diff --git "a/agentic_index_st/merged_18_to_36/docstore.json" "b/agentic_index_st/merged_18_to_36/docstore.json"
new file mode 100644--- /dev/null
+++ "b/agentic_index_st/merged_18_to_36/docstore.json"
@@ -0,0 +1 @@
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"file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "25f91279-1033-4bdd-81ed-2373ee198eae", "node_type": "1", "metadata": {}, "hash": "f5b73c616d8f7614272b21dac3c1cedbc38d97654578bc46cad095d115834201", "class_name": "RelatedNodeInfo"}}, "text": "\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{In situ synchrotron X-ray imaging of 4140 steel laser powder bed fusion }\n\n\n\\author{Andrew Bobel ${ }^{\\text {a,*, }}$ Louis G. Hector Jr. ${ }^{a}$, Isaac Chelladurai ${ }^{\\text {ab, }}$, Anil K. Sachdev ${ }^{a}$, Tyson Brown ${ }^{a}$,\\\\\nWhitney A. Poling ${ }^{a}$, Robert Kubic ${ }^{a}$, Benjamin Gould ${ }^{c}$, Cang Zhao ${ }^{d}$, Niranjan Parab ${ }^{d}$,\\\\\nAaron Greco ${ }^{\\mathrm{c}}$, Tao Sun ${ }^{\\mathrm{d}}$}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\def\\AA{\\mathring{\\mathrm{A}}}\n\n\\begin{document}\n\\maketitle\nFull Length Article\n\n${ }^{\\text {a Global Research and Development, General Motors, Warren MI 48092, USA }}$\n\n${ }^{\\mathrm{b}}$ Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA\n\n' Applied Materials Division, Argonne National Laboratory, Lemont, IL 60439, USA\n\n${ }^{\\mathrm{d}}$ X-ray Science Division, Argonne National Laboratory, Lemont, IL 60439, USA\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing (AM)\n\nSelective laser melting\n\n4140 steel\n\nHigh speed X-ray Imaging\n\nMicrostructure\n\nPorosity\n\n\\begin{abstract}\nA B S T R A C T An in situ synchrotron X-ray imaging technique was used to examine laser powder bed fusion (LPBF) of a chromemolybedum, AISI 4140, ferrite-bainite steel, from a moving laser source. Since 4140 has received only minimal attention in the AM literature, focus here was on the effects of melt pool dynamics, vapor cavity depths, build layer height, and the origin of porosity on the 4140 as-built microstructure. Four build parameter sets, which enabled variation of laser power, scan speed, laser spot size, and specific energy density (SED), were applied. Vapor cavity and melt pool depths were measured for each single-track laser scan. Direct imaging of the LPBF process demonstrated that the primary source of porosity in the build originates from incorporation of entrapped gas within the powder irrespective of build parameter set. High resolution SEM and EBSD demonstrated that the as-built microstructure did not vary significantly with build parameter set over a broad range of SED.", "start_char_idx": 0, "end_char_idx": 3112, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "25f91279-1033-4bdd-81ed-2373ee198eae": {"__data__": {"id_": "25f91279-1033-4bdd-81ed-2373ee198eae", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "52adb299-ffee-42d8-98ea-18a57070e646", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e3c88cdad0a4b6b342d1c8244afa920cee45c8f3aadb105a4722d4bb84cba88a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8026f792-08ff-4b67-9581-e8fd23ec4b2b", "node_type": "1", "metadata": {}, "hash": "6c573019702ff85237f49add8fdf812518f0f5bf51a9aa3adbf0ec4c458dc780", "class_name": "RelatedNodeInfo"}}, "text": "Since 4140 has received only minimal attention in the AM literature, focus here was on the effects of melt pool dynamics, vapor cavity depths, build layer height, and the origin of porosity on the 4140 as-built microstructure. Four build parameter sets, which enabled variation of laser power, scan speed, laser spot size, and specific energy density (SED), were applied. Vapor cavity and melt pool depths were measured for each single-track laser scan. Direct imaging of the LPBF process demonstrated that the primary source of porosity in the build originates from incorporation of entrapped gas within the powder irrespective of build parameter set. High resolution SEM and EBSD demonstrated that the as-built microstructure did not vary significantly with build parameter set over a broad range of SED. The fast solidification rates observed $(0.06-0.08 \\mathrm{~m} / \\mathrm{s})$ lead to fine martensite packet/block size distributions $(1-3 \\mu \\mathrm{m})$ with the potential for increased material strength.\n\\end{abstract}\n\n\\section*{1. Introduction}\nMetal additive manufacturing (AM) processes, such as laser powder bed fusion (LPBF), and direct energy deposition (DED), have demonstrated greater design flexibility, accuracy, part consolidation, and significant weight savings through topology optimized design compared to conventional manufacturing technologies. In particular, additive techniques for metal component production are very attractive in mobility industries [1], with current applications including motorsport components such as F1 gearboxes, suspension system mounting brackets, oil pump housings, exhaust manifolds and cylinder heads [2]. Capturing the full value of AM will include not only optimized component design, but also the use of unique low-cost additive materials which enable performance that would otherwise be impossible via current materials processing methods. A comprehensive review of additive manufacturing of metals was recently published by DebRoy et al. [3].\n\nThe predominant metal AM systems employ the LPBF process in which a high-power, moving laser source (e.g. ytterbium fiber laser) locally melts a thin layer of metallic powder spread layer-by-layer to build up complex 3D shapes. This process is highly dynamic, with rapid heating and cooling rates, complex transport phenomena (e.g. Marangoni\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:andrew.bobel@gm.com}{andrew.bobel@gm.com} (A. Bobel).\n}\n\nconvection, recoil pressure), powder ejection and re-distribution, powder porosity, and non-equilibrium phase transformations often resulting in high residual stresses and internal defects (e.g. lack of fusion, entrapped gas and/or keyhole porosity) in the built part. These defects can cause inconsistent performance and degrade mechanical properties in printed parts, requiring that they be reduced or eliminated to allow additive technologies to produce viable parts [4]. To understand the formation of these defects and associated non-equilibrium microstructures, it is critical to observe the complex dynamics inside the melt pool. Current real-time process monitoring in AM machines is limited to surface imaging; however, high-resolution, time-resolved X-ray imaging capable of monitoring the internal laser-material interaction of lab scale LPBF processes have recently been developed. This internal monitoring can provide data for alloy design modeling and for the creation of numerical models with sufficient fidelity to capture the laser-matter interaction and predict defect formation and mitigation and ultimately microstructural evolution and relevant mechanical properties [5,6].\n\nIn this paper, an in situ synchrotron X-ray imaging technique at Argonne National Laboratory's Advanced Photon Source (APS) beamline 32-ID-B $[7,8]$ was used to image the LPBF of AISI 4140, a chromemolybdenum steel. A ytterbium fiber laser beam was moved to produce\\\\\n$2 \\mathrm{~mm}$ long single-track scans on the surface of a 4140 build plate with and without powder. There are two features of this study that are of significant interest (1) Imaging occurred while the laser beam moved; (2) LPBF of 4140 has not been adequately addressed in the AM literature since previous studies have focused primarily on common AM alloys such as Al10SiMg, Ti-6Al-4V, and various stainless steels [7,9-13]. Two prior studies of note on 4140 include processing of single-walled deposits using laser engineered net shaping (LENS) [14] and finite element simulation and residual stress work focused on laser cladding [15].", "start_char_idx": 2306, "end_char_idx": 6922, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8026f792-08ff-4b67-9581-e8fd23ec4b2b": {"__data__": {"id_": "8026f792-08ff-4b67-9581-e8fd23ec4b2b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "25f91279-1033-4bdd-81ed-2373ee198eae", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "92e1db91ac2108e7fd09e6f283a7881d6d6c5b6c5a788cfea9bbc11d0a4f265b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "22755479-4a81-4b15-b2ff-93fafcf99dbb", "node_type": "1", "metadata": {}, "hash": "2770f83221617ff8fa96e0cc6f0500ad48b00071970493b771638ce32fde8831", "class_name": "RelatedNodeInfo"}}, "text": "A ytterbium fiber laser beam was moved to produce\\\\\n$2 \\mathrm{~mm}$ long single-track scans on the surface of a 4140 build plate with and without powder. There are two features of this study that are of significant interest (1) Imaging occurred while the laser beam moved; (2) LPBF of 4140 has not been adequately addressed in the AM literature since previous studies have focused primarily on common AM alloys such as Al10SiMg, Ti-6Al-4V, and various stainless steels [7,9-13]. Two prior studies of note on 4140 include processing of single-walled deposits using laser engineered net shaping (LENS) [14] and finite element simulation and residual stress work focused on laser cladding [15]. Unlike these more common AM material systems, 4140 has been used in a large volume of automotive applications, as detailed in Grassl et al. [16]. The common AM alloys either do not exhibit desired mechanical property combinations at room and elevated operating temperatures or are too richly alloyed to see wide spread use in automotive applications. Note that 4140 has superior toughness, good ductility and wear resistance, properties that render it suitable for a variety of applications in mobility industries.\n\nQuantitative information on the melt pool dynamics and vapor cavity depths, build layer height, and pore formation and entrapment were obtained for a series of build parameters (laser energy, spot size, and scan speed). The resulting as-built microstructure was analyzed using scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD) to first quantify grain size and then link the resulting microstructure to the build parameters. The in situ X-ray imaging technique captured the processes by which powder-induced and vaporization porosity occur. This data will provide an unprecedented understanding of the laser-material interaction, melt pool dynamics, and porosity defect development in 4140, and will further the optimization of build parameters to provide essentially porosity free additive manufactured parts as well as high fidelity computer models. The remainder of this paper is organized as follows: Section 2 provides background information on 4140 sample preparation and the in situ synchrotron X-ray imaging LPBF system, Section 3 details the results for LPBF of 4140 including melt pool and vapor cavity dynamics, microstructure, and porosity, Section 4 contains the summary remarks and main conclusions of the manuscript.\n\n\\section*{2. Methodology}\n\\subsection*{2.1. 4140 steel \\& characterization}\nThe composition of the 4140 powder (Carpenter Powder Products, Woonsocket, RI, USA) is $\\mathrm{Fe}-0.4 \\mathrm{C}-1.1 \\mathrm{Cr}-0.86 \\mathrm{Mn}-0.26 \\mathrm{Si}-0.19 \\mathrm{Mo}$ $-0.008 \\mathrm{P}-0.05 \\mathrm{O} \\mathrm{wt} \\%$. The shape of the powder particles is nominally\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5d6abf0de1bf85882ee9g-02(1)}\\\\\nrange. Thin 4140 plates were machined with EDM from conventionally processed 4140 bar stock, having a ferrite-bainite microstructure with a small amount of pearlite (see Fig. 5(a,Baseplate)), to use as baseplates for the powders. The plates were then polished to a mirror finish using a diamond polishing medium yielding an average thickness of $285 \\mu \\mathrm{m}$ and $325 \\mu \\mathrm{m}$, a height of $3.95 \\mathrm{~mm}$, and $30 \\mathrm{~mm}$ overall length. The thinner plates were used in the in situ LPBF experiments without powder to observe the melt pool in the solid material.\n\nA Zeiss NVision 40 focused-ion beam (FIB) field-emission microscope was used to image the post LPBF microstructures. Samples were mounted transverse and parallel to the beam scan direction and polished to $0.05 \\mu \\mathrm{m}$ with colloidal silica before EBSD imaging. EBSD data was collected using step sizes between $0.05 \\mu \\mathrm{m}$ and $0.08 \\mu \\mathrm{m}$ with ferrite as the reference crystal structure. The EBSD data was analyzed using the OIM TSL Analysis software. Inverse pole figure (IPF) maps, grain diameter, area, and orientations were examined for comparative studies between build parameters.", "start_char_idx": 6230, "end_char_idx": 10350, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "22755479-4a81-4b15-b2ff-93fafcf99dbb": {"__data__": {"id_": "22755479-4a81-4b15-b2ff-93fafcf99dbb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8026f792-08ff-4b67-9581-e8fd23ec4b2b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3988f35ee5dd38dc0deed54ce0853dd465326fc0ec6ee4339a5333b07ba83fdf", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fec593e6-0dc8-43d2-a7c2-f1940a8c2a7c", "node_type": "1", "metadata": {}, "hash": "b3d3ab32147cb5599a40afe1769e48949e3ddf1d5e1a832bcb95636cf0e0e3e8", "class_name": "RelatedNodeInfo"}}, "text": "The thinner plates were used in the in situ LPBF experiments without powder to observe the melt pool in the solid material.\n\nA Zeiss NVision 40 focused-ion beam (FIB) field-emission microscope was used to image the post LPBF microstructures. Samples were mounted transverse and parallel to the beam scan direction and polished to $0.05 \\mu \\mathrm{m}$ with colloidal silica before EBSD imaging. EBSD data was collected using step sizes between $0.05 \\mu \\mathrm{m}$ and $0.08 \\mu \\mathrm{m}$ with ferrite as the reference crystal structure. The EBSD data was analyzed using the OIM TSL Analysis software. Inverse pole figure (IPF) maps, grain diameter, area, and orientations were examined for comparative studies between build parameters. Prior to the data analysis, the raw EBSD datasets were processed to remove all low confidence index points $(\\leq 0.1)$ from the scan. Grains with a size less than 2 scan points (separated by the specified step size) were also removed. This cleared the dataset of noise in the form of badly indexed, pixelated points. Additionally, all edge grains and grains less than $1 \\mu \\mathrm{m}$ in diameter were not considered during grain size analysis from the exported dataset. Post EBSD, the laser processed samples were etched using a Nital ( $2 \\%$ nitric acid in methanol) to expose the microstructure and subsequently re-imaged.\n\n\\subsection*{2.2. Synchrotron X-ray imaging system for LPBF}\nThe in situ synchrotron X-ray imaging system, developed specifically for LPBF, was used for all tests. The main components of this system are a synchrotron X-ray imaging system, a laser system, a powder bed sample, and a stainless steel vacuum chamber. A short-period $(1.8 \\mathrm{~cm})$ undulator with the gap set to $12 \\mathrm{~mm}$ generated polychromatic X-rays with the first harmonic energy at $24.4 \\mathrm{keV}(\\lambda=0.508 \\AA)$. A pair of slits was used to define the area of the X-ray beam. The imaging detection system is composed of a LuAG:Ce scintillator ( $100 \\mu \\mathrm{m}$ thick), $45^{\\circ}$ reflection mirror, a relay lens, an objective lens (Edmund Optics Inc., Barrington, NJ), and a high-speed camera (Photron FastCam SA-Z, USA). X-ray images were converted to grey scale in the visible spectrum. Images were recorded\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-02}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-02(3)}\n\\end{center}\n\n(b)\n\nFig. 1. (a) Top down photograph of the miniature powder bed setup. (b) Schematic representation (not to scale) of the experimental set up (one carbon shim is not shown for clarity). (c) Top down view of the 4140 baseplates post laser scanning with the four build parameters. Laser scan direction was from left to right in this orientation.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-02(2)}\n\\end{center}\n\n(c)\\\\\nat a resolution of $1.974 \\mu \\mathrm{m} / \\mathrm{pixel}$, with a frame rate of $50 \\mathrm{kHz}$, and an exposure time of $1 \\mu$ s for each image.\n\nThe miniature powder bed sample, shown in Fig. 1(a), consists of two identical pieces of glassy carbon (vitreous) plates (Grade 22, Structure Probe Inc., USA) with a $1.0 \\mathrm{~mm}$ thickness and $4.0 \\mathrm{~mm}$ height to retain the powder on top of the 4140 baseplate. The gap width between the two plates is determined by the thickness of the 4140 baseplate. On top of the metal baseplate, 4140 powder is spread out evenly to a thickness of $\\sim 70 \\mu \\mathrm{m}$.", "start_char_idx": 9611, "end_char_idx": 13193, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fec593e6-0dc8-43d2-a7c2-f1940a8c2a7c": {"__data__": {"id_": "fec593e6-0dc8-43d2-a7c2-f1940a8c2a7c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "22755479-4a81-4b15-b2ff-93fafcf99dbb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f46a349361a9869a5f65b7484a638f0ae582c10b9498c8dbf98a97bc3ad0fb32", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8b9fdf63-0a46-4416-a8d6-95ec669828e9", "node_type": "1", "metadata": {}, "hash": "da640f8c4782e29f8bf64eb05404ed7f205632d4dd45a10a5664344fd42148f2", "class_name": "RelatedNodeInfo"}}, "text": "The miniature powder bed sample, shown in Fig. 1(a), consists of two identical pieces of glassy carbon (vitreous) plates (Grade 22, Structure Probe Inc., USA) with a $1.0 \\mathrm{~mm}$ thickness and $4.0 \\mathrm{~mm}$ height to retain the powder on top of the 4140 baseplate. The gap width between the two plates is determined by the thickness of the 4140 baseplate. On top of the metal baseplate, 4140 powder is spread out evenly to a thickness of $\\sim 70 \\mu \\mathrm{m}$. In experiments without powder, the carbon plates were not used, as the sole purpose of using them is too confine the powder layer.\n\nThe laser system consists of a ytterbium fiber laser (IPG YLR-500AC, USA) and a galvonometer laser scanner (IntelliSCAN ${ }_{\\mathrm{de}} 30$, SCANLAB GmbH, Puchheim, Germany). The fiber laser provided a Gaussian beam profile with a $1070 \\mathrm{~nm}$ wavelength and maximum nomial power of $520 \\mathrm{~W}$ in either continuous or pulsed scanning modes. At the focal spot, the laser beam size was $\\sim 56 \\mu \\mathrm{m}$. In the experiments, the sample was positioned 2 and $3.5 \\mathrm{~mm}$ below the laser focal plane to achieve spot sizes of $67 \\mu \\mathrm{m}$ and $88 \\mu \\mathrm{m}$, respectively. The spot size was measured as the diameter of the vapor cavity depression in the baseplate surface (i.e. without powder) in ancillary experiments with a stationary beam. The laser was operated in continuous scanning mode. This allowed variation of both scanning speed and laser power. The nominal fiber laser beam energy was varied between 156 and $364 \\mathrm{~W}$ and the laser scan speed varied from 300 to $600 \\mathrm{~mm} / \\mathrm{s}$, resulting in specific energy densities (SED) from $3.0-10.4 \\mathrm{~J} / \\mathrm{mm}^{2}$, where:\n\n$\\mathrm{SED}\\left[\\frac{\\mathrm{J}}{\\mathrm{mm}^{2}}\\right]=\\frac{\\text { Power }[\\mathrm{W}]}{\\text { Speed }[\\mathrm{mm} / \\mathrm{s}] * \\text { Diameter }[\\mathrm{mm}]}$\n\nFig. 1(b) is a schematic of the powder bed setup with the 4140 baseplate material positioned between two carbon plates (one carbon plate is omitted for clarity) with powder spread on top. Shown in Fig. 1(b) is the orientation of the laser with respect to the baseplate and powder, it's travel direction, and the generated laser trace where the powder and baseplate have been melted.\n\nThe powder bed sample is placed in a stainless-steel vacuum chamber. The laser beam transmits through a fused silica window, enters the chamber, and interacts with the miniature powder bed sample. The Xray beam enters and exits the chamber via two Kapton windows normal to the baseplate. Prior to the experiment, the chamber is pumped down below 500 mTorr and then back filled with Ar gas to inhibit oxidation of the metal powder and subsequent build. The sample, laser beam and $\\mathrm{X}$-ray beam are aligned using a set of stepper motors.\n\n\\section*{3. Results and discussion}\n\\subsection*{3.1. Build parameter sets}\nTable 1 lists four build parameter sets referred to as \"Skin\", \"Fill\", \"High-Energy (HE)\" and \"Keyhole\". These parameters were chosen to explore the effect of increasing the SED on the material interaction while emulating laser conditions expected in a commercial LPBF setup. The Skin parameter was chosen to emulate the low SED and fast scan speeds, as compared to a Fill parameter, typically used in the up-skin or downskin sections of a printed AM part, while the Fill parameter was chosen to produce a stable vapor cavity and resulting dense solidified layer. The HE parameter was chosen to evaluate the effect of increased laser power relative to the Fill parameter, while maintaining the spot size and scan speed of the Fill parameter. The Keyhole parameter was chosen to create the deep and narrow laser penetration typically seen in keyhole welding with intense beam energies.", "start_char_idx": 12719, "end_char_idx": 16544, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8b9fdf63-0a46-4416-a8d6-95ec669828e9": {"__data__": {"id_": "8b9fdf63-0a46-4416-a8d6-95ec669828e9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fec593e6-0dc8-43d2-a7c2-f1940a8c2a7c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a06d262a1332fd1cfd2119f4d0e7af96e931ed55f993f4696d0c6dfac00acd76", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "40b3ccda-2d91-48fa-9cc8-93b75b1ca165", "node_type": "1", "metadata": {}, "hash": "a31d3c85a3a8fcd099a6fa5638eda9ea2f1cbb2817f52fd012ccfa0ffdae64c2", "class_name": "RelatedNodeInfo"}}, "text": "Results and discussion}\n\\subsection*{3.1. Build parameter sets}\nTable 1 lists four build parameter sets referred to as \"Skin\", \"Fill\", \"High-Energy (HE)\" and \"Keyhole\". These parameters were chosen to explore the effect of increasing the SED on the material interaction while emulating laser conditions expected in a commercial LPBF setup. The Skin parameter was chosen to emulate the low SED and fast scan speeds, as compared to a Fill parameter, typically used in the up-skin or downskin sections of a printed AM part, while the Fill parameter was chosen to produce a stable vapor cavity and resulting dense solidified layer. The HE parameter was chosen to evaluate the effect of increased laser power relative to the Fill parameter, while maintaining the spot size and scan speed of the Fill parameter. The Keyhole parameter was chosen to create the deep and narrow laser penetration typically seen in keyhole welding with intense beam energies. Ancillary tests were performed on bare 4140 baseplates without powder to determine repeatability of melt pool dynamics and porosity formation independent of the added complexity of a powder layer. Results of one single-track laser scan performed with powder per parameter set follows, and the corresponding results were determined to be representative of results from two single-track laser scans using the same conditions. Fig. 1(c) shows top down views of the laser tracks in both a 4140 baseplate (top) and a powder layer (bottom). The laser beam was scanned across a $2 \\mathrm{~mm}$ long strip along the baseplate/powder bed such that the beam starts on the left side of the image and moves toward the right. Melted surfaces $2 \\mathrm{~mm}$ long are clearly visible on the top side of the plate where the laser pass occurred.\n\n\\subsection*{3.2. Melt pool and vapor cavity dynamics}\nThe X-ray beam entered the chamber transverse to the laser beam scan direction (see Fig. 1(b)), providing a side view of the powder bed setup. Fig. 2 shows selected difference images, i.e. frame \" $n$ \" subtracted from frame 0, during the laser scan process for the Fill (Fig. 2(a)), HE (Fig. 2(b)), and Keyhole (Fig. 2(c)) build parameter sets, with the vapor cavity outlined in blue and the melt pool liquid region outlined in red. The Skin parameter is not shown as no visible vapor cavity penetration into the baseplate was observed. The melt pool liquid boundary was determined by looking at a series of images and tracking the solidification front between the series. The melt pool geometry for all three parameter sets exhibits a decaying tail denoted by the red dashed line in each figure. The vapor cavity for the Fill and HE parameter sets follows a Gaussian profile that progressively widens and deepens. Alternatively, the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-03}\n\\end{center}\n\nFig. 2. X-ray images (with background subtraction) of the melt pool, keyhole and porosity in a 4140 baseplate (no powder) for three of the build parameters in Table 1. (a) Fill, (b) High-energy (HE), (c) Keyhole. The vapor cavity is outlined in blue and the melt pool in red. The laser beam scan is from left to right as indicated by the black arrow. Fill and HE parameters produce stable gaussian vapor cavities with long melt pool tails while Keyhole conditions lead to unstable vapor cavity necking which produced porosity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)\n\nTable 1\n\nBuild parameter sets for miniature powder bed system. SED = Specific Energy Density.", "start_char_idx": 15596, "end_char_idx": 19225, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "40b3ccda-2d91-48fa-9cc8-93b75b1ca165": {"__data__": {"id_": "40b3ccda-2d91-48fa-9cc8-93b75b1ca165", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8b9fdf63-0a46-4416-a8d6-95ec669828e9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2e949ea78b6ed62faf8d69e825febb3e3fda79d727a468d3bd73898f9978b429", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bfa95cad-9111-468f-9822-02cf0df04fb7", "node_type": "1", "metadata": {}, "hash": "10b887f4deb34eb7c74008a83e4ae4da1de42d21c5a9384f35b4f9abaa54c047", "class_name": "RelatedNodeInfo"}}, "text": "2. X-ray images (with background subtraction) of the melt pool, keyhole and porosity in a 4140 baseplate (no powder) for three of the build parameters in Table 1. (a) Fill, (b) High-energy (HE), (c) Keyhole. The vapor cavity is outlined in blue and the melt pool in red. The laser beam scan is from left to right as indicated by the black arrow. Fill and HE parameters produce stable gaussian vapor cavities with long melt pool tails while Keyhole conditions lead to unstable vapor cavity necking which produced porosity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)\n\nTable 1\n\nBuild parameter sets for miniature powder bed system. SED = Specific Energy Density.\n\n\\begin{center}\n\\begin{tabular}{lllll}\n\\hline\nBuild parameters & Laser power $(\\mathrm{W})$ & Scan speed $(\\mathrm{mm} / \\mathrm{s})$ & Spot size $(\\mu \\mathrm{m})$ & SED $\\left(\\mathrm{J} / \\mathrm{mm}^{2}\\right)$ \\\\\n\\hline\nSkin & 156 & 600 & $\\sim 88$ & 3.0 \\\\\nFill & 250 & 500 & $\\sim 88$ & 5.7 \\\\\nHigh-Energy (HE) & 364 & 500 & $\\sim 88$ & 8.3 \\\\\nKeyhole & 208 & 300 & $\\sim 67$ & 10.4 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nKeyhole parameter set generated a narrow and deep vapor cavity into the baseplate with an unstable cavity tip and rear wall (left side of the vapor cavity in the $\\mathrm{X}$-ray image). Observable necking of the vapor cavity is present in Fig. 2(c) where the complex melt flow and abrupt pressure change inside the keyhole lead to porosity formation in its wake. Vapor cavity collapse (described in further detail in Section 3.4) occurs when the cavity closes off and separates into a pore that becomes entrapped in the solidifying material while the keyhole geometry continues along the scan path until the laser is deactivated.\n\nA series of continuous X-ray images, which include those from Fig. 2, for the Fill, HE, and Keyhole parameter sets with and without 4140 powder were analyzed to track the melt pool and vapor cavity depths from image to image as the beam scanned across $2 \\mathrm{~mm}$ sections. The reported melt pool and vapor cavity depths were measured from the 4140 baseplate top surface to the maximum depth near the laser position during the melting process. The penetration depth into the 4140 baseplate by the Skin build parameter set was not clearly measurable and is not reported. Fig. 3(a) tracks the cavity depth (blue) and melt pool depth (red) for each build parameter as a function of time across the scan length for two cases: the baseplate alone (top) and the baseplate\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-04(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-04}\n\\end{center}\n\n(b)\n\nFig. 3. (a) Depth of the vapor cavity and melt pool as a function of time measured from the X-ray images for the Fill, HE, and Keyhole build parameters set with (top) and without (bottom) 4140 powder. (b) X-ray images of the 4140 LPBF after the laser scan was performed with powder. White arrows point to pores embedded in the newly solidified material as determined at higher magnifications. Note that much of the embedded porosity is not readily apparent because of the small size of the pores. Vapor cavity and melt pool depth increase with increasing SED while the difference between then is consistently $\\sim 20 \\mu \\mathrm{m}$. Porosity in the as-built material is primarily observed to originate from entrapped gas particles present in the powder.\\\\\nTable 2\n\nMeasured cavity and melt pool penetration depths using X-ray imaging. depths in units of $\\mu \\mathrm{m}$.", "start_char_idx": 18479, "end_char_idx": 22154, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bfa95cad-9111-468f-9822-02cf0df04fb7": {"__data__": {"id_": "bfa95cad-9111-468f-9822-02cf0df04fb7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "40b3ccda-2d91-48fa-9cc8-93b75b1ca165", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c6e5d634247ad62ab090e2522f78cf6023b4cbcf00a638567fdd9d6ff4adf19b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2b520c10-5e66-44b6-9638-df3f3bce59c2", "node_type": "1", "metadata": {}, "hash": "73c3b5c89df7ae54fadd1d82cf9a913aa8dfa5f242a2dde14bb1afafdf524da5", "class_name": "RelatedNodeInfo"}}, "text": "(a) Depth of the vapor cavity and melt pool as a function of time measured from the X-ray images for the Fill, HE, and Keyhole build parameters set with (top) and without (bottom) 4140 powder. (b) X-ray images of the 4140 LPBF after the laser scan was performed with powder. White arrows point to pores embedded in the newly solidified material as determined at higher magnifications. Note that much of the embedded porosity is not readily apparent because of the small size of the pores. Vapor cavity and melt pool depth increase with increasing SED while the difference between then is consistently $\\sim 20 \\mu \\mathrm{m}$. Porosity in the as-built material is primarily observed to originate from entrapped gas particles present in the powder.\\\\\nTable 2\n\nMeasured cavity and melt pool penetration depths using X-ray imaging. depths in units of $\\mu \\mathrm{m}$.\n\n\\begin{center}\n\\begin{tabular}{lllll}\n\\hline\n\\multicolumn{2}{l}{Build parameter} & Fill & High-Energy (HE) & Keyhole \\\\\n\\hline\nNo powder & Cavity depth & $53.4 \\pm 10.8$ & $128.3 \\pm 8.6$ & $251.7 \\pm 21.0$ \\\\\n & Melt pool depth & $77.5 \\pm 9.8$ & $149.3 \\pm 7.0$ & $272.2 \\pm 20.4$ \\\\\n & Depth difference & 24.1 & 21.0 & 20.5 \\\\\nWith & Cavity depth & $42.3 \\pm 6.7$ & $109.5 \\pm 5.3$ & $196.5 \\pm 16.0$ \\\\\npowder & Melt pool depth & $62.5 \\pm 7.3$ & $134.4 \\pm 5.5$ & $213.4 \\pm 13.7$ \\\\\n & Depth difference & 20.2 & 24.9 & 16.8 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nwith powder (bottom). The Keyhole build parameter has a slower scan speed (see Table 1) and thus more time was required to complete the $2 \\mathrm{~mm}$ scan. Fig. 3(a), suggests that for both cases, the maximum cavity and melt pool depths increase with increasing SED (Fill $<\\mathrm{HE}<$ Keyhole) and the distance between the maximum cavity and melt pool depths is nearly constant regardless of build parameter. The average vapor cavity and melt pool depths as measured across each $2 \\mathrm{~mm}$ laser scan using in situ X-ray imaging are summarized in Table 2, with the reported errors corresponding to one standard deviation. In the absence of powder, the average depth for both the vapor cavity and melt pool increases from $53 \\mu \\mathrm{m}$ and $78 \\mu \\mathrm{m}$, respectively, up to 252 and $272 \\mu \\mathrm{m}$, respectively, with increasing SED. With powder, the average depth for both the vapor cavity and melt pool depths increased from $42 \\mu \\mathrm{m}$ and $63 \\mu \\mathrm{m}$, respectively, up to $197 \\mu \\mathrm{m}$ and $213 \\mu \\mathrm{m}$, respectively. As compared to the laser scans without powder, the overall penetration depth into the baseplate material is reduced. Regardless of build parameter, the difference between the vapor cavity depth and the melt pool depth was measured to be $\\sim 20 \\mu \\mathrm{m}$ in all six tests without powder. It is important to note that the cavity and melt pool in the Keyhole parameter set exhibited large fluctuations in penetration depth during scanning both with and without powder. This is noted in the more than doubled standard deviation in the depth measurements in Table 2 as compared to the four Fill and HE parameter scans.\n\nThe measured average height of the powder manually added on top of the 4140 baseplate positioned between the two carbon plates (see Fig. 1(a)) is reported in Table 3 for all four build parameter sets. The powder height was measured from the top of the 4140 baseplate at a minimum of 40 locations across the $2 \\mathrm{~mm}$ long field of view of the X-ray images up to the top surface of any powder particles prior to scanning.", "start_char_idx": 21289, "end_char_idx": 24856, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2b520c10-5e66-44b6-9638-df3f3bce59c2": {"__data__": {"id_": "2b520c10-5e66-44b6-9638-df3f3bce59c2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bfa95cad-9111-468f-9822-02cf0df04fb7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1a7120117105733e82e8741622f0c70bba864f87f40e0c009906476fe72af96c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fe18e102-f2be-488b-880b-1d8aeb3db495", "node_type": "1", "metadata": {}, "hash": "23ae7fc0455fab778753f643b26ff19eee38f566550060e57d16610721922ec5", "class_name": "RelatedNodeInfo"}}, "text": "It is important to note that the cavity and melt pool in the Keyhole parameter set exhibited large fluctuations in penetration depth during scanning both with and without powder. This is noted in the more than doubled standard deviation in the depth measurements in Table 2 as compared to the four Fill and HE parameter scans.\n\nThe measured average height of the powder manually added on top of the 4140 baseplate positioned between the two carbon plates (see Fig. 1(a)) is reported in Table 3 for all four build parameter sets. The powder height was measured from the top of the 4140 baseplate at a minimum of 40 locations across the $2 \\mathrm{~mm}$ long field of view of the X-ray images up to the top surface of any powder particles prior to scanning. The initial powder height was fairly constant between the 4 different scan areas, varying from $64 \\mu \\mathrm{m}$ to $84 \\mu \\mathrm{m}$ (on average). The standard deviations in powder heights given in Table 3 across the $2 \\mathrm{~mm}$ scan areas (prior to scanning) are less than the average powder particle size. The largest deviation in powder height $(\\sim 20 \\mu \\mathrm{m})$ was in the Skin parameter set scan area which is less than the median powder particle size (d50 of $39.1 \\mu \\mathrm{m}$ ) demonstrating a consistent level of powder coverage in the miniature LPBF setup in Fig. 1(a).\n\nThe resulting build layer height post laser scan was measured from the original flat 4140 baseplate top surface to the top surface of the new 4140 solid layer at a minimum of 40 locations across the $2 \\mathrm{~mm}$ scan area. The average build layer height for all four build parameter sets is given in Table 3. The average build layer height between all four build parameters varied from $31 \\mu \\mathrm{m}$ to $45 \\mu \\mathrm{m}$, with no direct correlation to the SED. However, the average build layer height was found to correlate closely with the starting average powder height between the various scan areas. The highest initial powder height (Fill scan) resulted in the largest build layer height, and similarly, the smallest initial powder height (Keyhole scan) resulted in the smallest build layer height. Therefore, the height of the new layer of material seemingly depends only on the initial powder layer thickness, even though the melt pool depth into the baseplate varies directly with the SED. The average initial powder height to build layer height ratio across all build parameters was found to be $52 \\%$. This corresponds to a $12 \\%$ loss of material due to vaporization and spattering when compared to the random packing of equal spheres with a density of $64 \\%$.\n\nTable 3\n\nMeasured powder and build layer height with respect to the baseplate top surface from $\\mathrm{X}$-ray imaging.\n\n\\begin{center}\n\\begin{tabular}{lllll}\n\\hline\nBuild parameter & Skin & Fill & High-Energy (HE) & Keyhole \\\\\n\\hline\nPowder height $(\\mu \\mathrm{m})$ & $76.1 \\pm 19.5$ & $84.4 \\pm 13.8$ & $72.6 \\pm 9.7$ & $63.7 \\pm 11.3$ \\\\\nBuild layer height $(\\mu \\mathrm{m})$ & $38.3 \\pm 18.9$ & $45.5 \\pm 11.7$ & $40.0 \\pm 13.0$ & $31.5 \\pm 11.9$ \\\\\nBuild/Powder Ratio $(\\%)$ & 50.3 & 53.9 & 55.1 & 49.4 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-05}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-05(2)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-05(1)}\n\\end{center}\n\n(c)\n\nFig. 4.", "start_char_idx": 24101, "end_char_idx": 27638, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fe18e102-f2be-488b-880b-1d8aeb3db495": {"__data__": {"id_": "fe18e102-f2be-488b-880b-1d8aeb3db495", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2b520c10-5e66-44b6-9638-df3f3bce59c2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ed1aca67c774d735b1aa04a7d9e6825fdd6f68160cfd53b17dd0b9918e54d6b2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2a76004a-1db8-4fea-ac81-9d15e235f958", "node_type": "1", "metadata": {}, "hash": "026a15aeab2dece1b83968707a2f653e8acd7501625eb7f2b411ebe4cf97108b", "class_name": "RelatedNodeInfo"}}, "text": "4. Optical micrographs of etched 4140 baseplate and build layer cross-sections looking parallel to the laser beam scan direction (out of the page) for the (a) Fill, (b) HE, and (c) Keyhole build parameter sets. The large black circle in the Keyhole image is a pore. Dashed lines correspond to the melt boundary with the HAZ (red) and HAZ with the baseplate (yellow) as determined by the transition in microstructure. Melt pool geometry is of parabolic shape with the depth of the HAZ at the lowest point being $\\sim 25-30 \\mu \\mathrm{m}$ regardless of parameter set. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)\n\nX-ray images of the new build layer after laser scanning for all four build parameter sets are shown in Fig. 3(b). All images have a higher build layer height on the left side of the image where the laser was activated and decreases to the right where the laser was deactivated. This can be attributed to the beam being momentarily stationary on the left side as it ramps up in speed while moving to the right. This scan behavior leads to a larger melt pool in the baseplate and surrounding powder that's highly turbulent and tends to form a liquid \"bead\" once the beam starts scanning. This \"bead\" is more noticeable in the Skin parameter, since the \"bead\" tends to smooth out in the other build parameters due to the resulting larger and longer melt pools thereby reducing the surface tension which acts to spread the \"bead\" out. The surfaces resulting from the Fill, HE, and Keyhole parameter sets are relatively smooth; however, the Skin parameter set leaves a rougher surface with significantly more un-melted powder particles that adhere to the build layer. The reflectivity of the $2 \\mathrm{~mm}$ laser scanned surface in the photograph in Fig. 1(c) (with powder) highlights the smoother surface obtained from the Fill, HE, and Keyhole parameter sets as compared to the Skin parameter set.\n\n\\subsection*{3.3. Microstructure analysis}\nWelding of 4140 steel and the resulting microstructure is a common research topic of interest in the automotive community where fast cooling rates lead to hardening of the weld region and heat affected zone (HAZ) due to martensitic transformation $[17,18]$. However, the welding literature does not address 4140 powder. Arc welding of steels exhibits $\\sim 100{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ cooling rates [19] while laser welding exhibits cooling rates in upwards of $1000{ }^{\\circ} \\mathrm{C} / \\mathrm{s}$ [20]. These cooling rates are many orders of magnitude beneath those associated with $\\mathrm{AM}\\left(10^{5}-10^{6}{ }^{\\circ} \\mathrm{C} / \\mathrm{s}\\right)[9,21]$, and hence little to no inferences can be drawn about AM build microstructures from previous studies of weld microstructures. Here, we explore the relationship between build parameter sets, extreme cooling rates, and the resulting microstructure of the AM 4140 material in contrast to the manufactured 4140 bar stock baseplate material.\n\nWith a similar experimental setup, Calta et al. [12] indicated that the thermal boundary conditions may affect heat affected zones at Ti-6Al- $4 \\mathrm{~V}$ powder/glass carbon interfaces. Etched optical micrographs were taken to provide a view parallel to the laser scan direction (out of the page) as shown in Fig. 4 to observe the cross-sectional view of the melt pool. The micrographs highlight a section of the melt pool geometry for the (a) Fill, (b) HE, and (c) Keyhole parameter sets. The red dashed lines in each figure denote the boundary between the melted region and the HAZ, while the yellow dashed line is the boundary between the HAZ and the baseplate as determined by transitions in observable microstructure. Note that the HAZ in all build parameters sets shown extends to the glass carbon plates. However, the melt boundary region in only the HE and Keyhole build parameters extends to the glassy carbon plates. To mitigate any possible effects of thermal boundary conditions in our study, all high resolution EBSD and SEM were taken from the middle of the baseplates and build layers far from the glassy carbon plates. The maximum depth of the melt pool boundary as measured from the optical images in Fig.", "start_char_idx": 27636, "end_char_idx": 31921, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2a76004a-1db8-4fea-ac81-9d15e235f958": {"__data__": {"id_": "2a76004a-1db8-4fea-ac81-9d15e235f958", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fe18e102-f2be-488b-880b-1d8aeb3db495", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4288a9a5fec3eae28f1c5b946c634e0852db5dc19d7f590c63a148e333f8feca", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "580b37c6-d122-4dae-86fb-2ce5c0634ac6", "node_type": "1", "metadata": {}, "hash": "6d4195e49f58b45a1e1b4ca990f05716fd72725a54c0868b0f4266386366afae", "class_name": "RelatedNodeInfo"}}, "text": "4 to observe the cross-sectional view of the melt pool. The micrographs highlight a section of the melt pool geometry for the (a) Fill, (b) HE, and (c) Keyhole parameter sets. The red dashed lines in each figure denote the boundary between the melted region and the HAZ, while the yellow dashed line is the boundary between the HAZ and the baseplate as determined by transitions in observable microstructure. Note that the HAZ in all build parameters sets shown extends to the glass carbon plates. However, the melt boundary region in only the HE and Keyhole build parameters extends to the glassy carbon plates. To mitigate any possible effects of thermal boundary conditions in our study, all high resolution EBSD and SEM were taken from the middle of the baseplates and build layers far from the glassy carbon plates. The maximum depth of the melt pool boundary as measured from the optical images in Fig. 4 for the Fill parameter set was $\\sim 100 \\mu \\mathrm{m}$, for the HE parameter set $\\sim 176 \\mu \\mathrm{m}$, and for the Keyhole parameter set $\\sim 270 \\mu \\mathrm{m}$. These measurements are in very good agreement with the total depth (melt pool penetration and new layer height) as measured by X-ray imaging: $109 \\pm 19 \\mu \\mathrm{m}$ for the Fill parameter set, $174 \\pm 19 \\mu \\mathrm{m}$ for the HE parameter set, and $244 \\pm 26 \\mu \\mathrm{m}$ for the Keyhole parameter set as averaged across the length of the $2 \\mathrm{~mm}$ scan. The maximum depth of the HAZ was also measured from the optical micrographs Fig. 4. The HAZ depth for the Fill parameter set was found to be $\\sim 30 \\mu \\mathrm{m}$, for the HE parameter set $\\sim 28 \\mu \\mathrm{m}$, and for the Keyhole parameter set $\\sim 25 \\mu \\mathrm{m}$, indicating that the HAZ depth near the maximum penetration of the melt pool does not correlate strongly with build parameter SED. As can be seen in the optical images, the cross-sectional profiles of the melt pool and the HAZ were greatly affected by the location of the laser spot on the $\\sim 300 \\mu \\mathrm{m}$ thick baseplate. The melt pool and HAZ for the Fill and HE parameters take on the expected parabolic shape associated with LPBF and laser welding [21]. However, because the Keyhole parameter is of such a high SED (see Table 1) it appears to have melted the entire top surface of both the powder layer and baseplate, resulting in the parabolic shape only near the center of the laser scan. More work is needed to determine if the macroscopic features of the melt pool and HAZ have any bearing on material properties.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-06(7)}\n\\end{center}\n\nFig. 5. FE-SEM micrographs for post-build 4140 processed using the Fill parameter set looking transverse to the beam scan direction (scan direction runs left to right). The red dashed line corresponds to the boundary between the melted region and the HAZ while the yellow dashed line corresponds to the boundary between the HAZ region and the baseplate. (A) Top surface corresponding to solidified powder, (B) HAZ boundary region, (C) baseplate material close to the laser scan region, and (D) an image from the bottom of the baseplate far from the laser scan region. The baseplate microstructure is primarily ferrite-bainite. Upward solidification resulting in a primarily martensitic microstructure is observed post laser melting in (A) and (B), while the baseplate near (C) and far from (D) the melted region consists primarily of a mixture of ferrite and bainite. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)\\\\\nHigh resolution field emission SEM and EBSD were performed for the Fill, HE, and Keyhole parameters sets on samples with powder to determine the resulting grain structure post-build with no subsequent heat treatments. This was done for two different cross-sectional orientations with the sample normal: (1) transverse to the beam scan direction and (2) parallel to the beam scan direction.", "start_char_idx": 31013, "end_char_idx": 35076, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "580b37c6-d122-4dae-86fb-2ce5c0634ac6": {"__data__": {"id_": "580b37c6-d122-4dae-86fb-2ce5c0634ac6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2a76004a-1db8-4fea-ac81-9d15e235f958", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "66357fe6290079764ffc4fb9026a6b235bbc8320b155abd3fa0c642df52ef0b4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "15ccb9ed-2cdb-456a-a513-fc897dd3676a", "node_type": "1", "metadata": {}, "hash": "24332f5c4d28efb483d436bdba305ca480aa151b6e2ba1421485ac06ed024e3c", "class_name": "RelatedNodeInfo"}}, "text": "The baseplate microstructure is primarily ferrite-bainite. Upward solidification resulting in a primarily martensitic microstructure is observed post laser melting in (A) and (B), while the baseplate near (C) and far from (D) the melted region consists primarily of a mixture of ferrite and bainite. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)\\\\\nHigh resolution field emission SEM and EBSD were performed for the Fill, HE, and Keyhole parameters sets on samples with powder to determine the resulting grain structure post-build with no subsequent heat treatments. This was done for two different cross-sectional orientations with the sample normal: (1) transverse to the beam scan direction and (2) parallel to the beam scan direction. SEM micrographs for the Fill parameter set with powder, viewing transverse to the scan direction, are shown in Fig. 5, with the red dash line denoting the melt boundary and the yellow dashed line denoting the HAZ boundary as before. High magnification insets in Fig. 5(a) for the microstructure near the top surface are shown in (A), near the HAZ in (B), and for the baseplate near the HAZ in (C), and near the bottom of the baseplate far from the laser scan region in (D). Microstructures in insets A and B have upward branching solidification directionality from the baseplate. The as-built microstructure exhibits a fine branching network near the top surface in (A) while the microstructure in the HAZ (B) exhibits a notably coarser branching network. The lack of etching response to Nital in the HAZ near the baseplate (between inset B and the yellow dashed line in Fig. 5) suggests the HAZ contains fresh martensite after having cooled from an austenitic solidification structure $[22,23]$. The microstructures of the baseplate near the HAZ (inset C) and near the bottom of the baseplate (inset D) are indistinguishable, being a mixture of ferrite and bainite constituents with a small amount of pearlite evident by some lamellar carbides.\n\nHigh resolution FE-SEM etched micrographs of the as-built 4140 material oriented parallel to the beam path direction are shown in Fig. 6(a)(c) for the Fill, HE, and Keyhole parameters sets, respectively. As\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-06(5)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-06(1)}\n\\end{center}\n\n(d)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-06(2)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-06(4)}\n\\end{center}\n\n(e)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-06(3)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-06(6)}\n\\end{center}\n\n(f)\\\\\nFig. 6. FE-SEM micrographs and inverse pole figure (IPF) maps looking parallel to the beam scan direction (scan direction out of the page) from inside the melt area using the (a,d) Fill, (b,e) High Energy, and (c,f) Keyhole parameters. IPF maps have been filtered for confidence index $\\geq 0.1$. IPF maps ( $d, e, f)$ do not correspond to the same SEM image locations in (a,b,c). White-dashed outlines in (d-f) correspond to prior austenite grain boundaries (PAGs). Both equiaxed and elongated PAGs were observed in the as-build 4140 microstructure.", "start_char_idx": 34255, "end_char_idx": 37761, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "15ccb9ed-2cdb-456a-a513-fc897dd3676a": {"__data__": {"id_": "15ccb9ed-2cdb-456a-a513-fc897dd3676a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "580b37c6-d122-4dae-86fb-2ce5c0634ac6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "48f88225b1fa856aa181d2be1382799d1e6710f9a5bcfb3483601ef217a382f7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b203f552-e471-45fe-888b-9632024d5346", "node_type": "1", "metadata": {}, "hash": "f0b385510ae5957140b6d04dff079c07cbe56cc66e61e152b9ebfff28e089cc3", "class_name": "RelatedNodeInfo"}}, "text": "6. FE-SEM micrographs and inverse pole figure (IPF) maps looking parallel to the beam scan direction (scan direction out of the page) from inside the melt area using the (a,d) Fill, (b,e) High Energy, and (c,f) Keyhole parameters. IPF maps have been filtered for confidence index $\\geq 0.1$. IPF maps ( $d, e, f)$ do not correspond to the same SEM image locations in (a,b,c). White-dashed outlines in (d-f) correspond to prior austenite grain boundaries (PAGs). Both equiaxed and elongated PAGs were observed in the as-build 4140 microstructure.\n\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5d6abf0de1bf85882ee9g-06}\\\\\ndiscussed previously for the transverse micrographs in Fig. 5(a), the melt region microstructure is martensitic based on the appearance of substructure boundaries and light etching of the laths, which is most observable for the HE condition (Fig. 6(b)). The overall weak etching response is consistent with martensite that has undergone very little or no tempering $[22,23]$. The prior austenite grain boundaries (PAGs) and packet/block boundaries can be discerned from similarly oriented features in the IPF maps in Fig. 6(d)-(f) for the Fill, HE, and Keyhole parameters sets, respectively. It should be noted that these IPF maps are not of the same regions as shown in Fig. 6(a)-(c). Possible PAG boundaries have been highlighted in the IPF maps in Fig. 6(d-f) based on similarly oriented martensite packet/blocks. These PAGs show elongation in the build direction due to directional solidification from the Fill and HE parameters sets. The Keyhole parameter set however, does not appear to result in this strong directionality and consists of PAGs that have less anisotropy as outlined in Fig. 6(f). As observed from Xray imaging, the Keyhole parameter set produces a much larger and turbulent melt pool with a deep valley-like shape as in Fig. 2, which may be responsible for the morphology and directionality differences of the austenite grain growth as compared to the Fill and HE conditions. The morphology of the prior austenite grains (PAGs) as observed in these 4140 LPBF samples is comparable to 4140 material processed using LENS [14] where both equiaxed and elongated PAGs were observed in the as-build microstructure. The choice of build parameter sets and the resulting solidification associated with it therefore plays an important role in the grain anisotropy for this 4140 material during LPBF.\n\nSize analysis to determine the effect of build parameter set on the resulting martensite packet/blocks was performed. Size distributions for the Fill, HE, and Keyhole IPF maps (Fig. 6(d-f)) taken parallel to the laser scan direction are shown in Fig. 7(a)-(c). Packet/block diameters were taken from the OIM TSL Analysis software assuming a circular shape and averaged on a per count basis. The size distributions for the as-built material from the Fill, HE, and Keyhole parameter sets are narrow, with grains primarily between 1 and $3 \\mu \\mathrm{m}$ in diameter. The average diameter for each build parameter set is found to be $1.52 \\mu \\mathrm{m}$ for the Fill, $1.57 \\mu \\mathrm{m}$ for the HE, and $1.61 \\mu \\mathrm{m}$ for the Keyhole parameter sets. This is in contrast to the 4140 baseplate material which has a very broad grain size distribution between 1 and $25 \\mu \\mathrm{m}$, with about $98 \\%$ of the grains by count between 1 and $10 \\mu \\mathrm{m}$ in diameter and an average grain size $3.27 \\mu \\mathrm{m}$. The widths of the elongated PAGs (see Fig. $6(\\mathrm{~d}, \\mathrm{e})$ ) for the Fill and HE build parameter sets are on the order of $5 \\mu \\mathrm{m}$ or less.", "start_char_idx": 37216, "end_char_idx": 40854, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b203f552-e471-45fe-888b-9632024d5346": {"__data__": {"id_": "b203f552-e471-45fe-888b-9632024d5346", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "15ccb9ed-2cdb-456a-a513-fc897dd3676a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "08153a538417f526f53945336e94b1b310c6cd5b7b82042fea42bd31f715d65f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0c2a5f80-630b-4d87-a458-04ed72a62082", "node_type": "1", "metadata": {}, "hash": "be4d5b15bbe4b102b47562bf554094bd17bbac54f5155a7e0e62903adacee475", "class_name": "RelatedNodeInfo"}}, "text": "The average diameter for each build parameter set is found to be $1.52 \\mu \\mathrm{m}$ for the Fill, $1.57 \\mu \\mathrm{m}$ for the HE, and $1.61 \\mu \\mathrm{m}$ for the Keyhole parameter sets. This is in contrast to the 4140 baseplate material which has a very broad grain size distribution between 1 and $25 \\mu \\mathrm{m}$, with about $98 \\%$ of the grains by count between 1 and $10 \\mu \\mathrm{m}$ in diameter and an average grain size $3.27 \\mu \\mathrm{m}$. The widths of the elongated PAGs (see Fig. $6(\\mathrm{~d}, \\mathrm{e})$ ) for the Fill and HE build parameter sets are on the order of $5 \\mu \\mathrm{m}$ or less. While it was identified that the varying energy input of the build parameter sets played a direct role on the melt pool and vapor cavity size and shape, the choice of build parameter set during AM was found to have a very small effect on the block/packet size produced upon solidification. The fine block/packet size of the additive samples can be attributed to the very fast cooling rates. Based on the scan speed and the angle of the solidification front (i.e. the angle between the liquid-solid interface at the rear side of the melt pool and the sample top surface), the solidification rates in the Fill, HE, and Keyhole cases are about 0.08, 0.07, and $0.06 \\mathrm{~m} / \\mathrm{s}$, respectively. The lower solidification rate under the Keyhole parameter set results in a slightly larger block/packet size. Both packet and block size directly affect strength with finer packet and block sizes leading to higher strength [24,25], indicative of a potential increase in mechanical strength of the as-printed 4140 material via the Hall-Petch effect. It is interesting to note that Jamshidinia et al. [26] in their study of laser powder bed fusion of AISI 4140 on an EOS M280 concluded the as-built microstructure exhibited mechanical properties (yield strength, tensile strength, elongation, toughness) that were comparable to or superior to the conventionally processed and heat treated 4140.\n\n\\subsection*{3.4. Sources of porosity}\nMultiple forms of porosity have been observed in AM materials and can be summarized as two classes: process-induced porosity and powder-induced porosity. The process-induced pores are generally of two types: lack of fusion, and vaporization. Lack of fusion porosity is caused by insufficient melting of the powder layer and its adherence to the previously deposited layer. This is commonly caused by insufficient input energy conditions; however, this can also be caused by choices in scan strategy such as hatch spacing and adjacent scan path spacing. Pores that result from lack of fusion are generally quite large $(>100 \\mu \\mathrm{m})$ and are easily identifiable by their irregular shapes [27]. These were not explored in the present study because the in situ synchrotron X-ray experiments were limited to single layer build and viewing angles. Vaporization porosity, commonly referred to as keyhole porosity, can occur during the AM process due to excessive metal vaporization and the instability of the vapor cavity when operating under keyhole-mode laser melting conditions. These pores are caused by the collapse of the front and rear vapor cavity walls during these high energy input \"keyholemode\" conditions [28]. These keyhole pores tend to have a relatively large variation in size and shape, as illustrated in Fig. 2. The powderinduced pores refer to those that are transferred from the raw powders (often in gas atomized powders) to the build. When the powder melts, either from laser interaction or by encountering the melt pool, the pore is either able to escape the melt or gets pulled into it and trapped during solidification. This type of porosity is characterized by its near-spherical morphology.", "start_char_idx": 40229, "end_char_idx": 44012, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0c2a5f80-630b-4d87-a458-04ed72a62082": {"__data__": {"id_": "0c2a5f80-630b-4d87-a458-04ed72a62082", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b203f552-e471-45fe-888b-9632024d5346", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ec1ed047f55fb8e00ab840ab3273ffdab8cdff2371122cdc3e4637f290ce29c5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0f193409-7081-4058-98be-5555a4b3eb64", "node_type": "1", "metadata": {}, "hash": "0be333ad6e6e9dc9c4192977803451a8ecf14a98aae277eaf84fa23e496e6810", "class_name": "RelatedNodeInfo"}}, "text": "Vaporization porosity, commonly referred to as keyhole porosity, can occur during the AM process due to excessive metal vaporization and the instability of the vapor cavity when operating under keyhole-mode laser melting conditions. These pores are caused by the collapse of the front and rear vapor cavity walls during these high energy input \"keyholemode\" conditions [28]. These keyhole pores tend to have a relatively large variation in size and shape, as illustrated in Fig. 2. The powderinduced pores refer to those that are transferred from the raw powders (often in gas atomized powders) to the build. When the powder melts, either from laser interaction or by encountering the melt pool, the pore is either able to escape the melt or gets pulled into it and trapped during solidification. This type of porosity is characterized by its near-spherical morphology.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-07}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-07(1)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_5d6abf0de1bf85882ee9g-07(2)}\n\\end{center}\n\n(c)\n\nFig. 7. Martensite block diameter distributions looking parallel to the laser scan direction for the resulting as-built melt pool microstructures produced with the (d) Fill, (e) High Energy, and (f) Keyhole build parameter sets. The choice of build parameter was found to have little effect on the block size produced upon solidification with the average diameter being $1.52 \\mu \\mathrm{m}$ for the Fill, $1.57 \\mu \\mathrm{m}$ for the HE, and $1.61 \\mu \\mathrm{m}$ for the Keyhole parameter sets.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5d6abf0de1bf85882ee9g-08}\n\nFig. 8. Pore diameter distributions for internal 4140 powder porosity (open circles and dashed line) and pores in the newly solidified 4140 LPBF build material (filled circles and solid line) for all 4 build parameter sets: (a) Skin, (b) Fill, (c) High-Energy, and (d) Keyhole. Porosity in the as-built material matches primarily with entrapped gas present in the original powder; however, larger pores $(20-30 \\mu \\mathrm{m})$ are observed in the Keyholing condition resulting from vapor cavity necking.\\\\\nPorosity formation was monitored during the 4140 LPBF process for each build parameter set (see Table 1). Pores in both the new build layer and the baseplate were tracked and measured as they were trapped during solidification. In Fig. 3(b) the pores identified as trapped in the newly solidified material are marked with white arrows. Porosity on the right side of the X-ray image from the Skin build parameter set is too obscured by powder to be identified. Pore diameters were measured in the 4140 powder prior to the laser scanning and for all four build parameter sets post solidification when powder was present and are given in Fig. 8(a)-(d). Over all four scan sections, the average diameter for pores trapped in the original powder was measured to be $7.0 \\pm 2.3 \\mu \\mathrm{m}$ with the frequency distribution in Fig. 8 denoted by open circles and dashed line. The same powder porosity distribution is shown in all four plots for reference. The average pore diameter for the Skin build parameter set (Fig. 8(a)) was $7.2 \\pm 1.4 \\mu \\mathrm{m}, 6.6 \\pm 2.3 \\mu \\mathrm{m}$ for the Fill build parameter set (Fig. 8(b)), $8.6 \\pm 2.8 \\mu \\mathrm{m}$ for the HE build parameter set (Fig. 8(c)), and $10.2 \\pm 6.7 \\mu \\mathrm{m}$ for the Keyhole build parameter set (Fig. 8(d)).", "start_char_idx": 43143, "end_char_idx": 46727, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0f193409-7081-4058-98be-5555a4b3eb64": {"__data__": {"id_": "0f193409-7081-4058-98be-5555a4b3eb64", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0c2a5f80-630b-4d87-a458-04ed72a62082", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dcfb0e2e9b36a0d4ab6afb31b86aa2c69ee015bd263091d1572227bc9f68687a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1b8a27da-b3ef-48cd-85d1-6716d42d64b5", "node_type": "1", "metadata": {}, "hash": "7c81e7f273846365d2c7e877bd6cf3ff2ab9c0d291521590515b70c21b05ff11", "class_name": "RelatedNodeInfo"}}, "text": "Over all four scan sections, the average diameter for pores trapped in the original powder was measured to be $7.0 \\pm 2.3 \\mu \\mathrm{m}$ with the frequency distribution in Fig. 8 denoted by open circles and dashed line. The same powder porosity distribution is shown in all four plots for reference. The average pore diameter for the Skin build parameter set (Fig. 8(a)) was $7.2 \\pm 1.4 \\mu \\mathrm{m}, 6.6 \\pm 2.3 \\mu \\mathrm{m}$ for the Fill build parameter set (Fig. 8(b)), $8.6 \\pm 2.8 \\mu \\mathrm{m}$ for the HE build parameter set (Fig. 8(c)), and $10.2 \\pm 6.7 \\mu \\mathrm{m}$ for the Keyhole build parameter set (Fig. 8(d)). The average pore diameters for the Skin, Fill, and HE build parameter sets are similar to that of the internal porosity of the as-received powder (5-10 $\\mu \\mathrm{m}$ diameter). The Keyhole build parameter set has $70 \\%$ of the measured pores $<10 \\mu \\mathrm{m}$; however, a second distribution of pores is observed with diameters between $20 \\mu \\mathrm{m}$ and $30 \\mu \\mathrm{m}$. These larger pores are formed due to necking of the unstable vapor cavity produced during the laser scan process.\n\nDirect observation of pores from the X-ray images and from the pore size distribution suggest that the common source for most of the pores in the newly solidified material is from trapped gas porosity in the asreceived powder. Cunnighman et al. [29] reached a similar conclusion for electron beam melted Ti-6Al-4 V using X-ray microtomography by inference from porosity size distribution but without direct observation. Only the Keyhole laser scans revealed pores that were not observed to originate from the powder. This is consistent with the X-ray images of the laser scans without powder. Little to no porosity was observed in the Skin, Fill, and HE laser scans without powder present. Pores in the\\\\\nKeyhole build parameter scan without powder are due to excessive material vaporization and necking of the unstable vapor cavity (see Fig. 2). The source of both trapped gas and vaporization pores and the process by which they form in the build material is shown in a series of dynamic X-ray images in Fig. 9. The scale bars in Fig. 9(a) correspond to $50 \\mu \\mathrm{m}$. Shown are eight steps in a time sequence of a trapped gas powder pore from a previously ejected solid powder particle. The fact that this is a solid powder particle, and not liquid spatter, is made obvious by the presence of a \"satellite\" near the one o'clock position. The entrapped gas within this solid powder particle is pulled into the melt pool via Marangoni-driven flow during the HE build parameter laser scan. This is denoted by the red arrow that shows the pore trajectory, a white arrow is used to signify the pores final resting place within the build layer. The powder particle lands on the melt pool tail surface at $220 \\mu$ s, and is quickly melted thereby incorporating the trapped gas pore $(\\sim 12 \\mu \\mathrm{m}$ diameter) into the liquid region in less than $60 \\mu$ s from contact with the liquid surface ( $280 \\mu$ s image). The pore continues to get pulled into the melt ( $280 \\mu$ s to $580 \\mu$ s images) due to Marangoni convection in the melt pool tail. The pore continues to move until finally being trapped in the solidifying material (white arrow in $960 \\mu$ s image) about $75 \\mu \\mathrm{m}$ below the top solidified surface. The size of this particular pore remains unchanged. This source of porosity could certainly be minimized by using porosity-free raw powders. In addition, as shown in this case, ejected porous powder particles can lead to porosity inclusion elsewhere on the powder bed in a previously melted region. Using proper calibration of gas flow over the powder bed and/or innovative scan strategy could potentially minimize such porosity. The current miniature laser powder bed setup does not have a continuous flow of gas over the powder, thus enabling the observation of this effect in the small scan area. Note that the powder particles below the surface of the baseplate in Fig.", "start_char_idx": 46092, "end_char_idx": 50144, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1b8a27da-b3ef-48cd-85d1-6716d42d64b5": {"__data__": {"id_": "1b8a27da-b3ef-48cd-85d1-6716d42d64b5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0f193409-7081-4058-98be-5555a4b3eb64", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "788f35f7e3a5f3ba24b9e0b6997edfc355aa2293aa58a09a3d060194155cb3ea", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5c0bf03c-9386-41cd-8b02-a859cc9b6050", "node_type": "1", "metadata": {}, "hash": "662fe9ca9409c55301f552b69eb926ac67f5eb5808eb292e4786dc87b4ad099f", "class_name": "RelatedNodeInfo"}}, "text": "The pore continues to move until finally being trapped in the solidifying material (white arrow in $960 \\mu$ s image) about $75 \\mu \\mathrm{m}$ below the top solidified surface. The size of this particular pore remains unchanged. This source of porosity could certainly be minimized by using porosity-free raw powders. In addition, as shown in this case, ejected porous powder particles can lead to porosity inclusion elsewhere on the powder bed in a previously melted region. Using proper calibration of gas flow over the powder bed and/or innovative scan strategy could potentially minimize such porosity. The current miniature laser powder bed setup does not have a continuous flow of gas over the powder, thus enabling the observation of this effect in the small scan area. Note that the powder particles below the surface of the baseplate in Fig. 9 are trapped between the baseplate and the glassy carbon window and hence play no role in the build process.\n\nFig. 9(b) is a time sequence of difference images that show the formation of a pore from the collapse of the vapor cavity during a laser scan\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_5d6abf0de1bf85882ee9g-09}\n\n(b)\\\\\nFig. 9. Dynamic X-ray images of the LPBF process of 4140 for (a) the HE and (b) (background subtracted) Keyhole parameters. Each image sequence's first frame is set to $t=0$, with time steps given from that first image. In (a) the pore is within the dashed red circle with the red arrow in each image is used to indicate the pore trajectory, and the white arrow in the last frame denotes the pore's final resting place. Contrast has been enhanced in 400-960 $\\mu$ s to better show the pore. Image sequence in (b) is a divided image set to enhance the contrast in the baseplate. The red curve in the $240 \\mu$ s image denotes the melt pool top surface. All white scale bars in (a) are $50 \\mu \\mathrm{m}$ and in (b) are $100 \\mu \\mathrm{m}$. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) using the Keyhole build parameter set. The scale bars in Fig. 9(b) correspond to $100 \\mu \\mathrm{m}$. The vapor cavity is seen to fluctuate quite severely in the first $20 \\mu$ s of the image sequence. At $40 \\mu$ s neck formation occurs and at $60 \\mu$ s the neck collapses and a pore is left in the wake of the vapor cavity. At $80 \\mu$ s the pore is at its largest diameter ( $\\sim 45 \\mu \\mathrm{m})$ but it continues to shrink as material solidifies around it, leaving a semi-spherical shaped pore with a diameter of $\\sim 24 \\mu \\mathrm{m}$ at about $215 \\mu \\mathrm{m}$ below the melt pool surface (red curve in $240 \\mu$ s image).\n\nEliminating internal powder porosity and keyhole porosity conditions will be key for creating essentially porosity-free structures using AM. This is critical in fatigue limited parts where it has been previously demonstrated that cracks originating from porosity defects are detrimental to fatigue life [30]. Control of powder porosity is quite difficult in powders made using argon or nitrogen gas atomization and can vary from batch-to-batch. However, alternatives to gas atomization such as plasma atomization lead to powder with very little to no internal porosity [31]. Though keyhole-mode conditions can be avoided by the use of a correct set of build parameters, the occurrence of keyhole-like conditions can still occur due to subpar beam path handling, such as overlapping scan regions or beam turn-around conditions. Fine control of the beam path handling and correction of these occurrences during the pre-build process will be essential for mitigating the formation of unintended keyhole porosity.\n\n\\section*{4. Summary remarks and conclusions}\nIn situ high-speed synchrotron X-ray imaging of single-track laser passes demonstrates the importance of additive processing conditions on vapor cavity and melt pool formation, as-printed microstructure, and porosity defect formation on 4140 steel. Further experimentation to examine the heating and cooling profiles produced with varying energy input during the LPBF process of 4140 steel using IR imaging and in situ diffraction of the martensitic phase transformation are planned.", "start_char_idx": 49293, "end_char_idx": 53543, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5c0bf03c-9386-41cd-8b02-a859cc9b6050": {"__data__": {"id_": "5c0bf03c-9386-41cd-8b02-a859cc9b6050", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1b8a27da-b3ef-48cd-85d1-6716d42d64b5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "956a9d7c2bada204e015c23b1399f9f4d448e6d6392550e517cde7170831f45f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ec47eb59-3df5-4835-8228-f35ffc90ebde", "node_type": "1", "metadata": {}, "hash": "284427eb8c0df5ef02d7a5f73397aac9743383c5fc43db565e5d449a2dbb03bc", "class_name": "RelatedNodeInfo"}}, "text": "Though keyhole-mode conditions can be avoided by the use of a correct set of build parameters, the occurrence of keyhole-like conditions can still occur due to subpar beam path handling, such as overlapping scan regions or beam turn-around conditions. Fine control of the beam path handling and correction of these occurrences during the pre-build process will be essential for mitigating the formation of unintended keyhole porosity.\n\n\\section*{4. Summary remarks and conclusions}\nIn situ high-speed synchrotron X-ray imaging of single-track laser passes demonstrates the importance of additive processing conditions on vapor cavity and melt pool formation, as-printed microstructure, and porosity defect formation on 4140 steel. Further experimentation to examine the heating and cooling profiles produced with varying energy input during the LPBF process of 4140 steel using IR imaging and in situ diffraction of the martensitic phase transformation are planned.\n\nThe major conclusions from this study are as follows:\n\n\\begin{enumerate}\n  \\item Direct observation of laser powder bed fusion of AISI 4140 using synchrotron a X-ray imaging technique shows that porosity in the build layer originates primarily from entrapped gas present in the as-received powder irrespective of build parameter set.\n\n  \\item In the case of keyhole-mode build parameter conditions obtained with a high global energy density $\\left(10.4 \\mathrm{~J} / \\mathrm{mm}^{2}\\right)$, large pores $(20-$ $30 \\mu \\mathrm{m}$ ) due to vapor cavity necking are observed.\n\n  \\item Build parameter set did not cause a significant variation in as-built layer height. As noted in previous studies, the layer height was strongly correlated with the initial powder layer height resulting in an average build/powder height ratio of $52 \\%$.\n\n  \\item The vapor cavity and melt pool depth increased significantly by $365 \\%$ and $241 \\%$, respectively, with an increase in global energy density $\\left(5.7-10.4 \\mathrm{~J} / \\mathrm{mm}^{2}\\right.$ ); yet the difference in depth between the vapor cavity and melt pool was consistently $\\sim 20 \\mu \\mathrm{m}$.\n\n  \\item Solidification rates in the Fill, HE, and Keyhole cases are about $0.08,0.07$, and $0.06 \\mathrm{~m} / \\mathrm{s}$, respectively, resulting in martensite block/packet size distributions between 1 and $3 \\mu \\mathrm{m}$ in the as-built material and did not vary significantly with build parameter set. These fine packet/block size distributions potentially suggest a high material strength in the as-printed condition as expected from the Hall-Petch effect.\n\n\\end{enumerate}\n\n\\section*{Acknowledgments}\nThe authors thank Kamel Fezzaa and Alex Deriy at the APS for their assistance with beamline experiments. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office\\\\\nof Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. I. Birko kindly performed sample preparation for microstructure and imaging. C. Enloe and J. Coryell provided the authors with their expertise on ferrous microstructures.\n\n\\section*{Declaration of interest}\nNone.\n\n\\section*{References}\n[1] C.K. Chua, K.F. Leong, 3D Printing and Additive Manufacturing: Principles and Applications, in: World Scientific Publishing Co. Pte. Ltd., New Jersey, 5th ed., 2015.\n\n[2] N. Guo, M.C. 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Sci. 92 (2018) 112224, doi:10.1016/j.pmatsci.2017.10.001.", "start_char_idx": 52578, "end_char_idx": 56396, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ec47eb59-3df5-4835-8228-f35ffc90ebde": {"__data__": {"id_": "ec47eb59-3df5-4835-8228-f35ffc90ebde", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5c0bf03c-9386-41cd-8b02-a859cc9b6050", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6dd6952aebcb938d28b9e1ebcbbe5ba07d5f3ac9cfc0ce3d414f12a8856951af", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f22b2b3d-7d5a-4f99-963e-14255a0b9a63", "node_type": "1", "metadata": {}, "hash": "715ce1ffdcc0bfab94f8f4f985675e6d6476b4ea22c5c19ab5ebdf3644dec64e", "class_name": "RelatedNodeInfo"}}, "text": "Pte. 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Commun.", "start_char_idx": 55922, "end_char_idx": 58483, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f22b2b3d-7d5a-4f99-963e-14255a0b9a63": {"__data__": {"id_": "f22b2b3d-7d5a-4f99-963e-14255a0b9a63", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ec47eb59-3df5-4835-8228-f35ffc90ebde", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b87d80dd35796d523d6028f71f0208451434f16f6d212361cc8fc8b44a88c03f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "80e9106f-e9a1-4b93-95d4-e9b9bfae1431", "node_type": "1", "metadata": {}, "hash": "f1c180b590fc40d6f60a39a8a7071193da8ee57bd42e4c75617b267202fcde61", "class_name": "RelatedNodeInfo"}}, "text": "[10] C.L.A. 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Stephens, J.K. Lim, Fatigue Crack Growth and Retardation in the Welded HAZ of 4140 Steel, Weld. Res. Suppl (1990) 294-304.\n\n[19] W.E. Lukens, R.A. Marris, E.C. Dunn, Infrared Temperature Sensing of Cooling Rates for Arc Welding Control, 1982.\n\n[20] J. Xie, Dual Beam Laser Welding, Weld. Res 81 (2002) 223-230 doi:10-2002-XIE-s.\n\n[21] U. Tradowsky, J. White, R.M. Ward, N. Read, W. Reimers, M.M. Attallah, Selective laser melting of AlSi10Mg: Influence of post-processing on the microstructural and tensile properties development, Mater. Des. 105 (2016) 212-222, doi:10.1016/j.matdes.2016.05.066.\n\n[22] D. De Knijf, R. Petrov, C. F\u00f6jer, L.A.I. Kestens, Effect of fresh martensite on the stability of retained austenite in quenching and partitioning steel, Mater. Sci. Eng. A 615 (2014) 107-115, doi:10.1016/j.msea.2014.07.054.\n\n[23] M.J. Santofimia, L. Zhao, R. Petrov, C. Kwakernaak, W.G. Sloof, J. 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Rollett, Evaluating the Effect of Processing Parameters on Porosity in Electron Beam Melted Ti-6Al-4V via Synchrotron X-ray Microtomography 68 (2016) 2-9, doi:10.1007/s11837-015-1802-0.\n\n[28] W.E. King, H.D. Barth, V.M. Castillo, G.F. Gallegos, J.W. Gibbs, D.E. Hahn, C. Kamath, A.M. Rubenchik, Observation of keyhole-mode laser melting in laser powderbed fusion additive manufacturing, J. Mater. Process. Technol. 214 (2014) 29152925, doi:10.1016/j.jmatprotec.2014.06.005.\n\n[29] A. Nicolas, A.D. Rollett, E. Anagnostou, R. Cunningham, M.D. Sangid, E. Fodran, J. Madsen, Analyzing the effects of powder and post-processing on porosity and properties of electron beam melted Ti-6Al-4V, Mater. Res. Lett. 5 (2017) 516-525, doi:10.1080/21663831.2017.1340911.", "start_char_idx": 60021, "end_char_idx": 62543, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "86eb0aa7-89d1-410c-855f-6b2789a8b403": {"__data__": {"id_": "86eb0aa7-89d1-410c-855f-6b2789a8b403", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "80e9106f-e9a1-4b93-95d4-e9b9bfae1431", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f634a5bec8a8314f657f93c4be89b8bfee946458c672ce554a830e670130cc75", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "69557b64-a80e-4286-8059-2a1b07e70d4a", "node_type": "1", "metadata": {}, "hash": "7a2d28d1936e6ba412195e24eff3916264295ed3d778b5a0f2e260f3ce64f71c", "class_name": "RelatedNodeInfo"}}, "text": "Gallegos, J.W. Gibbs, D.E. Hahn, C. Kamath, A.M. Rubenchik, Observation of keyhole-mode laser melting in laser powderbed fusion additive manufacturing, J. Mater. Process. Technol. 214 (2014) 29152925, doi:10.1016/j.jmatprotec.2014.06.005.\n\n[29] A. Nicolas, A.D. Rollett, E. Anagnostou, R. Cunningham, M.D. Sangid, E. Fodran, J. Madsen, Analyzing the effects of powder and post-processing on porosity and properties of electron beam melted Ti-6Al-4V, Mater. Res. Lett. 5 (2017) 516-525, doi:10.1080/21663831.2017.1340911.\n\n[30] Q. Wang, D. Apelian, D. Lados, Fatigue behavior of A356-T6 aluminum cast alloys. Part I. Effect of casting defects, J. Light Met. 1 (2001) 73-84, doi:10.1016/S1471-5317(00)00008-0.\n\n[31] M.N. Ahsan, A.J. Pinkerton, R.J. Moat, J. Shackleton, A comparative study of laser direct metal deposition characteristics using gas and plasma-atomized Ti-6Al-4V powders, Mater. Sci. Eng. A 528 (2011) 7648-7657, doi:10.1016/j.msea.2011.06.074.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{multirow}\n\n\\title{Journal Pre-proof }\n\n\n\\author{Louca R. 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Goossens*, Brecht Van Hooreweder\\\\\nKU Leuven, Mechanical Engineering Department, Member of Flanders Make\\\\\nCelestijnenlaan 300 - 3001 Leuven - Belgium}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nA virtual sensing approach for monitoring meltpool dimensions using high speed coaxial imaging during laser powder bed fusion of metals\n\nLouca R. Goossens, Brecht Van Hooreweder\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-01}\n\\end{center}\n\nPII:\n\nS2214-8604(21)00088-9\n\nDOI:\n\n\\href{https://doi.org/10.1016/j.addma.2021.101923}{https://doi.org/10.1016/j.addma.2021.101923}\n\nReference: ADDMA101923\n\nTo appear in: Additive Manufacturing\n\nReceived date: 1 October 2020\n\nRevised date: 22 January 2021\n\nAccepted date: 16 February 2021\n\nPlease cite this article as: Louca R. Goossens and Brecht Van Hooreweder, A virtual sensing approach for monitoring melt-pool dimensions using high speed coaxial imaging during laser powder bed fusion of metals, Additive Manufacturing, (2020) doi:\\href{https://doi.org/10.1016/j.addma.2021.101923}{https://doi.org/10.1016/j.addma.2021.101923}\n\nThis is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.\n\n(C) 2020 Published by Elsevier.\n\n\\section*{A virtual sensing approach for monitoring melt-pool dimensions using high speed coaxial imaging during laser powder bed fusion of metals }\n\n\n\\begin{abstract}\nMetal parts produced by Laser Powder Bed Fusion (L-PBF) are frequently used for demanding applications. To meet stringent safety and certification requirements, a better understanding of melt-pool behavior and stability during processing is desired. This work presents a novel, fast and economically feasible virtual sensing approach for accurate estimation of melt-pool depth and width during L-PBF of metals. In a first step, the melt-pool width is determined by GPU-based processing of images from a high-speed coaxial camera monitoring system. In a second step, a physics-based analytical model is used to calculate the melt-pool depth-to-width ratio from the processing conditions and material properties. In a third and last step, the results from the first two steps are combined to estimate the melt-pool depth. Experimental validation of these predicted melt-pool dimensions is performed on 316L SS single layer strips that are consecutively produced, cross-sectioned, polished and etched to reveal the actual melt-pool boundaries.", "start_char_idx": 63492, "end_char_idx": 67051, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "af3e2abc-f8ba-488d-820b-3d26d2c5fd3f": {"__data__": {"id_": "af3e2abc-f8ba-488d-820b-3d26d2c5fd3f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "69557b64-a80e-4286-8059-2a1b07e70d4a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cd4ccf10a02d9fc4120ad0064557612d69d39c4744f857d90269765e43fb4232", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d11e51ec-70b6-4a6b-bbee-76159f7c1fd9", "node_type": "1", "metadata": {}, "hash": "cb90b58542398977ae61c0f6c5158a685a7f15081df3996b2f4fb07b23b7d4dd", "class_name": "RelatedNodeInfo"}}, "text": "To meet stringent safety and certification requirements, a better understanding of melt-pool behavior and stability during processing is desired. This work presents a novel, fast and economically feasible virtual sensing approach for accurate estimation of melt-pool depth and width during L-PBF of metals. In a first step, the melt-pool width is determined by GPU-based processing of images from a high-speed coaxial camera monitoring system. In a second step, a physics-based analytical model is used to calculate the melt-pool depth-to-width ratio from the processing conditions and material properties. In a third and last step, the results from the first two steps are combined to estimate the melt-pool depth. Experimental validation of these predicted melt-pool dimensions is performed on 316L SS single layer strips that are consecutively produced, cross-sectioned, polished and etched to reveal the actual melt-pool boundaries. The results\n\\end{abstract}\n\n\\footnotetext{${ }^{*}$ Corresponding author\n\nEmail address: Louca.Goossens@kuleuven. be (Louca R. Goossens)\n}\nindicate an average relative error on the predicted melt-pool depth of $9.9 \\%$ and $2.8 \\%$ for the full L-PBF parameter range and for the optimal parameter range respectively. This gives confidence in the predictive capabilities of a virtual sensing approach using coaxial camera images for the assessment of the melt-pool depth and process stability.\n\nKeywords: , L-PBF, monitoring, melt-pool, image processing, metals\n\n\\section*{1. Introduction}\nLaser Powder Bed Fusion (L-PBF), also referred to as Selective Laser Melting (SLM), is an Additive Manufacturing technique (AM). As a production process it offers distinct advantages over conventional manufacturing techniques. In particular it allows for the production of very complex geometries directly from a CAD model. Applications are typically found in highly demanding industries such as aerospace and the medical industry. One of the main challenges all AM technologies face is the issue of quality assurance and certification. Due to the nature of the layer-based process, defects such as porosity can manifest themselves throughout the entire volume of the produced component. The occurrence of such defects can lead\n\nto unwanted variations in the mechanical properties and as such affect final product performance so far as to reducing it to scrap [1]. Typically, timeand cost-ineffective post production quality control techniques such as X-ray computed tomography are necessary to guarantee that the final component meets the required specification.\n\nIn this work a virtual sensing approach is presented and validated for 316L Stainless Steel (SS). Virtual sensing, at its core, is the combination of sensor\\\\\nand model data in order to achieve feasible and/or economical alternatives to costly or impossible to measure physical quantities [2]. In this two-pronged strategy, melt-pool modeling, and coaxial camera monitoring are combined in order to estimate, in situ, the melt-pool depth and width during L-PBF of metals.\n\nExtracting melt-pool widths from camera images has shown to be a promising method for achieving confidence in L-PBF part quality. Lane et al. have presented several methods which can be used to calibrate and characterize the spatial resolution of a coaxial camera system for determining the melt-pool temperature, cooling rates and dimensions $[3,4]$. While, Zheng et al. showed that using an infrared camera with a limited frame rate, the melt-pool width can be determined from an infrared image for Ti$6 \\mathrm{~V}-4 \\mathrm{Al}$ [5]. However, a significant calibration with microscopy results was required and only a limited processing range was examined. Other authors applied machine learning techniques on coaxial camera images, with the aim of detecting anomalies in the melt-pool shape. Kwon et al. showed that that the quantification of melt-pool images using deep neural networks could be utilized to determine whether the process is in normal or abnormal state [6]. Also, Yuan et al. demonstrated that using a two-step machine learning approach the track width, standard deviation and track continuity could be predicted without the need for ex situ measurements [7]. Directly quantifying the melt-pool depth in situ proves to be more challenging. Indeed, one of the most prevalent quoted downsides of coaxial camera monitoring is a lack of the melt-pool depth information [8, 1]. For in situ melt-pool depth\\\\\nmeasurements, transmission X-ray imaging is the method of choice for many authors $[9,10,11,12,13,14]$.", "start_char_idx": 66115, "end_char_idx": 70705, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d11e51ec-70b6-4a6b-bbee-76159f7c1fd9": {"__data__": {"id_": "d11e51ec-70b6-4a6b-bbee-76159f7c1fd9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "af3e2abc-f8ba-488d-820b-3d26d2c5fd3f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ff7a5f10db4cf2a9ef5c60b0689e94069635bcbee6cfba005e6d51957406cf28", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c5ae6c92-062c-482f-83ea-c8dd068241ce", "node_type": "1", "metadata": {}, "hash": "86b006c452a31b3f8d56cb8e78aa031e9a435e039a54fba1994def4a8271b40d", "class_name": "RelatedNodeInfo"}}, "text": "Other authors applied machine learning techniques on coaxial camera images, with the aim of detecting anomalies in the melt-pool shape. Kwon et al. showed that that the quantification of melt-pool images using deep neural networks could be utilized to determine whether the process is in normal or abnormal state [6]. Also, Yuan et al. demonstrated that using a two-step machine learning approach the track width, standard deviation and track continuity could be predicted without the need for ex situ measurements [7]. Directly quantifying the melt-pool depth in situ proves to be more challenging. Indeed, one of the most prevalent quoted downsides of coaxial camera monitoring is a lack of the melt-pool depth information [8, 1]. For in situ melt-pool depth\\\\\nmeasurements, transmission X-ray imaging is the method of choice for many authors $[9,10,11,12,13,14]$. While it provides high quality temporal and spatial information, the technique is associated with high costs and stringent safety measures, making it economically unattractive in a manufacturing environment and limiting the applicability to specialized laboratories. An alternative to measure the depth directly is proposed by Fleming and Allen et al. They show that with the combined use of inline coherent imaging and direct laser absorptance measurements, conduction and keyhole modes can be clearly distinguished on the basis of their time-resolved measurements $[15,16]$. As such, in situ measurements of the melt-pool geometry still prove difficult in a production environment.\n\nThe second part of the virtual sensing methodology is the modeling component. The modeling of $\\mathrm{L}-\\mathrm{PBF}$ is a well-researched topic, where the aim is to achieve a relationship between the inputs and outputs of the system. In this case, the processing conditions, machine parameters, and powder/material properties can be considered as the input. The resulting solidified melt-pool geometry (width, depth) can either be directly interpreted as the output or indirectly linked to final part density. In general, models can be datadriven (DD) or physics based. In data-driven models, inputs and outputs are linked through a series of observations or experiments typically yielding a set of algebraic expressions. Previously, authors have reported a successful application of these techniques, typically employing a Neural Network (NN) or a machine learning approach $[7,6,17]$. While DD models have shown great promise under specific operating conditions, they are often unable to\\\\\nuncover the underlying physical principles. Furthermore, with a plethora of different machine builders, powder producers, varying environmental conditions and part geometries, there is a substantial risk of construing misleading or erroneous relationships due to the inherent properties of the materials, machines and additionally the circumstantial conditions of the experiments. This makes DD models vulnerable to changing conditions. It also limits their scaling capability, relying heavily on large and reliable datasets for achieving acceptable performance in previously \"untrained\" conditions. Models based on physics, on the other hand, are expressed through a set of equations, be it differential or partial differential equations. These models attempt to incorporate the relevant physical and continuity equations that describe the phenomena under investigation. One of the advantages of physics-based models is the inherent reliability they bring over a large range of conditions without the need for new data or costly experiments when changes are made to the process or environmental conditions, e.g. a change of L-PBF machine or powder producer. Contrary to DD models, physics-based models don't yield immediate algebraic expressions relating the input and output. Depending on the desired outcome, the equations can either be numerically solved using Finite-Element or -Volume (FE/FV) methods or the models can be strategically simplified and solved analytically. The FE/FV approach has already shown to yield high-fidelity results corresponding well with experimental data $[18,19,20]$. In a similar fashion, analytical models have been found to unveil underlying trends with relation to the melt-pool dimensions and processing conditions [21, 22, 23, 24, 25]. For virtual sensing, any kind of model capable of linking processing conditions and melt-pool dimensions\\\\\nwould suffice. Taking into account computational efficiency and generality of the model, an analytical model, as introduced by Fabbro [24] is used in this study.\n\nIn conclusion, this paper presents and validates a methodology for estimating melt-pool width and depth during L-PBF of metals. The first section describes the monitoring setup and the model employed. After which, in the second section, the model performance is validated using metallographic cross sections.", "start_char_idx": 69839, "end_char_idx": 74740, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c5ae6c92-062c-482f-83ea-c8dd068241ce": {"__data__": {"id_": "c5ae6c92-062c-482f-83ea-c8dd068241ce", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d11e51ec-70b6-4a6b-bbee-76159f7c1fd9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7e6a1a1a78b76b4d1cf00ff0aa63894bcb2eccb9c790646e0878dc19013601d1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c834a981-2750-40cd-a1ca-4ae0ac2f8360", "node_type": "1", "metadata": {}, "hash": "177e0928c97a2147502a56b1add8e0ac4a46ea51f31fc424d52c868a5b8e82f4", "class_name": "RelatedNodeInfo"}}, "text": "The FE/FV approach has already shown to yield high-fidelity results corresponding well with experimental data $[18,19,20]$. In a similar fashion, analytical models have been found to unveil underlying trends with relation to the melt-pool dimensions and processing conditions [21, 22, 23, 24, 25]. For virtual sensing, any kind of model capable of linking processing conditions and melt-pool dimensions\\\\\nwould suffice. Taking into account computational efficiency and generality of the model, an analytical model, as introduced by Fabbro [24] is used in this study.\n\nIn conclusion, this paper presents and validates a methodology for estimating melt-pool width and depth during L-PBF of metals. The first section describes the monitoring setup and the model employed. After which, in the second section, the model performance is validated using metallographic cross sections. The third section describes the comparison of the width measurements extracted from the camera images, and the metallographic widths. Finally, in the last section, the model data and camera images are combined and the predicted melt-pool depth is compared with the depth as obtained by metallographic analysis.\n\n\\section*{2. Materials and methods}\n\\subsection*{2.1. Materials, thermophysical properties and process parameters}\nIn this work, an in-house developed L-PBF machine is used. A detailed description of the specifications and setup are given in section 2.2. The powder material used, is gas atomized 316L SS powder with a size distribution between $10-45 \\mu \\mathrm{m}$. This material is chosen for validating the predicted meltpool depths in this work, as melt-pool boundaries of L-PBF 316L SS can be easily visualized after cross-sectioning, polishing and chemical etching.\n\nSingle layer strips $(10 \\times 2[\\mathrm{~mm}])$ are scanned on top of a larger 316L SS\n\nL-PBF substrate $(25 \\times 15 \\times 1.5[\\mathrm{~mm}])$. These are all simultaneously pro-\\\\\nduced in a single production run, with no delay between the production of the substrate and the strips, as to mimic realistic processing conditions. Each of the 6 different substrates produced, contains 8 such strips. This makes a total of 48 distinct strips. For each strip, different combinations of laser power and scan speed are applied. The parameters range from 100 to $600 \\mathrm{~W}$ in increments of $100 \\mathrm{~W}$ for the applied laser power and 400 to $1100 \\mathrm{~mm} / \\mathrm{s}$ with increments of $100 \\mathrm{~mm} / \\mathrm{s}$ for the scan speed. The layer thickness is set at $30 \\mu \\mathrm{m}$ and a hatch spacing of $105 \\mu \\mathrm{m}$ is applied. The vectors are scanned in the long direction $(10 \\mathrm{~mm}$ ) with a zig-zag strategy. Labels are applied to each substrate and below each single layer strip in order to differentiate them later on. The sample geometry is shown in Figure 1. To evaluate the melt-pool dimensions post-production, the samples are cut using wire EDM near the center of the strip's long axis. The sample cross sections are subsequently polished and electrochemical etching is applied for 30 seconds using an aqueous solution of $10 \\%$ oxalic acid at 7 V. Finally, a Keyence VHX$6000^{\\circledR}$ optical microscope is used to measure the melt-pool depth and width dimensions. For each strip, 7 individual melt-pools are measured in order to evaluate the process stability.\n\nFor the predictive modeling component, the relevant thermophysical properties of bulk 316L SS material are taken from [26] with exception of the optical absorption, which is taken from [27]. The values are taken for solid material near the melting temperature. A summary of these properties is shown in Table 1.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-09}\n\\end{center}\n\nFigure 1: A rendering of the produced sample geometry, for clarity, the height of the single layer strips are not to scale.", "start_char_idx": 73864, "end_char_idx": 77790, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c834a981-2750-40cd-a1ca-4ae0ac2f8360": {"__data__": {"id_": "c834a981-2750-40cd-a1ca-4ae0ac2f8360", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c5ae6c92-062c-482f-83ea-c8dd068241ce", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dd04588bb261d0706f1978cb6733b4f67e292b9cc05aaca99d7dc18741f6fff0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a8c672ee-9c64-4d1e-b8af-80cf6d8f5ee3", "node_type": "1", "metadata": {}, "hash": "e66473a4a74287ab491802469915172b59679ee93cb9818c282051dbfe5d5373", "class_name": "RelatedNodeInfo"}}, "text": "For each strip, 7 individual melt-pools are measured in order to evaluate the process stability.\n\nFor the predictive modeling component, the relevant thermophysical properties of bulk 316L SS material are taken from [26] with exception of the optical absorption, which is taken from [27]. The values are taken for solid material near the melting temperature. A summary of these properties is shown in Table 1.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-09}\n\\end{center}\n\nFigure 1: A rendering of the produced sample geometry, for clarity, the height of the single layer strips are not to scale.\n\n\\begin{center}\n\\begin{tabular}{|l|c|c|c|}\n\\hline\n\\multicolumn{1}{|c|}{Property} & Value & Units & Symbol \\\\\n\\hline\nDensity & 7269 & $\\mathrm{~kg} / \\mathrm{m}^{3}$ & $\\rho$ \\\\\n\\hline\nThermal Conductivity & 31.1 & $W /(\\mathrm{m} * \\mathrm{~K})$ & $k$ \\\\\n\\hline\nHeat Capacity & 710 & $\\mathrm{~J} /(\\mathrm{kg} * \\mathrm{~K})$ & $\\mathrm{C}$ \\\\\n\\hline\nLiquidus Temperature & 1690 & $K$ & $T m$ \\\\\n\\hline\nEvaporation Temperature & 3090 & $K$ & $T b$ \\\\\n\\hline\nOptical Absorption & 0.34 & - & $A$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 1: Summary of the relevant thermophysical properties of bulk 316L SS taken from $[26,27]$.\n\n\\subsection*{2.2. Experimental setup}\n\\subsection*{2.2.1. Optical train}\nFor this research an in-house developed L-PBF machine is used. The core of the optical train is a $1 \\mathrm{~kW}$ fiber laser with a wavelength of $1080 \\mathrm{~nm}$. The system's focal length is $340 \\mathrm{~mm}$ and has a measured $1 / e^{2}$ spot size of 37.5 $\\mu \\mathrm{m}$. The general layout of the monitoring setup is similar to those previously published by $[28,29,30]$ be it with newer and upgraded components. For clarity, a brief description of the constituents and working principle is given here.\n\nThe optical path consists out of a forward propagation part and a backwards propagation part as schematically shown in Figure 2. The optical pathways are separated by wavelength using a thin-film interference filter with a 950 $\\mathrm{nm}$ cut-on wavelength (b). In forward propagation, the laser beam (a) is guided and focused onto the powder-bed (e). Starting from the laser source, the beam passes through the thin-film filter (b) after which it is positioned and focused by a galvanometer scanner (c) in conjunction with an f-theta lens (d). In operation, a melt-pool is created (e) and in accordance with Planck's law, emits what is referred to as process light [31]. The emitted process light is partially recaptured by the f-theta lens and travels back up to the thin-film interference filter (b). Here the process light below $950 \\mathrm{~nm}$ is reflected and thus separated from the laser light. The remainder of the process light is then directed towards the backward propagation part of the optical train. The main components of the backward propagation part are a high speed CMOS camera [32] (h) and a large area silicon photodiode sensor (g). The process light is evenly distributed among the two using a 50/50 beam splitter\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-11}\n\\end{center}\n\nFigure 2: Schematic layout of the coaxial monitoring system in the L-PBF setup.\n\n(f). Additionally, both sensors are band pass filtered in a range of 800 to 950 $\\mathrm{nm}$. This prevents any stray ambient and laser light from interfering with the measurements.\n\n\\subsection*{2.2.2.", "start_char_idx": 77151, "end_char_idx": 80643, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a8c672ee-9c64-4d1e-b8af-80cf6d8f5ee3": {"__data__": {"id_": "a8c672ee-9c64-4d1e-b8af-80cf6d8f5ee3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c834a981-2750-40cd-a1ca-4ae0ac2f8360", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9c01bbc6db268470a215cbbe24da37ed702f51eb726b20fe719018875461a462", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "adb3ac17-577c-43c6-83d6-a2b6baea6a29", "node_type": "1", "metadata": {}, "hash": "9d4f599c03acb230b500bb0390fb0bc382b82b4d5af6075e570231f023a3c816", "class_name": "RelatedNodeInfo"}}, "text": "The remainder of the process light is then directed towards the backward propagation part of the optical train. The main components of the backward propagation part are a high speed CMOS camera [32] (h) and a large area silicon photodiode sensor (g). The process light is evenly distributed among the two using a 50/50 beam splitter\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-11}\n\\end{center}\n\nFigure 2: Schematic layout of the coaxial monitoring system in the L-PBF setup.\n\n(f). Additionally, both sensors are band pass filtered in a range of 800 to 950 $\\mathrm{nm}$. This prevents any stray ambient and laser light from interfering with the measurements.\n\n\\subsection*{2.2.2. Data acquisition}\nDue to the highly localized energy input and the high processing speeds involved, the L-PBF process is characterized by high temporal and spatial temperature gradients. This results in the highly dynamic melt-pool behavior typically associated with L-PBF. Several authors have measured and reported the relevant time scales for melt-pool flow behavior using high speed x-ray imaging and/or multi-physics simulations $[12,13,11,10,18,14]$. With the exception of the keyhole collapsing when the laser power source is cut off [13], the relevant time scales are shown to be in the order of tens to hundreds of $\\mu \\mathrm{s}$. This implies that the acquisition rate should be in the same range,\\\\\nat least, if the melt-pool dynamics are desired to be captured. A second requirement is having the potential to capture the entire build process. This is rooted in the ascertainment that for optimal processing parameters, densities typically exceed $99.9 \\%$. This would result in a low probability of defect detection when only short snapshots are considered. To fulfill both of these requirements a custom data acquisition system was developed, capable of sustaining continuous processing and recording of monitoring data. This system is built up using a custom FPGA based frame grabber/processor linked to a fiber coupled Network-Attached Storage (NAS). The NAS is equipped with a RAID 0 array of four 1 TB Solid State Disks (SSD), resulting in a sustainable data rate up to $1 \\mathrm{~GB} / \\mathrm{s}$ and a total capacity of $4 \\mathrm{~TB}$. The camera interface used is the \"Full\" configuration Camera-Link ${ }^{\\circledR}$ interface, capable of data rates of up to $850 \\mathrm{MB} / \\mathrm{s}$ [33]. Balancing the availability of light, resolution and frame rate, the acquisition speed for the camera is set at 50 $\\mu$ s or expressed alternatively, 20.000 frames per second (fps).\n\n\\subsection*{2.3. Image processing}\nThe images captured by the coaxial camera are 8-bit gray-scale images, measuring 120 by 120 pixels in size. The calibrated pixel size is $11.8 \\mu \\mathrm{m}$, resulting in a field of view of 1416 by $1416 \\mu \\mathrm{m}$. An example image showing a representative melt-pool is presented in Figure 3. The melt-pool is shown to be slightly off-center in the $\\mathrm{x}$-direction, this is due to the discrete $\\mathrm{x}$-offsetting capabilities of the camera, for the region of interest selection (modulo 80) [32]. To extract the melt-pool width, a series of image processing steps are applied. The image processing is done using MATLAB ${ }^{\\circledR}$ [34]. Due to the large amount of frames that need to be processed, the individual processing\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-13}\n\\end{center}\n\nFigure 3: A representative raw image taken at $20.000 \\mathrm{fps}$ using a coaxial camera in the KU Leuven L-PBF setup and showing a melt-pool traveling upwards.\n\nsteps were carefully selected and a balance was struck between the computational efficiency and the measurement accuracy. As Graphical Processing Units (GPUs) are specifically designed to be efficient in the processing of images, individual processing steps capable of leveraging the CUDA ${ }^{\\circledR}$ GPU library [35] are preferred.", "start_char_idx": 79920, "end_char_idx": 83945, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "adb3ac17-577c-43c6-83d6-a2b6baea6a29": {"__data__": {"id_": "adb3ac17-577c-43c6-83d6-a2b6baea6a29", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a8c672ee-9c64-4d1e-b8af-80cf6d8f5ee3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "83a5e498bc9b7aa86161ca9fc08a714aa74ef8e8baa3d1603bd50d84a194099e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fb6842fb-c224-48a5-8b6a-073a6c23e1cb", "node_type": "1", "metadata": {}, "hash": "8f7614160e0735c2ee97aabc3f24c835f1b84157c318b5af94ccb8e6835324f2", "class_name": "RelatedNodeInfo"}}, "text": "The image processing is done using MATLAB ${ }^{\\circledR}$ [34]. Due to the large amount of frames that need to be processed, the individual processing\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-13}\n\\end{center}\n\nFigure 3: A representative raw image taken at $20.000 \\mathrm{fps}$ using a coaxial camera in the KU Leuven L-PBF setup and showing a melt-pool traveling upwards.\n\nsteps were carefully selected and a balance was struck between the computational efficiency and the measurement accuracy. As Graphical Processing Units (GPUs) are specifically designed to be efficient in the processing of images, individual processing steps capable of leveraging the CUDA ${ }^{\\circledR}$ GPU library [35] are preferred. This way, also simultaneous parallel processing of different frames is possible, enabling the entire processing chain to be scalable and capable of running tasks in parallel. Combined with the high computational efficiency, this will ensure that the algorithms and processing steps are transferable to an on-line system where frames can be processed on-line, extending the capabilities from monitoring and off-line analysis to on-line monitoring and control. The processing steps for determining the melt-pool depth are discussed further in section 2.4.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-14}\n\\end{center}\n\nFigure 4: Image processing workflow; a) Original image, b) Sobel edge detection, c) Addition of the center line, d) Boolean \"and\" operation, e) Overlay of original image and melt-pool outline.\n\nAs a frame can contain more than one object due to the occurrence of spatter or due to break up of the melt-pool tail, the first step in the image processing is to filter out the melt-pool outline. This is done using a combination of an edge detection using the Sobel operator [36], and the relative location of the laser in the frame. The Sobel operator consists out of two kernels to be convoluted with the original image. The operation results in the approximate derivative for each pixel in the horizontal and vertical direction. By combining both directions, the total derivative of the original image is acquired. Based on this derivative or gradient image, edges in the original image are identified. Figure 4.b shows the result of this operation. There are some distinct advantages to using edge detection compared to fixed value thresholding. First, no calibration is required for different materials or alloys since the boundary is defined by the gradient and not the absolute grey value. Second, erroneous extraction due to variance in the intensity is reduced to a minimum. Such variances could be the results of melt-pool plume or spatter ejection. After the edge detection step, the resulting image is binary, with only the melt-pool outline remaining. As the camera is synchronized with the scanner controls, the direction of travel can be determined for each frame. With the knowledge of the beam center and the direction of travel available, a line with single pixel width is construed across the frame. This line is referred to as the ruler-line and is perpendicular to the direction of travel and passes through the laser beam center. As the analytical solution for the temperature field of a moving Gaussian beam shows, perpendicular to the direction of travel and passing through the laser beam center is where the maximum of the melt-pool width occurs [37]. The melt-pool width can\\\\\nthus be extracted by calculating the distance between the two intersection points of the ruler-line and the melt-pool outline. The intersecting points are determined using a Boolean \"AND\" operation. An extra operation is still required due to the fact that both the outline and the ruler-line are of single pixel width, and single pixel width elements can intersect without the need for overlapping pixels as shown in Figure 5.a. The line is therefore diluted using a square structuring element of two by two pixels as demonstrated in Figure 5.b. This guarantees the existence of, at least, one intersection point. Figure 4.e shows a composite image where the melt-pool outline and accompanying width line are superimposed on the original image. As seen, the melt-pool outline and width measurement correspond well with the original melt-pool image. The time complexity of the proposed workflow is dominated by that of the edge detection, which is $\\mathrm{O}(\\mathrm{n} \\log (\\mathrm{n}))$ with $\\mathrm{n}$ being the total number of elements.", "start_char_idx": 83184, "end_char_idx": 87750, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fb6842fb-c224-48a5-8b6a-073a6c23e1cb": {"__data__": {"id_": "fb6842fb-c224-48a5-8b6a-073a6c23e1cb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "adb3ac17-577c-43c6-83d6-a2b6baea6a29", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "95ae61ba9cd2cb5ebda7485fcd96496b7a374960927476fa0aff41e37022d112", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bf25a380-ee65-40d5-a324-b0e678fb702a", "node_type": "1", "metadata": {}, "hash": "c204358c2a46a6b23914826277f814b19ad45d8a93c68184547a6418ff36cd6f", "class_name": "RelatedNodeInfo"}}, "text": "The intersecting points are determined using a Boolean \"AND\" operation. An extra operation is still required due to the fact that both the outline and the ruler-line are of single pixel width, and single pixel width elements can intersect without the need for overlapping pixels as shown in Figure 5.a. The line is therefore diluted using a square structuring element of two by two pixels as demonstrated in Figure 5.b. This guarantees the existence of, at least, one intersection point. Figure 4.e shows a composite image where the melt-pool outline and accompanying width line are superimposed on the original image. As seen, the melt-pool outline and width measurement correspond well with the original melt-pool image. The time complexity of the proposed workflow is dominated by that of the edge detection, which is $\\mathrm{O}(\\mathrm{n} \\log (\\mathrm{n}))$ with $\\mathrm{n}$ being the total number of elements. The remaining steps are $\\mathrm{O}(1)$ assuming parallel execution of the Boolean \"AND\" operation.\n\nExpanding the presented work-flow to also measure the melt-pool length is trivial. Indeed, a rotation of 90 degrees on the ruler line is sufficient. However, determining and validating the melt-pool length is challenging for a number of reasons. First of all, the melt-pool length in process, is a dynamic condition of which no direct measurable trace remains in the post-process condition. This encumbers the validation of online melt-pool length measurements. Secondly, the work-flow presented here utilizes a Sobel operator for edge detection. Figure 6 shows an illustrative raw melt-pool image (a), and the resulting convolution of that image and the horizontal Sobel oper-\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3ea5497605dea1905837g-17}\n\nFigure 5: a) Two single pixel elements (melt outline and the ruler-line) without a pixel in common, even though intersection is clearly present b) Application of the dilution operator on the ruler-line ensures the existence of pixel overlap for intersecting elements.\n\nator (b). The convoluted image shows two different regions, with the first being the melt-pool depression, and the second, downstream of the first, is the melt-pool tail. It is clear that the melt-pool depression yields a strong edge well suited for a reliable dimensional measurement of the melt-pool width. However, along the scanning axis, the extent of the depression does not truthfully represent the melt-pool length. Numerous transmission X-ray imaging studies $[9,10,11,12,13,14]$ and works employing $\\mathrm{FE} / \\mathrm{FV}$ simulations $[18,19,20]$ indeed confirm that molten material remains present and eventually consolidates in the tail section of the melt-pool. As is clear from Figure $6 \\mathrm{~b})$, the coaxial camera is able to register the melt-pool tail. However, the edge it provides is very weak. This directly affects the accuracy and robustness of the measurement method. For the aforementioned reasons, in this work, only the melt-pool width is extracted from the camera images.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3ea5497605dea1905837g-18}\n\nFigure 6: a) A representative raw melt-pool image, b) The convolution of the raw image and the horizontal Sobel operator, showing a strong edge for the melt-pool depression, and weak edges for the melt-pool tail.\n\n\\subsection*{2.4. Melt-pool modeling}\nThe analytic scaling law model used to predict the melt-pool depth-towidth ratios $(e / d)$ is taken from Fabbro $[25,24]$. It is construed using several simplifying strategic hypotheses, which can be summarized as follows:\n\n\\begin{enumerate}\n  \\item The power absorbed by the melt-pool $(P \\times A)$ is equal to the product of the laser beam power $P$, and the material absorption coefficient $A$, taken at the laser's wavelength.\n\n  \\item The melt-pool transverses the substrate at a steady state scan speed $V$ with an initial substrate temperature of $T_{0}$.\n\n  \\item The inner boundary of the melt-pool geometry, or keyhole is considered to be a vertical cylinder with a diameter $d$, equal to the laser spot size and with a length of $e$, representative of the melt-pool depth.", "start_char_idx": 86833, "end_char_idx": 91020, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bf25a380-ee65-40d5-a324-b0e678fb702a": {"__data__": {"id_": "bf25a380-ee65-40d5-a324-b0e678fb702a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fb6842fb-c224-48a5-8b6a-073a6c23e1cb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e2050fe61e8dde2ec2157ca9aff2329bed977e57f794e7a2455a1eb2664a4607", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a0ae04f6-69a0-40d8-9326-11742f1c2567", "node_type": "1", "metadata": {}, "hash": "42b895458acce7d2c032712c49611ca04d36dc33b79ce3e841a7dde83bd223fc", "class_name": "RelatedNodeInfo"}}, "text": "Melt-pool modeling}\nThe analytic scaling law model used to predict the melt-pool depth-towidth ratios $(e / d)$ is taken from Fabbro $[25,24]$. It is construed using several simplifying strategic hypotheses, which can be summarized as follows:\n\n\\begin{enumerate}\n  \\item The power absorbed by the melt-pool $(P \\times A)$ is equal to the product of the laser beam power $P$, and the material absorption coefficient $A$, taken at the laser's wavelength.\n\n  \\item The melt-pool transverses the substrate at a steady state scan speed $V$ with an initial substrate temperature of $T_{0}$.\n\n  \\item The inner boundary of the melt-pool geometry, or keyhole is considered to be a vertical cylinder with a diameter $d$, equal to the laser spot size and with a length of $e$, representative of the melt-pool depth.\n\n  \\item The inner wall temperature of the melt-pool is constant and remains at $T_{v}$ which is the material boiling temperature.\n\n  \\item The melt-pool behavior is characterized by some additional thermophysical properties. Being the heat capacity $C[J /(k g * K)]$, the density $\\rho\\left[\\mathrm{kg} / \\mathrm{m}^{3}\\right]$ and the thermal conductivity $k[W /(m * K)]$.\n\n\\end{enumerate}\n\nFor these hypotheses the Vashy-Buckingham $\\pi$ theorem is applied and a solution for the thermal model is found. This yield the expression for the depth-to-width ratio $R$ found in equation 1. For a full derivation of this solution, the reader is referred to preceding publications by Fabbro et al. $[24,25]$.\n\nFrom condition \\# 3 and \\# 4 it's clear that the employed model assumes the process to be governed by keyhole mode melting. Where the recoil pressure generates a cylindrical void about the size of the laser beam diameter. While the inner wall temperature boundary conditions is set at boiling temperature, necessary to sustain the recoil pressure and subsequent keyhole. The model thus attempts to describe the resulting solidified melt-pool shapes through modeling of the generated keyhole as a result of the recoil pressure. It should be noted that the melt-pool width in LPBF is often much larger than the beam diameter and exhibits a parabole-like cross section as opposed to the proposed cylindrical shape. Nevertheless, Fabbro et al. have shown that a good correspondence with experimental results for both laser welding and LPBF are achieved $[24,25]$.\n\n\n\\begin{equation*}\nR=\\frac{e}{d}=\\frac{R_{0}}{1+\\frac{V}{V_{0}}} \\tag{1}\n\\end{equation*}\n\n\nwith:\n\n$$\nR_{0}=\\frac{A \\times P}{n \\times d \\times k \\times\\left(T_{v}-T_{0}\\right)}, V_{0}=\\frac{2 \\times n \\times k}{m \\times d \\times \\rho \\times C}\n$$\n\nwhere\n\n$A$ is the material absorption coefficient at the laser wavelength\n\n$P$ is the laser power $[W]$\n\n$k$ is the thermal conductivity $[W /(m * K)]$\n\n$T_{v}$ is the evaporation temperature $[K]$\n\n$T_{0}$ is the substrate temperature $[K]$\n\n$d$ is the beam diameter $[m]$\n\n$\\rho$ is the material density $\\left[\\mathrm{kg} / \\mathrm{m}^{3}\\right]$\n\n$C$ is the material heat capacity $[J /(k g * K)]$\n\nThe parameters $m$ and $n$ in equation 1 are a function of the P\u00e9clet range for the given processing conditions. They are derived from a 2D FE-analysis, as no analytical solution for the power conducted through the cylindrical melt-pool surface exists. The numerical solution is approximated by a linear function, where the factors $m$ and $n$ are a piecewise approximate function dependent on the P\u00e9clet number [24], with the P\u00e9clet number being expressed as :\n\n\n\\begin{equation*}\nP e=\\frac{V \\times \\rho \\times C \\times d}{2 \\times k} \\tag{2}\n\\end{equation*}\n\n\nFor the given conditions and parameters in section 2.1, the P\u00e9clet number ranges between $1.2 \\leq P e \\leq 3.4$.", "start_char_idx": 90215, "end_char_idx": 93914, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a0ae04f6-69a0-40d8-9326-11742f1c2567": {"__data__": {"id_": "a0ae04f6-69a0-40d8-9326-11742f1c2567", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bf25a380-ee65-40d5-a324-b0e678fb702a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4d779a4a0e992f304a269c08ffba095fa347792b1189828b4a9463a8f841773e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b4d9e60b-9742-4773-9d3e-56acde20fab0", "node_type": "1", "metadata": {}, "hash": "d89afa22d767b6c10bb066a39965cc991077581cd820ad7d713d6f0b15170649", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{equation*}\nP e=\\frac{V \\times \\rho \\times C \\times d}{2 \\times k} \\tag{2}\n\\end{equation*}\n\n\nFor the given conditions and parameters in section 2.1, the P\u00e9clet number ranges between $1.2 \\leq P e \\leq 3.4$. In this range, $m$ and $n$ are set to $m=5$ and $n=3[24]$. Finally, to estimate the substrate temperature $T_{0}$, the maximum of the recorded baseplate temperatures is selected as a reference. The temperature was measured in process using a type $\\mathrm{K}$ thermocouple mounted to the bottom of the baseplate. A temperature of $T_{0} \\approx 473 \\mathrm{~K}$ was reached near the end.\n\nOverall, errors in the input parameters propagate linearly, except for the beam diameter $(d)$, which exhibits a quadratic behavior, making it the most critical and sensitive parameter in all of the equation.\n\n\\section*{3. Results and discussion}\n\\subsection*{3.1. Metallographic analysis of the melt-pool dimensions}\nFigure 7 displays a number of illustrative vertical cross sections of the etched 316L SS parts produced by L-PBF. The metallographic images in Figure 7 a-b-c shown here, were taken at the same magnification. Looking at these cross sections, a large span of melt-pool dimensions is observed, with Figure 7 a. showing rather shallow melt-pools in conduction mode melting $(R=0.59)$, Figure 7 b. showing some melt-pools near the optimal processing parameters $(R=2.54)$, and finally, Figure $7 \\mathrm{c}$. showing some very\n\nhigh aspect ratio melt-pools which are deep into the keyhole mode melting regime $(R=4.43)$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3ea5497605dea1905837g-22}\n\nFigure 7: Illustrative vertical cross sections showing melt-pool dimensions of etched 316L SS L-PBF parts for a range of processing conditions including a) $100 \\mathrm{~W}-800 \\mathrm{~mm} / \\mathrm{s}$, b) $300 \\mathrm{~W}-800 \\mathrm{~mm} / \\mathrm{s}$, c) $600 \\mathrm{~W}-800 \\mathrm{~mm} / \\mathrm{s}$, d) Definition of metallographic melt-pool dimensions.\n\nFigure 7 d. shows the definition of the melt-pool dimensions, indicating that the width $d$ and depth $e$ are measured at the original substrate level. The width is measured between the melt-pool boundaries along a horizontal line, while the depth is defined as the distance between the top surface of the original substrate and the bottom of the melt-pool boundary. The aspect ratios $(e / d)$ are calculated from the obtained mean values for $e$ and $d$. Table A. 1 shows the measured melt-pool dimensions and aspect ratios for the given range of L-PBF processing parameters. The melt-pool depths for the processing parameters of $600 \\mathrm{~W}, 400-500 \\mathrm{~mm} / \\mathrm{s}$ are linearly extrapolated as their depth exceeded the substrate thickness. The measured melt-pool $e / d$ ratios range from 0.47 up to 5.65. All samples show the expected morphological/dimensional evolution of the melt-pool, except for the parameters sets of $600 \\mathrm{~W}$ and 1000-1100 mm/s. Here a sudden drop in the $e / d$ ratio is observed (4.68 to 1.68) which cannot be explained by the change in energy density. Figure 8 shows the cross sections of interest, revealing unstable, broad and shallow melt-pools. A possible explanation here is the onset of hydrodynamic instabilities as a result of the melt-pool elongating under higher scan speeds and laser power. This results in high length to width ratios $(\\geq \\pi)$, which can in turn cause Plateau - Rayleigh instabilities. This effect is often referred to as \"humping\" in laser welding and sets an upper boundary on the maximum processing speed at elevated laser power levels [38, 39].\n\n\\subsection*{3.2.", "start_char_idx": 93702, "end_char_idx": 97344, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b4d9e60b-9742-4773-9d3e-56acde20fab0": {"__data__": {"id_": "b4d9e60b-9742-4773-9d3e-56acde20fab0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a0ae04f6-69a0-40d8-9326-11742f1c2567", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fcb085226f5223ab0c6bca89bfab7f7a4eb52b356ebd18cf64187acffe529219", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7386d140-8cef-4595-83b3-392543af8da4", "node_type": "1", "metadata": {}, "hash": "fb3243842c71058028a748a2366e363b5b3bead53a9e61c9931e779401f392aa", "class_name": "RelatedNodeInfo"}}, "text": "Here a sudden drop in the $e / d$ ratio is observed (4.68 to 1.68) which cannot be explained by the change in energy density. Figure 8 shows the cross sections of interest, revealing unstable, broad and shallow melt-pools. A possible explanation here is the onset of hydrodynamic instabilities as a result of the melt-pool elongating under higher scan speeds and laser power. This results in high length to width ratios $(\\geq \\pi)$, which can in turn cause Plateau - Rayleigh instabilities. This effect is often referred to as \"humping\" in laser welding and sets an upper boundary on the maximum processing speed at elevated laser power levels [38, 39].\n\n\\subsection*{3.2. Model validation}\nTo assess the model's predictive qualities, the measured $e / d$ ratios are compared to the predicted $e / d$ ratios. Figure 9, shows a 3D mapping of the results with on the $\\mathrm{x}$ - and $\\mathrm{y}$-axis the scan speed and laser power, and with\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3ea5497605dea1905837g-24}\n\nFigure 8: Vertical cross-sections of etched 316L SS L-PBF parts showing unstable shallow melt-pools for a) $600 \\mathrm{~W}-1000 \\mathrm{~mm} / \\mathrm{s}$ and b) $600 \\mathrm{~W}-1100 \\mathrm{~mm} / \\mathrm{s}$, possibly due to hydrodynamic instability sometimes referred to as \"humping\" in laser welding.\n\nthe z-axis denoting the melt-pool depth-to-width ratio $(e / d)$. For clarity, the measured ratios are linearly interpolated between the vertices of the green plane. The gray plane indicates the models' predicted ratios. As seen qualitatively, a good fit is observed between the measured and predicted ratios. To quantify the model performance, the relative errors are calculated as follows: err $=\\left(R_{\\text {meas }}-R_{\\text {predict }}\\right) / R_{\\text {meas }}$. This definition of relative error is maintained throughout the remainder of the text.\n\nThe average relative error over the whole processing range is $-14.3 \\%$, with a standard deviation of $40 \\%$. The largest residual is $-208 \\%$ for $600 \\mathrm{~W}$, $1100 \\mathrm{~mm} / \\mathrm{s}$ for which the predicted ratio is 3.32 and the measured is 1.08 . This processing range includes two zones where the difference between the predicted and measured melt-pool dimensions is relatively large :\n\n\\begin{itemize}\n  \\item Zone 1 , is the processing range corresponding to $600 \\mathrm{~W}$ and $400-500$ $\\mathrm{mms} / \\mathrm{s}$. For this range, the metallographic depths are extrapolated depths as mentioned in Table A. 1 due to them exceeding the sample\n\\end{itemize}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-25(1)}\n\\end{center}\n\nb)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-25}\n\\end{center}\n\nFigure 9: Comparisons of the calculated and measured aspect ratio $e / d$, in function of the laser power $P$ and scan speed $V$. Expressed in a) as a heat map of the relative error, and in b) as a three-dimensional comparison showing the \"model ratios\" and \"Metallographic ratios\".\\\\\nthickness. As such, they do not represent the actual melt-pool characteristics and are considered unreliable measurement data.\n\n\\begin{itemize}\n  \\item Zone 2, is the processing range corresponding to $600 \\mathrm{~W}$ and 1000-1100 $\\mathrm{mm} / \\mathrm{s}$ which is related to the observed instabilities as shown in Figure 8. The scaling law model employed doesn't take into account the physics involved in the dynamic \"humping\" process, hence the model is unable to predict the occurrence of such instabilities and is indeed expected to show poor predictive capacities.", "start_char_idx": 96671, "end_char_idx": 100328, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7386d140-8cef-4595-83b3-392543af8da4": {"__data__": {"id_": "7386d140-8cef-4595-83b3-392543af8da4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b4d9e60b-9742-4773-9d3e-56acde20fab0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "fde68667e5f6c5cb6164f0f932620f822ac788753651f453cb9d301190b60434", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3cdbe651-de11-47e7-85fc-87d1171945aa", "node_type": "1", "metadata": {}, "hash": "27046dfc075aa94271a760bfd1664a057e0fc866493fe9e9767fb4cd33e511aa", "class_name": "RelatedNodeInfo"}}, "text": "Expressed in a) as a heat map of the relative error, and in b) as a three-dimensional comparison showing the \"model ratios\" and \"Metallographic ratios\".\\\\\nthickness. As such, they do not represent the actual melt-pool characteristics and are considered unreliable measurement data.\n\n\\begin{itemize}\n  \\item Zone 2, is the processing range corresponding to $600 \\mathrm{~W}$ and 1000-1100 $\\mathrm{mm} / \\mathrm{s}$ which is related to the observed instabilities as shown in Figure 8. The scaling law model employed doesn't take into account the physics involved in the dynamic \"humping\" process, hence the model is unable to predict the occurrence of such instabilities and is indeed expected to show poor predictive capacities.\n\\end{itemize}\n\nWith the exclusion of the results from zone 1 and 2, the relative error amounts to $-4.6 \\%$, with a standard deviation of $18.9 \\%$. The highest residual is $-59.11 \\%$ for $200 \\mathrm{~W}, 1100 \\mathrm{~mm} / \\mathrm{s}$ for which the predicted ratio is 1.11 and the measured ratio is 0.696 . This large relative error is also to be expected. The observed geometry for these conditions is similar to the one shown in Figure 7 a., where a conduction mode melting regime together with its characteristic shape is presented. The conduction mode melt-pool shape differs strongly from the proposed cylindrical keyhole geometry, voiding simplifying hypothesis \\# 3 in section 2.4 .\n\nIn general, the predicted depth-to-width ratios are biased slightly towards overestimation. Examining the standard deviation on the relative error and comparing it to the standard deviations of the metallographic measurements, similar magnitudes are observed. With the average of the relative standard deviations for the measured depths and widths being $12.16 \\%$ and $9.69 \\%$, respectively. This illustrates the limitation of the steady state conditions assumed by the model employed here, which cannot completely capture the real complex and dynamic relation between processing parameters $P$ and $V$\\\\\nand the resulting melt-pool characteristics $e$ and $d$. This can, in part, also explain the observed standard deviation of the relative model error. Furthermore, the steady state assumption limits generalization of the model in transient situations, such as those occurring at the start and stop of a vector of for geometries that accumulate heat. For the start-stop behavior, the dynamics of the hardware components and the opening and closing behavior of the melt-pool play a vital role in the evolution of the melt-pool dimensions. While heat accumulating features such as overhangs, or insufficient support material can significantly increase the temperature above the expected substrate temperature. No such mechanisms are included in the steady state formulation and as a result, the model performance can be expected to deviate largely from the results presented here.\n\n\\subsection*{3.3. Camera measurements}\nFor each of the processing conditions, the melt-pool widths are extracted from the camera images using the method described in section 2.3. The number of samples per parameter set is only dependent on the scan speed as the acquisition rate is fixed at 20.000 frames per second. The number of images\n\nper condition ranges between 9167 and 3472 for $400 \\mathrm{~mm} / \\mathrm{s}$ and $1100 \\mathrm{~mm} / \\mathrm{s}$ respectively. The average values and standard deviations for the melt-pool widths extracted from the camera images are reported in Table A.2.\n\nFigure 10 shows the metallographic melt-pool width compared to the camera melt-pool width for the examined processing range. The average relative error is $-2.8 \\%$ with a standard deviation of $18.5 \\%$. As seen, the results correspond well, with a slight tendency for underestimation at high energy densities and overestimation at lower energy densities. This effect is par-\\\\\ntially a result of the change in the image gradient of the melt-pool, as the melt-pool temperature changes with the processing conditions, so does the emitted intensity, changing the overall contrast. This is due to the fixed linear dynamic range of the camera sensor, which influences the perceived object size in extreme dark-light contrasts [32]. Additionally, Lane et al. showed that changes is the melt-pool cooling rates, due to changes in the processing parameters, are observable in melt-pool camera images [40].", "start_char_idx": 99600, "end_char_idx": 104006, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3cdbe651-de11-47e7-85fc-87d1171945aa": {"__data__": {"id_": "3cdbe651-de11-47e7-85fc-87d1171945aa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7386d140-8cef-4595-83b3-392543af8da4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ba4e98895b812cd18e7087a75d7b3046429fe0825390b14a7e6b8d48a4c31584", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "edbf5ebb-00de-4d75-9d8e-42d2c84c3d9b", "node_type": "1", "metadata": {}, "hash": "f94f7b7fd3c95f8edbdf8106e2b67997d9199d2ca3090dbff1efe954dd29d04b", "class_name": "RelatedNodeInfo"}}, "text": "Figure 10 shows the metallographic melt-pool width compared to the camera melt-pool width for the examined processing range. The average relative error is $-2.8 \\%$ with a standard deviation of $18.5 \\%$. As seen, the results correspond well, with a slight tendency for underestimation at high energy densities and overestimation at lower energy densities. This effect is par-\\\\\ntially a result of the change in the image gradient of the melt-pool, as the melt-pool temperature changes with the processing conditions, so does the emitted intensity, changing the overall contrast. This is due to the fixed linear dynamic range of the camera sensor, which influences the perceived object size in extreme dark-light contrasts [32]. Additionally, Lane et al. showed that changes is the melt-pool cooling rates, due to changes in the processing parameters, are observable in melt-pool camera images [40]. As the cooling rate and overall contrast determine the observed gradient in the camera images, the extracted width can deviate, as the algorithm relies on the approximate derivatives of the image for edge detection. As such, the underestimation for large melt-pools and overestimation for small melt-pool can be explained partly. Furthermore, considering the limited camera resolution of $11.8 \\mu \\mathrm{m}$ and the melt-pool width ranging between $\\approx 70 \\mu \\mathrm{m} \\leq d \\leq 220 \\mu \\mathrm{m}$, a measurement error of only a single pixel can result in a large relative error, i.e. $\\approx 16.8 \\% \\leq$ err $\\leq 5.4 \\%$. Despite this high sensitivity, the highest relative error is $-54 \\%$ for $400 \\mathrm{~W}, 1100 \\mathrm{~mm} / \\mathrm{s}$ with a metallographic width of $114.29 \\mu \\mathrm{m}$ and camera width of $176.05 \\mu \\mathrm{m}$. This implies an error of about 6 pixels in total (5.23 exact), or 3 pixels on either edge of the melt-pool. Hence it is to be expected that the measurement accuracy can still be improved by adopting techniques/technologies that improves the dynamic range such as high-dynamic-range imaging, automatic shutter speed adjustments or by further increasing the pixel resolution [41].\n\nAdditionally, a comparison is made between the Relative Standard Deviations (RSD) of the metallographic widths and the camera widths. The 2-D correlation coefficient was found to be 0.8. As seen in Figure 11, the gen-\\\\\na)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-29(1)}\n\\end{center}\n\nb)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-29}\n\\end{center}\n\nFigure 10: Comparisons of the calculated and measured camera widths, in function of the laser power $P$ and scan speed $V$. Expressed in a) as a heat map of the relative error, and in b) as a three-dimensional comparison showing the \"camera width\" and \"Metallographic width\".\\\\\neral trends of the camera width standard deviations correspond well to those of the metallographic measurements. However, the camera measurements exhibit an offset towards higher standard deviations. This contradicts the expectation that for the camera measurements the standard deviation is expected to be smaller, as the sample size is comparatively larger than that of the metallographic measurements. However, the larger standard deviations can be explained by examining the specific measurement conditions. Firstly, the measurement resolution of the camera measurements is about an order of magnitude lower than the metallographic measurements. The resulting discretization errors, by default, increase the observed standard deviation for the camera measurements. Additionally, the camera measurements also include the transient effects of the formation and closure of the melt-pool. These dynamic effects span about ten frames for a total vector length of 200 frames $(1000 \\mathrm{~mm} / \\mathrm{s}, 10 \\mathrm{~mm}, 20.000 \\mathrm{fps})$. While they have a limited effect on the mean, they are expected to have a more outspoken effect on the standard deviation. In contrast, the metallographic cross sections are taken near the center of the long axis, at steady state input conditions.", "start_char_idx": 103107, "end_char_idx": 107262, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "edbf5ebb-00de-4d75-9d8e-42d2c84c3d9b": {"__data__": {"id_": "edbf5ebb-00de-4d75-9d8e-42d2c84c3d9b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3cdbe651-de11-47e7-85fc-87d1171945aa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e54b05d010d5681eb9cd5bfa17809a5a20b41166543db548b5b87380e5e503a0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9a38284a-6175-4586-80c3-ba10abccf617", "node_type": "1", "metadata": {}, "hash": "22bde88b494b633495baff5589c4a0b325efcb68429e2cedffc92895376e819f", "class_name": "RelatedNodeInfo"}}, "text": "However, the larger standard deviations can be explained by examining the specific measurement conditions. Firstly, the measurement resolution of the camera measurements is about an order of magnitude lower than the metallographic measurements. The resulting discretization errors, by default, increase the observed standard deviation for the camera measurements. Additionally, the camera measurements also include the transient effects of the formation and closure of the melt-pool. These dynamic effects span about ten frames for a total vector length of 200 frames $(1000 \\mathrm{~mm} / \\mathrm{s}, 10 \\mathrm{~mm}, 20.000 \\mathrm{fps})$. While they have a limited effect on the mean, they are expected to have a more outspoken effect on the standard deviation. In contrast, the metallographic cross sections are taken near the center of the long axis, at steady state input conditions. Thirdly, part of melt-pool image can be distorted by the harsh environmental conditions, such as the presence of the melt-pool plume, spatter ejections and powder particles. All of the aforementioned arguments contribute to the higher relative standard deviation of the camera measurements. Still, despite the offset, the good correspondence of the standard deviations implies that variations in the melt-pool width are also detected as variations in the camera images. As such, the camera images can prove to be a valuable tool in assessing the process stability.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-31}\n\\end{center}\n\nFigure 11: 3D comparison of the Relative Standard Deviations (RSD) on the camera and metallographic melt-pool widths in function of the laser power $P$ and scan speed $V$.\n\n\\subsection*{3.4. Virtual sensing results}\nFinally, the modeling results and the camera measurements are combined. To assess the melt-pool depth for a given processing condition, the camera width $\\left(d_{\\text {camera }}\\right)$ is extracted from the image and the melt-pool ratio $(R)$ is taken from the model. The estimated melt-pool depth is expressed as follows:\n\n$$\ne_{\\text {est }}=R \\times d_{\\text {camera }}\n$$\n\nThe comparison between the metallographic depth and the estimated depth is given in Figure 12. With exception of the processing conditions in the \"humping\" regime, the estimated depths are close to the measured depths. The average relative error equals $9.9 \\%$ with a standard deviation of $30.8 \\%$. The high standard deviation is the result of the underperformance of both the model and the camera at the extremities of the processing range ex-\\\\\namined. The largest residual amounts to $121.6 \\%$ for 200 W, 1100 mm/s. For these conditions, both the model and the camera overestimate the melt-pool dimensions. Indeed the processing range examined is very large and deviates largely from what is considered to being an optimal processing range. If a second assessment is made using a smaller subsection of the processing parameters, in the vicinity of the optimal conditions $(250 \\mathrm{~W}, 600 \\mathrm{~mm} / \\mathrm{s})$ i.e. ranging from $200-400 \\mathrm{~W}$ and $500-700 \\mathrm{~mm} / \\mathrm{s}$, an average error of $2.8 \\%$ and standard deviation of $8.18 \\%$ is recorded. This demonstrates a significant improvement of the overall fit compared to the full range of processing parameters. For the reduced range the highest residual is only $11.5 \\%$ for 300 W, $600 \\mathrm{~mm} / \\mathrm{s}$. In absolute values, this translates to an error of $\\approx 50 \\mu \\mathrm{m}$ for a total depth of $\\approx 450 \\mu \\mathrm{m}+/-11 \\mu \\mathrm{m}$.\n\nThese results demonstrate the effectiveness and value of the virtual sensing approach presented in this work. With the exception of the camera pixel size, no calibrations were necessary or performed. The model is fed with typical data sheet material and machine properties, and the melt-pool widths are extracted using a series of straightforward, commonplace and scalable image processing steps. Nevertheless, the measured melt-pool width and predicted depth correspond well with metallographic measurements over a very wide range of processing parameters.", "start_char_idx": 106373, "end_char_idx": 110547, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9a38284a-6175-4586-80c3-ba10abccf617": {"__data__": {"id_": "9a38284a-6175-4586-80c3-ba10abccf617", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "edbf5ebb-00de-4d75-9d8e-42d2c84c3d9b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8ec885ebd159587f93dad7bf3d94eeba2b8456ea6405517084a55790344200b4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "11b8c831-281e-4d18-8ddd-47ea9afc1742", "node_type": "1", "metadata": {}, "hash": "416f33650709d459010db6cdae28c513e25dfab0825c341774e3bbaa9f054405", "class_name": "RelatedNodeInfo"}}, "text": "For the reduced range the highest residual is only $11.5 \\%$ for 300 W, $600 \\mathrm{~mm} / \\mathrm{s}$. In absolute values, this translates to an error of $\\approx 50 \\mu \\mathrm{m}$ for a total depth of $\\approx 450 \\mu \\mathrm{m}+/-11 \\mu \\mathrm{m}$.\n\nThese results demonstrate the effectiveness and value of the virtual sensing approach presented in this work. With the exception of the camera pixel size, no calibrations were necessary or performed. The model is fed with typical data sheet material and machine properties, and the melt-pool widths are extracted using a series of straightforward, commonplace and scalable image processing steps. Nevertheless, the measured melt-pool width and predicted depth correspond well with metallographic measurements over a very wide range of processing parameters.\n\nThe ability to determine the melt-pool dimensions without the need for destructive testing is of great use, for instance, for fast determination of a suitable processing parameter window. For the experiments performed in this work, the time required to process all the data and to generate the pro-\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-33(1)}\n\\end{center}\n\nb)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-33}\n\\end{center}\n\nFigure 12: Comparisons of the predicted and and metallographic melt-pool depth in function of the laser power $P$ and scan speed $V$. Expressed in a) as a heat map of the relative error, and in b) as a three-dimensional comparison showing the \"Predicted depth\" and \"Metallographic depth\".\\\\\ncess maps for the melt-pool width and depth was less than five minutes on a desktop computer equipped with a NVIDEA QUADRO M4000 ${ }^{\\circledR}$. Of these five minutes about two were spent on the image processing, which amounts to an average of about $5 \\mathrm{~ms}$ per frame. These processing times are negligible compared to the time consuming experimental approach for generating processing maps using traditional parameter optimization techniques. Those traditional techniques usually involve the manufacturing of many samples with different processing parameters, after which those samples are removed from the baseplate, cross-sectioned, polished, and etched for microstructural analysis.\n\nAdditionally, the observed 2D correlation (0.8) between the standard deviation of the camera and the metallographic measurements is promising for the application of this virtual sensing approach in the field of on-line monitoring and control. Indeed, the correlation suggests that instabilities in the melting behavior are also observed by the camera, suggesting that the melt-pool dimensions can be accurately assessed frame by frame. This in combination with the fact that the camera runs at a high frame rate and is synchronized with the scanner positions, resulting in highly resolved measurements ( $50 \\mu \\mathrm{m}$ at $1000 \\mathrm{~mm} / \\mathrm{s}$ ), could reveal the occurrence of defects due to the variation of the melt-pool dimensions in a highly localized manner.\n\nRegarding the expandability of the methodology to other materials and L-PBF machines, several authors have demonstrated the generality of scaling law models over different materials and different AM setups. For the\\\\\nmodel used in this work, Fabbro et al. showed good correspondence with experimental results for different materials and processes such as St 35 steel, INC 625, Ti-6Al-4V and $\\mathrm{Cu}[24,25]$. Similarly Rubenchick et al. have shown that with a scaling law model pertaining to conduction mode melting, a good model fit can be achieved with experimental data from different machines and materials [23]. Additionally, other authors have reported that using normalized enthalpy formulations, experimental data can be collapsed into a single curve for different processing conditions, materials and machines [21, 22, 42]. This strengthens the belief that these types of models describe a universal relationship for linking L-PBF process conditions with melt-pool size and shape.\n\nOverall, the final accuracy of the virtual sensing methodology is contingent on the individual accuracy of the modeling component and the camera width measurements. Both these components propagate their errors linearly, with the beam diameter being the only input parameter showing nonlinear behavior. Hence, further improvement to either of these components will benefit the overall performance. For the camera measurements, it is shown that the limited resolution and varying illumination conditions are restricting factors.", "start_char_idx": 109734, "end_char_idx": 114360, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "11b8c831-281e-4d18-8ddd-47ea9afc1742": {"__data__": {"id_": "11b8c831-281e-4d18-8ddd-47ea9afc1742", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9a38284a-6175-4586-80c3-ba10abccf617", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e2551d84524189582bdd7dd322c4ce6e58ac574776e989d3fc586f714c9609d6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "303d05d3-45b2-4cd0-9973-2254f88a16df", "node_type": "1", "metadata": {}, "hash": "fb6a24a46802ee0c97cb3ade91bb5759737d5d1637c13ef980c895bd5b510ec4", "class_name": "RelatedNodeInfo"}}, "text": "Similarly Rubenchick et al. have shown that with a scaling law model pertaining to conduction mode melting, a good model fit can be achieved with experimental data from different machines and materials [23]. Additionally, other authors have reported that using normalized enthalpy formulations, experimental data can be collapsed into a single curve for different processing conditions, materials and machines [21, 22, 42]. This strengthens the belief that these types of models describe a universal relationship for linking L-PBF process conditions with melt-pool size and shape.\n\nOverall, the final accuracy of the virtual sensing methodology is contingent on the individual accuracy of the modeling component and the camera width measurements. Both these components propagate their errors linearly, with the beam diameter being the only input parameter showing nonlinear behavior. Hence, further improvement to either of these components will benefit the overall performance. For the camera measurements, it is shown that the limited resolution and varying illumination conditions are restricting factors. For the modeling component, omitting fluid behavior physics such as Plateau-Rayleigh instabilities, Marangoni convection and viscosity [43], but also the lack of ray propagation effects, can cause the approximation errors observed. Moreover, in a production setting, the range of processing parameters will be much smaller, and both the model and camera are shown to have better performance near the optimal parameter set. Nevertheless,\\\\\nas modeling and simulation of L-PBF advance and camera sensor technology improves, so will the accuracy of the virtual sensing methodology as demonstrated here.\n\n\\section*{4. Conclusions}\nMeeting the stringent quality and repeatability standards typical for high end industries is a challenging task for L-PBF produced parts. In this sense, the ability to assess the melt-pool dimensions (width and depth) is of great interest. As components produced by L-PBF are essentially the combination of many individually stacked weld lines, the overlap and penetration depth determine to great extent the final part density and quality $[44,43,1]$. In this work, the results for determining the melt-pool width and depth using a virtual sensing approach are presented, for which the relative errors and standard deviations are summarized in Table 2. It is shown that for L-PBF 316L SS, melt-pool widths can be extracted over large range of processing parameters (100-600 W and 400-1100 mm/s), using a coaxial camera setup at high frame rates. The extracted widths show good correlation with metallographic cross sections with an average relative error of $-2.8 \\%$. Additionally, the depth is predicted with high accuracy by combining the analytic scaling law model from Fabbro et al. [24, 25] for melt-pool ratios and the extracted melt-pool widths from the coaxial camera. For the full parameter range the average relative error on the predicted depth is $9.9 \\%$. If a smaller processing range, closer to the optimal processing parameters, is examined, then the relative error on the predicted depth decreases to $2.8 \\%$. This gives confidence in the predictive capabilities of a virtual sensing approach using coaxial\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|}\n\\hline\n\\begin{tabular}{c}\nMetallographic \\\\\nvalidation of : \\\\\n\\end{tabular} & \\begin{tabular}{c}\nInvestigated \\\\\nparameter \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage error \\& standard deviation \\\\\nfull range \\\\\n\\end{tabular} & \\begin{tabular}{c}\nAverage error \\& standard deviation \\\\\nreduced range \\\\\n\\end{tabular} \\\\\n\\hline\n\\multirow{2}{*}{Analytical model} & \\begin{tabular}{c}\ndepth /width \\\\\n$(\\mathrm{R}=\\mathrm{e} / \\mathrm{d})$ \\\\\n\\end{tabular} & err : $-14.3 \\%$ & err : $-4.6 \\%$ \\\\\n\\hline\n\\multirow{2}{*}{} & width & std : $40 \\%$ & std : $18.9 \\%$ \\\\\n\\hline\n\\multirow{2}{*}{Virtual sensing} & (d) & std : $18.5 \\%$ & $/$ \\\\\n & (e) & err : $9.9 \\%$ & err : $2.8 \\%$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 2: Summary of the metallographic validations for the model ratios, camera widths and virtual sensed depths.\n\ncamera images for the assessment of the melt-pool depth.", "start_char_idx": 113252, "end_char_idx": 117448, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "303d05d3-45b2-4cd0-9973-2254f88a16df": {"__data__": {"id_": "303d05d3-45b2-4cd0-9973-2254f88a16df", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "11b8c831-281e-4d18-8ddd-47ea9afc1742", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0b79c62940c7bc1ef7d9c497cc3094ba1783a3a94f71ce699f856f6bb00b1fa7", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2fd61136-811f-4c8b-af64-ddee2eec3033", "node_type": "1", "metadata": {}, "hash": "b9d2ac50becc9ede39f9b13d077bc6e72cf504863590b5b7c37020763c757bd2", "class_name": "RelatedNodeInfo"}}, "text": "camera images for the assessment of the melt-pool depth. Furthermore, the data revealed a remarkable correlation between the standard deviation on the metallographic measurements and the camera measurements, implying that instabilities in the melt-pool dimensions are observable through examination of the camera images. Further research is required to evaluate if the virtual sensing approach can also be applied in a frame by frame, monitoring and control setting. Finally, the virtual sensing methodology presented here can also be applied to other AM and more general materials processing techniques, such as electron beam and directed energy deposition additive manufacturing, but also laser and electron beam welding/cutting.\n\n\\section*{Acknowledgments}\nThis research was funded by KU Leuven internal funds and by the agency Flanders Innovation \\& Entrepreneurship (VLAIO) through the Flanders Make project MONICON (HBC.2016.0459). The authors would like to gratefully acknowledge Yannis Kinds and Sam Buls for their knowledge, support and help on the experimental setup, Seren Senol for her assistance in the metallographic sample preparation, Viktor Coen for his contributions in analytical melt-pool modeling, and finally, Jean-Pierre Kruth for the fruitful and valuable discussions on the topic of L-PBF process monitoring.\n\nAppendix A. Metallographic and camera extracted melt-pool dimensions\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-40}\n\\end{center}\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|c|c|c|c|}\n\\hline\n\\begin{tabular}{l}\nLaser Power $[\\mathrm{W}] \\backslash$ \\\\\nScan speed $[\\mathrm{mm} / \\mathrm{s}]$ \\\\\n\\end{tabular} & 100 & 200 & 300 & 400 & 00 & 600 \\\\\n\\hline\n400 & \\[\n\\begin{aligned} & 138.56 \\\\ &+- \\\\ &\\end{aligned}\n\\] & \\begin{tabular}{r}\n140.48 \\\\\n$+/-21.645$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n177.03 \\\\\n$+/-21.326$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n141.07 \\\\\n$+/-31.622$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n172.89 \\\\\n$+/-19.375$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n138.5 \\\\\n$+/-36.656$ \\\\\n\\end{tabular} \\\\\n\\hline\n500 & \\begin{tabular}{r}\n125.05 \\\\\n$+/-19.5$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n136.31 \\\\\n$+/-20.989$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n159.94 \\\\\n$+/-20.936$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n143.03 \\\\\n$+/-46.268$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n158.41 \\\\\n$+/-26.128$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n127.33 \\\\\n$+/-44.004$ \\\\\n\\end{tabular} \\\\\n\\hline\n600 & \\[\n\\begin{aligned} & 112.53 \\\\ + & --18.528\\end{aligned}\n\\] & \\begin{tabular}{c}\n135.15 \\\\\n$+/-19.763$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n145.32 \\\\\n$+/-19.48$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n137.74 \\\\\n$+/-34.003$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n144.96 \\\\\n$+/-26.952$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n128.01 \\\\\n$+/-39.197$ \\\\\n\\end{tabular} \\\\\n\\hline\n700 & \\begin{tabular}{r}\n99.673 \\\\\n$+/-18.698$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n141.24 \\\\\n$+/-19.493$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n136.95 \\\\\n$+/-19.", "start_char_idx": 117392, "end_char_idx": 120399, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2fd61136-811f-4c8b-af64-ddee2eec3033": {"__data__": {"id_": "2fd61136-811f-4c8b-af64-ddee2eec3033", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "303d05d3-45b2-4cd0-9973-2254f88a16df", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cd0794caecd7a2e332fcf01ad8fde769a44c57181258974875282144dae3b80c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "19a9c5f5-1985-4ed8-93bf-17f82aae6b1c", "node_type": "1", "metadata": {}, "hash": "f5afd400acec538f65b9518e48e8e0ca6b4b38b733df05f9887a8beae18208db", "class_name": "RelatedNodeInfo"}}, "text": "763$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n145.32 \\\\\n$+/-19.48$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n137.74 \\\\\n$+/-34.003$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n144.96 \\\\\n$+/-26.952$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n128.01 \\\\\n$+/-39.197$ \\\\\n\\end{tabular} \\\\\n\\hline\n700 & \\begin{tabular}{r}\n99.673 \\\\\n$+/-18.698$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n141.24 \\\\\n$+/-19.493$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n136.95 \\\\\n$+/-19.61$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n145.86 \\\\\n$+/-30.048$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n138.2 \\\\\n$+/-25.709$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n142.13 \\\\\n$+/-37.199$ \\\\\n\\end{tabular} \\\\\n\\hline\n800 & \\[\n\\begin{aligned} & 90.581 \\\\ &+- \\\\ &\\end{aligned}\n\\] & \\begin{tabular}{r}\n152.04 \\\\\n$+/-20.332$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n132.41 \\\\\n$+/-22.427$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n156.86 \\\\\n$+/-29.798$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n136.32 \\\\\n$+/-31.164$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n155.69 \\\\\n$+/-37.599$ \\\\\n\\end{tabular} \\\\\n\\hline\n900 & \\begin{tabular}{r}\n84.738 \\\\\n$+/-19.428$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n160.57 \\\\\n$+/-19.763$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n131.29 \\\\\n$+/-27.027$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n162.5 \\\\\n$+/-22.237$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n136.28 \\\\\n$+/-35.573$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n165.08 \\\\\n$+/-40.146$ \\\\\n\\end{tabular} \\\\\n\\hline\n1000 & \\begin{tabular}{r}\n79.306 \\\\\n$+\\quad-20.231$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n162.26 \\\\\n$+/-22.118$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n127.85 \\\\\n$+/-29.934$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n169.34 \\\\\n$+/-24.643$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n137.16 \\\\\n$+/-44.62$ \\\\\n\\end{tabular} & \\[\n\\begin{aligned} & 195.53 \\\\ + & -81.597\\end{aligned}\n\\] \\\\\n\\hline\n11 & \\begin{tabular}{r}\n73.111 \\\\\n$+/-21.874$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n168.34 \\\\\n$+/-24.261$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n123.63 \\\\\n$+/-33.178$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n176.06 \\\\\n$+/-34.127$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n140.97 \\\\\n$+/-59.318$ \\\\\n\\end{tabular} & \\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-41}\n \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable A.", "start_char_idx": 119966, "end_char_idx": 122161, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "19a9c5f5-1985-4ed8-93bf-17f82aae6b1c": {"__data__": {"id_": "19a9c5f5-1985-4ed8-93bf-17f82aae6b1c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2fd61136-811f-4c8b-af64-ddee2eec3033", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e4dcb0fbf926fdf5f12f239cb36e4ae5c01cf726ea674255f348f22f70e7c70a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d399ed90-ab5f-4309-a047-93e5a02f4a49", "node_type": "1", "metadata": {}, "hash": "4435f6b19bed996774fc495d2ac268215250ba18ef737841a53dbd4356623e4a", "class_name": "RelatedNodeInfo"}}, "text": "597\\end{aligned}\n\\] \\\\\n\\hline\n11 & \\begin{tabular}{r}\n73.111 \\\\\n$+/-21.874$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n168.34 \\\\\n$+/-24.261$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n123.63 \\\\\n$+/-33.178$ \\\\\n\\end{tabular} & \\begin{tabular}{c}\n176.06 \\\\\n$+/-34.127$ \\\\\n\\end{tabular} & \\begin{tabular}{r}\n140.97 \\\\\n$+/-59.318$ \\\\\n\\end{tabular} & \\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-41}\n \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable A.2: Average measured camera melt-pool widths and standard deviations expressed in micrometers.\n\n\\section*{References}\n[1] S. 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Van Humbeeck, Part and material properties in selective laser melting of metals, 16th International Symposium on Electromachining, ISEM 2010 (2010) 3-14.", "start_char_idx": 133191, "end_char_idx": 135508, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "883a1e54-d50d-4e70-82b3-bf06b47dc436": {"__data__": {"id_": "883a1e54-d50d-4e70-82b3-bf06b47dc436", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "73bbbe2d-2dcc-4574-9bd8-36d1f45d2b4d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5bafbe3853975e7824cf9f8f112561dbdac485dcbb3821761a1d053aa4997ee2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3f15db3e-c9e7-4d03-ba34-161d947c600c", "node_type": "1", "metadata": {}, "hash": "b2fb0302fef44f19978cc992023cd50b363a26e95b1b2f9de1ff7c37020a028f", "class_name": "RelatedNodeInfo"}}, "text": "URL \\href{https://doi.org/10.1016/j}{https://doi.org/10.1016/j} .addma.2018.08.006\n\n[43] J. P. Kruth, G. Levy, F. Klocke, T. H. Childs, Consolidation phenomena in laser and powder-bed based layered manufacturing, CIRP Annals - Manufacturing Technology 56 (2) (2007) 730-759. doi:10.1016/j.cirp.2007.10.004.\n\n[44] J. P. Kruth, M. Badrossamay, E. Yasa, J. Deckers, L. Thijs, J. Van Humbeeck, Part and material properties in selective laser melting of metals, 16th International Symposium on Electromachining, ISEM 2010 (2010) 3-14.\n\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_3ea5497605dea1905837g-51.jpg?height=4429&width=6951&top_left_y=760&top_left_x=16}\n\nd: melt-pool width\\\\\nMetallographic Validation\\\\\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_3ea5497605dea1905837g-51.jpg?height=9132&width=12804&top_left_y=4656&top_left_x=3248}\n\n\\section*{VIRTUAL SENSING}\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_3ea5497605dea1905837g-51.jpg?height=4562&width=7071&top_left_y=14725&top_left_x=9267}\n\ne*: melt-pool depth\\\\\n\\texttt{https://cdn.mathpix.com/cropped/2024_03_10_3ea5497605dea1905837g-51.jpg?height=16992&width=9826&top_left_y=790&top_left_x=15519}\n\n\\section*{AUTHORS STATEMENT}\nLouca Goossens: Conceptualization, investigation, formal analysis, visualization, validation, supervision, writing - original draft. Brecht Van Hooreweder: Supervision, funding acquisition, resources, project management, writing - review and editing\n\n\\section*{Declaration of interests}\n$\\boxtimes$ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n$\\square$ The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3ea5497605dea1905837g-53}\n\\end{center}\n\n\\section*{HIGHLIGHTS}\n\\begin{itemize}\n  \\item Melt-pool stability and dimensions are linked to in-situ coaxial camera monitoring images\n  \\item Coaxial melt-pool monitoring yields accurate estimates of melt-pool width\n  \\item Analytical models are suitable for fast calculation of melt-pool depth/with ratios\n  \\item Virtual sensing is promising for fast and accurate melt-pool depth estimation\n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{multirow}\n\n\\title{Correlation of meltpool characteristics and residual stresses at high laser intensity for metal lpbf process }\n\n\n\\author{Alexandre Staub ${ }^{a *}$, Adriaan B. Spierings ${ }^{a}$, Konrad Wegener ${ }^{b}$\\\\\n${ }^{a}$ Inspire, Innovation Center for Additive Manufacturing Switzerland (icams), St. Gallen,\\\\\nSwitzerland, ${ }^{b}$ ETH Zurich, Institute of Machine Tools and Manufacturing, Zurich,\\\\\nSwitzerland}\n\\date{}", "start_char_idx": 134979, "end_char_idx": 138183, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3f15db3e-c9e7-4d03-ba34-161d947c600c": {"__data__": {"id_": "3f15db3e-c9e7-4d03-ba34-161d947c600c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "883a1e54-d50d-4e70-82b3-bf06b47dc436", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4e766ef88e8b4bc1f748f6d45945e5f36cdbf49ba11a36029371ad642cb9ab7b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5c2b2d70-440d-4324-b48c-977a70deea94", "node_type": "1", "metadata": {}, "hash": "5196cf56d63acc7f309d7ab4ce0c826c73a696261a3c12bc6213d034d26378ef", "class_name": "RelatedNodeInfo"}}, "text": "\\author{Alexandre Staub ${ }^{a *}$, Adriaan B. Spierings ${ }^{a}$, Konrad Wegener ${ }^{b}$\\\\\n${ }^{a}$ Inspire, Innovation Center for Additive Manufacturing Switzerland (icams), St. Gallen,\\\\\nSwitzerland, ${ }^{b}$ ETH Zurich, Institute of Machine Tools and Manufacturing, Zurich,\\\\\nSwitzerland}\n\\date{}\n\n\n\\begin{document}\n\\maketitle\nSee discussions, stats, and author profiles for this publication at: \\href{https://www.researchgate.net/publication/328411432}{https://www.researchgate.net/publication/328411432}\n\nArticle in Advances in Materials and Processing Technologies $\\cdot$ October 2018 Dol: 10.1080/23740688.2018.1535643\n\nCITATIONS\n\n7\n\n3 authors:\n\nAlexandre Staub\n\ninspire AG\n\n5 PUBLICATIONS 8 CITATIONS\n\nSEE PROFILE\n\nKonrad Wegener\n\nETH Zurich\n\n485 PUBLICATIONS 5,645 CITATIONS\n\nSEE PROFILE\n\nSome of the authors of this publication are also working on these related projects:\n\nGPU-Enhanced Metal Cutting Simulation Using Advanced Meshfree Methods View project\n\nDLPCC Direct Laser Processing of Ceramic Composite View project\\\\\nAdriaan B. Spierings\n\ninspire $A G$\n\n52 PUBLICATIONS 1,952 CITATIONS\n\nSEE PROFILE\n\n\\section*{Correlation of Meltpool Characteristics and Residual Stresses at High Laser Intensity for Metal LPBF Process }\n*Corresponding author: \\href{mailto:staub@inspire.ethz.ch}{staub@inspire.ethz.ch}\n\n\\section*{Correlation of Meltpool and Residual Stresses at High Laser Intensity for Metal LPBF Process}\nSelective Laser Melting (SLM) commonly referred as Metal Laser Powder Bed Fusion (LPBF) processes, proved in the last decade to be suitable for the manufacturing of complex metallic components. In order to fulfil industrial needs from various industries (e.g. aerospace, tooling, energy production, medical), Machine manufacturers have increased the productivity of the LPBF-process mainly by increasing the number and maximum power of lasers. However, this strategy also affects the magnitude of residual stresses generated in the consolidated material. This study analyses the residual stresses in SS316L components by XRD measurement, where a correlation to the meltpool dimensions could be found and verified for different laser power and scan speeds. The results provide fundamentals to assess the gain in productivity, and to establish generic guidelines for the optimization of residual stresses at high laser power.\n\nKeywords: additive manufacturing, laser powder bed fusion, residual stresses, XRD, meltpool, SS316L\n\n\\section*{Introduction}\nSelective Laser Melting (SLM) (PBF-LB/M according to ISO/ASTM DIS 52900:2018), commonly Laser Powder Bed Fusion (LPBF) is one of the most promising Additive Manufacturing (AM) technologies for the manufacturing of metallic three-dimensional structures having typical sizes from tenths of millimetres to tenths of centimetres [1]. Bourell et al. [2] presented a review of the different AM-processes and highlighted the remaining bottlenecks. Schmidt et al. [3] also discussed the opportunities and limitations of the LPBF process. Notably the residual stresses remaining in the parts are identified by Patterson et al. [4] as a bottleneck for further technology development. Indeed, the high stress levels in the parts can lead to build job interruption in case of in-process deformation, or to critical part distortions once they are removed from the build plate. In fact, no prediction of the final part accuracy is possible without the knowledge of the residual stress state, which is greatly influenced by the part geometry and the build-up strategy. In addition, the residual stresses limit their industrial performance during use.\n\nIndependently from the manufacturing technique, all metallic materials are subject to residual stresses either coming from mechanical or thermal solicitation during\\\\\nthe manufacturing process. Complex residual stress states in LPBF originate from the high temperature gradient induced by the high intensity laser process, and according to Kruth et al. [5] strongly depends on the Marangoni convection. Indeed, the extremely fast temperature change in the process is leading to two phenomena.", "start_char_idx": 137877, "end_char_idx": 141988, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5c2b2d70-440d-4324-b48c-977a70deea94": {"__data__": {"id_": "5c2b2d70-440d-4324-b48c-977a70deea94", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3f15db3e-c9e7-4d03-ba34-161d947c600c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ce368d978edd13ae7ec645f5c97d3b694af34d796f91e462041e7a345d9e2529", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "af551e81-7173-4350-95d1-3e68a2b8fa5b", "node_type": "1", "metadata": {}, "hash": "04c999aad253475b2527c6e284114de04116d047255a7a13e40e60aa35f2781a", "class_name": "RelatedNodeInfo"}}, "text": "[4] as a bottleneck for further technology development. Indeed, the high stress levels in the parts can lead to build job interruption in case of in-process deformation, or to critical part distortions once they are removed from the build plate. In fact, no prediction of the final part accuracy is possible without the knowledge of the residual stress state, which is greatly influenced by the part geometry and the build-up strategy. In addition, the residual stresses limit their industrial performance during use.\n\nIndependently from the manufacturing technique, all metallic materials are subject to residual stresses either coming from mechanical or thermal solicitation during\\\\\nthe manufacturing process. Complex residual stress states in LPBF originate from the high temperature gradient induced by the high intensity laser process, and according to Kruth et al. [5] strongly depends on the Marangoni convection. Indeed, the extremely fast temperature change in the process is leading to two phenomena. Both the temperature gradient mechanism (TGM) during the heating phase and a thermal shrinkage of the solidified melt-pool during the cooling phase yield to the formation of high residual stresses as a result of surrounding solid material constraining the solidification of the molten material [6].\n\nA lot of research has been performed to characterise residual stresses induced by the LPBF process. The different mechanisms of residual stresses formation are having different scales, and are classified in three types as proposed by Withers et al. [7], being the atomic level (type III), the grain level (type II) and the macroscopic level (type I). For each stress type specific tools and methods for quantification are used, which do not permit the quantification of the other types. The residual stresses studied in most of the literature about the LPBF process are from type I, being macro-scale stresses, as these stresses are the most relevant in terms of part deformation. Measurement methods such as geometrical deformation permit a qualitative assessment of the residual stresses magnitude using a beam curvature after removal of the support structure binding to the build plate, as used by Safronov et al. [8], while Ghasri-Khouzani et al. [9] used the overall deformation of disk artefacts for the same purpose. However, the use of neutron diffraction $[9,10]$ or the hole drilling method [11] permit a better understanding of the residual stress profiles over the depth of a sample. Casavola et al. [11] identified that due to the partial re-melting of the layers through the build, residual stresses would be reduced in the depth of the sample. Bartlett et al. [12] proposed a new methodology to in-situ monitor residual stresses during the LPBF-process, by using digital image correlation. These results permit to establish stress maps for simple geometries. The authors also highlighted the high dependencies of the stress state on the geometry of the sample. X Ray Diffraction (XRD) measurements have been performed to assess the stress state in a surface near region, hence within the last top-layer of the sample. Vrancken et al. [13] used XRD to identify that the main stress direction is in the scan direction, while Mercelis et al. [6] applied chemical etching to assess the stress state of layers beneath the top layer, giving information about the stress profile. Numerous analytical studies [14-16] analysed the effects of different scanning strategies on residual stress reduction, concluding that\\\\\nthe reduction of the scanning vector length and the application of a chessboard island scan strategy are beneficial for stress reduction.\n\nHowever, so far not sufficient work has been put into the characterisation of the residual stresses for higher laser intensities, and the dependency of residual stresses from the properties of the melt-pool created by the laser beam. Hence, this paper intends to advance the state of the art in the comprehension of these phenomena. By the characterisation of the residual stresses and the correlation with the meltpool dimensions, this paper aims at providing a comparison basis for the understanding of the residual stresses in LPBF at various laser powers using a constant methodology.\n\n\\section*{Materials and Methods}\n\\section*{Sample definition and LPBF parameters}\n10x10x10mm $\\mathrm{mm}^{3}$ cube samples were produced in SS316L, as a widely adopted material in metal additive manufacturing. A ConceptLaser M2 machine, equipped with a SPI 400W Nd-YAG laser source operated in continuous wave mode, was used. The laser spot diameter in the processing plane was $116 \\mu \\mathrm{m}$.", "start_char_idx": 140977, "end_char_idx": 145644, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "af551e81-7173-4350-95d1-3e68a2b8fa5b": {"__data__": {"id_": "af551e81-7173-4350-95d1-3e68a2b8fa5b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5c2b2d70-440d-4324-b48c-977a70deea94", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1a882dd0f1466e99fd61d6f305eb98711eb49f2b6f57180c1a8ddfb811dcece6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1222b383-9970-4bc0-b5cb-57cd0e6c8326", "node_type": "1", "metadata": {}, "hash": "545500b0f0a7a8f38b8ec9fa1c16a20289456a35a29902251a6b2245fb621eb2", "class_name": "RelatedNodeInfo"}}, "text": "Hence, this paper intends to advance the state of the art in the comprehension of these phenomena. By the characterisation of the residual stresses and the correlation with the meltpool dimensions, this paper aims at providing a comparison basis for the understanding of the residual stresses in LPBF at various laser powers using a constant methodology.\n\n\\section*{Materials and Methods}\n\\section*{Sample definition and LPBF parameters}\n10x10x10mm $\\mathrm{mm}^{3}$ cube samples were produced in SS316L, as a widely adopted material in metal additive manufacturing. A ConceptLaser M2 machine, equipped with a SPI 400W Nd-YAG laser source operated in continuous wave mode, was used. The laser spot diameter in the processing plane was $116 \\mu \\mathrm{m}$. The slicing thickness $(L)$ and hatching distance ( $h$ ) were respectively of $40 \\mu \\mathrm{m}$ and $90 \\mu \\mathrm{m}$. The classic meander scanning strategy with a $90^{\\circ}$ rotation applied between each layer was chosen as it has been shown to be the most promising strategy for high laser intensities [17].\n\nPrior to the analysis of meltpool characteristics and residual stress state, a process window for a material density of $\\rho \\geq 99.5 \\%$ was developed for each laser power level $(P)$. By the variation of the scanning speed $(v)$ samples were produced and measured for $\\mathrm{P}=$ $100 \\mathrm{~W}, 150 \\mathrm{~W}, 200 \\mathrm{~W}, 250 \\mathrm{~W}, 300 \\mathrm{~W}$, and $350 \\mathrm{~W}$. The common characteristics to all process windows is that they use the same volumetric energy density range, $e_{d}$, as defined in Equation (1).\n\n\n\\begin{equation*}\ne_{d}=\\frac{P}{L * h * v}\\left(\\mathrm{~J} \\cdot \\mathrm{mm}^{-3}\\right) \\tag{1}\n\\end{equation*}\n\n\n\\section*{Analysis}\nThe material density analysis was performed with a non-destructive density measurement methodology using Archimedes' principle applied in acetone. As pointed out by\n\nSpierings et al. [18] this analysis is easy and yields to quick and reliable results in comparison to other analysis methods, e.g. X-ray neutron imaging, or optical micrograph analysis.\n\nThe meltpool characteristics were analysed by a cutting, embedding, polishing and etching procedure in the transversal plane. After ODS (oxide dispersion solution) polishing down to $\\mathrm{Ra}=50 \\mathrm{~nm}$ the samples were etched for $30 \\mathrm{~s}$ using V2A etchant (Schmitz-Metallographie, Germany). The analysis was performed using an optical light microscope Leica DM6 at various magnifications.\n\nThree different samples per laser power level were selected for the residual stress state quantification. For comparison purposes, the three samples will each have respectively the same energy density for each laser power. The samples are produced using energy densities, $e_{d}$, of 43,62 and $79 \\mathrm{~J} / \\mathrm{mm}^{3}$, and having all a material density $\\rho \\geq$ 99\\% (see arrows on Figure 1).\n\nThe residual stresses were measured using an X Ray Diffractometer Stresstech Xstress 3000 G3 using Mn radiation at wavelength of $0.2103 \\mathrm{~nm}$, equipped with a $1 \\mathrm{~mm}$ diameter collimator. The measurements of the samples are obtained for a $2 \\theta$ value of $152.3^{\\circ}$, at nine different tilt angles being: $0^{\\circ}, \\pm 18,3^{\\circ}, \\pm 26,4^{\\circ}, \\pm 33,0^{\\circ}, \\pm 39,0^{\\circ}$. The total exposure time is $65 \\mathrm{~s}$. The two principal in-plane directions $\\sigma_{11}$ and $\\sigma_{22}$ are computed and the resulting stress is deduced.\n\nStress relieve operations were realised at a temperature of $800^{\\circ} \\mathrm{C}$ followed by a natural furnace cooling [19].", "start_char_idx": 144888, "end_char_idx": 148524, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1222b383-9970-4bc0-b5cb-57cd0e6c8326": {"__data__": {"id_": "1222b383-9970-4bc0-b5cb-57cd0e6c8326", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "af551e81-7173-4350-95d1-3e68a2b8fa5b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9f5cfdd48aafa091b78b338f0362575d69a89bdccc79a30af1884ae5a69301b5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3f2cfa3f-11e0-41cc-b1e9-6995f4426bbc", "node_type": "1", "metadata": {}, "hash": "833602fc09a1628a219e664b2f52b52f122a95bc8091ce77708ed672e9b54aec", "class_name": "RelatedNodeInfo"}}, "text": "The measurements of the samples are obtained for a $2 \\theta$ value of $152.3^{\\circ}$, at nine different tilt angles being: $0^{\\circ}, \\pm 18,3^{\\circ}, \\pm 26,4^{\\circ}, \\pm 33,0^{\\circ}, \\pm 39,0^{\\circ}$. The total exposure time is $65 \\mathrm{~s}$. The two principal in-plane directions $\\sigma_{11}$ and $\\sigma_{22}$ are computed and the resulting stress is deduced.\n\nStress relieve operations were realised at a temperature of $800^{\\circ} \\mathrm{C}$ followed by a natural furnace cooling [19].\n\n\\section*{Results and Discussion}\n\\section*{Process window development}\nIn order to keep comparable results, the energy density range to establish the processing windows is kept the same for all laser powers. Consequently, and knowing the fixed parameter presented above, it is impossible to establish a suitable processing window for a laser power of $100 \\mathrm{~W}$, as shown on Figure 1. This is due to the meltpool size being not large enough to correctly connect to the neighbouring scan tracks, resulting in connection defects and correspondingly a high material porosity. Indeed, it has been shown in previous studies that such energy density range could easily process SS316L, but only\\\\\nwith other process parameters, notably a smaller hatch distance and layer thickness.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c897e4a312c10ccc8db6g-07}\n\\end{center}\n\nFigure 1. Relative Material density-gain curve along the energy density for several laser powers.\n\nAll the other five processing windows developed for $\\mathrm{P}=150 \\mathrm{~W}$ to $350 \\mathrm{~W}$ successfully reached the expected material density level and the above-described samples were used for residual stresses measurement.\n\n\\section*{Meltpool Characteristics}\nThe meltpool dimensions were measured in the cross section of the samples, averaged and represented using elliptical shapes, representing all typical meltpool geometries, as in the present data set there were no \"bell shaped\" meltpool observed due to the selected manufacturing parameters. The aspect ratio $(A R)$, being the ratio between the width and the depth of the sample, was calculated to highlight the meltpool shape. An $A R>1$ represents shallow and flat meltpools, while $A R<1$ represents deep and thin meltpools. The characteristics of the meltpools are summarized in Table 1.\n\n\\begin{center}\n\\begin{tabular}{cccc}\n\\hline\n$P[W]$ & $E d\\left[\\mathrm{~J} / \\mathrm{mm}^{3}\\right]$ & $A R$ & Area $[\\mu \\mathrm{m} 2]$ \\\\\n\\hline\n\\multirow{3}{*}{150} & 43 & 1.53 & 10033 \\\\\n & 62 & 1.51 & 19554 \\\\\n & 79 & 1.64 & 22616 \\\\\n\\hline\n\\multirow{3}{*}{200} & 43 & 1.15 & 13344 \\\\\n & 62 & 1.13 & 24951 \\\\\n & 79 & 1.30 & 24362 \\\\\n\\hline\n\\multirow{3}{*}{250} & 43 & 1.28 & 16496 \\\\\n & 62 & 0.95 & 22425 \\\\\n & 79 & 1.19 & 46863 \\\\\n\\hline\n & 43 & 1.28 & 23164 \\\\\n & 62 & 0.81 & 20793 \\\\\n & 79 & 0.71 & 29863 \\\\\n\\hline\n & 43 & 1.10 & 24075 \\\\\n350 & 62 & 0.67 & 28612 \\\\\n & 79 & 0.64 & 34508 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nTable 1. Meltpools characteristics in the different processing conditions\n\nAs shown in Figure 2, meltpool shapes tend to elongate in depth with increasing laser power assuming a constant energy density. Typical $A R$ values are between 1.51 to 0.67 for an energy density, $e_{d}$, of $62 \\mathrm{~J} / \\mathrm{mm}^{3}$.", "start_char_idx": 148020, "end_char_idx": 151331, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3f2cfa3f-11e0-41cc-b1e9-6995f4426bbc": {"__data__": {"id_": "3f2cfa3f-11e0-41cc-b1e9-6995f4426bbc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1222b383-9970-4bc0-b5cb-57cd0e6c8326", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6cb50525d592c03d9f5ab091b7ccd07349c3a12741e400519a4adab6f88a4293", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6a348269-fc0b-44d4-a44d-f585c9f0cd26", "node_type": "1", "metadata": {}, "hash": "72fa7234b10428ea34ae59596dbeb11460169822c470e9dd1676e2d9dfafadd5", "class_name": "RelatedNodeInfo"}}, "text": "Meltpools characteristics in the different processing conditions\n\nAs shown in Figure 2, meltpool shapes tend to elongate in depth with increasing laser power assuming a constant energy density. Typical $A R$ values are between 1.51 to 0.67 for an energy density, $e_{d}$, of $62 \\mathrm{~J} / \\mathrm{mm}^{3}$. For each laser power $P$ in the power range [150 W; $250 \\mathrm{~W}$ ], the $A R$ tends to increase with the corresponding energy density increase, in the domain where the consolidated material is considered dense ( $\\rho \\geq 99 \\%)$. While for higher laser power $\\mathrm{P}>250 \\mathrm{~W}$ the contrary effect is observed. Therefore, the assumption can be made that this change in the meltpool shape is linked to a change in the dynamic behaviour of the meltpool during the liquid phase and its energy dissipation to the surrounding material, thus influencing the residual stress state. Once a threshold of $\\mathrm{P}=$ $250 \\mathrm{~W}$ is exceeded, and for energy densities permitting to produce dense material, the welding mode switches from convection to keyhole welding, as discussed by King et al. [20] and Staub et al.[17], resulting in more elongated and deeper meltpool shapes.\n\nThe increase in the energy brought to the powder layer, considering a constant laser power, will also increase the area of the meltpool cross-section as shown in Table 1. Indeed, the time given to the growth of the meltpool per unit of length is longer for a higher energy density due to the slower scanning speed. This volume increase goes along with a change in the aspect ratio $A R$, showing the tendency of the meltpool not to increase its width proportionally to the depth. This anisotropic growth of the meltpool size is related to the given laser spot diameter that is comparable or slightly smaller than the\\\\\nmeltpool width, thus explaining the tendency of the meltpool to switch to the keyhole mode.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c897e4a312c10ccc8db6g-09}\n\\end{center}\n\nFigure 2. Meltpool characteristics at different laser powers and energy densities.\n\n\\section*{Residual stresses}\nFigure 3 shows the residual stresses in dependence of the aspect ratio. A steady increase of the residual stress state can be observed for increasing $A R$. A flatter meltpool induces higher residual stresses on the surface due to its larger width in comparison to a deeper and thinner meltpool. This leads to the conclusion that deeper meltpools are beneficial for lower in-plane residual stresses. However, this measurement does not give any insights on the residual stresses in the build direction, which might be increased by the meltpool elongation.\n\nAt a laser power of $\\mathrm{P}=250 \\mathrm{~W}$ the residual stresses are stable through the increase of the energy input and in the magnitude of the yield stress of the bulk material. This behaviour has also to be correlated with the meltpool characteristics, which show relatively large but stable meltpools for this parameter set.\n\nFor the other laser powers, except for $\\mathrm{P}=350 \\mathrm{~W}$ were the stresses increase with the energy input, $e_{d}$, the residual stress state shows the same behaviour. The samples having a lower material density result in lower residual stresses, due to a different mechanical behaviour arising from the higher pore concentration. The residual stresses increase for samples having a relative material density $\\rho \\geq 99.5 \\%$ and decrease again for even higher energy inputs. This effect arise from the increase of the sample temperature\\\\\nat higher energy density, thus increasing the ductility of the material and lowering the resulting residual stresses.\n\nRemoving approximately $-150 \\mu \\mathrm{m}$ by etching the sample produced using $250 \\mathrm{~W}$ with an energy density $62 \\mathrm{~J} / \\mathrm{mm}^{3}$, hence removing the last molten layer leaves a zone that was not remolten by the last scan tracks. This allows the measurement of residual stresses within the material, yielding to a resulting stress of $593 \\mathrm{MPa}$ at a depth of the meltpool bottom. This drastic increase of the stresses compared to measurements done at a surfacenear region highlights the complexity of the stress distribution in LPBF-produced samples.", "start_char_idx": 151021, "end_char_idx": 155306, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6a348269-fc0b-44d4-a44d-f585c9f0cd26": {"__data__": {"id_": "6a348269-fc0b-44d4-a44d-f585c9f0cd26", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3f2cfa3f-11e0-41cc-b1e9-6995f4426bbc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1c79f5d47ce99196c53b4ed1f6eb12dcacddb2a2974eacdf22eb85d9b41af7d1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ba566317-1c11-4377-9d5e-b45622806cf0", "node_type": "1", "metadata": {}, "hash": "7f823a48b0583e5f4fe54ffc2418fe1420e6489e484c1ec16fdbff8087476193", "class_name": "RelatedNodeInfo"}}, "text": "This effect arise from the increase of the sample temperature\\\\\nat higher energy density, thus increasing the ductility of the material and lowering the resulting residual stresses.\n\nRemoving approximately $-150 \\mu \\mathrm{m}$ by etching the sample produced using $250 \\mathrm{~W}$ with an energy density $62 \\mathrm{~J} / \\mathrm{mm}^{3}$, hence removing the last molten layer leaves a zone that was not remolten by the last scan tracks. This allows the measurement of residual stresses within the material, yielding to a resulting stress of $593 \\mathrm{MPa}$ at a depth of the meltpool bottom. This drastic increase of the stresses compared to measurements done at a surfacenear region highlights the complexity of the stress distribution in LPBF-produced samples. The highest temperature of the meltpool is found at its bottom according to Zhang et al. [21]. The even steeper temperature gradient in the neighbourhood of the meltpool bottom explains this drastic increase in residual stresses.\n\nThe stress-relived samples, produced at $300 \\mathrm{~W}$, showed small residual stresses in the magnitude of $50 \\mathrm{MPa}$, proving the reliability of the measurement for this study.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c897e4a312c10ccc8db6g-10}\n\\end{center}\n\nFigure 3. Residual stresses measured at different laser powers in dependence of the meltpool aspect ratio.\n\n\\section*{Conclusion}\nThis study investigates the meltpool size and shape in dependence of the laser power at comparable processing conditions (i.e. constant scanning strategies and energy input range) and correlates them with the meltpool shape and area. Several effects are identified:\n\n(1) The shape and area, of the meltpool correlate with the residual stresses on the top layer of the sample. Thereby, larger and flatter meltpools induce higher in-plane stresses in both directions.\n\n(2) The higher laser intensities influence single-track residual stresses. Nevertheless, the overall increase of the temperature of the sample appears to be beneficial for the relief of stresses. For this reason, for a proper comparison of stress measurement data, the temperature of the samples needs to be considered, which is highly dependent of the volume, geometry and orientation of the part.\n\n(3) The complexity of the residual stresses also needs to be investigated in the build direction in order to draw optimisation guidelines for the LPBF process.\n\nThe results of this study tend to favour the keyhole melting mode as beneficial for lower residual stresses. In addition, detrimental effects of the keyhole welding mode, such as e.g. the formation of keyhole porosity, and typical complex features on real AM-parts, e.g. fine lattice structures, and the quality of overhanging surfaces, which are more complex to manufacture at high laser intensities should be considered.\n\nThis study serves as a basis for further development of simulation models taking into account the meltpool characteristics. The results are also a contribution to the general optimisation of the LPBF process. Nevertheless, a visual inspection permits to realise that the residual stress state needs to be compared to other dimensions in order to optimise the process. Residual stress reduction cannot be the only goal to improve the LPBF process. Further work to correlate different physical dimension such as residual stresses in build direction, surface quality of overhanging surface, mechanical behaviour are necessary to lead the optimisation of the process.\n\n\\section*{Acknowledgments}\nThe authors would like to kindly acknowledge the company Stresstech GmbH for leading fast and effective XRD measurements of the samples.\n\n\\section*{References}\n[1] D. Herzog, V. Seyda, E. Wycisk, and C. Emmelmann, \"Additive manufacturing of metals,\" Acta Materialia, Article vol. 117, pp. 371-392, 2016.\n\n[2] D. Bourell et al., \"Materials for additive manufacturing,\" CIRP Annals Manufacturing Technology, Article vol. 66, no. 2, pp. 659-681, 2017.\n\n[3] M. Schmidt et al., \"Laser based additive manufacturing in industry and academia,\" CIRP Annals, Article vol. 66, no. 2, pp. 561-583, 2017.\n\n[4] A. E. Patterson, S. L. Messimer, and P. A. Farrington, \"Overhanging Features and the SLM/DMLS Residual Stresses Problem: Review and Future Research Need,\" Technologies, vol.", "start_char_idx": 154538, "end_char_idx": 158876, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ba566317-1c11-4377-9d5e-b45622806cf0": {"__data__": {"id_": "ba566317-1c11-4377-9d5e-b45622806cf0", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6a348269-fc0b-44d4-a44d-f585c9f0cd26", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6ff3bd9b289d6b5777648959f01259a4fae456ff264d91fcc3d6a3bb1209cf83", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "215eeed2-4ecf-4f96-a6ef-17ed22b1d679", "node_type": "1", "metadata": {}, "hash": "dc736c34d124fdf3d8094a16da9fdc7fda9ee30bbf7f4854764810a44a138c7b", "class_name": "RelatedNodeInfo"}}, "text": "117, pp. 371-392, 2016.\n\n[2] D. Bourell et al., \"Materials for additive manufacturing,\" CIRP Annals Manufacturing Technology, Article vol. 66, no. 2, pp. 659-681, 2017.\n\n[3] M. Schmidt et al., \"Laser based additive manufacturing in industry and academia,\" CIRP Annals, Article vol. 66, no. 2, pp. 561-583, 2017.\n\n[4] A. E. Patterson, S. L. Messimer, and P. A. Farrington, \"Overhanging Features and the SLM/DMLS Residual Stresses Problem: Review and Future Research Need,\" Technologies, vol. 5, no. 2, 2017.\n\n[5] J. P. Kruth, L. Froyen, J. Van Vaerenbergh, P. Mercelis, M. Rombouts, and B. Lauwers, \"Selective laser melting of iron-based powder,\" Journal Of Materials Processing Technology, vol. 149, no. 1-3, pp. 616-622, Jun 102004.\n\n[6] P. Mercelis and J. P. Kruth, \"Residual stresses in selective laser sintering and selective laser melting,\" Rapid Prototyping Journal, Article vol. 12, no. 5, pp. 254-265, 2006.\n\n[7] P. J. Withers and H. K. D. H. Bhadeshia, \"Residual stress part 2 - Nature and origins,\" Materials Science and Technology, Review vol. 17, no. 4, pp. 366-375, 2001 .\n\n[8] V. A. Safronov, R. S. Khmyrov, D. V. Kotoban, and A. V. Gusarov, \"Distortions and residual stresses at layer-by-layer additive manufacturing by fusion,\" Journal of Manufacturing Science and Engineering, Transactions of the ASME, Article vol. 139, no. 3, 2017, Art. no. 031017.\n\n[9] M. Ghasri-Khouzani et al., \"Experimental measurement of residual stress and distortion in additively manufactured stainless steel components with various dimensions,\" Materials Science and Engineering A, Article vol. 707, pp. 689-700, 2017.\n\n[10] D. W. Brown, J. D. Bernardin, J. S. Carpenter, B. Clausen, D. Spernjak, and J. M. Thompson, \"Neutron diffraction measurements of residual stress in additively manufactured stainless steel,\" Materials Science and Engineering A, Article vol. 678, pp. 291-298, 2016.\n\n[11] C. Casavola, S. L. Campanelli, and C. Pappalettere, \"Preliminary investigation on distribution of residual stress generated by the selective laser melting process,\" Journal of Strain Analysis for Engineering Design, Article vol. 44, no. 1, pp. 93104, 2009.\n\n[12] J. L. Bartlett, B. P. Croom, J. Burdick, D. Henkel, and X. Li, \"Revealing mechanisms of residual stress development in additive manufacturing via digital image correlation,\" Additive Manufacturing, Article vol. 22, pp. 1-12, 2018.\n\n[13] B. Vrancken, R. Wauthle, J. P. Kruth, and J. Van Humbeeck, \"Study of the influence of material properties on residual stress in selective laser melting,\" in 24th International SFF Symposium - An Additive Manufacturing Conference, SFF 2013, 2013, pp. 393-407.\n\n[14] K. Dai and L. Shaw, \"Distortion minimization of laser-processed components through control of laser scanning patterns,\" Rapid Prototyping Journal, Article vol. 8, no. 5, pp. 270-276, 2002.\n\n[15] B. Cheng, S. Shrestha, and K. Chou, \"Stress and deformation evaluations of scanning strategy effect in selective laser melting,\" Additive Manufacturing, Article vol. 12, pp. 240-251, 2016.\n\n[16] Y. Liu, Y. Yang, and D. Wang, \"A study on the residual stress during selective laser melting (SLM) of metallic powder,\" International Journal of Advanced Manufacturing Technology, Article in Press pp. 1-10, 2016.", "start_char_idx": 158386, "end_char_idx": 161643, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "215eeed2-4ecf-4f96-a6ef-17ed22b1d679": {"__data__": {"id_": "215eeed2-4ecf-4f96-a6ef-17ed22b1d679", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ba566317-1c11-4377-9d5e-b45622806cf0", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4ec129e3d33c3f5144faaa8c5cb033ce60242921a21f316f949598db0c2cbb91", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "da73f521-2cfb-4113-8eb7-c2a63deaa713", "node_type": "1", "metadata": {}, "hash": "eec733af6328c32399de3b5bf6f42155061593e8e19a197cb5dbc9c2d74a88d3", "class_name": "RelatedNodeInfo"}}, "text": "393-407.\n\n[14] K. Dai and L. Shaw, \"Distortion minimization of laser-processed components through control of laser scanning patterns,\" Rapid Prototyping Journal, Article vol. 8, no. 5, pp. 270-276, 2002.\n\n[15] B. Cheng, S. Shrestha, and K. Chou, \"Stress and deformation evaluations of scanning strategy effect in selective laser melting,\" Additive Manufacturing, Article vol. 12, pp. 240-251, 2016.\n\n[16] Y. Liu, Y. Yang, and D. Wang, \"A study on the residual stress during selective laser melting (SLM) of metallic powder,\" International Journal of Advanced Manufacturing Technology, Article in Press pp. 1-10, 2016.\n\n[17] A. Staub, A. B. Spierings, and K. Wegener, \"Selective Laser Melting at High Laser Intensity: Overhang Surface Characterization and Optimization \" in Direct Digital Manufacturing Conference, Berlin, 2018, vol. ISBN 978-3-8396-1320-7.\n\n[18] A. B. Spierings, M. Schneider, and R. Eggenberger, \"Comparison of density measurement techniques for additive manufactured metallic parts,\" Rapid Prototyping Journal, Article vol. 17, no. 5, pp. 380-386, 2011.\n\n[19] T. Kurzynowski, K. Gruber, W. Stopyra, B. Ku\u017anicka, and E. Chlebus, \"Correlation between process parameters, microstructure and properties of $316 \\mathrm{~L}$ stainless steel processed by selective laser melting,\" Materials Science and Engineering A, Article vol. 718, pp. 64-73, 2018.\n\n[20] W. E. King et al., \"Observation of keyhole-mode laser melting in laser powderbed fusion additive manufacturing,\" Journal of Materials Processing Technology, Article vol. 214, no. 12, pp. 2915-2925, 2014.\n\n[21] D. Zhang, P. Zhang, Z. Liu, Z. Feng, C. Wang, and Y. Guo, \"Thermofluid field of molten pool and its effects during selective laser melting (SLM) of Inconel 718 alloy,\" Additive Manufacturing, Article vol. 21, pp. 567-578, 2018.\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Pressure dependence of the laser-metal interaction under laser powder bed fusion conditions probed by in situ X-ray imaging }\n\n\n\\author{Nicholas P. Calta ${ }^{\\mathrm{a}, *}$, Aiden A. Martin ${ }^{\\mathrm{a}}$, Joshua A. Hammons ${ }^{\\mathrm{a}}$, Michael H. Nielsen ${ }^{\\mathrm{a}}$,\\\\\nTien T. Roehling ${ }^{a}$, Kamel Fezzaa ${ }^{b}$, Manyalibo J. Matthews ${ }^{a}$, Jason R. Jeffries ${ }^{a}$, Trevor M. Willey ${ }^{a}$,\\\\\nJonathan R.I. Lee ${ }^{\\mathrm{a}, *}$\\\\\n${ }^{a}$ Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA, 94550, United States\\\\\n${ }^{\\mathrm{b}}$ X-ray Science Division, Argonne National Laboratory, 9700 S Cass Avenue, Argonne, IL, 60439, United States}\n\\date{}", "start_char_idx": 161026, "end_char_idx": 164020, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "da73f521-2cfb-4113-8eb7-c2a63deaa713": {"__data__": {"id_": "da73f521-2cfb-4113-8eb7-c2a63deaa713", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "215eeed2-4ecf-4f96-a6ef-17ed22b1d679", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ca63df1589519c5c4fc615acaa687289786f7f78ec094b520c1ed4c1f3122e3f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "83abd372-6674-4a6e-a69f-a7e24b9bf041", "node_type": "1", "metadata": {}, "hash": "d7d63862a0d64ea060f27aac18e4abd8edb94e84875d7dc1a4dc033895038e6b", "class_name": "RelatedNodeInfo"}}, "text": "%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\n\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing\n\nLaser powder bed fusion\n\nSurface tension\n\nPressure\n\nLaser material interaction\n\n\\begin{abstract}\nA B S T R A C T Laser powder bed fusion (LPBF) additive manufacturing and laser welding are powerful metal processing techniques with broad applications in advanced sectors such as the biomedical and aerospace industries. One common process variable that can tune laser-material interaction dynamics in these two techniques is adjustment of the composition and pressure of the atmosphere in which the process is conducted. While some of the physical mechanisms that are governed by the ambient pressure are well known from the welding literature, it remains unclear how these mechanisms extend to the distinct process conditions of LPBF. In situ studies of the differences in subsurface structure and behavior are essential for understanding the effects of gas pressure and composition on the LPBF processes. This article reports the use of in situ X-ray imaging to directly probe the morphological evolution of the liquid-vapor interface during laser melting as a function of ambient pressure and oxygen partial pressure under LPBF conditions in $316 \\mathrm{~L}$ steel, Ti-64, aluminum 6061, and Nickel 400. We observe significant changes in melt pool morphology as a function of pressure. Furthermore, similar changes in morphology occur due to an increase in oxygen partial pressure in the process atmosphere. Temperature- and composition-dependent changes in surface tension of the liquid metal drive this change in behavior, which has the potential to influence defect creation and final morphology in LPBF parts.\n\\end{abstract}\n\n\\section*{1. Introduction}\nLaser powder bed fusion (LPBF) additive manufacturing relies on a high-power laser to melt thin layers of metal powder into a specific 2D shape. This process is then repeated hundreds to thousands of times to produce a 3D part in a layer-by-layer fashion. While industrial adoption of this technology is accelerating [1], unanswered questions remain about the detailed mechanisms that govern the laser-material interaction central to the process. While a good deal of insight is transferrable from existing laser welding literature, most LPBF occurs in a different processing regime than typical laser welding conditions so the governing mechanisms are subtly different [2].\n\nOne common process variable used to influence laser weld characteristics is the ambient pressure [3]. Adjusting the pressure of the cover gas has a significant influence on weld depth at slow scan speeds typical of laser welding, but this influence diminishes at higher scan speeds more typical of LPBF [4,5]. These fluid dynamics have been extensively investigated in the context of welding, where at sufficiently low scan speeds the melt depth under vacuum can be twice as much as that observed at atmospheric pressure [5]. The behavior in the slow scanning regime has been investigated by ex situ sample analysis to determine melt depth [4,6], in situ X-ray imaging [7-9], in situ optical imaging [10-12], and modelling [6,13] in the context of laser welding, with studies primarily focused on the deep penetration regime relevant to keyhole welding. The melt pool depth is ultimately governed by vapor depression depth, which is primarily influenced by the balance between vapor recoil pressure of metal vaporization and the surface tension of the liquid metal [6,13-15].", "start_char_idx": 164023, "end_char_idx": 168160, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "83abd372-6674-4a6e-a69f-a7e24b9bf041": {"__data__": {"id_": "83abd372-6674-4a6e-a69f-a7e24b9bf041", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "da73f521-2cfb-4113-8eb7-c2a63deaa713", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f05c00a58ac053445c52163de3714d59c53e72c08126cbfee4408dd95a87979d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "20a294a9-493c-4f54-8d9f-99f6c4f8a380", "node_type": "1", "metadata": {}, "hash": "a7bac68d6e85de86c727de2ffd2a14a07b4595159806ff9f8aa59f1514461f22", "class_name": "RelatedNodeInfo"}}, "text": "Adjusting the pressure of the cover gas has a significant influence on weld depth at slow scan speeds typical of laser welding, but this influence diminishes at higher scan speeds more typical of LPBF [4,5]. These fluid dynamics have been extensively investigated in the context of welding, where at sufficiently low scan speeds the melt depth under vacuum can be twice as much as that observed at atmospheric pressure [5]. The behavior in the slow scanning regime has been investigated by ex situ sample analysis to determine melt depth [4,6], in situ X-ray imaging [7-9], in situ optical imaging [10-12], and modelling [6,13] in the context of laser welding, with studies primarily focused on the deep penetration regime relevant to keyhole welding. The melt pool depth is ultimately governed by vapor depression depth, which is primarily influenced by the balance between vapor recoil pressure of metal vaporization and the surface tension of the liquid metal [6,13-15]. High speed optical imaging [16] and studies of powder denudation [17] illustrate powder is blown away from the melt pool at low pressure, while it is entrained in the gas flow and drawn inward towards the melt at high pressure. This difference is due to changes in the balance between expansion of the metal vapor plume and gas entrainment of the surrounding Ar cover gas present at atmospheric pressures. However, the subsurface dynamics and vapor\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding authors.\n\\end{itemize}\n\nE-mail addresses: \\href{mailto:calta1@1lnl.gov}{calta1@1lnl.gov} (N.P. Calta), \\href{mailto:lee204@1lnl.gov}{lee204@1lnl.gov} (J.R.I. Lee).\n}\ndepression behavior have not been investigated in detail as a function of pressure in the fast scanning regime. Understanding changes to melt pool flow is essential to understand the solidification conditions of the welded region and the resulting microstructure, which ultimately dictates the properties of the final part.\n\nHigh speed X-ray imaging probes subsurface fluid dynamics that cannot be directly observed with other in situ tools and has been applied to both laser welding [7-9,18] and LPBF [19-21]. X-ray imaging experiments based on both synchrotron and laboratory sources have investigated keyhole dynamics [8,22], pore formation [23], and hot cracking in deep penetration laser welding [7]. Recent imaging studies focused on the LPBF process have investigated high speed phenomena related to keyhole dynamics and pore formation [24], keyhole geometry as a function of laser scan parameters in Ti-6Al-4 V (Ti-64) [25], the correlation between vapor depression shape and spatter behavior [26], solidification dynamics in spot welding [20], pore formation dynamics due to scan geometry effects [27], and melt behavior in deep powder beds [21]. While some of these studies used variable pressure conditions during their investigations [24], none explicitly investigated the influence of cover gas pressure and composition on the melt pool dynamics observed. In this article, we use high speed X-ray imaging to probe changes in the laser-material interaction relevant to both laser welding and LPBF as a function of both laser scan parameters and ambient pressure. These experiments include studies of $316 \\mathrm{~L}$ steel, Ti64, Nickel 400, and Al6061 under vacuum, $\\sim 97 \\mathrm{kPa}$ high purity Ar, and $\\sim 97 \\mathrm{kPa}$ Ar with $13,000 \\mathrm{ppm} \\mathrm{O}_{2}$ partial pressure. The behavior of the vapor-liquid interface significantly changes under vacuum conditions and atmospheric pressure Ar cover gas. These differences are primarily caused by changes in flow behavior and surface tension dominated by changes in surface temperature of the melt pool as a function of pressure. Additional experiments probe the effects of oxygen partial pressure on LPBF melt pool dynamics. Increases in oxygen partial pressure induce subtle but similar changes to the vapor-liquid interface, highlighting the importance of surface tension changes due to either temperature or oxygen content in determining melt pool behavior.\n\n\\section*{2. Methods}\nTransmission X-ray imaging experiments were performed using a custom-built LPBF testbed system described in detail by Martin et al. [24]. It consists of a vacuum chamber with an anti-reflective coated optical window for the laser to enter and Be windows on each side to allow the X-ray beam to transmit through the chamber.", "start_char_idx": 167187, "end_char_idx": 171618, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "20a294a9-493c-4f54-8d9f-99f6c4f8a380": {"__data__": {"id_": "20a294a9-493c-4f54-8d9f-99f6c4f8a380", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "83abd372-6674-4a6e-a69f-a7e24b9bf041", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ee8efd74cbb3e9626e7133f2fdfcb5bf8370a3531a44af8380056bb0790f23de", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c765a071-13cd-4ccf-8d8e-1ce9bbd3bd36", "node_type": "1", "metadata": {}, "hash": "98333c3203ed51315e3267dbcd289b1493c46acbe0d0789da70dfaabb15d2077", "class_name": "RelatedNodeInfo"}}, "text": "The behavior of the vapor-liquid interface significantly changes under vacuum conditions and atmospheric pressure Ar cover gas. These differences are primarily caused by changes in flow behavior and surface tension dominated by changes in surface temperature of the melt pool as a function of pressure. Additional experiments probe the effects of oxygen partial pressure on LPBF melt pool dynamics. Increases in oxygen partial pressure induce subtle but similar changes to the vapor-liquid interface, highlighting the importance of surface tension changes due to either temperature or oxygen content in determining melt pool behavior.\n\n\\section*{2. Methods}\nTransmission X-ray imaging experiments were performed using a custom-built LPBF testbed system described in detail by Martin et al. [24]. It consists of a vacuum chamber with an anti-reflective coated optical window for the laser to enter and Be windows on each side to allow the X-ray beam to transmit through the chamber. A $1070 \\mathrm{~nm}$ continuous wave (CW) process laser (IPG Photonics, YLR-500-AC) was directly coupled via a collimator (IPG Photonics, D25) to a three-axis galvanometer scanner system (Nutfield Technologies, 3XB scan head), which directed the process laser to the sample position inside the LPBF testbed chamber. Laser powers reported here refer to output power at the laser and expected optical losses through the system are estimated to be $\\sim 3 \\%$. The experiments used two slightly different beam diameters: $45 \\pm 5 \\mu \\mathrm{m}$ and $55 \\pm 5 \\mu \\mathrm{m}$ (D46, or $1 / e^{2}$ diameter for a perfectly Gaussian beam). Pressure was monitored by a Piezo and Micro Pirani combination pressure gauge (MKS Instruments, 910 DualTrans) and regulated by a mass flow controller for the addition of Ar gas and a turbo molecular vacuum pump (Pfeiffer HiCube 80). Oxygen partial pressure was monitored by an oxygen vacuum probe (XS22, ZIROX Sensoren und Elektronik GmbH). Samples were aligned to the X-ray beam with translation stages (Attocube, AG) positioned inside the vacuum chamber. Samples consisted of a single plate of $316 \\mathrm{~L}$ stainless steel $(380 \\mu \\mathrm{m}$ or $508 \\mu \\mathrm{m}$, Maudlin \\& Son Mfg. Co., Inc.), Nickel 400 alloy $(508 \\mu \\mathrm{m}$, United States Brass \\& Copper, $28-34 \\% \\mathrm{Cu},<2.5 \\%$ $\\mathrm{Fe},<2 \\% \\mathrm{Mn},<0.5 \\% \\mathrm{Si},<0.3 \\% \\mathrm{C}$, balance Ni), aluminum 6061 ( $635 \\mu \\mathrm{m}$, ThyssenKrupp Materials NA, Inc.) or Ti-64 alloy $(508 \\mu \\mathrm{m}$, Performance Titanium Group) sandwiched between two $300 \\mu \\mathrm{m}$ thick glassy carbon plates (22 grade, SPI Supplies) held in place by set screws.\\\\\nIn some instances, the glassy carbon plates were not used and only the metal sample was secured in place with the set screws. Two thicknesses of $316 \\mathrm{~L}$ steel plates were used as samples, and comparisons at $800 \\mathrm{~mm} /$ $s$ to determine the effect of thermal boundary conditions observed negligible differences in vapor depression behavior at powers up to $400 \\mathrm{~W}$. After a sample was placed in the chamber, it was evacuated to less than $0.13 \\mathrm{kPa}$ and subsequently either (i) backfilled with Ar (ultra high purity, $99.999 \\%$ ) and maintained at a pressure between 93 and $100 \\mathrm{kPa}$ under a constant Ar gas flow of 500 standard cubic centimeters per minute $(\\mathrm{sccm})$ combined with dynamic purging using a roughing pump (ambient), (ii) backfilled with Ar, opened the chamber door to admit a significant volume of air to the chamber, then closed the door and held at a constant pressure of $\\sim 101 \\mathrm{kPa}$ under a constant Ar gas flow of $500 \\mathrm{sccm}$ (oxygen poisoned), or (iii) continuously evacuated with a turbo pump until the pressure reached less than $1.3 \\times 10^{-3} \\mathrm{~Pa}$ (vacuum).", "start_char_idx": 170637, "end_char_idx": 174484, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c765a071-13cd-4ccf-8d8e-1ce9bbd3bd36": {"__data__": {"id_": "c765a071-13cd-4ccf-8d8e-1ce9bbd3bd36", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "20a294a9-493c-4f54-8d9f-99f6c4f8a380", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6da81d3179c7fefad58d06ba69f9dc9b476c051e50b6cb61074178f2f96e1d19", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ece7c03d-6fd5-43f2-94dc-4eaf208bc3ac", "node_type": "1", "metadata": {}, "hash": "2e409207c9a2adfb3f0f5d35247433f246c8ddadabde1ee9569d24480fb5c60a", "class_name": "RelatedNodeInfo"}}, "text": "After a sample was placed in the chamber, it was evacuated to less than $0.13 \\mathrm{kPa}$ and subsequently either (i) backfilled with Ar (ultra high purity, $99.999 \\%$ ) and maintained at a pressure between 93 and $100 \\mathrm{kPa}$ under a constant Ar gas flow of 500 standard cubic centimeters per minute $(\\mathrm{sccm})$ combined with dynamic purging using a roughing pump (ambient), (ii) backfilled with Ar, opened the chamber door to admit a significant volume of air to the chamber, then closed the door and held at a constant pressure of $\\sim 101 \\mathrm{kPa}$ under a constant Ar gas flow of $500 \\mathrm{sccm}$ (oxygen poisoned), or (iii) continuously evacuated with a turbo pump until the pressure reached less than $1.3 \\times 10^{-3} \\mathrm{~Pa}$ (vacuum).\n\nX-ray imaging experiments were conducted at the Dynamic Compression Sector (beamline 35-ID) and sector 32 (beamline 32-ID) at the Advanced Photon Source at Argonne National Laboratory. The Xray source operated in either 324 bunch mode with 22 ps X-ray pulses separated by a $11.47 \\mathrm{~ns}$ or 24 bunch mode with $33.5 \\mathrm{ps}$ X-ray pulses separated by $153 \\mathrm{~ns}$ between pulses. These X-ray pulse length in both modes are root mean squared pulse durations [28]. In both cases, the detector system was not explicitly synchronized to the X-ray pulse because the phenomena investigated occur on an order of magnitude longer time scale than the pulse spacings. Experiments at 35-ID used the full X-ray spectrum from a U17.2 undulator with a peak energy of approximately $24 \\mathrm{keV}$ [24] while experiments at 32-ID used a U18 undulator with roughly the same peak energy. A millisecond X-ray shutter was used to protect the sample and detector system from prolonged Xray exposure. For detection, the X-rays are converted to visible light by a $100 \\mu \\mathrm{m}$ thick LuAG:Ce scintillator (Crytur), which is then diverted out of the X-ray beam path by a silver-coated optical mirror, collected by a long working distance objective lens, and split into four duplicate images by beam splitters (Thor Labs, BSW10R). Each of these four image copies is imaged by a tube lens onto a Princeton Instruments PIMAX4:1024i iCCD camera. Two different objective and tube lens assemblies were used: a $7.5 \\times$ magnification, 0.21 NA objective lens (Mitutoyo plan apo infinity corrected long working distance objective, \\#66-383) paired with a $400 \\mathrm{~mm}$ effective focal length tube lens yielding $15 \\times$ total magnification, and a $10 \\times, 0.28$ NA objective lens (Mitutoyo plan apo infinity corrected long working distance objective, \\#46-144) paired with a $200 \\mathrm{~mm}$ effective focal length tube lens yielding $10 \\times$ total magnification. Raw X-ray absorption image data were reduced to highlight changes in attenuation during the process by dividing the uncorrected absorption image at time $t\\left(A_{t}\\right)$ by an initial image of the sample collected prior to laser processing $\\left(A_{0}\\right)$ to obtain a difference image ( $A_{\\text {diff }}$ ) using Eq. (1):\n\n$A_{\\text {diff }}=\\frac{\\ln \\left(A_{t}\\right)}{\\ln \\left(A_{0}\\right)}$\n\nThis procedure generates a difference image $A_{\\text {diff }}$ where dark regions represent a decrease in X-ray attenuation and light regions represent an increase in X-ray attenuation. In addition to absorption contrast, phase contrast enhances the visibility of material interfaces. The uncertainty of identifying the location of vapor depression edges is approximately $3-5 \\mu \\mathrm{m}$, depending on magnification. Vapor depression geometry was quantified using measurements of depth $(D)$, length at the sample surface $(L)$, and length at half depth $\\left(L_{h}\\right)$ as illustrated in Fig. 1a. These measurements were used to calculate vapor depression aspect ratio $R=$ $D / L_{h}$.", "start_char_idx": 173710, "end_char_idx": 177571, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ece7c03d-6fd5-43f2-94dc-4eaf208bc3ac": {"__data__": {"id_": "ece7c03d-6fd5-43f2-94dc-4eaf208bc3ac", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c765a071-13cd-4ccf-8d8e-1ce9bbd3bd36", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "79d497bc2322218f1d06db253854468ba21df6f7721b43522e0c6087c8c142c3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1757141a-492e-421a-9220-cc6203b0f5cb", "node_type": "1", "metadata": {}, "hash": "3845ba3901b92f262adbce005822cbad5b1d0195fd298ebc555e7dae2d467f89", "class_name": "RelatedNodeInfo"}}, "text": "(1):\n\n$A_{\\text {diff }}=\\frac{\\ln \\left(A_{t}\\right)}{\\ln \\left(A_{0}\\right)}$\n\nThis procedure generates a difference image $A_{\\text {diff }}$ where dark regions represent a decrease in X-ray attenuation and light regions represent an increase in X-ray attenuation. In addition to absorption contrast, phase contrast enhances the visibility of material interfaces. The uncertainty of identifying the location of vapor depression edges is approximately $3-5 \\mu \\mathrm{m}$, depending on magnification. Vapor depression geometry was quantified using measurements of depth $(D)$, length at the sample surface $(L)$, and length at half depth $\\left(L_{h}\\right)$ as illustrated in Fig. 1a. These measurements were used to calculate vapor depression aspect ratio $R=$ $D / L_{h}$.\n\nImages recorded for Al6061, Ti-64, and 316 L stainless steel were framed such that the surface of the sample plate was clearly observed in the upper half of the image, ideally $\\sim 1 / 4$ of the distance from the top of the image to allow study of the surface and sub-surface regions of the metal. In contrast, the high attenuation of $\\sim 24 \\mathrm{keV}$ photons by Nickel\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-03}\n\nFig. 1. Vapor depression geometry of $316 \\mathrm{~L}$ steel as a function of power for $800 \\mathrm{~mm} / \\mathrm{s}$ scan speed. (a) Illustration of the three measurements used in this manuscript: vapor depression depth $(D)$ vapor depression surface length $(L)$, and vapor depression length at half depth $\\left(L_{h}\\right)$. (b) Vapor depression surface length at $1.3 \\times 10^{-3} \\mathrm{~Pa}$ (vacuum) and $\\sim 97 \\mathrm{kPa}$ (ambient). (c) vapor depression depth for both pressures. (d) vapor depression aspect ratio ( $D / L_{h}$ ) for both pressures.\n\n400 required framing the surface of the plate with the very top of the image. This geometry permits the extended exposure times required for suitable signal to noise to analyze the sub-surface of Nickel 400 without detector saturation in regions where photons are unattenuated by the sample.\n\nWhile the solid-liquid interface is not clearly discernable in the in situ imaging, optical microscope images of ex situ metallographic cross sections were used to quantify the melt pool dimensions for a small subset of samples. These samples were cross-sectioned using a watercooled, low-speed diamond cut-off saw, and then mounted in epoxy. The samples were then ground using SiC paper down to 1200 grit, and polished using $3 \\mu \\mathrm{m}$ and $1 \\mu \\mathrm{m}$ polycrystalline diamond suspension. Final vibratory polishing was performed using $0.05 \\mu \\mathrm{m}$ colloidal silica. The samples were etched electrolytically using a $10 \\%$ oxalic acid solution at $6 \\mathrm{~V}$.\n\n\\section*{3. Results}\n\\subsection*{3.1. Stainless steel melt pool behavior as a function of pressure and oxygen partial pressure}\nThe contrasting vapor depression geometries as a function of laser power between the two pressure regimes are quantified in Fig. 1. In an ambient pressure Ar atmosphere, the in situ X-ray imaging of $316 \\mathrm{~L}$ steel illustrates behavior that is expected based on existing welding literature $[5,8,9]$. The vapor depression depth (and the corresponding melt pool depth) increases linearly with increasing power (Fig. 1c). During this increase, the vapor depression does not substantially change shape. At the lowest powers, the vapor depression is very shallow, does not extend far in the scan direction, and extends essentially straight downward into the substrate (Fig. 2a). As the laser power increases, both the depth and the length of the vapor depression increase (Fig. 2b). This larger depression remains stable up to $\\sim 300 \\mathrm{~W}$, extending straight downward into the melt pool. Above $300 \\mathrm{~W}$, the deeper and longer vapor depression becomes unstable, with ripples moving up and down the back of the vapor depression (Fig. 2c, g).", "start_char_idx": 176793, "end_char_idx": 180782, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1757141a-492e-421a-9220-cc6203b0f5cb": {"__data__": {"id_": "1757141a-492e-421a-9220-cc6203b0f5cb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ece7c03d-6fd5-43f2-94dc-4eaf208bc3ac", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a867de766cb343942e245ca45e2cfc29b9ef416a465a7c39ad5a19713738f2d9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "391c82b6-5174-4bf9-8291-4055e1c10351", "node_type": "1", "metadata": {}, "hash": "2e05d437eb3afc5a3d653f22730147b3454926f08eed0ccb9685b7354456b1f0", "class_name": "RelatedNodeInfo"}}, "text": "The vapor depression depth (and the corresponding melt pool depth) increases linearly with increasing power (Fig. 1c). During this increase, the vapor depression does not substantially change shape. At the lowest powers, the vapor depression is very shallow, does not extend far in the scan direction, and extends essentially straight downward into the substrate (Fig. 2a). As the laser power increases, both the depth and the length of the vapor depression increase (Fig. 2b). This larger depression remains stable up to $\\sim 300 \\mathrm{~W}$, extending straight downward into the melt pool. Above $300 \\mathrm{~W}$, the deeper and longer vapor depression becomes unstable, with ripples moving up and down the back of the vapor depression (Fig. 2c, g). These ripples on the back of the melt pool correlate with small waves on the melt pool surface, similar to behavior observed in welding $\\mathrm{Al}$ alloys via ultrafast radiography [24]. In addition to the instability of the vapor-liquid interface on the back of the vapor depression, the base of the vapor depression curves backwards. These observations are consistent with literature reports of high-speed optical imaging of laser welding at high velocities as well as reports of additive manufacturing under essentially the same conditions with powder added to the substrate $[10,16]$. Despite the instabilities observed in the vapor-liquid interface at the melt pool surface, no pores were observed in $316 \\mathrm{~L}$ steel under the ambient pressure conditions investigated here.\n\nUnder vacuum, the behavior of the steel melt pool exhibits both strong similarities and significant differences relative to those observed under ambient pressure of Ar. The vapor depression depth displays a linear increase with laser power consistent the behavior observed under ambient pressure, and the mean depth values under the two pressure regimes are very similar. Ex situ measurements of the melt pool depth are also very similar for the two pressure cases. This behavior is expected for laser welding at reduced pressure at high scan speeds [6]. The identical vapor depression and melt pool depths in this study indicate that the conditions studied here are in the fast welding regime, where the penetration depth is no longer sensitive to the pressure of the cover gas.\n\nWhile the depth of the vapor depression is consistent between the two pressures, other features of the vapor depression geometry are strikingly different between the two cases. At low powers the length of the vapor depression is much larger at low pressure (Fig. 2d, e) than under ambient conditions (Fig. 2a, b), leading to a low aspect ratio vapor depression. As the laser power increases above $150 \\mathrm{~W}$, the wide vapor depression collapses to form a vapor depression that appears similar to what is observed in the ambient pressure case, a deep depression with a high aspect ratio (Fig. 2f) that is closely comparable with the vapor depression under ambient pressure (Fig. 2c). At high powers the vapor depression under vacuum conditions does not exhibit the same ripples at the vapor-liquid interface observed at ambient pressure, and the curve at the bottom of the vapor depression is more pronounced. The vapor depression aspect ratio is consistently higher in the ambient pressure case than the vacuum case. Furthermore, no pore formation is apparent under vacuum, similar to ambient pressure observations.\n\nThe in situ X-ray images presented here provide information about the depth and length of the vapor depression as a function of processing conditions, but the data do not have sufficient signal to noise to permit an estimate of the width of the vapor depression along the axis of the Xray beam, perpendicular to the scan direction. Therefore, ex situ metallographs of selected conditions in 316L steel were collected to measure melt pool depth and width as comparisons for vapor depression dimensions. Since melt pool depth correlates strongly with vapor depression depth (Fig. 3a), it is anticipated that melt pool width correlates with vapor depression width. As expected, melt pool widths for both pressures increase with increasing laser power (Fig. 3b). However, melt pools are consistently wider under ambient pressure than in vacuum, indicating that the low aspect ratio, long vapor depression observed at lower powers in the vacuum experiments is not an isotropic expansion of the depression but rather an extension in the scan direction only.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-04(1)}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3a4788fbcdcfe3f23744g-04}\n\\end{center}\n\nFig. 2.", "start_char_idx": 180028, "end_char_idx": 184732, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "391c82b6-5174-4bf9-8291-4055e1c10351": {"__data__": {"id_": "391c82b6-5174-4bf9-8291-4055e1c10351", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1757141a-492e-421a-9220-cc6203b0f5cb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cf2751b37b6e009498f4fdc85a48b5324b1241d1901084d28605ed5a16e41492", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "24b76d11-4a9c-4982-b705-34f84935c642", "node_type": "1", "metadata": {}, "hash": "324017e8723127d7f1cf5aac1312d084880c22e727d901c4c31555966737767b", "class_name": "RelatedNodeInfo"}}, "text": "Since melt pool depth correlates strongly with vapor depression depth (Fig. 3a), it is anticipated that melt pool width correlates with vapor depression width. As expected, melt pool widths for both pressures increase with increasing laser power (Fig. 3b). However, melt pools are consistently wider under ambient pressure than in vacuum, indicating that the low aspect ratio, long vapor depression observed at lower powers in the vacuum experiments is not an isotropic expansion of the depression but rather an extension in the scan direction only.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-04(1)}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3a4788fbcdcfe3f23744g-04}\n\\end{center}\n\nFig. 2. In situ X-ray difference images ( $A_{\\text {diff }}$ ) of the vapor depression in $316 \\mathrm{~L}$ stainless steel with a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. Each image represents the change in density relative to the starting sample such that dark regions represent less material and light regions represent more material, with additional phase contrast at material interfaces. These images illustrate ambient pressure behavior of the vapor depression at (a) $100 \\mathrm{~W}$, (b) $150 \\mathrm{~W}$, and (c) $400 \\mathrm{~W}$ as well as behavior in vacuum conditions at (d) $100 \\mathrm{~W}$, (e) $150 \\mathrm{~W}$, and (f) $400 \\mathrm{~W}$. Panels (a)-(f) use the same scale. (g) Higher magnification view with adjusted contrast of the vapor depression at $400 \\mathrm{~W}$ under an $\\mathrm{Ar}$ atmosphere shown in panel (c). The arrow highlights the instability on the back of the vapor depression.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-04(2)}\n\nFig. 3. Comparison of melt pool and vapor depression dimensions in $316 \\mathrm{~L}$ steel. (a) Vapor depression depth compared with melt pool depth. (b) Vapor depression length compared to melt pool width, measured at the substrate surface. All melt pool dimensions are measured by ex situ metallography, while vapor depression measurements are based on in situ X-ray imaging.\n\nFig. 4 illustrates $316 \\mathrm{~L}$ vapor depression geometries as a function of oxygen partial pressure at $\\sim 101 \\mathrm{kPa}$ with a scan speed of $1000 \\mathrm{~mm} / \\mathrm{s}$. The shape metrics of vapor depression length, depth, and aspect ratio agree quite well in an atmosphere of $10 \\mathrm{ppm}_{2}$ case and $13,000 \\mathrm{ppm}$ $\\mathrm{O}_{2}$ at $200 \\mathrm{~W}$ and $300 \\mathrm{~W}$. At $400 \\mathrm{~W}$, however, the depression is significantly longer and deeper in an atmosphere of $10 \\mathrm{ppm} \\mathrm{O}_{2}$ case than in the $13,000 \\mathrm{ppm}$ case. This leads to a higher aspect ratio vapor\n\ndepression in the $10 \\mathrm{ppm} \\mathrm{O}_{2}$ case and the shape is qualitatively different as well, illustrated in Fig. 4d and e.\n\n\\subsection*{3.2. Nickel 400 melt pool behavior as a function of pressure}\nVapor depression behavior in Nickel 400 for scan speeds of $800 \\mathrm{~mm} / \\mathrm{s}$ (Fig. 5) is very similar to what is observed in $316 \\mathrm{~L}$ steel. The framing of the Ni alloy plate with the surface at the very top of the radiography images described previously can lead to significant errors in measurement of the surface length. Therefore, the length at half depth is used as an alternative measure when discussing the Ni alloy experiments (Fig. 5a). The vapor depression depth exhibits a linear increase with increasing power for both ambient pressure and vacuum. The difference in measured vapor depression depth is quite small between the two cases, with marginally deeper vapor depressions observed at ambient pressure. However, the vapor depression length (and therefore aspect ratio) exhibits significantly different behavior between the two pressures.", "start_char_idx": 183980, "end_char_idx": 187840, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "24b76d11-4a9c-4982-b705-34f84935c642": {"__data__": {"id_": "24b76d11-4a9c-4982-b705-34f84935c642", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "391c82b6-5174-4bf9-8291-4055e1c10351", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6ba16ee08b7c2842c1a495fb9c0535d12a25070118b7403ca185656c621a4f94", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "31e36ef3-3330-4557-ad9f-733ee8ce3708", "node_type": "1", "metadata": {}, "hash": "0799db05b56fd31ba6a2eea6deab35e72c831c564e4bc48073f2986eb01453dc", "class_name": "RelatedNodeInfo"}}, "text": "Nickel 400 melt pool behavior as a function of pressure}\nVapor depression behavior in Nickel 400 for scan speeds of $800 \\mathrm{~mm} / \\mathrm{s}$ (Fig. 5) is very similar to what is observed in $316 \\mathrm{~L}$ steel. The framing of the Ni alloy plate with the surface at the very top of the radiography images described previously can lead to significant errors in measurement of the surface length. Therefore, the length at half depth is used as an alternative measure when discussing the Ni alloy experiments (Fig. 5a). The vapor depression depth exhibits a linear increase with increasing power for both ambient pressure and vacuum. The difference in measured vapor depression depth is quite small between the two cases, with marginally deeper vapor depressions observed at ambient pressure. However, the vapor depression length (and therefore aspect ratio) exhibits significantly different behavior between the two pressures. At ambient pressure, vapor depression length exhibits an approximately linear increase with increasing power, leading to an increase in vapor depression aspect ratio until $250 \\mathrm{~W}$, above which the aspect ratio remains relatively constant. Under vacuum, however, vapor depression length increases sharply at low power, reaches a maximum at $200 \\mathrm{~W}$ and drops slowly at $250 \\mathrm{~W}$ and above. The result is a transition in the vapor depression aspect ratio starting at $250 \\mathrm{~W}$ from low to high aspect ratio. This transition is similar to the behavior observed in $316 \\mathrm{~L}$ steel, but with the transition to a high aspect ratio vapor depression occurring at a higher power in Nickel 400 (Fig. 5c). Vapor depression aspect ratio is consistently higher under ambient pressure than under vacuum.\n\n\\subsection*{3.3. Al6061 melt pool behavior as a function of pressure}\nThe behavior observed in Al6061 as a function of pressure (Fig. 6) deviates significantly from the behavior of 316 L steel and Nickel 400 . At powers below $200 \\mathrm{~W}$, no vapor depression was observed. For both pressures, the vapor depression depth increases linearly as power increases above $200 \\mathrm{~W}$. The vapor depression length remains essentially constant as a function of power, although the fluctuations in length (as quantified by the standard deviation of length measurements, represented by error bars in Fig. 6a) are more significant at ambient pressure than under vacuum. The vapor depression aspect ratio at $200 \\mathrm{~W}$, the lowest power where a depression is observed, is $\\sim 11$, significantly higher than the values of 2-4 observed in $316 \\mathrm{~L}$ and Nickel alloy at low power. This aspect ratio indicates a narrow and deep vapor depression and increases with increasing power. No vapor depression\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-05(1)}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_3a4788fbcdcfe3f23744g-05(3)}\n\\end{center}\n\nFig. 4. $316 \\mathrm{~L}$ steel vapor depression geometry as a function of oxygen partial pressure at $1000 \\mathrm{~mm} / \\mathrm{s}$. (a) Vapor depression length. (b) Vapor depression depth. (c) Vapor depression aspect ratio. (d) Image of the vapor depression produced by a laser power of $400 \\mathrm{~W}$ in a 10 ppm $\\mathrm{O}_{2}$ environment. e Image of the vapor depression produced by a laser power of $400 \\mathrm{~W}$ in a $13,000 \\mathrm{ppm}_{2}$ environment. The scale of panels (d) and (e) is the same.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-05}\n\nFig. 5. Vapor depression geometry measurements for Nickel 400 alloy with a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. (a) Vapor depression length at half depth, (b) vapor depression depth, and (c) vapor depression aspect ratio, calculated based on length at half depth.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-05(2)}\n\nFig. 6.", "start_char_idx": 186907, "end_char_idx": 190864, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "31e36ef3-3330-4557-ad9f-733ee8ce3708": {"__data__": {"id_": "31e36ef3-3330-4557-ad9f-733ee8ce3708", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "24b76d11-4a9c-4982-b705-34f84935c642", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0df854f97d8b1a68f8d3e8613beee8ba3c2dbeb2b02c69da0fc7c3c13a031b7f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1af6623b-d46a-4748-933e-fdcfc51cf127", "node_type": "1", "metadata": {}, "hash": "4f360bcfb83766a52e13783a32c0b2a1e876d6fb764616548218fc0146f2abaa", "class_name": "RelatedNodeInfo"}}, "text": "e Image of the vapor depression produced by a laser power of $400 \\mathrm{~W}$ in a $13,000 \\mathrm{ppm}_{2}$ environment. The scale of panels (d) and (e) is the same.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-05}\n\nFig. 5. Vapor depression geometry measurements for Nickel 400 alloy with a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. (a) Vapor depression length at half depth, (b) vapor depression depth, and (c) vapor depression aspect ratio, calculated based on length at half depth.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-05(2)}\n\nFig. 6. Vapor depression geometry in Al6061 at a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. (a) Vapor depression surface width as a function of power. (b) vapor depression depth as a function of power. (c) Vapor depression aspect ratio as a function of power.\n\nshape transition occurred, in contrast to the behavior in $316 \\mathrm{~L}$ steel and Nickel 400. Large standard deviations in the aspect ratio (Fig. 6c) arise from fluctuations in the vapor depression length. While aspect ratios for all powers are not significantly different between the vacuum and ambient cases, aspect ratio values for ambient pressure are slightly higher than those observed under vacuum.\n\n\\subsection*{3.4. Ti-64 melt pool behavior as a function of pressure and oxygen partial pressure}\nVapor depression geometries of Ti-64 at two different scan speeds are illustrated in Fig. 7. At 800 mm/s Ti-64 behaves similarly to what is observed in Al6061, with no distinct transition in vapor depression geometry observed as a function of power. Depth increases linearly with laser power and the depression length again remains essentially constant with power. Furthermore, depression length values exhibit minimal change as a function of power and are similar in both pressure cases. Consequently the aspect ratio is high, above 8 at the lowest point, and increases with increasing power. No transition of the vapor depression shape is observed at this scan speed, and the aspect ratio values for the vacuum and ambient cases are nearly identical.\n\nTo investigate the morphology transition in Ti-64 further, the vapor depression geometry as a function of power was measured at a scan speed of $1200 \\mathrm{~mm} / \\mathrm{s}$. These experiments used a slightly larger beam size than the experiments performed at $800 \\mathrm{~mm} / \\mathrm{s}, \\sim 45 \\mu \\mathrm{m}$ vs $\\sim 55 \\mu \\mathrm{m}$ beam diameter. As observed at lower scan speeds, depth increases linearly with increasing power, and the difference in overall depth between the two pressures studied here is small. Interestingly, the depression length under vacuum is much larger than at ambient pressure, leading to consistently higher aspect ratios in the ambient pressure case. While a sharp transition in aspect ratio is not observed, the shape of the vapor depression differs between the two pressures in ways that are not well captured by the shape metrics used here. At ambient pressure a kink is present in the rear surface of the vapor depression and is more pronounced at high power (Fig. 7d), while under vacuum the rear surface of the vapor depression is relatively straight (Fig. 7e).\n\nFig. 8 contrasts the vapor depression geometry for Ti-64 under high purity $\\mathrm{Ar}$ with a low oxygen content $4 \\mathrm{ppm}$ and in an oxygen-rich $\\mathrm{Ar}$ environment $13,000 \\mathrm{ppm}$. Consistent differences are observed between the two oxygen partial pressures. The vapor depression is longer in the $4 \\mathrm{ppm} \\mathrm{O}_{2}$ case, by between $15 \\%$ and $30 \\%$ at half depth (Fig. 8a) and $40 \\%-180 \\%$ at the pool surface not shown, although the depression length at melt pool surface exhibits significant fluctuations. The vapor depression depth at $13,000 \\mathrm{ppm}_{2}$ is $10 \\%-15 \\%$ deeper than the vapor depression at $4 \\mathrm{ppm}_{2}$ (Fig. 8b), leading to a higher aspect ratio vapor depression at the high $\\mathrm{O}_{2}$ partial pressure (Fig. 8c).", "start_char_idx": 190238, "end_char_idx": 194294, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1af6623b-d46a-4748-933e-fdcfc51cf127": {"__data__": {"id_": "1af6623b-d46a-4748-933e-fdcfc51cf127", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "31e36ef3-3330-4557-ad9f-733ee8ce3708", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "021f3672d6a6563bebf9015a9a376e7c3ed6af8bb8b77391722a2b0d40a1b8a6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bf9910c0-1f81-42eb-b84c-ba6a159e7203", "node_type": "1", "metadata": {}, "hash": "f7b3b33130b6a7a4bd1862e038c9abd12b0bcb81307fc859b3ca393d55434639", "class_name": "RelatedNodeInfo"}}, "text": "Consistent differences are observed between the two oxygen partial pressures. The vapor depression is longer in the $4 \\mathrm{ppm} \\mathrm{O}_{2}$ case, by between $15 \\%$ and $30 \\%$ at half depth (Fig. 8a) and $40 \\%-180 \\%$ at the pool surface not shown, although the depression length at melt pool surface exhibits significant fluctuations. The vapor depression depth at $13,000 \\mathrm{ppm}_{2}$ is $10 \\%-15 \\%$ deeper than the vapor depression at $4 \\mathrm{ppm}_{2}$ (Fig. 8b), leading to a higher aspect ratio vapor depression at the high $\\mathrm{O}_{2}$ partial pressure (Fig. 8c). In addition to the quantitative differences in the vapor depression size, the melt pool behavior far from the laser impact point is also significantly affected by the change in oxygen partial pressure. In the $4 \\mathrm{ppm}$ case (Fig. 8d), the vapor depression looks very similar to what is observed at $1200 \\mathrm{~mm} / \\mathrm{s}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-06(2)}\n\nFig. 7. Ti-64 vapor depression geometry as a function of pressure for both $800 \\mathrm{~mm} / \\mathrm{s}$ and $1200 \\mathrm{~mm} / \\mathrm{s}$ scan speeds. (a) Vapor depression length at half depth. (b) Vapor depression depth. (c) Vapor depression aspect ratio. (d) Image of the vapor depression produced by a laser power of $250 \\mathrm{~W}$ and a scan speed of $1200 \\mathrm{~mm} / \\mathrm{s}$ at ambient pressure. The white arrow indicates the kink described in the text (e) Image of the vapor depression produced by a laser power of $250 \\mathrm{~W}$ and a scan speed of $1200 \\mathrm{~mm} / \\mathrm{s}$ under vacuum. The scale of panels (d) and (e) is the same.\n\nin Fig. 7d with a long, shallow tail to the rear of the vapor depression. Under high oxygen partial pressure (Fig. 8e), this tail is not present and instead is replaced by a surface wave that protrudes above the surface of the sample followed by a second, much smaller, depression. This depression, marked with an arrow in Fig. 8e, is observed at both 200 and $300 \\mathrm{~W}$ at $1000 \\mathrm{~mm} / \\mathrm{s}$ and is more pronounced at higher power.\n\n\\subsection*{3.5. Surface features of $316 \\mathrm{~L}$ steel and Nickel 400 weld tracks}\nAn additional contrast between behavior at ambient pressure and under vacuum appears in the formation of surface roughness, or balling, of the melt pool behind the vapor depression. Balling becomes more pronounced at high power (above $150 \\mathrm{~W}$ ) under vacuum but is not observed at ambient pressure, demonstrating that the effect observed by Bidare et al. does not depend on the presence of powder [16]. Fig. 9a illustrates a line profile along the scan direction comparing $316 \\mathrm{~L}$ tracks produced under both ambient and vacuum conditions with a laser power of $300 \\mathrm{~W}$ and a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. To quantify the periodicity of surface features, we use the 1D fast Fourier transform (FFT) of the line profile of track height, omitting the start and end of the melt track to avoid artifacts introduced by edge effects. We define the balling length, or distance between peaks in the surface profile of the single track, as the distance corresponding to the highest amplitude peak in the 1D FFT, and use the FFT amplitude as a metric for the strength of balling. Fig. $9 \\mathrm{~b}$ and $\\mathrm{c}$ show the balling length computed by a 1D FFT of the linear height profile and the mean square amplitude of the FFT peak as a function of power. Balling length under vacuum increases dramatically with power until $\\sim 200 \\mathrm{~W}$ and remains relatively constant as power continues to increase. Qualitatively similar balling behavior occurs in the case of Nickel 400 (Fig. 9d and e).", "start_char_idx": 193701, "end_char_idx": 197476, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bf9910c0-1f81-42eb-b84c-ba6a159e7203": {"__data__": {"id_": "bf9910c0-1f81-42eb-b84c-ba6a159e7203", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1af6623b-d46a-4748-933e-fdcfc51cf127", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c0fcb1980fdb3b9e23668033b7741542cf0717d873376ca28bc57a355f8865bc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "cf295f43-3bfd-47ff-9b38-7785c33f9580", "node_type": "1", "metadata": {}, "hash": "130f281ee48732bf99fa46e946d1feac2ca81d765002405c425036b986166278", "class_name": "RelatedNodeInfo"}}, "text": "We define the balling length, or distance between peaks in the surface profile of the single track, as the distance corresponding to the highest amplitude peak in the 1D FFT, and use the FFT amplitude as a metric for the strength of balling. Fig. $9 \\mathrm{~b}$ and $\\mathrm{c}$ show the balling length computed by a 1D FFT of the linear height profile and the mean square amplitude of the FFT peak as a function of power. Balling length under vacuum increases dramatically with power until $\\sim 200 \\mathrm{~W}$ and remains relatively constant as power continues to increase. Qualitatively similar balling behavior occurs in the case of Nickel 400 (Fig. 9d and e). At ambient pressure essentially no balling is observed, as indicated by FFT peak magnitudes below 1 for all powers. Under vacuum, balling length is relatively constant at $\\sim 600 \\mu \\mathrm{m}$ for the cases where significant balling occurs. As is the case in steel, a stronger balling tendency is observed with increased power. While the onset of strong balling under vacuum coincides with the collapse of the vapor depression length in $316 \\mathrm{~L}$ steel (Fig. 1b), the vapor depression collapse does not occur at the same power as the onset of strong balling in Nickel 400 so these phenomena\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-06}\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-06(1)}\n\nFig. 8. Ti-64 vapor depression geometry as a function of oxygen partial pressure at $1000 \\mathrm{~mm} / \\mathrm{s}$. (a) Vapor depression length at half depth. (b) Vapor depression depth. (c) Vapor depression aspect ratio at half depth. (d) Image of the vapor depression produced by a laser power of $300 \\mathrm{~W}$ in a $4 \\mathrm{ppm}_{2}$ environment. e Image of the vapor depression produced by a laser power of $300 \\mathrm{~W}$ in a $13,000 \\mathrm{ppm} \\mathrm{O}_{2}$ environment, with the second depression far from the laser focus location marked with an arrow. The scale of panels (d) and (e) is the same.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-07}\n\nFig. 9. Surface features of melted tracks in $316 \\mathrm{~L}$ steel. (a) Compared line profiles of vacuum and ambient melt tracks produced with $300 \\mathrm{~W}$ laser power and $800 \\mathrm{~mm} /$ s scan speed in $316 \\mathrm{~L}$. (b) balling lengths as a function of power for $316 \\mathrm{~L}$ at a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. (c) the magnitude of the FFT peak corresponding to the balling lengths shown in panel (b). (d) balling lengths as a function of power for Nickel 400 at a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. (e) the magnitude of the FFT peak corresponding to the balling lengths shown in panel (d).\n\nare likely not causally linked.\n\n\\section*{4. Discussion}\nThe vapor depression shape at both pressures is determined by the combination of melt pool surface tension and the interaction of the metal vapor jet with the surface of the melt pool. The metal vapor jet is ejected from the melt pool where the laser hits the melt pool surface and is directed in the direction opposite the laser scan vector at an angle determined by the laser scan speed and the angle of the front surface of the vapor depression $[14,25,29,30]$. Recoil pressure from the vapor jet pushes the liquid metal surface down into the melt pool, creating a vapor depression. Recoil pressure is given by Eq.", "start_char_idx": 196809, "end_char_idx": 200283, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "cf295f43-3bfd-47ff-9b38-7785c33f9580": {"__data__": {"id_": "cf295f43-3bfd-47ff-9b38-7785c33f9580", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bf9910c0-1f81-42eb-b84c-ba6a159e7203", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2390c40e570ecca7f319cc8026fbf54d75a2c5dfd0e303279a4f1da0f2a84414", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e627fd8f-216b-4a11-93c4-dfa06aec22d6", "node_type": "1", "metadata": {}, "hash": "d1eaf0ed3900b876fd5cffa84adbe2fd0f52829216b29a534311563cafa7d5db", "class_name": "RelatedNodeInfo"}}, "text": "(d) balling lengths as a function of power for Nickel 400 at a scan speed of $800 \\mathrm{~mm} / \\mathrm{s}$. (e) the magnitude of the FFT peak corresponding to the balling lengths shown in panel (d).\n\nare likely not causally linked.\n\n\\section*{4. Discussion}\nThe vapor depression shape at both pressures is determined by the combination of melt pool surface tension and the interaction of the metal vapor jet with the surface of the melt pool. The metal vapor jet is ejected from the melt pool where the laser hits the melt pool surface and is directed in the direction opposite the laser scan vector at an angle determined by the laser scan speed and the angle of the front surface of the vapor depression $[14,25,29,30]$. Recoil pressure from the vapor jet pushes the liquid metal surface down into the melt pool, creating a vapor depression. Recoil pressure is given by Eq. (2), which is derived from kinetic theory [31]:\n\n$P_{r}=P^{*} e^{\\lambda\\left(\\frac{1}{T_{b}}-\\frac{1}{T_{s}}\\right)}$\n\nWhere $P_{r}$ is the recoil pressure, $P^{*}$ is ambient pressure, $\\lambda$ is the evaporation energy, $T_{b}$ is the equilibrium boiling point of the liquid at $P^{*}$, and $T_{s}$ is the surface temperature of the liquid metal. The metal vapor ejected by the vapor jet impacts the rear wall of this vapor depression, forcing it backwards and causing the vapor depression to lengthen. The length of the vapor depression is determined by the balance between the momentum transferred from the metal vapor jet to the liquid surface and the surface tension of the liquid metal. It is also influenced by the stability of the curved liquid metal surface itself, which is proportional to surface energy expressed as the closing pressure of the keyhole $\\mathrm{P}_{\\mathrm{c}}[13,32]$\n\n$P_{c} \\sim \\frac{\\gamma}{a}$\n\nWhere $\\gamma$ represents specific surface energy and $a$ represents the curvature of the melt pool surface, which is proportional to the laser spot size and also influenced by the shape of the vapor depression. In this formalism, curvature $a$ is inversely related to the radius of curvature of the liquid surface, such that $a=0$ for a perfectly flat surface.\n\nAt low power, the vapor depression is much longer under vacuum conditions than under ambient conditions. This primarily arises because of the difference in melt pool surface temperature and therefore surface tension, which leads to an increase in the laser power required to produce sufficient vapor recoil pressure to overcome $P_{c}$. At reduced pressures the boiling point of the metal under thermodynamic equilibrium decreases as described by the Clausius-Clapeyron equation $[16,33]:$\n\n$\\ln \\left(\\frac{P_{2}}{P_{1}}\\right)=\\frac{L_{\\text {vap }}}{R}\\left(\\frac{1}{T_{1}}-\\frac{1}{T_{2}}\\right)$\\\\\nWhere $L_{\\text {vap }}$ is the latent heat of vaporization, $R$ is the ideal gas constant, and $\\left(P_{1}, T_{1}\\right)$ and $\\left(P_{2}, T_{2}\\right)$ are two points on the vaporization/condensation boundary of the pressure - temperature phase diagram. Since the temperature of the melt pool is limited by evaporative cooling [15], the reduced boiling temperature reduces the peak temperature of the melt pool and therefore surface temperatures throughout the melt. These temperature changes are quite significant: in the case of $316 \\mathrm{~L}$ steel the equilibrium boiling point drops from $\\sim 3090 \\mathrm{~K}$ at $101.3 \\mathrm{kPa}$ $[16,34]$ to $\\sim 1463 \\mathrm{~K}$ at $1.3 \\times 10^{-3} \\mathrm{~Pa}$. The actual peak temperature of the melt surface is likely higher in both cases due to non-equilibrium superheating and local pressure effects, but these estimates provide a reasonable approximation of the temperature differences in the melt pool for the two cases. In the liquid metals investigated in this study, surface tension decreases linearly as a function of temperature [35]. The melt pool under vacuum therefore has a higher surface tension than under ambient conditions. The higher surface tension forces the melt pool surface towards a flatter geometry, which manifests as a low aspect ratio vapor depression.", "start_char_idx": 199406, "end_char_idx": 203525, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e627fd8f-216b-4a11-93c4-dfa06aec22d6": {"__data__": {"id_": "e627fd8f-216b-4a11-93c4-dfa06aec22d6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "cf295f43-3bfd-47ff-9b38-7785c33f9580", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "02866a64e28fa7398d418a25b91a2b3b1ba86da01eafdf06e61556b83b7027f5", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "21f563e6-04bc-4682-bab0-b76804d19eb9", "node_type": "1", "metadata": {}, "hash": "236d9b0967b2614d809d69854a29d1dd36f0e8ad613414af8485b5da4de3d267", "class_name": "RelatedNodeInfo"}}, "text": "These temperature changes are quite significant: in the case of $316 \\mathrm{~L}$ steel the equilibrium boiling point drops from $\\sim 3090 \\mathrm{~K}$ at $101.3 \\mathrm{kPa}$ $[16,34]$ to $\\sim 1463 \\mathrm{~K}$ at $1.3 \\times 10^{-3} \\mathrm{~Pa}$. The actual peak temperature of the melt surface is likely higher in both cases due to non-equilibrium superheating and local pressure effects, but these estimates provide a reasonable approximation of the temperature differences in the melt pool for the two cases. In the liquid metals investigated in this study, surface tension decreases linearly as a function of temperature [35]. The melt pool under vacuum therefore has a higher surface tension than under ambient conditions. The higher surface tension forces the melt pool surface towards a flatter geometry, which manifests as a low aspect ratio vapor depression. This shape reduces the surface energy by reducing the curvature of the melt pool surface in the vapor depression. In terms of Eq. (3), this corresponds to a decrease in $\\gamma$ at reduced pressure, which leads to lower $a$ for a given $P_{c}$. At sufficiently high power, the local pressure at the bottom of the vapor depression is dominated by the metal vapor flux from the vapor jet. Above this critical laser power, which is different for each material, surface tension effects are less important and the high local vapor pressure creates a deep, high aspect ratio keyhole. Above this critical laser power the geometry difference between the vacuum and ambient cases is small, as observed in the strong similarities between the high power conditions under both pressure regimes (Figs. 1d, $5 \\mathrm{c}, 6 \\mathrm{c}, 7 \\mathrm{c}$ ). In spite of these similarities, most materials still exhibit a slightly higher aspect ratio vapor depression in the ambient pressure case when compared to vacuum. In addition to surface tension, temperature has a strong influence on the viscosity of the melt pool. In the case of $316 \\mathrm{~L}$ steel, the change in melt pool surface temperatures due to the lower boiling point leads to greater than fivefold increase of viscosity if the liquid [34]. Therefore, the melt pool under vacuum conditions requires a greater recoil force to deform fluid flow and develop a high aspect ratio vapor depression. While the recoil pressure and therefore metal vapor flux are both lower in the vacuum case, the mean free path of the metal vapor in vacuum is much longer than at ambient pressure.\n\nThe introduction of oxygen in the cover gas has a significant effect on the flow behavior near the vapor depression, because even small increases in oxygen content lead to large decreases in the surface tension of liquid metals [36,37]. Vapor depression morphology changes between low $\\sim 10 \\mathrm{ppm}$ and high 13,000 ppm oxygen partial pressure in both Ti-64 and 316 L steel, although the magnitude of these changes\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_3a4788fbcdcfe3f23744g-08}\n\nFig. 10. Comparison of vapor depression shapes as a function of normalized enthalpy. (a) Vapor depression depth of $316 \\mathrm{~L}$ and Ti-64 plotted as a function of normalized enthalpy. (b) Vapor depression aspect ratio plotted as a function of normalized enthalpy.\n\nvaries significantly between the two materials. In Ti-64, morphological differences associated with the two oxygen levels were observed at all laser powers and scan speeds investigated Fig. 8), with higher oxygen content leading to a higher aspect ratio vapor depression. In $316 \\mathrm{~L}$, however, differences in melt pool morphology only became pronounced at $400 \\mathrm{~W}$ (at $1000 \\mathrm{~mm} / \\mathrm{s}$ ), the highest power level investigated (Fig. 4). The magnitude of this effect varies from metal to metal due to the varying oxygen affinity between metal alloys. A precise description of this observation is complicated by the fact that surface tension has a non-monotonic relationship with temperature for some levels of oxygen contamination [36], and the exact oxygen content of the material is influenced significantly by surface oxidation prior to laser melting. The fine details of this vapor depression behavior as a function of oxygen content becomes even more difficult to predict in a full-scale LPBF build, where control of surface oxidation and moisture uptake of the feedstock powder is a significant challenge. Within the scope of Eq.", "start_char_idx": 202653, "end_char_idx": 207100, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "21f563e6-04bc-4682-bab0-b76804d19eb9": {"__data__": {"id_": "21f563e6-04bc-4682-bab0-b76804d19eb9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e627fd8f-216b-4a11-93c4-dfa06aec22d6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b1645704262a7905870a506a7e2f919b8fdc98dcba69bd58cc51669d37d8cf7e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7dd4ab0c-ddf6-4204-b86f-7ada0f5a203d", "node_type": "1", "metadata": {}, "hash": "7b853208ddc099a6ff8d0fdfa333dc1e86bbdf3b02789a5eb78f5abebfec7f88", "class_name": "RelatedNodeInfo"}}, "text": "In $316 \\mathrm{~L}$, however, differences in melt pool morphology only became pronounced at $400 \\mathrm{~W}$ (at $1000 \\mathrm{~mm} / \\mathrm{s}$ ), the highest power level investigated (Fig. 4). The magnitude of this effect varies from metal to metal due to the varying oxygen affinity between metal alloys. A precise description of this observation is complicated by the fact that surface tension has a non-monotonic relationship with temperature for some levels of oxygen contamination [36], and the exact oxygen content of the material is influenced significantly by surface oxidation prior to laser melting. The fine details of this vapor depression behavior as a function of oxygen content becomes even more difficult to predict in a full-scale LPBF build, where control of surface oxidation and moisture uptake of the feedstock powder is a significant challenge. Within the scope of Eq. (3), for a given pressure, the presence of oxygen increases $\\gamma$, thereby increasing the curvature of the vapor depression $a$ and leading to higher vapor depression aspect ratios.\n\nIn addition to quantitative differences in vapor depression size, oxygen partial pressure also causes changes in the melt flow behavior that are not captured by vapor depression size measurements. These changes are most clear in Ti-64, the more oxygen-sensitive of the two metals. Fig. 8d and e illustrates the development of a small surface wave followed by a relatively shallow secondary depression, $\\sim 30 \\mu \\mathrm{m}$ deep and $\\sim 100-150 \\mu \\mathrm{m}$ behind the back of the primary vapor depression, in the oxygen poisoned case but not the Ar case. This secondary depression is not formed due to recoil pressure but is instead formed due to changes to the melt pool flow induced by changes in the local surface tension of the oxygen-reacted melt surface. This secondary depression is remarkably stable, appearing constantly with some fluctuation at $200 \\mathrm{~W}$ and $300 \\mathrm{~W}$ in high oxygen content environments for Ti-64. Notably, this feature is not present in the pure Ar case, so it is apparently stabilized by the oxygen rich atmosphere. This discrepancy highlights the influence of the surface tension of the metal on vapor depression geometry, as oxygen contamination only influences the surface tension of the melt pool, not the magnitude of recoil pressure or surface temperature of the melt.\n\nWe speculate that the formation of the secondary depression is driven by a peak in the local surface tension of the melt immediately behind the vapor depression due to a balance between temperature effects and oxygen saturation effects. Oxygen transport into the vapor depression itself is limited by the metal vapor flux from evaporative cooling, so oxygen uptake on the metal surface becomes much more pronounced on the melt pool surface behind the vapor depression than in the depression itself. Moving backwards from the vapor depression, the temperature of the melt pool falls, increasing surface tension. However, the oxygen content of the surface simultaneously increases, which decreases surface tension. This balance leads to a peak in surface tension shortly behind the vapor depression, which pulls in nearby liquid to form a small bump in the melt pool surface immediately behind the vapor depression, and also forming the secondary depression behind it (Fig. 8e).\n\nThe laser power threshold for the transition between the low aspectratio vapor depression observed at low power and the high aspect-ratio depression observed at high power varies based on the material. This behavior is expected, because the shape of the vapor depression is primarily influenced by liquid vaporization energy, surface tension, and viscosity of the liquid metal near the boiling point. These parameters vary significantly from material to material, so the threshold powers for vapor depression behavior will be material-dependent. One formalism for comparing laser melting parameters across different materials is the normalized enthalpy approach, which uses a scaling law to account for different materials properties [2,27,38-40] given by Eq. (5):\n\n$\\frac{\\Delta H}{h_{s}}=\\frac{A P}{\\pi \\rho C T_{m} \\sqrt{D u r^{3}}}$\n\nWhere $\\Delta H$ is the specific enthalpy of melting, $h_{s}$ is the enthalpy at melting, $A$ is material absorptivity, $P$ is the laser power, $\\rho$ is the material density, $C$ is the specific heat capacity, $T_{m}$ is the equilibrium melting temperature, $D$ is the thermal diffusivity, $u$ is scan speed, and $r$ is the $1 /$ $e$ radius of the laser.", "start_char_idx": 206205, "end_char_idx": 210789, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7dd4ab0c-ddf6-4204-b86f-7ada0f5a203d": {"__data__": {"id_": "7dd4ab0c-ddf6-4204-b86f-7ada0f5a203d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "21f563e6-04bc-4682-bab0-b76804d19eb9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "20c7dac81f98a768f4e27de95991be3e4bb8ae05d78b98457edb9a845b080791", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "531010eb-1910-47e1-ab25-979b7a9946e3", "node_type": "1", "metadata": {}, "hash": "ab00205159df917e4962c7fff0ef2d2fcbdcd8f8a8433a04e27b188c3bf39433", "class_name": "RelatedNodeInfo"}}, "text": "One formalism for comparing laser melting parameters across different materials is the normalized enthalpy approach, which uses a scaling law to account for different materials properties [2,27,38-40] given by Eq. (5):\n\n$\\frac{\\Delta H}{h_{s}}=\\frac{A P}{\\pi \\rho C T_{m} \\sqrt{D u r^{3}}}$\n\nWhere $\\Delta H$ is the specific enthalpy of melting, $h_{s}$ is the enthalpy at melting, $A$ is material absorptivity, $P$ is the laser power, $\\rho$ is the material density, $C$ is the specific heat capacity, $T_{m}$ is the equilibrium melting temperature, $D$ is the thermal diffusivity, $u$ is scan speed, and $r$ is the $1 /$ $e$ radius of the laser. Since normalized enthalpy has been successfully used to predict the keyhole transition threshold at ambient pressure in Ti-64, Inconel alloys, and $316 \\mathrm{~L}$ [38], it is expected to capture the observed morphology transition. A comparison of the parameters used for Ti-64 and 316 L is shown in Fig. 10. Nickel 400 is omitted from this comparison because not all of the required materials properties are available to compute normalized enthalpy. The normalized enthalpy scaling predicts vapor depression depth (Fig. 10a), although with a greater spread of the data than was observed by Ye et al [38]. This slight discrepancy may be because of a slight systematic difference in the relationship between vapor depression depth and melt pool depth in Ti-64 and 316 L steel. However, the normalized enthalpy scaling does not predict changes in the vapor depression shape, even within a single material such as Ti-64 (Fig. 10b). This is because the shape of the vapor depression depends on variables that are not explicitly accounted for in the normalized enthalpy scaling, which was developed primarily to predict melt pool shape rather than the shape of the vapor depression. The most important factors not accounted for in the normalized enthalpy scaling are the surface tension of the liquid and the change in angle of the front wall of the vapor depression as a function of scan speed, which is known to heavily influence the vapor depression\\\\\ngeometry [25].\n\nEffects caused by changes in surface tension and melt viscosity are also evident in the high-power regime, above the power threshold for the vapor depression geometry transition in the vacuum case. In both Nickel alloy and $316 \\mathrm{~L}$, the vacuum conditions exhibit significant balling behavior. This arises due to the formation of waves on the surface of the melt pool due to fluid flow effects enabled by the lower surface temperature, and consequently higher surface tension, under vacuum that do not occur under ambient pressure. As reported by Bidare et al. [16], this balling is not caused by the Raleigh-Plateau instability but rather by waves formed by changes to the melt pool flow near the edges of the melt pool. The mechanism that causes this large scale, periodic balling is distinct from much finer surface features described by Martin et al that correlate with instabilities on the back wall of the vapor depression [24].\n\nWhile the vapor depression length differs between the vacuum case and the ambient case at low powers, the vapor depression and melt pool depths for the two pressures are the same within experimental uncertainties. Such close comparison indicates that the balance between vapor recoil pressure, which exerts a downward force on the liquid surface to form the vapor depression, and surface tension, which exerts an opposing force on the liquid surface, does not change significantly between vacuum and ambient. This contrasts with reported behavior at lower scan speeds, where reduced pressure increases weld penetration depths by as much as a factor of two [5].\n\nA possible alternate explanation is that under vacuum, the vapor jet expands uniformly, becoming less directional than what is observed at ambient pressure. If this were the case, the vapor depression is expected to be wider perpendicular to the scan direction under vacuum in addition to the lengthening observed via X-ray imaging. As illustrated by Fig. 3, the melt pools are consistently wider for the ambient case than for the vacuum case. This behavior suggests that uniform gas expansion does not have a strong influence on the vapor depression geometry, and that the surface temperature of the melt pool under vacuum is lower than at ambient pressure. Therefore, we discount the possibility that uniform gas expansion of the metal vapor plays a significant role in causing the change in vapor depression geometry between vacuum and ambient pressure.\n\n\\section*{5.", "start_char_idx": 210142, "end_char_idx": 214733, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "531010eb-1910-47e1-ab25-979b7a9946e3": {"__data__": {"id_": "531010eb-1910-47e1-ab25-979b7a9946e3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7dd4ab0c-ddf6-4204-b86f-7ada0f5a203d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0bd794839d6e348fa3c4848ea995580dd64b1f73e48c8a6d14c351570aa33ea1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3ccfffdb-b318-46af-89f4-ea0efc38aa60", "node_type": "1", "metadata": {}, "hash": "f3e0879dc5eb1cf2f46189c330ae6ecad3bff9b2973431141bae64bd15a1c11a", "class_name": "RelatedNodeInfo"}}, "text": "This contrasts with reported behavior at lower scan speeds, where reduced pressure increases weld penetration depths by as much as a factor of two [5].\n\nA possible alternate explanation is that under vacuum, the vapor jet expands uniformly, becoming less directional than what is observed at ambient pressure. If this were the case, the vapor depression is expected to be wider perpendicular to the scan direction under vacuum in addition to the lengthening observed via X-ray imaging. As illustrated by Fig. 3, the melt pools are consistently wider for the ambient case than for the vacuum case. This behavior suggests that uniform gas expansion does not have a strong influence on the vapor depression geometry, and that the surface temperature of the melt pool under vacuum is lower than at ambient pressure. Therefore, we discount the possibility that uniform gas expansion of the metal vapor plays a significant role in causing the change in vapor depression geometry between vacuum and ambient pressure.\n\n\\section*{5. Conclusions}\nThis article reports the melt pool flow behavior during laser melting as a function of the process atmosphere pressure and composition. At low energy density, significantly different vapor depression morphologies are observed under vacuum and ambient pressure conditions while at high energy densities the vapor depression morphology very similar under vacuum and ambient pressure. These differences in surface geometry are best quantified by the vapor depression aspect ratio. This behavior was observed in $316 \\mathrm{~L}$ steel, Nickel 400, and Ti-64 but not in Al6061. The details of the behavior and magnitude of the change as a function of power vary depending on material and scan speed. We attribute these differences primarily to changes in the surface tension of the liquid metal. The surface tension changes because the boiling temperature, and therefore melt pool surface temperature, are lower at reduced pressure. We also observe contrasting flow behavior in cases where the atmosphere has a significant $\\mathrm{O}_{2}$ partial pressure when compared to a pure Ar atmosphere, and also attribute these changes primarily to the influence of oxygen uptake on liquid metal surface tension. The subsurface observations reported here complement previous optical experiments and modelling studies and further improve our understanding of the physics of the laser-material interactions central to both LPBF and laser welding.\n\n\\section*{CRediT authorship contribution statement}\nNicholas P. Calta: Conceptualization, Formal analysis,\\\\\nInvestigation, Writing - original draft, Visualization, Methodology. Aiden A. Martin: Conceptualization, Formal analysis, Investigation, Writing - review \\& editing, Software, Methodology. Joshua A. Hammons: Conceptualization, Formal analysis, Investigation, Writing review \\& editing, Software. Michael H. Nielsen: Investigation, Writing - review \\& editing. Tien T. Roehling: Investigation, Writing - review \\& editing. Kamel Fezzaa: Writing - review \\& editing, Resources. Manyalibo J. Matthews: Conceptualization, Writing - review \\& editing. Jason R. Jeffries: Conceptualization, Writing - review \\& editing. Trevor M. Willey: Conceptualization, Writing - review \\& editing, Investigation, Funding acquisition. Jonathan R.I. Lee: Conceptualization, Writing - review \\& editing, Investigation, Supervision, Project administration, Funding acquisition.\n\n\\section*{Declaration of Competing Interest}\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n\\section*{Acknowledgements}\nThis work was performed under the auspices of the U.S. Department of Energy (DOE) by Lawrence Livermore National Laboratory (LLNL) under Contract No. DE-AC52-07NA27344. This publication is based upon work performed at the Dynamic Compression Sector (DCS), which is operated by Washington State University under the U.S. Department of Energy/National Nuclear Security Administration award no. DENA0002442. This research used resources of the Advanced Photon Source, a DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357. The authors gratefully acknowledge valuable discussions with W. King, S. Khairallah, and A. Rubenchik, sample preparation by the LLNL Precision Machine Shop, and beamtime support from N. Sinclair, P. Rigg, D. Rickerson, J. Klug, and N. Weir at DCS and A. Deriy at APS sector 32. LLNL-JRNL-788222. 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Rollett, A.D.", "start_char_idx": 224072, "end_char_idx": 226537, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5eb1a0c6-9ee2-4c17-84a2-8a802d242267": {"__data__": {"id_": "5eb1a0c6-9ee2-4c17-84a2-8a802d242267", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "917e15b9-27e4-4c57-8c28-31884144da6b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "416f9f91f035709b43b7ba5d43c65bde69ede47051221b4255c98a1478f73dcc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "901bd390-d6fc-4a49-a023-6778a665802f", "node_type": "1", "metadata": {}, "hash": "db9bee73677ade5c78ef8dab11a77a3d8b084721039f5bc569655c69d40385d6", "class_name": "RelatedNodeInfo"}}, "text": "Matthews, Dynamics of pore formation during laser powder bed fusion additive manufacturing, Nat. 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King, S.S.", "start_char_idx": 226028, "end_char_idx": 228643, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "901bd390-d6fc-4a49-a023-6778a665802f": {"__data__": {"id_": "901bd390-d6fc-4a49-a023-6778a665802f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5eb1a0c6-9ee2-4c17-84a2-8a802d242267", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a9b3fbdaf9a114f6669013805c3a358de2423f90855ba55d562e30b0b47a7309", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "708ff2d1-d13a-44b4-ad60-1423299012e4", "node_type": "1", "metadata": {}, "hash": "ed56c49f7d468734c05f2cc98a33487bf081dcae70969fd70b18bdf738adac22", "class_name": "RelatedNodeInfo"}}, "text": "Phys. 107 (2010) 014910, \\href{https://doi.org/10.1063/1.3275047}{https://doi.org/10.1063/1.3275047}.\n\n[38] J. Ye, S.A. Khairallah, A.M. Rubenchik, M.F. Crumb, G. Guss, J. Belak, M.J. Matthews, Energy coupling mechanisms and scaling behavior associated with laser powder bed fusion additive manufacturin, AdvEngMater.21, 2019, 1900185. \\href{https://doi.org/10.1002/adem}{https://doi.org/10.1002/adem}. 201900185.\n\n[39] A.M. Rubenchik, W.E. King, S.S. Wu, Scaling laws for the additive manufacturing, J. Mater. Process. Technol. 257 (2018) 234-243, \\href{https://doi.org/10.1016/j}{https://doi.org/10.1016/j}. jmatprotec.2018.02.034.\n\n[40] D.B. Hann, J. Iammi, J. Folkes, A simple methodology for predicting laser-weld properties from material and laser parameters, J. Phys. D Appl. Phys. 44 (2011) 445401, , \\href{https://doi.org/10.1088/0022-3727/44/44/445401}{https://doi.org/10.1088/0022-3727/44/44/445401}.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{3-Dimensional heat transfer modeling for laser powder-bed fusion additive manufacturing with volumetric heat sources based on varied thermal conductivity and absorptivity }\n\n\n\\author{Zhidong Zhang, Yuze Huang, Adhitan Rani Kasinathan, Shahriar Imani Shahabad, Usman Ali,\\\\\nYahya Mahmoodkhani, Ehsan Toyserkani*}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nFull length article\n\nMulti-Scale Additive Manufacturing Lab, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada\n\n\\begin{itemize}\n  \\item Eight 3D heat sources used for simulating Laser Powder-Bed Fusion are compared.\n  \\item New equations for varied thermal conductivity and laser absorptivity is proposed.\n  \\item The varied thermal conductivity and absorptivity expressions can be linear functions.", "start_char_idx": 228192, "end_char_idx": 230968, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "708ff2d1-d13a-44b4-ad60-1423299012e4": {"__data__": {"id_": "708ff2d1-d13a-44b4-ad60-1423299012e4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "901bd390-d6fc-4a49-a023-6778a665802f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "f241f915dadb1e630e5d38e1d163da69148f39999876d594595d19063a08a254", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c18b92c5-32e4-4170-baf5-4348fea0be40", "node_type": "1", "metadata": {}, "hash": "924089de2c7c85f8f84cc9506aa18a413efdad164136b04bca206c4266e587cb", "class_name": "RelatedNodeInfo"}}, "text": "\\item New equations for varied thermal conductivity and laser absorptivity is proposed.\n  \\item The varied thermal conductivity and absorptivity expressions can be linear functions.\n\\end{itemize}\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing\n\nLaser powder-bed fusion\n\nHeat transfer modeling\n\nVolumetric heat sources\n\nVaried laser absorptivity\n\nAnisotropically enhanced thermal conductivity\n\n\\begin{abstract}\nA B S T R A C T In this article, a 3-dimensional heat-transfer finite element model for Laser Powder-Bed Fusion (LPBF) was developed for accurately predicting melt pool dimensions and surface features. The sole deployment of trial-anderror experiments for arriving at optimal process parameters is very costly and time-consuming, thus the developed model can be used to reduce the process/material development costs. A literature review of heat source models was presented. Eight commonly used heat source models are evaluated and compared. All of their simulated depths are smaller than the experimental result, which may be due to the melt pool convection and inconstant laser absorptivity in the reality during the experiment. In order to enable the numerical model to predict melt pool dimensions for different combinations of process parameters, a novel model including expressions of varied anisotropically enhanced thermal conductivity and varied laser absorptivity is proposed and verified by both the melt pool dimensions and track surface morphology. It is found that the heat source expressions can be linear while causing the simulation results to be in better agreement with both experimental melt pool dimensions and track surface morphology.\n\\end{abstract}\n\n\\section*{1. Introduction}\nLaser Powder-Bed Fusion (LPBF) is a commercially available Additive Manufacturing (AM) process. It is regarded as one of the most common processes for direct metal fabrication [1]. In LPBF, geometrically complex parts can be produced by selectively melting layers of powder. Nevertheless, wide industrial applications of LPBF are hindered by several limitations, including porosity defects resulted from lack of fusion, keyhole collapse, and balling [2], and residual stress which causes distortion and failure of the final products due to high thermal gradients $[3,4]$. Therefore, machine process parameter optimization becomes a critical task.\n\nHowever, the sole deployment of trial-and-error experiments to determine optimal process parameters is very costly and time-consuming [5] since there will be a large number of coupon samples with different combinations of process parameters, such as laser power, scanning speed, powder layer thickness, hatch spacing, preheating temperature, and scanning patterns. Therefore, numerical simulations of the LPBF process are widely investigated.\n\nThe physical phenomena associated in a melt pool are highly complicated, mainly controlled by mass and heat transfer. The heating and cooling rates are extremely high due to the fast-moving laser irradiation on the powder particles [6]. In addition, the dynamic melt pool development beneath the powder-bed [7], phase change dynamics from liquid to vapor and plasma [8], and powder particles drawn by high-speed metal vapor flux [9] and capillary effects exist in the melt\n\\footnotetext{*Corresponding author at: Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.\n\nE-mail address: \\href{mailto:ehsan.toyserkani@uwaterloo.ca}{ehsan.toyserkani@uwaterloo.ca} (E. Toyserkani).\n}\npool. Therefore, fine-scale numerical models [10,11], which included several details, such as laser-ray tracing in randomly distributed particles and thermal fluid dynamics, have been built in order to simulate several complex melt pool behaviors. However, the computational cost for such simulations is extremely high. For example, the work done in [10] employed ALE3D (developed in Lawrence Liverpool National Laboratory) massively-parallel code which consumes on the order 100,000 CPU-h [5], and the work done in [11] took $140 \\mathrm{~h}$ for only $4 \\mathrm{~ms}$ simulation of the process.\n\nTherefore, for reducing the computational time, effective simulation models with certain approximations and assumptions to predict the dimensions of melt pools (e.g. melt pool width and depth) have been proposed. For simplification, instead of employing laser-ray tracing method in randomly distributed particles, the heat source has been usually assumed as volumetric heat source models, and the powder layer is presumed as homogeneous bulk materials with effective powder-layer material properties. In the literature, researchers have employed various heat sources.", "start_char_idx": 230787, "end_char_idx": 235522, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c18b92c5-32e4-4170-baf5-4348fea0be40": {"__data__": {"id_": "c18b92c5-32e4-4170-baf5-4348fea0be40", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "708ff2d1-d13a-44b4-ad60-1423299012e4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "094e2c572398741ddbd158425dd936556c62dfebf84c5228dfe4dfb9d0807645", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d27069e7-cfb1-4b09-9138-a944fe15258d", "node_type": "1", "metadata": {}, "hash": "03e6ddc8d60dca141a58ba0b76d36bfa6b3543dd34481ad14ce9adf2b5591f4c", "class_name": "RelatedNodeInfo"}}, "text": "However, the computational cost for such simulations is extremely high. For example, the work done in [10] employed ALE3D (developed in Lawrence Liverpool National Laboratory) massively-parallel code which consumes on the order 100,000 CPU-h [5], and the work done in [11] took $140 \\mathrm{~h}$ for only $4 \\mathrm{~ms}$ simulation of the process.\n\nTherefore, for reducing the computational time, effective simulation models with certain approximations and assumptions to predict the dimensions of melt pools (e.g. melt pool width and depth) have been proposed. For simplification, instead of employing laser-ray tracing method in randomly distributed particles, the heat source has been usually assumed as volumetric heat source models, and the powder layer is presumed as homogeneous bulk materials with effective powder-layer material properties. In the literature, researchers have employed various heat sources. These heat sources can be categorized into two groups based on their characteristics, namely (a) Geometrically Modified Group (GMG); and, (b) Absorptivity Profile Group (APG). In GMG, different geometries are used to mimic the actual shape of the heat source, such as cylinder shape [12], semi-sphere [13], semi-ellipsoid [13,14], and conical shape [15]. For example, the work in [12] built up a volumetric heat source model with the consideration of the optical-penetration depth (OPD) of the laser beam into the powder-bed, where the shape of the heat source is a cylinder. Bruna-Rosso et al. [14] implemented the semi-ellipsoid heat source model, which was proposed firstly by Goldak et al. [13], in the LPBF simulation. The model showed good agreement with the experimental results. Wu et al. [15] proposed a conical shape of the heat source for arc welding, which is comparable to the LPBF process, and derived a good set of data in accordance with experimental results. On the other hand, in APG, the powder-bed of LPBF is viewed as an optical medium and the laser beam is assumed to be absorbed gradually along the depth of the powder layer. Therefore, several absorptivity profiles have been proposed, such as radiation transfer equation [6], absorptivity derived by the Monte Carlo method [16], linearly decaying equation [17], and exponentially decaying equation [18]. In APG, the heat source models are not constrained in specific geometries, and their general form is that two-dimensional Gaussian distribution is on the top surface while the laser beam is absorbed along the depth of the powder-bed based on the absorptivity functions. Gusarov et al. [6] presented a mathematical approach for effectively estimating the laser radiation scattering and absorption in powder layers and developed a volumetric heat source based on the radiation transfer. In the work done in [18], a heat source model was presented, which follows a Gaussian profile on the Cartesian coordinates, and an exponentially decaying profile along the z-direction. The effective heat source models presented in the literature are computationally efficient and accurate while being compared to the corresponding experimental results. However, a comparison report is not found in the literature. Heat source modeling is regarded as one of the key factors that influence not only the melt pool dimensions but also thermal variables [18], e.g. the cooling rate, etc. Therefore, comparisons of heat sources used in simulation of the LPBF process are necessary.\n\nIn addition to computation acceleration, thermal fluid dynamics, such as mass convection in the melt pool during LPBF, can be approximated effectively by the anisotropically enhanced thermal conductivity method [19]. The anisotropically enhanced thermal conductivity method could effectively improve the prediction precision of melt pool dimensions. However, its further investigation is still critical since it may be changed from one set of process parameters to others. Lastly, laser absorptivity is one of the most uncertain parameters during the numerical modeling as discussed in [5,6]. All the simulation models mentioned in the above literature employed constant absorptivity, which may not be the case in reality. The laser absorption factor is influenced not only by the powder particle size and distribution but also the angle of incidence that varies due to the dynamic melt pool surface [20]. Trapp et al. [20] and Matthews et al. [21] studied the absorptivity in LPBF using experimental approaches. The variation of absorptivity was observed very large from 0.3 up to near 0.7 dependent on process parameters.", "start_char_idx": 234605, "end_char_idx": 239187, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d27069e7-cfb1-4b09-9138-a944fe15258d": {"__data__": {"id_": "d27069e7-cfb1-4b09-9138-a944fe15258d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c18b92c5-32e4-4170-baf5-4348fea0be40", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "de6b0e564296b40b43ad51a190565a987d72403ced41a592679212fc61a7e7b1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8ac8d2d0-1e73-453d-b5e1-792b75b35b61", "node_type": "1", "metadata": {}, "hash": "5c33abf902ecee8c18e6bcd6bbf3b8a48ce4220bfb65a6010f4d7bb061444d9f", "class_name": "RelatedNodeInfo"}}, "text": "The anisotropically enhanced thermal conductivity method could effectively improve the prediction precision of melt pool dimensions. However, its further investigation is still critical since it may be changed from one set of process parameters to others. Lastly, laser absorptivity is one of the most uncertain parameters during the numerical modeling as discussed in [5,6]. All the simulation models mentioned in the above literature employed constant absorptivity, which may not be the case in reality. The laser absorption factor is influenced not only by the powder particle size and distribution but also the angle of incidence that varies due to the dynamic melt pool surface [20]. Trapp et al. [20] and Matthews et al. [21] studied the absorptivity in LPBF using experimental approaches. The variation of absorptivity was observed very large from 0.3 up to near 0.7 dependent on process parameters. As seen in their results, for specefic range of process parameters, the absorptivity was directly proportional to the laser power. However, there is still a lack of clear expressions correlating the absorptivity and the process parameters. Besides, investigations on more different kinds of materials are still needed.\n\nTherefore, the present study gives a summary and comparison of the heat source models commonly used by researchers in the literature. In addition, to the authors' best knowledge, it is the first attempt to develop a model including expressions of varied anisotropically enhanced thermal conductivity and varied laser absorptivity. For the model validation, melt pool dimensions and track surface morphology, e.g. track stability [22] and ripple angle [18] can be used as significant indicators since they determine the final product quality and can be quantified by experimental results at the same time. Thus, the validity of the proposed approach is verified by the melt pool dimensions and track surface morphology.\n\n\\section*{2. Background to heat transfer modeling utilized in LPBF}\n\\subsection*{2.1. Governing equations}\nThe governing expression for 3D heat transfer processes can generally be as follows,\n\n$\\rho c \\frac{\\partial T}{\\partial t}=\\frac{\\partial}{\\partial x}\\left(k_{x} \\frac{\\partial T}{\\partial x}\\right)+\\frac{\\partial}{\\partial y}\\left(k_{y} \\frac{\\partial T}{\\partial y}\\right)+\\frac{\\partial}{\\partial z}\\left(k_{z} \\frac{\\partial T}{\\partial z}\\right)+Q(x, y, z, t)$\n\nwhere $\\rho$ is the material density $\\left[\\mathrm{kg} / \\mathrm{m}^{3}\\right], \\mathrm{c}$ is the specific heat $[\\mathrm{J} / \\mathrm{kgK}], T$ is the current temperature $[\\mathrm{K}], t$ is the time $[\\mathrm{s}], x, y$, and $z$ are the coordinates in the reference system [m], $k_{\\mathrm{x}}, k_{\\mathrm{y}}$, and $k_{\\mathrm{z}}$ are the thermal conductivity $[\\mathrm{W} / \\mathrm{mK}]$ of $\\mathrm{x}, \\mathrm{y}$, and $\\mathrm{z}$-axis direction, and $\\mathrm{Q}(x, y, z, t)$ is the internal heat generation per unit volume $\\left[\\mathrm{W} / \\mathrm{m}^{3}\\right]$.\n\nBecause of the preheating of the substrate, the initial temperature ( $\\mathrm{T}_{\\text {base }}$ ) of the substrate and the powder layer was considered as $353[\\mathrm{~K}]$. The ambient temperature $\\left(\\mathrm{T}_{0}\\right)$ distribution of the environment during LPBF can be set to $293[\\mathrm{~K}]$.\n\nConvective heat losses $\\left(q_{\\mathrm{c}}\\right)$ were considered as follows,\n\n$q_{c}=-h_{c}\\left(T_{\\text {sur }}-T_{0}\\right)$\n\nwhere $h_{\\mathrm{c}}$ is the convective heat transfer coefficient $\\left[\\mathrm{W} /\\left(\\mathrm{m}^{2} \\mathrm{~K}\\right)\\right]$, and $T_{\\text {sur }}$ is the surface temperature $[\\mathrm{K}]$.", "start_char_idx": 238281, "end_char_idx": 241926, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8ac8d2d0-1e73-453d-b5e1-792b75b35b61": {"__data__": {"id_": "8ac8d2d0-1e73-453d-b5e1-792b75b35b61", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d27069e7-cfb1-4b09-9138-a944fe15258d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6bf68344e5596c7ea5274b3f84fcec0fb0fe87f61739bc1823270658a3671fc9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "55098998-dc6b-442b-9edc-83e3b9a8314a", "node_type": "1", "metadata": {}, "hash": "433ab435ec3ed6cb36e7f59aeec4f1750e606ce912aba4333aafd5a440d96533", "class_name": "RelatedNodeInfo"}}, "text": "Because of the preheating of the substrate, the initial temperature ( $\\mathrm{T}_{\\text {base }}$ ) of the substrate and the powder layer was considered as $353[\\mathrm{~K}]$. The ambient temperature $\\left(\\mathrm{T}_{0}\\right)$ distribution of the environment during LPBF can be set to $293[\\mathrm{~K}]$.\n\nConvective heat losses $\\left(q_{\\mathrm{c}}\\right)$ were considered as follows,\n\n$q_{c}=-h_{c}\\left(T_{\\text {sur }}-T_{0}\\right)$\n\nwhere $h_{\\mathrm{c}}$ is the convective heat transfer coefficient $\\left[\\mathrm{W} /\\left(\\mathrm{m}^{2} \\mathrm{~K}\\right)\\right]$, and $T_{\\text {sur }}$ is the surface temperature $[\\mathrm{K}]$.\n\nRadiative heat losses $\\left(q_{\\mathrm{r}}\\right)$ were accounted for by using StefanBoltzmann law:\n\n$q_{r}=-\\varepsilon \\sigma\\left(T_{\\text {sur }}^{4}-T_{0}^{4}\\right)$\n\nwhere $\\varepsilon$ is the emissivity of the powder-bed, and $\\sigma$ is Stefan-Boltzmann constant for radiation.\n\n\\subsection*{2.2. Heat source models}\nIt is important to establish an appropriate heat source model of LPBF simulations since the heat source will not only influence the geometries of melt pools but also probably have an impact on the mechanical performance of final products. Heat source models used in LPBF simulations is a laser beam which is usually assumed to be twodimensional Gaussian [23]. The beam irradiance at any point $(x, y)$ at time $t$ for the fundamental transverse electromagnetic mode $\\left(\\mathrm{TEM}_{00}\\right)$ can be expressed as,\n\n$I(x, y, t)=\\frac{2 \\beta P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{(x-v \\cdot t)^{2}+y^{2}}{r_{l}^{2}}\\right]$\\\\\nwhere $P$ is the power of the stationary laser source, $r_{l}$ is the radius of the laser beam, $(x, y)$ are the coordinates of the heat source, $v$ is the scanning velocity and $\\beta$ is the laser-beam absorptivity.\n\nHowever, it may be improper to employ the two-dimensional heat source to simulate LPBF, because the laser scanning over metal powder can penetrate into the powder-bed [6]. In other words, laser energy is deposited not only on the top surface of a powder-bed but inside the powder-bed. Thus, volumetric heat sources should be considered in order to describe the laser penetration into powders [18].\n\nEight heat source models will be discussed and compared to investigate which heat source model is the most suitable one for LPBF simulations, the Optical Penetration Depth (OPD) method [12], threedimensional Gaussian distribution [13], ellipsoidal distribution [13], conical heat source [15], radiation transfer method [6,24], absorptivity function method [16], linearly decaying heat source [17], and exponentially decaying heat source [18]. They can, however, be categorized into two groups: 1) geometrically modified group including the first four heat sources; and, 2) absorptivity profile group containing the last four heat sources.\n\n\\subsection*{2.2.1. GMG: Geometrically modified group}\nSince the Gaussian laser beam can penetrate into and reflect in the powder layers, a practical method to describe this process is to change the shape of the heat source from two-dimensional surfaces to threedimensional geometries, which can be cylindrical, semi-spherical, semiellipsoidal, and conical shapes.\n\n2.2.1.1. GMG.1: Cylindrical shape heat source model. The shape of the laser beam in LPBF is usually circular so that it is relatively straightforward to employ a 3D cylindrical heat source. The authors in [12] proposed to employ a uniform energy distribution for the heat source in the cylinder volume influenced by the Optical Penetration Depth (OPD). The OPD is defined as the depth where the laser intensity drops to $1 / e(\\approx 36.8 \\%)$ of the laser beam intensity absorbed on the top surface of the powder-bed. The schematic plot of the cylindrical heat source model is plotted in Fig. 1a.", "start_char_idx": 241283, "end_char_idx": 245108, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "55098998-dc6b-442b-9edc-83e3b9a8314a": {"__data__": {"id_": "55098998-dc6b-442b-9edc-83e3b9a8314a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8ac8d2d0-1e73-453d-b5e1-792b75b35b61", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "47489b2946ec451a6c82d224f039e65d748bd015ceef46f7dca7954d2b8161ff", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c4b9ea3f-4a95-485c-ae2e-4da0c271dfc5", "node_type": "1", "metadata": {}, "hash": "39f9ed6cafe4c2a4564dc6495397ab943d9986a0989a5f14efd27100b00fbe06", "class_name": "RelatedNodeInfo"}}, "text": "2.2.1.1. GMG.1: Cylindrical shape heat source model. The shape of the laser beam in LPBF is usually circular so that it is relatively straightforward to employ a 3D cylindrical heat source. The authors in [12] proposed to employ a uniform energy distribution for the heat source in the cylinder volume influenced by the Optical Penetration Depth (OPD). The OPD is defined as the depth where the laser intensity drops to $1 / e(\\approx 36.8 \\%)$ of the laser beam intensity absorbed on the top surface of the powder-bed. The schematic plot of the cylindrical heat source model is plotted in Fig. 1a. Therefore, the heat source intensity can be expressed as,\n\n$I(x, y, z)=\\beta P / V, \\quad V=S \\times \\alpha_{O P D} \\times O P D$\n\nwhere $x, y$, and $z$ are the variables of the three dimensions, $\\beta$ is the absorptivity of laser beam, $P$ is the laser power (W), $V$ is the volume exposed by the laser beam $\\left(\\mathrm{m}^{3}\\right), S$ is the area of the laser spot $\\left(\\mathrm{m}^{2}\\right)$, and $\\alpha_{O P D}$ is the correction factor for the assumed OPD. In this work, the OPD is chosen to be the layer thickness $20 \\mu \\mathrm{m}$, and the correction factor $\\alpha$ is assumed to be 1 because of a lack of data for stainless steel $17-4 \\mathrm{PH}$.\n\n2.2.1.2. GMG.2: Semi-spherical shape heat source model. As known, the laser beam has a two-dimensional Gaussian intensity distribution [23]. In the case that a three-dimensional heat source should be considered, a semi-spherical Gaussian distribution of energy density $\\left(\\mathrm{W} / \\mathrm{m}^{3}\\right)$ would be a step toward a more precise model [13]. The schematic plot of the heat source model is plotted in Fig. 1b. As shown in [13], the expression of a 3D Gaussian distribution of the laser beam is as follows,\n\n$I(x, y, z)=q_{0} \\cdot \\exp \\left[-2 \\frac{x^{2}+y^{2}+z^{2}}{r_{l}^{2}}\\right]$\n\nwhere $q_{0}$ is a coefficient, derived by the energy balance. Based on the conservation of energy, the total energy input should be equal to the integration of intensity over the semi-infinite domain,\n\n$\\beta \\cdot P \\cdot=\\int_{0}^{\\infty} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} q_{0} \\cdot \\exp \\left[-2 \\frac{x^{2}+y^{2}+z^{2}}{r^{2}}\\right] d x d y d z$\n\nThus, the expression of $q_{o}$ should be, $q_{0}=\\frac{2^{5 / 2} \\beta \\cdot P}{\\pi^{3 / 2} r_{l}^{3}}$\n\nAfter replacing $q_{o}$ in Eq. (6) by Eq. (8), the final expression of the intensity distribution can be obtained as,\n\n$I(x, y, z)=\\frac{2^{5 / 2} \\beta \\cdot P}{\\pi^{3 / 2} \\eta^{3}} \\exp \\left[-2 \\frac{x^{2}+y^{2}+z^{2}}{\\eta^{2}}\\right]$\n\n2.2.1.3. GMG.3: Semi-ellipsoidal shape heat source model. The 3D Gaussian heat source is in semi-spherical shape; however, the melt pool in LPBF is often far from a spherical shape. In order to more accurately simulate the melt pool dimensions, the semi-ellipsoidal power distribution proposed by Goldak et al. [13] originally for the welding process has been employed and investigated, as shown in Fig. 1c.", "start_char_idx": 244510, "end_char_idx": 247514, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c4b9ea3f-4a95-485c-ae2e-4da0c271dfc5": {"__data__": {"id_": "c4b9ea3f-4a95-485c-ae2e-4da0c271dfc5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "55098998-dc6b-442b-9edc-83e3b9a8314a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1621c89e11a50f2d934d6d78adab5297abddcb450597a9b2417892bda23048e4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "edab5012-041f-4868-bdc7-e8928382fd55", "node_type": "1", "metadata": {}, "hash": "26f898542e6fbd74bcc4ccd097b69f0574e7c7b8410af8c0737a0c2921ec1f5b", "class_name": "RelatedNodeInfo"}}, "text": "(6) by Eq. (8), the final expression of the intensity distribution can be obtained as,\n\n$I(x, y, z)=\\frac{2^{5 / 2} \\beta \\cdot P}{\\pi^{3 / 2} \\eta^{3}} \\exp \\left[-2 \\frac{x^{2}+y^{2}+z^{2}}{\\eta^{2}}\\right]$\n\n2.2.1.3. GMG.3: Semi-ellipsoidal shape heat source model. The 3D Gaussian heat source is in semi-spherical shape; however, the melt pool in LPBF is often far from a spherical shape. In order to more accurately simulate the melt pool dimensions, the semi-ellipsoidal power distribution proposed by Goldak et al. [13] originally for the welding process has been employed and investigated, as shown in Fig. 1c. As shown in [13], the ellipsoidal distribution is a Gaussian distribution in an ellipsoid with semi-axes $a, b$, and $c$ and center at $(0,0$, 0 ),\n\n$I(x, y, z)=q_{0} \\cdot \\exp \\left[-2\\left(\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}+\\frac{z^{2}}{c^{2}}\\right)\\right]$\n\nwhere $a, b, c$ are semi-axes parallel to the coordinate axes $x, y, z$.\n\nSimilar to the 3D Gaussian distribution, $q_{0}$ is as follows,\n\n$q_{0}=\\frac{2^{5 / 2} \\beta \\cdot P}{\\pi^{3 / 2} a b c}$\n\nThus, the final expression of the intensity distribution can be written as,\n\n$I(x, y, z)=\\frac{2^{5 / 2} \\beta \\cdot P}{\\pi^{3 / 2} a b c} \\exp \\left[-2\\left(\\frac{x^{2}}{a^{2}}+\\frac{y^{2}}{b^{2}}+\\frac{z^{2}}{c^{2}}\\right)\\right]$\n\nAccording to the researchers [13], the front part of the ellipsoid could be different from the rear part in order to coincide with some experimental situations. Thus the double ellipsoidal power density distribution was proposed. The front part of the ellipsoid can be expressed as,\n\n$I_{f}(x, y, z)=f_{f} \\cdot \\frac{2^{5 / 2} \\beta \\cdot P}{\\pi^{3 / 2} a_{f} b c} \\exp \\left[-2\\left(\\frac{x^{2}}{a_{f}^{2}}+\\frac{y^{2}}{b^{2}}+\\frac{z^{2}}{c^{2}}\\right)\\right]$\n\nwhile the rear part of the ellipsoid can be written as follows,\n\n$I_{r}(x, y, z)=f_{r} \\cdot \\frac{2^{5 / 2} \\beta \\cdot P}{\\pi^{3 / 2} a_{r} b c} \\exp \\left[-2\\left(\\frac{x^{2}}{a_{r}^{2}}+\\frac{y^{2}}{b^{2}}+\\frac{z^{2}}{c^{2}}\\right)\\right]$\n\nwhere $a_{f}$ and $a_{r}$ are the semi-axes of the front and rear ellipsoids, respectively. It should be noted that $f_{f}+f_{r}=2$, because,\n\n\n\\begin{align*}\n\\beta \\cdot P & =\\frac{1}{2} \\int_{0}^{\\infty} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} I_{f}(x, y, z) d x d y d z+\\frac{1}{2} \\int_{0}^{\\infty} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} I_{r}(x, y, z) d x d y d z \\\\\n& =f_{f} \\frac{\\beta \\cdot P}{2}+f_{r} \\frac{\\beta \\cdot P}{2} \\tag{15}\n\\end{align*}\n\n\n2.2.1.4. GMG.4: Conical shape heat source model.", "start_char_idx": 246896, "end_char_idx": 249450, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "edab5012-041f-4868-bdc7-e8928382fd55": {"__data__": {"id_": "edab5012-041f-4868-bdc7-e8928382fd55", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c4b9ea3f-4a95-485c-ae2e-4da0c271dfc5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2764fb32d2acfd9284ae59ae971bb57176edbf15f2bf839e7801f33d7f3fa939", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ea46afe6-4a8d-4b0d-93d6-fcf3450c6cff", "node_type": "1", "metadata": {}, "hash": "d697d6a7d7dc5bec8d211a65e4a099cf2097a38d4fc6ccaddc3588cfe3253ad0", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{align*}\n\\beta \\cdot P & =\\frac{1}{2} \\int_{0}^{\\infty} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} I_{f}(x, y, z) d x d y d z+\\frac{1}{2} \\int_{0}^{\\infty} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} I_{r}(x, y, z) d x d y d z \\\\\n& =f_{f} \\frac{\\beta \\cdot P}{2}+f_{r} \\frac{\\beta \\cdot P}{2} \\tag{15}\n\\end{align*}\n\n\n2.2.1.4. GMG.4: Conical shape heat source model. In the welding area, researchers [15,25] have employed conical shape heat source to simulate the welding process. Based on the inherent similarity between welding and LPBF, this model can be applied for simulating the LPBF process. The schematic plot of the conical heat source model is plotted in Fig. 1(d).\n\nAs shown in [15,25], the mathematical expression of the heat source can be written as,\n\n$I(x, y, z)=q_{0} \\cdot \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{0}^{2}}\\right], \\quad r_{0}(z)=r_{e}+\\frac{z}{H}\\left(r_{e}-r_{i}\\right)$\n\nwhere $r_{e}$ and $r_{i}$ are the radius at the top and bottom, respectively. Based on the conservation of energy, the total energy input should be equal to\\\\\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04(3)}\n\\end{center}\n\n(e)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04(6)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04}\n\\end{center}\n\n(f)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04(1)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04(5)}\n\\end{center}\n\n(g)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04(2)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04(7)}\n\\end{center}\n\n(h)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-04(4)}\n\\end{center}\n\nFig. 1. The schematic of the heat source models, (a) cylindrical shape; (b) semi-spherical shape; (c) semi-ellipsoidal shape; (d) conical shape, (e) radiation transfer method; (f) ray-tracing method; (g) linearly decaying method; (h) exponentially decaying method.\n\nthe integration of intensity over the conical shape domain,\n\n$\\beta \\cdot P=\\int_{-H}^{0} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} q_{0} \\cdot \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{0}^{2}}\\right] d x d y d z$\n\nUsing Eq.", "start_char_idx": 249070, "end_char_idx": 251529, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ea46afe6-4a8d-4b0d-93d6-fcf3450c6cff": {"__data__": {"id_": "ea46afe6-4a8d-4b0d-93d6-fcf3450c6cff", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "edab5012-041f-4868-bdc7-e8928382fd55", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6d4ad592699ae5fd00d4f1637c4fea05d328c485b00a481af9b346a38f52b167", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7e6a011a-b534-4f33-8406-cafe69997b5c", "node_type": "1", "metadata": {}, "hash": "b78f6644dc9fedc89f37f548b264985229ea0edc00d764369672ce4203c71264", "class_name": "RelatedNodeInfo"}}, "text": "1. The schematic of the heat source models, (a) cylindrical shape; (b) semi-spherical shape; (c) semi-ellipsoidal shape; (d) conical shape, (e) radiation transfer method; (f) ray-tracing method; (g) linearly decaying method; (h) exponentially decaying method.\n\nthe integration of intensity over the conical shape domain,\n\n$\\beta \\cdot P=\\int_{-H}^{0} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} q_{0} \\cdot \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{0}^{2}}\\right] d x d y d z$\n\nUsing Eq. (17), an expression for $q_{0}$ can be derived,\n\n$q_{0}=\\frac{6 \\beta \\cdot P}{\\pi H\\left(r_{e}^{2}+r_{e} r_{i}+r_{i}^{2}\\right)}$\n\nAfter replacing $q_{o}$ in Eq. (16) by Eq. (18), the final expression of the intensity distribution can be obtained as,\n\n$I(x, y, z)=\\frac{6 \\beta \\cdot P}{\\pi H\\left(r_{e}^{2}+r_{e} r_{i}+r_{i}^{2}\\right)} \\cdot \\exp \\left[-2 \\cdot \\frac{x^{2}+y^{2}}{r_{0}^{2}}\\right]$\n\n\\subsection*{2.2.2. APG. Absorptivity profile group}\nDuring LPBF, a laser beam can penetrate into a depth of a powderbed, while it is being absorbed gradually along the depth of the powder layer. Therefore, the powder-bed can be viewed as an optical medium, whose optical absorptivity would be described by absorptivity profiles. The heat source models in this group are not constrained in specific geometries as those in GMG, as shown in Fig. 1(e-h). Their general form is that the two-dimensional Gaussian distribution is on the top surface while the laser beam is absorbed along the depth of the powder layer. It can be written as follows,\n\n$I(x, y, z)=\\frac{2 P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{l}^{2}}\\right] \\cdot f(z)$\n\nwhere $f(z)=d \\beta / d z$ is the absorptivity profile function. $\\beta(z)$ is the absorptivity coefficient function.\n\n2.2.2.1. APG.1: Radiation transfer equation method. The onedimensional radiation transfer equation proposed by Gusarov et al.\\\\\n[6] is implemented and investigated. Based on the fact that laser can penetrate into a depth of a powder-bed, this approach resembles the powder-bed with a thickness of $z_{\\text {bed }}$ with an optical media with an extinction coefficient of $\\eta$. The schematic plot of this source model is plotted in Fig. 1(e).\n\nAs developed in [6], the volumetric heat source due to radiation transfer is,\n\n$I(x, y, z)=\\frac{2 P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{l}^{2}}\\right] \\cdot f_{1}(z), f_{1}(z)=\\left(-\\eta \\cdot \\frac{d q}{d \\xi}\\right)$\n\nwhere $\\xi=\\eta \\cdot z$ is the dimensionless local depth coordinate, and $q$ is the dimensionless form of net radiative energy flux density and is described as,", "start_char_idx": 251044, "end_char_idx": 253644, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7e6a011a-b534-4f33-8406-cafe69997b5c": {"__data__": {"id_": "7e6a011a-b534-4f33-8406-cafe69997b5c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ea46afe6-4a8d-4b0d-93d6-fcf3450c6cff", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8d5573cf440532520a6590812833303c323bd7a71a522dbf288e64d85d41986f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bcb5078c-669c-4984-b115-f9e810bc25d9", "node_type": "1", "metadata": {}, "hash": "6b02ab094a019fdae84fe34d5976c7a1a78dd233241db6a40336fe194e693624", "class_name": "RelatedNodeInfo"}}, "text": "The schematic plot of this source model is plotted in Fig. 1(e).\n\nAs developed in [6], the volumetric heat source due to radiation transfer is,\n\n$I(x, y, z)=\\frac{2 P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{l}^{2}}\\right] \\cdot f_{1}(z), f_{1}(z)=\\left(-\\eta \\cdot \\frac{d q}{d \\xi}\\right)$\n\nwhere $\\xi=\\eta \\cdot z$ is the dimensionless local depth coordinate, and $q$ is the dimensionless form of net radiative energy flux density and is described as,\n\n\n\\begin{align*}\nq= & \\frac{\\gamma a_{s}}{(4 \\gamma-3) D}\\left\\{\\left(1-\\gamma^{2}\\right) \\exp [-\\lambda] \\cdot\\left[\\left(1-a_{s}\\right) \\exp \\left[-2 a_{s} \\xi\\right]+\\left(1+a_{s}\\right) \\exp \\left[2 a_{s} \\xi\\right]\\right]\\right. \\\\\n& -(3+\\gamma \\exp [-2 \\lambda]) \\\\\n& \\left.\\times\\left\\{\\left[1+a_{s}-\\gamma\\left(1-a_{s}\\right)\\right] \\exp \\left[2 a_{s}(\\lambda-\\xi)\\right]+\\left[1-a_{s}-\\gamma\\left(1+a_{s}\\right)\\right] \\exp \\left[2 a_{s}(\\xi-\\lambda)\\right]\\right\\}\\right\\} \\\\\n& -\\frac{3(1-\\gamma)(\\exp [-\\xi]-\\gamma \\exp [\\xi-2 \\lambda])}{4 \\gamma-3} \\tag{22}\n\\end{align*}\n\n\nwhere $\\lambda=\\eta z_{\\text {bed }}$ refers to the optical thickness for the powder-bed, $a_{s}=\\sqrt{1-\\gamma}, \\gamma$ is the hemispherical reflectivity in the dense form, and $D$ is described as,\n\n\n\\begin{align*}\nD & =\\left(1-a_{s}\\right)\\left[1-a_{s}-\\gamma\\left(1+a_{s}\\right)\\right] \\exp \\left[-2 a_{s} \\lambda\\right] \\\\\n& -\\left(1+a_{s}\\right)\\left[1+a_{s}-\\gamma\\left(1-a_{s}\\right)\\right] \\exp \\left[2 a_{s} \\lambda\\right] \\tag{23}\n\\end{align*}\n\n\nThe extinction coefficient $\\eta$ is given as,\n\n$\\eta=S_{p} / 4$\n\nwhere $S_{p}$ is the specific powder surface per unit pore volume, $z_{b e d}$ is the layer thickness. $\\gamma$ is 0.7 [6], $S_{p}$ is regarded as $\\pi / r_{\\text {powder }}$, and $r_{\\text {powder }}$ is the average powder radius.\n\n2.2.2.2. APG.2: Ray-tracing method. The above method represents an analytical way to derive the absorptivity profile function. The absorptivity profile function can also be acquired by numerical methods. Tran et al. [16] built up a powder-bed model with randomly distributed particles and calculated the absorptivity profile function by means of Monte Carlo ray-tracing simulations. As developed in [16] and shown in Fig. 1(f), the volumetric heat source model can be formulated as,\n\n$I(x, y, z)=\\frac{2 P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{l}^{2}}\\right] \\cdot f_{2}(z)$\n\nwhere $f_{2}(z)=d \\beta / d z$ is the absorptivity function derived by the Monte Carlo ray-tracing simulation.\n\n2.2.2.3. APG.3: Linearly decaying equation method. Besides the two methods presented above for deriving the absorptivity profile, Ladani et al. [17] employed a linearly decaying function (see Fig.", "start_char_idx": 253179, "end_char_idx": 255884, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bcb5078c-669c-4984-b115-f9e810bc25d9": {"__data__": {"id_": "bcb5078c-669c-4984-b115-f9e810bc25d9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7e6a011a-b534-4f33-8406-cafe69997b5c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2119a244f86669da3db749be625e5aac8f1d2eb79d6c9c58bde93755d96a02f4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bbddbd84-b6fd-4b6c-9bdd-5fa3bccdce27", "node_type": "1", "metadata": {}, "hash": "a9c898943fea14f1121e5a7339cbcf15cf0af35724c7f2d12946bf90e8e76e4a", "class_name": "RelatedNodeInfo"}}, "text": "As developed in [16] and shown in Fig. 1(f), the volumetric heat source model can be formulated as,\n\n$I(x, y, z)=\\frac{2 P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{l}^{2}}\\right] \\cdot f_{2}(z)$\n\nwhere $f_{2}(z)=d \\beta / d z$ is the absorptivity function derived by the Monte Carlo ray-tracing simulation.\n\n2.2.2.3. APG.3: Linearly decaying equation method. Besides the two methods presented above for deriving the absorptivity profile, Ladani et al. [17] employed a linearly decaying function (see Fig. 1(g)) to describe the absorptivity profile as,\n\n$I(x, y, z)=\\frac{2 P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{l}^{2}}\\right] \\cdot f_{3}(z), \\quad f_{3}(z)=\\frac{2 \\beta}{\\delta}\\left(1-\\frac{z}{\\delta}\\right)$\n\nwhere $\\delta$ is the beam penetration depth. In this work, the penetration depth is equal to the layer thickness.\n\n2.2.2.4. APG.4: Exponentially decaying equation method. Similarly, an exponentially decaying heat source (see Fig. 1(h)) was used by Liu et al. [18]. The specific expression is as follows,\n\n$I(x, y, z)=\\frac{2 P}{\\pi r_{l}^{2}} \\exp \\left[-2 \\frac{x^{2}+y^{2}}{r_{l}^{2}}\\right] \\cdot f_{4}(z), \\quad f_{4}(z)=\\frac{\\beta}{H} \\cdot \\exp \\left[-\\frac{|z|}{H}\\right]$\n\nwhere $H$ is regarded as the powder layer thickness.\n\n\\subsection*{2.2.3. Summary of heat models}\nThe eight heat source models are summarized in Table 1.\n\n\\subsection*{2.3. Material properties}\nTwo phases of Stainless Steel 17-4PH (SS17-4PH), the powder state and the solidified state, were considered in this simulation. The effective thermal conductivity of the powder-bed is much smaller than that of bulk material. For the used material in this study, the effective thermal conductivity is typically from 0.1 to $0.2 \\mathrm{~W} / \\mathrm{mK}$ at room temperature, which is around $1 \\%$ of the bulk thermal conductivity (i.e., $10.5 \\mathrm{~W} / \\mathrm{mK}$ ). In addition, the effective thermal conductivity is mainly dependent on the size and morphology of the powders [12,23,26]. Therefore, the effective thermal conductivity in this work is expressed as follows,\n\n$k_{\\text {powder }}=\\left\\{\\begin{array}{c}0.01 \\times k_{\\text {solid }}, \\quad T<T_{m} \\\\ k_{\\text {solid }}, \\quad T>=T_{m}\\end{array}\\right.$\n\nwhere $T_{\\mathrm{m}}$ is the melting temperature. $k_{\\text {powder }}$ and $k_{\\text {solid }}$ are the thermal conductivity of the powder phase and solid phase, respectively.\n\nAs the powder-bed is regarded as a mixture of solid powder (SS174PH) and gas (argon) phases, the density of SS17-4PH powder may be derived by:\n\n$\\rho_{\\text {powder }}=(1-\\varphi) \\rho_{\\text {solid }}+\\varphi \\cdot \\rho_{\\text {gas }}$\n\nwhere $\\varphi$ is the porosity of SS17-4PH powder, and is chosen as 0.53 based on the work done by $[5,27,28]$, $\\rho_{\\text {solid }}$ is the density of the SS17$4 \\mathrm{PH}$ bulk material, and $\\rho_{\\text {gas }}$ is the density of argon gas.", "start_char_idx": 255369, "end_char_idx": 258280, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bbddbd84-b6fd-4b6c-9bdd-5fa3bccdce27": {"__data__": {"id_": "bbddbd84-b6fd-4b6c-9bdd-5fa3bccdce27", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bcb5078c-669c-4984-b115-f9e810bc25d9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dc5d326d2d77612762f6815c42ef3978a255175a7cc40bbd50996d5d41157b68", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0d930e3b-45a2-4fae-95a3-9017333b6bf1", "node_type": "1", "metadata": {}, "hash": "c95fda4d18c479e67981a1a17fde3a8c666dc355f58f1e2a1923a4bfdc2fe489", "class_name": "RelatedNodeInfo"}}, "text": "$k_{\\text {powder }}$ and $k_{\\text {solid }}$ are the thermal conductivity of the powder phase and solid phase, respectively.\n\nAs the powder-bed is regarded as a mixture of solid powder (SS174PH) and gas (argon) phases, the density of SS17-4PH powder may be derived by:\n\n$\\rho_{\\text {powder }}=(1-\\varphi) \\rho_{\\text {solid }}+\\varphi \\cdot \\rho_{\\text {gas }}$\n\nwhere $\\varphi$ is the porosity of SS17-4PH powder, and is chosen as 0.53 based on the work done by $[5,27,28]$, $\\rho_{\\text {solid }}$ is the density of the SS17$4 \\mathrm{PH}$ bulk material, and $\\rho_{\\text {gas }}$ is the density of argon gas. Since the density of argon gas is very low compared with that of SS17-4PH, it can be omitted, the density of SS17-4PH may be considered as follows,\n\n$\\rho_{\\text {powder }}=(1-\\varphi) \\rho_{\\text {solid }}$\n\nThe heat capacity of the powder-bed may be then calculated using [12] and,\n\n$\\rho_{\\text {powder }} C_{\\text {powder }}=(1-\\varphi) \\rho_{\\text {solid }} C_{\\text {solid }}+\\varphi \\cdot \\rho_{\\text {gas }} C_{\\text {gas }}$\n\nwhere $C_{\\text {powder }}, C_{\\text {solid }}$, and $C_{\\text {gas }}$ are the heat capacity of the powder-bed, gas phase, and solid phase, respectively. Similarly, by omitting the gas phase due to its low density, the heat capacity of the powder-bed is regarded as equal to the heat capacity of the solid phase. Fig. 2a-c show the temperature dependent material properties of material SS17-4PH [29] and Fig. 2d depicts those of the base plate, material mild carbon steel [30]. The effective capacity method [2] was employed in this work. The heat capacity due to latent heat during material phase\n\nTable 1\n\nSummary of mathematical representations of laser-beam heat sources.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-05}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-06(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-06(2)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-06}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-06(3)}\n\\end{center}\n\n(d)\n\nFig. 2. Temperature-dependent thermal material properties (a) density of SS17-4PH; (b) thermal conductivity of SS17-4PH; (c) heat capacity of SS17-4PH; (d) material properties of mild carbon steel.", "start_char_idx": 257666, "end_char_idx": 260145, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0d930e3b-45a2-4fae-95a3-9017333b6bf1": {"__data__": {"id_": "0d930e3b-45a2-4fae-95a3-9017333b6bf1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bbddbd84-b6fd-4b6c-9bdd-5fa3bccdce27", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "64fe2f7d160dc5da0d5129545ce326039187a77141a0ebfb1dc86b6ad2f2b20c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3ac8d2cc-30c0-4090-9ff9-c9ccf26cd8fd", "node_type": "1", "metadata": {}, "hash": "09a679898fb25198f3dbdd2a8b0668e7ed2785f868af5d08161536aada3178ad", "class_name": "RelatedNodeInfo"}}, "text": "2. Temperature-dependent thermal material properties (a) density of SS17-4PH; (b) thermal conductivity of SS17-4PH; (c) heat capacity of SS17-4PH; (d) material properties of mild carbon steel.\n\nchange can be specified as\n\n$C=\\left\\{\\begin{array}{cc}C_{\\text {solid }}, \\quad T \\leqslant T_{S} \\\\ C_{\\text {solid }}+2 \\cdot L_{f}\\left(T-T_{S}\\right) /\\left(T_{l}-T_{S}\\right)^{2}, & T_{S}<T \\leqslant T_{l} \\\\ C_{\\text {solid }}+2 \\cdot L_{v}\\left(T-T_{l}\\right) /\\left(T_{v}-T_{l}\\right)^{2}, & T_{l}<T \\leqslant T_{v}\\end{array}\\right.$\n\nwhere $C_{\\text {solid }}$ is the specific heat of the material at solidus temperature, $L_{f}$ and $L_{v}$ are the latent heat of fusion and vaporization, $T_{s}, T_{l}$, and $T_{v}$ are the solidus, liquidus, and vaporization temperatures.\n\nFurthermore, a model related to two material properties was proposed for better predicting melt pool dimensions, anisotropically enhanced thermal conductivity $k$ and the effective absorptivity of continuous laser light $\\beta$. To the authors' best knowledge, this is the first work that considers the both varied anisotropically enhanced thermal conductivity and laser absorptivity in the LPBF modeling. The melt pool dimensions can be described in terms of linear functions to the deposited energy density for several process-parameter regions, which is consistent with the findings in [31]. The deposited energy during the laser dwell time $\\tau=2 r_{l} / v$ is $\\beta P \\tau$, where $r_{l}$ is the laser beam radius. This energy is deposited in a volume, whose depth can be regarded as the heating depth, $H D R \\cdot l_{t h}$, where $H D R=\\sqrt{ }(4 \\alpha \\tau) / l_{t h}, \\alpha$ is the diffusivity, and $l_{t h}$ is layer thickness, according to [32]. The volume is expressed as $V=\\pi r_{l}^{2} \\sqrt{ }(\\sqrt{ }(4 \\alpha \\tau))$. Therefore, the absorbed energy density $e_{m}$ is derived by dividing the deposited energy $\\beta P \\tau$ by $V$, $e_{m}=\\frac{\\beta}{\\pi \\sqrt{2 \\alpha r_{l}^{3}}} \\cdot \\frac{P}{\\sqrt{v}}=C \\cdot \\frac{P}{\\sqrt{v}}$\n\nwhere $C$ is a coefficient, which is $\\beta /\\left(\\pi \\cdot \\sqrt{ }\\left(2 \\alpha r_{l}^{3}\\right)\\right)$. Since $\\alpha$ during the analysis in [32] and $\\beta$ in [31] were regarded as constants, it can be found that the energy density is proportional to the ratio of the laser power to the root of velocity, $P / \\sqrt{ } v$.\n\nTherefore, the melt pool dimensions are proportional to $P / \\sqrt{ } v$. However, physical explanations behind it were not fully understood, and simulation results with isotropic thermal conductivity $k$ and constant absorptivity $\\beta$ are not consistent with the experimental results, which will be deliberated in-detail in the discussion section. For improving the accuracy of simulation results, a novel model of the material properties is proposed that the absorptivity, $\\beta$, and the anisotropically enhanced factors of thermal conductivity, $\\lambda_{x}, \\lambda_{y}$, and $\\lambda_{z}$, are assumed to be simple linear algebraic equations of $P / \\sqrt{ } v$ based on experimental results The anisotropically enhanced thermal conductivity discussed in [19] was employed to approximate the contribution of the melt pool convection to melt pool dimensions. During the LPBF process, an important contributory mode of heat transfer is the melt pool convection, which may change the melt pool dimensions and influence the temperature distribution in a melt pool [33,34]. Using the anisotropically enhanced thermal heat conductivity could improve the dimension accuracy of melt pool simulation results $[18,19]$.", "start_char_idx": 259953, "end_char_idx": 263548, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "3ac8d2cc-30c0-4090-9ff9-c9ccf26cd8fd": {"__data__": {"id_": "3ac8d2cc-30c0-4090-9ff9-c9ccf26cd8fd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0d930e3b-45a2-4fae-95a3-9017333b6bf1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c716c2ca785b44cca3472198d6f8f963e6e5b48ef7e3d00f07424e74db8898b4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c99680f0-ec7f-4e41-923a-4031e2cd2bd4", "node_type": "1", "metadata": {}, "hash": "c05345bcff73f2a54f9f1be1fef23704a4e17e4516e47fbc39b4228b1c5a1f0f", "class_name": "RelatedNodeInfo"}}, "text": "For improving the accuracy of simulation results, a novel model of the material properties is proposed that the absorptivity, $\\beta$, and the anisotropically enhanced factors of thermal conductivity, $\\lambda_{x}, \\lambda_{y}$, and $\\lambda_{z}$, are assumed to be simple linear algebraic equations of $P / \\sqrt{ } v$ based on experimental results The anisotropically enhanced thermal conductivity discussed in [19] was employed to approximate the contribution of the melt pool convection to melt pool dimensions. During the LPBF process, an important contributory mode of heat transfer is the melt pool convection, which may change the melt pool dimensions and influence the temperature distribution in a melt pool [33,34]. Using the anisotropically enhanced thermal heat conductivity could improve the dimension accuracy of melt pool simulation results $[18,19]$. The anisotropically enhanced thermal conductivity can be expressed as follows,\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-07(1)}\n\\end{center}\n\nFig. 3. Geometry and mesh used in the finite element simulation.\n\n$k_{x}=\\lambda_{x} k, \\quad k_{y}=\\lambda_{y} k, \\quad k_{z}=\\lambda_{z} k$\n\nwhere $\\lambda_{x}, \\lambda_{y}$, and $\\lambda_{z}$ are the anisotropically enhanced factors of thermal conductivity $k$. They are dependent on the temperature in the melt pool and derived based on experiments.\n\n$\\left\\{\\begin{array}{c}\\lambda_{x}=\\lambda_{y}=\\lambda_{z}=1, \\quad T<T_{\\text {melting }} \\\\ \\lambda_{x}=1, \\quad \\lambda_{y}=f_{y}(P, v), \\lambda_{z}=f_{z}(P, v), \\quad T \\geqslant T_{\\text {melting }}\\end{array}\\right.$\n\nwhere $f_{y}$ and $f_{z}$ are functions of laser power $P[\\mathrm{~W}]$ and scanning speed $v$ $[\\mathrm{mm} / \\mathrm{s}]$.\n\nIn this work, a linear function of the enhanced factor of thermal conductivity, $\\lambda_{z}$, is proposed and described as,\n\n$\\lambda_{z}=a_{1} \\frac{P}{\\sqrt{v}}+b_{1}$\n\nThe enhanced factor of thermal conductivity $\\lambda_{y}$, which influences the width of melt pool, is formulated slightly different from $\\lambda_{z}$ since the width of melt pool is proportional only to velocity $v$ and not globally proportional to $P / \\sqrt{ } v$,\n\n$\\lambda_{y}=\\left\\{\\begin{array}{c}a_{2} v+b_{2}, \\quad v \\leqslant v_{a} \\\\ 1, \\quad v>v_{a}\\end{array}\\right.$\n\nwhere $v_{a}, a_{1}, b_{1}, a_{2}$, and $b_{2}$ are also parameters and will be determined by experimental results. The melt pool width may be governed by the same physics that causes the melt pool to be more sensitive to the scanning speed rather than the laser power. However, further studies on the correlation of the melt pool dynamics and the width are needed.\n\nSecondly, the effective absorptivity $\\beta$ of continuous laser light can also influence the melt pool dimensions significantly [20]. It typically can vary greatly based on different combinations of laser powers and scanning speeds. The recoil pressure-induced surface depression may lead to an increase in absorption of the laser light [20].\n\nThe absorptivity $\\beta$ in the present work is also proposed to be a linear equation and can be written as,\n\n$\\beta=a_{3} \\frac{P}{\\sqrt{v}}+b_{3}$\n\nwhere $a_{3}$ and $b_{3}$ are coefficients to be determined by experiment. The variation of the effective absorptivity was specified as $0.48-0.65$, which are comparable with the data from [20].\n\n\\section*{3. Numerical model configuration}\nThe present study is proposed to estimate the geometries of the melt pool under the substrate top surface. Using the commercial software package, COMSOL 5.2 Multiphysics, simulations were performed considering non-linear transient thermal analyses within the metal powder and the base plate.", "start_char_idx": 262681, "end_char_idx": 266393, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c99680f0-ec7f-4e41-923a-4031e2cd2bd4": {"__data__": {"id_": "c99680f0-ec7f-4e41-923a-4031e2cd2bd4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3ac8d2cc-30c0-4090-9ff9-c9ccf26cd8fd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9ac8fc2dfdede6aa6e4d95a4232c4c155ec78068ca602c575e13f38bd054c09a", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "118bfede-ef65-44f6-b3ac-c4202bb327a7", "node_type": "1", "metadata": {}, "hash": "b5b4f1804d5abb603dec0e448e43de85c301095e35b4f0557e83138def8ce4ec", "class_name": "RelatedNodeInfo"}}, "text": "The recoil pressure-induced surface depression may lead to an increase in absorption of the laser light [20].\n\nThe absorptivity $\\beta$ in the present work is also proposed to be a linear equation and can be written as,\n\n$\\beta=a_{3} \\frac{P}{\\sqrt{v}}+b_{3}$\n\nwhere $a_{3}$ and $b_{3}$ are coefficients to be determined by experiment. The variation of the effective absorptivity was specified as $0.48-0.65$, which are comparable with the data from [20].\n\n\\section*{3. Numerical model configuration}\nThe present study is proposed to estimate the geometries of the melt pool under the substrate top surface. Using the commercial software package, COMSOL 5.2 Multiphysics, simulations were performed considering non-linear transient thermal analyses within the metal powder and the base plate. The dimensions of the solid substrate in the simulation were $2000 \\times 1000 \\times 500 \\mu \\mathrm{m}$, and those of the powder layer were appointed to be $2000 \\times 1000 \\times 20 \\mu \\mathrm{m}$. To prevent the thermal shock problem, it is important that the simulation domain should be considered adequately large to ensure that a stable melt pool is achieved in the simulation. The thermal shock problem imposes a relatively short-term effect on the simulation zone for pure thermal analyses that may cause numerical instabilities if the melt pool is not fully developed $[35,36]$. The powder layer thickness was chosen as $20 \\mu \\mathrm{m}$ since it is one of the commonly used layer thickness. The material of the solid substrate was mild carbon steel, and the powder layer was Stainless Steel 17-4PH. Tetrahedral elements were employed for meshing both the solid substrate and the metal powder layer. The laser beam diameter was $100 \\mu \\mathrm{m}$. The eight volumetric heat sources discussed previously were employed in the simulation, while the exponentially decaying heat source was employed in the further simulations, where both varied anisotropically enhanced thermal conductivity and absorptivity were also considered. According to a series of convergence trials, the laser-beam interaction region was meshed with $20 \\mu \\mathrm{m}$ elements, while the other regions were filled with coarser elements in order to improve the computational efficiency. In this study, the adaptive time step algorithm was used with an initial time step of $7 \\mu$ s. An adaptive time step allows users to give a reference time step, where the software changes the time step based on the convergence state during simulation. The minimum and maximum values for the time step used in numerical simulations was between $0.2 \\mu$ s and $6 \\mu$ s. In order to accelerate the simulations, only half of the geometry was built based on symmetry, since the domain is symmetric about the vertical plane containing the laser-beam moving line, as presented in Fig. 3. The symmetry constraint was set on the symmetric plane. In addition, radiative (Eq. (2)) and convective (Eq. (3)) heat losses at the top surface of the powder layer to the ambient air were considered. The convective heat transfer coefficient and the emissivity coefficient were chosen as $15 \\mathrm{~W} / \\mathrm{mK}$ [37] and 0.5 [38], respectively. The ambient temperature was set to $293 \\mathrm{~K}$. The other sides of the domain were specified as a fixed preheating temperature, $353 \\mathrm{~K}$.\n\n\\section*{4. Experimental procedures}\nExperiments were carried out on an EOS M 290 LPBF machine. Its chamber was filled with argon atmosphere during the manufacturing process. The EOS M 290 has a $400 \\mathrm{~W}$ fiber laser. The transverse electromagnetic mode of the laser beam is $\\mathrm{TEM}_{00}$ indicating a single mode laser, and the beam spot diameter is $100 \\mu \\mathrm{m}$. The powder used in this study is the gas atomized Stainless Steel 17-4PH powder with a particle size of $16 \\sim 64 \\mu \\mathrm{m}$. The scanning electron microscopy (SEM) image (Fig. 4) of Stainless Steel 17-4PH powder particles shows that they were almost spherical in shape.", "start_char_idx": 265601, "end_char_idx": 269624, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "118bfede-ef65-44f6-b3ac-c4202bb327a7": {"__data__": {"id_": "118bfede-ef65-44f6-b3ac-c4202bb327a7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c99680f0-ec7f-4e41-923a-4031e2cd2bd4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9d0a2cef8f3a22f1f4b4d8623d2fcc81bb79cd281f17acbeaab4e69f4547f128", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "81440fea-98bf-4949-9e8f-8cdcecaa1674", "node_type": "1", "metadata": {}, "hash": "abce13ba67592681abcb17623242f180cbfc8669b01c819ce7ee10f5dd15102f", "class_name": "RelatedNodeInfo"}}, "text": "The other sides of the domain were specified as a fixed preheating temperature, $353 \\mathrm{~K}$.\n\n\\section*{4. Experimental procedures}\nExperiments were carried out on an EOS M 290 LPBF machine. Its chamber was filled with argon atmosphere during the manufacturing process. The EOS M 290 has a $400 \\mathrm{~W}$ fiber laser. The transverse electromagnetic mode of the laser beam is $\\mathrm{TEM}_{00}$ indicating a single mode laser, and the beam spot diameter is $100 \\mu \\mathrm{m}$. The powder used in this study is the gas atomized Stainless Steel 17-4PH powder with a particle size of $16 \\sim 64 \\mu \\mathrm{m}$. The scanning electron microscopy (SEM) image (Fig. 4) of Stainless Steel 17-4PH powder particles shows that they were almost spherical in shape.\n\nIn order to validate the numerical simulation results, several single-\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-07}\n\\end{center}\n\nFig. 4. SEM image of the stated powders.\n\nTable 2\n\nParameters for the tests of single line scanning.\n\n\\begin{center}\n\\begin{tabular}{llllllllll}\n\\hline\nLaser power, $P[\\mathrm{~W}]$ & 170 & 195 & 220 &  &  &  &  &  \\\\\n\\hline\nScanning speed, $v[\\mathrm{~mm} / \\mathrm{s}]$ & 600 & 700 & 800 & 900 & 1000 & 1100 & 1200 & 1300 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\ntrack experiments were conducted. The current design of experiment (DOE) included combinations of different process parameters, including laser power and scanning speed. According to the literature [39-44], the laser power used by other researchers are generally from 190 to $200 \\mathrm{~W}$, for 17-4 PH stainless steel. As such, only laser powers close to this range were studied, which were 170,195 , and $220 \\mathrm{~W}$. The scanning speed range was from 600 to $1300 \\mathrm{~mm} / \\mathrm{s}$. The corresponding selections of the processing parameters are shown in Table 2. The combinations of the process parameters were categorized into 3 groups, as exhibited in Fig. 5a. In order to avoid randomness, each set of parameters was repeated five times, as shown in Fig. 5 b.\n\nAll the single tracks were cross-sectioned in the middle of the scan line perpendicular to the laser-scan direction. The samples were mounted, polished, and etched by using $5 \\%$ Nital. The melt pool dimensions (width and depth) and the single-track surface profiles were measured by a laser scanning confocal microscope. For measuring the melt pool dimensions, each of the produced single tracks was mounted, cross-sectioned, and measured, as shown in Fig. 6.\n\n\\section*{5. Results and discussion}\n\\subsection*{5.1. Heat source model comparisons}\nHeat transfer simulations with the eight heat sources (GMG1 to GMG4 and APG1 to APG4) listed in Table 1 were performed with laser power and scanning speed of $195 \\mathrm{~W}$ and $800 \\mathrm{~mm} / \\mathrm{s}$ respectively which were used in the literature [39,44]. The layer thickness of $20 \\mu \\mathrm{m}$ was used. Fig. 7a shows the melt pool dimensions of experimental and simulation results. The left and right show the melt pool width and depth respectively. For the melt pool width, all the simulation results with the eight heat source models are within the experimental variation range. The maximum melt pool width error is $7.4 \\%$ (GMG1). However, for the depth, all of the simulation results are over $40 \\%$ smaller than the experimental results.", "start_char_idx": 268859, "end_char_idx": 272260, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "81440fea-98bf-4949-9e8f-8cdcecaa1674": {"__data__": {"id_": "81440fea-98bf-4949-9e8f-8cdcecaa1674", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "118bfede-ef65-44f6-b3ac-c4202bb327a7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "aa4b55457b825de734b7257116b437c52e441cd8c51e63b1bd2e99013c5f660e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a45f20b2-1ce2-4214-b856-d25386282f5a", "node_type": "1", "metadata": {}, "hash": "49f7ec2839f3316856277a2915f6dcbe4f6fb05922a716e78a1b6edf813a7202", "class_name": "RelatedNodeInfo"}}, "text": "Heat source model comparisons}\nHeat transfer simulations with the eight heat sources (GMG1 to GMG4 and APG1 to APG4) listed in Table 1 were performed with laser power and scanning speed of $195 \\mathrm{~W}$ and $800 \\mathrm{~mm} / \\mathrm{s}$ respectively which were used in the literature [39,44]. The layer thickness of $20 \\mu \\mathrm{m}$ was used. Fig. 7a shows the melt pool dimensions of experimental and simulation results. The left and right show the melt pool width and depth respectively. For the melt pool width, all the simulation results with the eight heat source models are within the experimental variation range. The maximum melt pool width error is $7.4 \\%$ (GMG1). However, for the depth, all of the simulation results are over $40 \\%$ smaller than the experimental results.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-08(2)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-08}\n\\end{center}\n\nFig. 6. Melt pool cross-section.\n\nIn GMG, GMG1 results in the largest width but the smallest depth. In contrast, GMG4 leads to the smallest width but the largest depth. The results of GMG2 and GMG3 are almost identical ( $0 \\%$ in width, $2.5 \\%$ in depth), because the semi-axes $b$ and $c$, which may influence melt pool width and depth correspondingly, were chosen as the same as the radius $r_{l}$. The melt pool dimensions derived in GMG may be further improved by carefully setting the parameters of the heat source models, for example by increasing the height of the conical shape to make the simulated melt pool deeper.\n\nIn APG, the absorptivity profile in APG2 is originally from ray tracing method [16], while that in APG1 is derived by mathematical analysis [6]. APG1 and APG2 have very similar melt pool dimensions (1.7\\% in width, $2.7 \\%$ in depth). Since these two models were designed for predicting melt pools in the conduction mode [16] where the melt pool convection is not significant, the melt pool depths are near $50 \\%$ smaller than the experimental result. In addition, APG4's melt pool is a little bit deeper, while the error still is very large, over $40 \\%$.\n\nBesides, Fig. $7 \\mathrm{~b}$ shows the maximum temperature for the eight heat source models. The two highest maximum temperature, GMG1 and APG3, correspond to the two largest melt pool widths respectively. Since the laser energy melted the material and formed the melt pool, the energy deposition distribution influences melt pool dimensions and\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-08(1)}\n\\end{center}\n\n(b)\n\nFig. 5. The configuration of single tracks on the substrate, (a) design of experiments, (b) the single tracks actually printed.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-09(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-09}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-09(5)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-09(2)}\n\\end{center}\n\n(d)\n\nFig. 7. Comparisons of the heat source models, (a) melt pool dimensions, (b) maximum temperature, (c) energy deposited in the powder layer, (d) energy deposited beyond $40 \\mu \\mathrm{m}$ depth.", "start_char_idx": 271467, "end_char_idx": 274901, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a45f20b2-1ce2-4214-b856-d25386282f5a": {"__data__": {"id_": "a45f20b2-1ce2-4214-b856-d25386282f5a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "81440fea-98bf-4949-9e8f-8cdcecaa1674", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3f3c5e598c6f0bf4e753022a61e14be4e9526dac968d7277cce4f27a13e7b646", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "505af7d1-79d3-42ec-aff5-1dc3f968bfb6", "node_type": "1", "metadata": {}, "hash": "c30ce15405b37edc77764d86ece8f680f14b94546c1dd011a5194d681a65f88e", "class_name": "RelatedNodeInfo"}}, "text": "7. Comparisons of the heat source models, (a) melt pool dimensions, (b) maximum temperature, (c) energy deposited in the powder layer, (d) energy deposited beyond $40 \\mu \\mathrm{m}$ depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-09(3)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-09(4)}\n\\end{center}\n\n(b)\n\nFig. 8. Comparison of melt pool depths between simulations by two methods, (a) the traditional method in literature, (b) the method proposed in this work considering anisotropically enhanced thermal conductivities and varied absorptivities.\n\nas well as the maximum temperature. The energy deposition in the powder layer is plotted in Fig. 7c. It can be seen that the two maximum energy deposition models are GMG1 and APG3 as well, which correspond to the trends of the maximum melt pool width and maximum temperature. In addition, the smallest energy deposition from GMG4 results in smallest melt pool width as well as one of the smallest maximum temperature. Therefore, a conclusion can be derived that there is a positive correlation between either the melt pool width or the maximum temperature and the energy deposition in the powder layer. In other words, the more energy is deposited in the powder layer, the wider melt pool and high maximum temperature are. Furthermore, Fig. $7 \\mathrm{~d}$ plots the energy deposition in the region beyond the melt pool\\\\\n$170 \\mathrm{~W}$\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-10}\n\\end{center}\n\n$195 \\mathrm{~W}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_0862f05ef1456ffe25f0g-10(1)}\n\n$220 \\mathrm{~W}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_0862f05ef1456ffe25f0g-10(2)}\n\nFig. 9. Melt pool shapes of single tracks on one layer of powder particles at different laser power and process speed combinations.\n\ndepths, which is chosen as $40 \\mu$. Comparing Fig. 7d to Fig. 7a manifests the heat sources GMG2 GMG3 GMG4 and APG4, which have larger energy deposition in this region than the remaining four, result in deeper melt pools. It seems that more energy is deposited in a deeper domain, the deeper melt pools are derived in the simulations. Even though it is not a restricted rule since the numerical simulations are nonlinear, the trend is obvious that there is a positive correlation between the melt pool depth and the energy deposition in the region beyond $40 \\mu \\mathrm{m}$ depth.\n\nIn GMG, GMG4 may be potential to make a more accurate prediction by increasing the cone's height. However, there would be another factor, the bottom radius. To derive the optimal parameters for GMG4 may take numbers of trial and errors. In addition, the energy input is constrained in the specific geometry may need further physical explanations. In APG, APG1 and APG2 are originally designed for conduction mode and their expressions are more complex than APG3 and APG4. Besides, APG3 has less accurate prediction than APG4. Therefore, APG4 will be chosen as the heat source for the following simulations.\n\nIt should be noted that all of the simulated depths are over $40 \\%$ smaller than the experimental result, even by using APG4. The discrepancy between simulation and experimental results may even increase under some combinations of laser power and scanning speed. For example, Fig. 8a shows the simulated and experimental depth with the same power but under different scanning speed with APG4. The difference between the simulation and experimental results are larger with decreasing the scanning speed. All of these could be explained by the underestimation of the contribution of melt pool convection to the heat transfer model.", "start_char_idx": 274712, "end_char_idx": 278488, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "505af7d1-79d3-42ec-aff5-1dc3f968bfb6": {"__data__": {"id_": "505af7d1-79d3-42ec-aff5-1dc3f968bfb6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a45f20b2-1ce2-4214-b856-d25386282f5a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b1775e07b16253d746a74c8ce2c7e10d53cd3a1b7272a824174760d232f79449", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4e9d6123-d615-4a73-88a5-0f740d0134bc", "node_type": "1", "metadata": {}, "hash": "56b8c9f68c9fa1689f82dc29383bd7527db761f477a4d108fc428b5264c62274", "class_name": "RelatedNodeInfo"}}, "text": "In APG, APG1 and APG2 are originally designed for conduction mode and their expressions are more complex than APG3 and APG4. Besides, APG3 has less accurate prediction than APG4. Therefore, APG4 will be chosen as the heat source for the following simulations.\n\nIt should be noted that all of the simulated depths are over $40 \\%$ smaller than the experimental result, even by using APG4. The discrepancy between simulation and experimental results may even increase under some combinations of laser power and scanning speed. For example, Fig. 8a shows the simulated and experimental depth with the same power but under different scanning speed with APG4. The difference between the simulation and experimental results are larger with decreasing the scanning speed. All of these could be explained by the underestimation of the contribution of melt pool convection to the heat transfer model. As the discussion in $[18,19]$ about the anisotropically enhanced thermal conductivity, incorporating the melt pool convection effect into the analysis by choosing appropriate anisotropically enhanced thermal conductivity is helpful to describe both temperature and temperature-gradient distributions correctly. For example, Fig. 8b shows the results derived from the model proposed in this paper, and a better match between simulation and experimental results is obtained. Further detailed discussion of the melt pool prediction will be\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-11(2)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-11}\n\\end{center}\n\nFig. 10. Experimental results of melt pool dimensions with different laser powers and scanning velocities, (a) melt pool width, (b) melt pool depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-11(3)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-11(1)}\n\\end{center}\n\n(b)\n\nFig. 11. Experimental results of melt pool dimensions as functions of $P / \\sqrt{ } v$, (a) melt pool width, (b) melt pool depth.\n\nTable 3\n\nCoefficients in the approximation equations of anisotropically enhanced thermal conductivity and varied absorptivity.\n\n\\begin{center}\n\\begin{tabular}{lllllll}\n\\hline\n$a_{1}$ & $b_{1}$ & $a_{2}$ & $b_{2}$ & $a_{3}$ & $b_{3}$ & $v_{a}(\\mathrm{~mm} / \\mathrm{s})$ \\\\\n\\hline\n2.1095 & -6.9460 & -0.0036 & 4.96 & 0.0398 & 0.2921 & 1100 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nillustrated in the later sections.\n\n\\subsection*{5.2. Prediction of melt pool dimensions}\nIn order to study the effect of the LPBF process parameters, e.g. laser power $(P)$ and scanning velocity $(v)$ on melt pool dimensions, experiments were carried out with the process parameters listed in Table 2. The melt pool width and depth were measured through the analysis of the microscopic images as shown in Fig. 6. Several melt pool profiles are shown in Fig. 9, which covers the whole range of the process parameters. The trend of melt pool dimensions with different process parameters can be observed, for example, the melt pool is the biggest with the largest power and the smallest speed, and the melt pool is the smallest with the smallest power and the largest speed. Furthermore, the whole experimental results of the melt pool width and depth with three laser powers $(170,195,220 \\mathrm{~W})$ and varied speed $(600-1300 \\mathrm{~mm} /$ s) are plotted in Fig. 10a-b.\n\nFig. 10 shows that the melt pool width and depth reduce with increasing scanning speeds. This is observed for all powers. Moreover, with a higher laser power, the melt pool depths are deeper, as shown in Fig. 10b where the red curve is above the others.", "start_char_idx": 277597, "end_char_idx": 281360, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4e9d6123-d615-4a73-88a5-0f740d0134bc": {"__data__": {"id_": "4e9d6123-d615-4a73-88a5-0f740d0134bc", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "505af7d1-79d3-42ec-aff5-1dc3f968bfb6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "782015c90dca6644965f4415c4ab1a86d9b02c0665402a9d5fa900736f6b5da0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5ee1d536-7a47-40a0-88cc-0f6aa0658e8a", "node_type": "1", "metadata": {}, "hash": "cda2599133f20c4aebbbe876af51914dbed9527de1df3a2c4b4eaf40457c03a6", "class_name": "RelatedNodeInfo"}}, "text": "6. Several melt pool profiles are shown in Fig. 9, which covers the whole range of the process parameters. The trend of melt pool dimensions with different process parameters can be observed, for example, the melt pool is the biggest with the largest power and the smallest speed, and the melt pool is the smallest with the smallest power and the largest speed. Furthermore, the whole experimental results of the melt pool width and depth with three laser powers $(170,195,220 \\mathrm{~W})$ and varied speed $(600-1300 \\mathrm{~mm} /$ s) are plotted in Fig. 10a-b.\n\nFig. 10 shows that the melt pool width and depth reduce with increasing scanning speeds. This is observed for all powers. Moreover, with a higher laser power, the melt pool depths are deeper, as shown in Fig. 10b where the red curve is above the others. The melt pool widths tend to increase less obviously, as shown in Fig. 10a, where the red curve and the blue curve are relatively close for all the scanning speeds.\n\nFig. 11 presents the experimental results of melt pool dimensions as functions of $P / \\sqrt{ } v$. Interestingly, the data of melt pool depth, which shows uncertain patterns in Fig. 10b, collapses to a linear line as shown in Fig. 11b. As for the melt pool width, it is not converged into a single curve but is formed into three similar curves with close maximum and minimum value. The inability to converge to a master curve for melt pool widths could be due to other physical parameters that affect the melt pool width more than the laser power and velocity.\n\nExperimental melt pool width and depth results, shown in this section, were used to calibrate and validate single track LPBF simulations using heat source model APG4. As the discussion previously about Fig. 8, a lack of considering anisotropically enhanced thermal conductivity and varied absorptivity, may cause the simulation results diverged from the experimental ones. In order to predict the melt pool dimensions more accurately as the experimental results, the model shown in Eq. (38), Eq. (36), and Eq. (37) was employed, in which the absorptivity $\\beta$ and the anisotropically enhanced factors of thermal\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-12(2)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-12}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-12(1)}\n\\end{center}\n\n(c)\n\nFig. 12. Comparisons of melt pool dimensions at different power (a) $P=170 \\mathrm{~W}$, (b) $P=170 \\mathrm{~W}$, (c) $P=220 \\mathrm{~W}$.\n\nTable 4\n\nProposed model validation and comparison of simulation results with experimental data.", "start_char_idx": 280541, "end_char_idx": 283277, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5ee1d536-7a47-40a0-88cc-0f6aa0658e8a": {"__data__": {"id_": "5ee1d536-7a47-40a0-88cc-0f6aa0658e8a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4e9d6123-d615-4a73-88a5-0f740d0134bc", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6d94722f7a8c019cca797241f9579f0751400ce0f55ab83d1eb337929f3657ce", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "064a2edc-4463-410f-a61c-916b416ff7d7", "node_type": "1", "metadata": {}, "hash": "eeadab12d04b662aa8a0bfa917537ac509531c94a8708228e10954d643f17d25", "class_name": "RelatedNodeInfo"}}, "text": "12. Comparisons of melt pool dimensions at different power (a) $P=170 \\mathrm{~W}$, (b) $P=170 \\mathrm{~W}$, (c) $P=220 \\mathrm{~W}$.\n\nTable 4\n\nProposed model validation and comparison of simulation results with experimental data.\n\n\\begin{center}\n\\begin{tabular}{lllllll}\n\\hline\nPower (W) & \\begin{tabular}{l}\nMin \\\\\nError \\\\\nWidth \\\\\n$(\\%)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMin \\\\\nError \\\\\nDepth \\\\\n$(\\%)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMax \\\\\nError \\\\\nWidth \\\\\n$(\\%)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nMax \\\\\nError \\\\\nDepth \\\\\n$(\\%)$ \\\\\n\\end{tabular} & \\begin{tabular}{l}\nAverage \\\\\nError \\\\\nWidth (\\%) \\\\\n\\end{tabular} & \\begin{tabular}{l}\nAverage \\\\\nError \\\\\nDepth (\\%) \\\\\n\\end{tabular} \\\\\n\\hline\n170 & 0.8 & 2.35 & 6.3 & 22.6 & 3.7 & 11.6 \\\\\n195 & 0.22 & 0.11 & -3.4 & -5.9 & 1.6 & 4.3 \\\\\n220 & 0.57 & 0.37 & 4.5 & 10.7 & 3.3 & 6.1 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nconductivity $\\lambda_{y y}$ and $\\lambda_{z z}$ are formulated in simple linear equations of $P /$ $\\checkmark v$. The coefficients (Table 3 ) in these three equations are obtained by matching numerical results with experimental results. It should be noted that with the coefficients, the variation of the effective absorptivity is calculated as $0.48-0.65$ by Eq.(37), which are comparable with the data from $[20,21]$.\n\nFig. 12a-c show the comparison of the melt pool dimensions between the simulation (sim) and experimental (exp) results at a laser power of $170 \\mathrm{~W}, 195 \\mathrm{~W}$, and $220 \\mathrm{~W}$, respectively. Results from Fig. 12 show good agreement with experimental results. The melt pool width and depth error between simulation and experimental results are listed in Table 4. As seen in Table 4, when the model proposed consisted of Eq. (38), Eq. (36), and Eq. (37) was included, all average error of the melt pool width is within $4 \\%$. The average error of melt pool depth is within $7 \\%$ for $195 \\mathrm{~W}$ and $220 \\mathrm{~W}$. The $170 \\mathrm{~W}$ has a larger error, which may be due to measuring error. In addition, $170 \\mathrm{~W}$ resulted in smallest melt pool depth, so the absolute error should be comparable to those of $195 \\mathrm{~W}$ and $220 \\mathrm{~W}$.\n\nThe simulation (sim) and experimental (exp) results are also plotted together in Fig. 13 as functions of $P / v v$, where it is proved that the proposed model can predict the trend of the melt pool dimensions very well. Results presented in Fig. 13b show that the melt pool depth is proportional to $P / \\sqrt{ } v$. Therefore, the melt pool depth $d$ can be approximated with the following equation,\n\n$d=k_{d} \\cdot \\frac{P}{\\sqrt{v}}+k_{i}$\n\nwhere $k_{d}$ is the slope and $k_{i}$ is the y-intercept. It should be noted that Eq. (39) is similar to the expression of the absorbed energy density shown in Eq. (33), which implies the melt pool depth may be a linear function of the absorbed energy density $e_{m}$. However, since the $C$ in Eq.", "start_char_idx": 283047, "end_char_idx": 285994, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "064a2edc-4463-410f-a61c-916b416ff7d7": {"__data__": {"id_": "064a2edc-4463-410f-a61c-916b416ff7d7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5ee1d536-7a47-40a0-88cc-0f6aa0658e8a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c9bd064751d705bedd826ef17e0bbf3d4d7824c5498e4aee04e298f7645140de", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5c17b4fb-a4df-407b-80f8-21a74d7b16f5", "node_type": "1", "metadata": {}, "hash": "ea0b26e225bd04ea42ef9ee59638daa544cf3b1dd0cb7de1a49cf806d68285de", "class_name": "RelatedNodeInfo"}}, "text": "13 as functions of $P / v v$, where it is proved that the proposed model can predict the trend of the melt pool dimensions very well. Results presented in Fig. 13b show that the melt pool depth is proportional to $P / \\sqrt{ } v$. Therefore, the melt pool depth $d$ can be approximated with the following equation,\n\n$d=k_{d} \\cdot \\frac{P}{\\sqrt{v}}+k_{i}$\n\nwhere $k_{d}$ is the slope and $k_{i}$ is the y-intercept. It should be noted that Eq. (39) is similar to the expression of the absorbed energy density shown in Eq. (33), which implies the melt pool depth may be a linear function of the absorbed energy density $e_{m}$. However, since the $C$ in Eq. (33) consists of the absorptivity and thermal conductivity $k\\left(\\alpha=k / \\rho C_{p}\\right)$, which are all variables in this proposed model, $e_{m}$ as a function to $P / \\sqrt{ } v$ should be evaluated by substituting the absorptivity $\\beta$ (Eq. (38)) and the enhanced factors of thermal conductivity $\\lambda_{z z}$ (Eq. (36)) into it.\n\nFig. 14 depicts the absorbed energy density $e_{m}$ versus $P / V v$, from which the approximately linear behavior for a large portion of the range could be observed. Therefore, the conclusion can be proved as discussed in $[31,45]$ that melt pool depth is proportional to the absorbed energy density for a range of the input process parameters. Furthermore, since during simulation, laser absorptivity is regarded as a linear function of the parameter $P / \\sqrt{ } v$ as shown in Eq. (38), it may prove that the absorptivity in the laser scanning process may be increasing with larger $P / \\sqrt{ } v$ value, as illustrated in [20]. This phenomenon may be explained by the reason that at higher intensities, a deeper depressed surface would be formed by the vapor recoil pressure in the melt pool,\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-13}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-13(2)}\n\\end{center}\n\n(b)\n\nFig. 13. Comparison between the numerical and experimental results of melt pool dimensions as functions of $P / \\sqrt{ } v$, (a) melt pool width, (b) melt pool depth.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-13(1)}\n\\end{center}\n\nFig. 14. Absorbed energy density vs. $P / \\sqrt{ } v$.\n\nso that the laser interacts with the deeper and steeper walls, leading to less reflection of the laser beam and increased energy absorption. It is necessary to note that the left end of the curve in Fig. 14 seems to be nonlinear, which is belonged to $170 \\mathrm{~W}$, and this nonlinearity may be another reason why the error of $170 \\mathrm{~W}$ shown in Table 4 is larger than those of $195 \\mathrm{~W}$ and $220 \\mathrm{~W}$. However, further investigation on the applicable range of this proposed model should be addressed in the future work.\n\n\\subsection*{5.3. Printed track surfaces}\nFig. 15 shows the 3D surfaces of experimental samples for different combinations of process parameters. The ripple, for example in 1-1, is almost in a triangle shape and it indicates the shape of the isotherm curves. From Fig. 15a, it can be observed that the triangle-shaped pattern of ripple becomes not clear when the scanning speed is increased to $800 \\mathrm{~mm} / \\mathrm{s}$, which may imply that the single tracks are becoming unstable. The similar phenomena happened at the laser power of $195 \\mathrm{~W}$ (Fig. 15b) and $220 \\mathrm{~W}$ (Fig.", "start_char_idx": 285337, "end_char_idx": 288845, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5c17b4fb-a4df-407b-80f8-21a74d7b16f5": {"__data__": {"id_": "5c17b4fb-a4df-407b-80f8-21a74d7b16f5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "064a2edc-4463-410f-a61c-916b416ff7d7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5641d1a581375a4431f96a291c6396cd6f2ee359d6f16d3756c57264fb06e039", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6402d7f9-b954-4059-a797-2929e9c5983b", "node_type": "1", "metadata": {}, "hash": "95f24b32b0037ada1e7fd80e74bd1e5c84aa25e2fa9fc27ee54c7bc95a4237b3", "class_name": "RelatedNodeInfo"}}, "text": "However, further investigation on the applicable range of this proposed model should be addressed in the future work.\n\n\\subsection*{5.3. Printed track surfaces}\nFig. 15 shows the 3D surfaces of experimental samples for different combinations of process parameters. The ripple, for example in 1-1, is almost in a triangle shape and it indicates the shape of the isotherm curves. From Fig. 15a, it can be observed that the triangle-shaped pattern of ripple becomes not clear when the scanning speed is increased to $800 \\mathrm{~mm} / \\mathrm{s}$, which may imply that the single tracks are becoming unstable. The similar phenomena happened at the laser power of $195 \\mathrm{~W}$ (Fig. 15b) and $220 \\mathrm{~W}$ (Fig. 15c), while the thresholds of the scanning speed that cause instability are around $1000 \\mathrm{~mm} / \\mathrm{s}$, which are larger than that with the laser power of $170 \\mathrm{~W}$.\n\nAs highlighted in [46], \"The Plateau-Rayleigh analysis of the capillary instability of a circular cylinder of a liquid points out that the cylinder is stable\" when the stability condition is satisfied [46]. The necessary and sufficient condition of stability is $\\pi D / L>1$, where $D$ is the diameter of the cylinder and $L$ is the wavelength. $\\pi D$ represents the circumference of the cylinder cross-section. In this work, the circumference can be regarded as the perimeter of a melt pool cross-section, and the wavelength is assumed to be the length of a melt pool. Therefore, the melt pool stability can be predicted by calculating the ratio of the circumference and the length of the melt pools in numerical simulations, which is shown as follows,\n\nStability $=\\frac{C_{m p}}{L_{m p}}$\n\nwhere $C_{m p}$ is the circumference of a melt pool, and $L_{m p}$ is the length of the melt pool.\n\nFig. 16 provides the numerical results of stability calculated based on Eq. (40). The data points above the red dash line imply stable melt tracks, while those below imply that the melt tracks may be unstable. As seen in Fig. 16, the first several single tracks with smaller scanning speed tend to be stable for all the three laser powers, and melt pool stability is inclined to decrease with increasing scanning speed. Generally, the predicted results are consistent with that of the experimental results shown in Fig. 15, except that the stability of single tracks at the laser power of $170 \\mathrm{~W}$ seems to be a little bit overestimated.\n\nFor comparing with the form of ripples and isotherm curves, an angle $\\theta$ [18] is defined as depicted in Fig. 17. $\\theta$ is the tail angle of a triangle ripple. In order to reduce the randomness, five measurements on a single track were averaged. For the track with the laser power of $195 \\mathrm{~W}$ and scanning speed of $800 \\mathrm{~mm} / \\mathrm{s}$, the experimental $\\theta$ is in the range of $23^{\\circ}-32^{\\circ}$, as displayed in Fig. 17a. The numerical result of $\\theta$ is $22^{\\circ}$. Therefore, the simulated value is close to the experimental value, and the percentage of the difference between them is $20 \\%$.\n\nFig. 18 shows the ripple-angle ( $\\theta$ ) comparison of experimental results and numerical data for all stable tracks with the numbering of 1-1, $1-2,2-1$ to $2-4$, and $3-1$ to $3-4$. All the simulated ripple angles are smaller than those of the experiment; however, they are either within or close to the range of experimental results. For the tracks with the laser power of $195 \\mathrm{~W}$, the maximum difference of angles in experimental data is $17.3 \\%$, and for $220 \\mathrm{~W}$, it is $18.13 \\%$. The maximum error between the experimental and simulated results is $22 \\%$, which was derived from sample $1-2$ with $170 \\mathrm{~W}$ and $700 \\mathrm{~mm} / \\mathrm{s}$. The similar trend of ripple angles $\\theta$ with a specific power versus scanning speed can be observed from the experimental and simulated values, for example, $\\theta$ decreases with the scanning speed.", "start_char_idx": 288128, "end_char_idx": 292105, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6402d7f9-b954-4059-a797-2929e9c5983b": {"__data__": {"id_": "6402d7f9-b954-4059-a797-2929e9c5983b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5c17b4fb-a4df-407b-80f8-21a74d7b16f5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4832fc0a6ed9b61e09954fd0db5aa490ad6a9317f020b095d37f2ebc558e3512", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "aa23ba1a-476d-4345-aab5-ae3885c3cc53", "node_type": "1", "metadata": {}, "hash": "b0c9e4e827f07537b301a3521ec7c004ddc1915f0426f6c1c41ed6c254aa49b3", "class_name": "RelatedNodeInfo"}}, "text": "All the simulated ripple angles are smaller than those of the experiment; however, they are either within or close to the range of experimental results. For the tracks with the laser power of $195 \\mathrm{~W}$, the maximum difference of angles in experimental data is $17.3 \\%$, and for $220 \\mathrm{~W}$, it is $18.13 \\%$. The maximum error between the experimental and simulated results is $22 \\%$, which was derived from sample $1-2$ with $170 \\mathrm{~W}$ and $700 \\mathrm{~mm} / \\mathrm{s}$. The similar trend of ripple angles $\\theta$ with a specific power versus scanning speed can be observed from the experimental and simulated values, for example, $\\theta$ decreases with the scanning speed. The reason can be ascribed to the fact that with the higher scanning speed, the temperature gradient could be smaller and the isotherm curves are elongated with a smaller\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-14(3)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-14(1)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-14}\n\\end{center}\n\n(c)\n\nFig. 15. Experimental 3D surfaces of the single tracks at different laser power, (a) $170 \\mathrm{~W}$, (b) $195 \\mathrm{~W}$, (c) $\\mathrm{P}=220 \\mathrm{~W}$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-14(2)}\n\\end{center}\n\nFig. 16. Prediction of melt-track stability based on the simulated melt pool data.\n\nripple angle $\\theta$. Moreover, the tracks with a specific scanning speed versus power ended up with very close angles, e.g. the group of tracks $1-1,2-1$, and $3-1$, and the group of tracks $1-2,2-2$, and $3-2$. For the group with the scanning speed of $600 \\mathrm{~mm} / \\mathrm{s}$, tracks 1-1, 2-1, and 3-1, the maximum difference in the experimental data is only $4.66 \\%$. For scanning speed of $700 \\mathrm{~mm} / \\mathrm{s}$, tracks 1-2, 2-2, and 3-2 have a maximum difference of $5.9 \\%$. This is probably attributed to the reason that laser power may have less influence on the ripple angles than scanning speed.\n\nIn the future, a larger range of process parameters such as laser power and scanning speed should be considered in order to further validate the proposed model. Besides, the influence of powder layer thickness on melt pool profiles and track morphology would be investigated. Then the proposed 3D FEM model can be implemented for multiple-track and even multiple-layer situations of the LPBF process.\n\n\\section*{6. Conclusions}\nA 3D heat-transfer finite element model for LPBF was developed for accurately predicting melt pool dimensions and surface features. Based on the literature review, eight heat source models are used for the numerical modeling of LPBF and can be categorized as 1) geometrically modified group (GMG); and, 2) absorptivity profile group (APG). Experiments were carried out to validate the simulation results. All the eight heat source models lead to over $40 \\%$ shallower melt pools compared with the experiments.\n\nIn order to improve the model performance, a novel mathematical\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-15(1)}\n\\end{center}\n\nFig. 17. Ripple-angle $\\theta$ comparison of a track with process parameter $195 \\mathrm{~W}$ and $800 \\mathrm{~mm} / \\mathrm{s}$, (a) experimental result, (b) numerical result.", "start_char_idx": 291404, "end_char_idx": 294884, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "aa23ba1a-476d-4345-aab5-ae3885c3cc53": {"__data__": {"id_": "aa23ba1a-476d-4345-aab5-ae3885c3cc53", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6402d7f9-b954-4059-a797-2929e9c5983b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a48919942181722b00fb6d71e9e04927d6acdd85e6fddfff1fd43e8aaf543141", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8a617a3e-232a-494f-85c7-0139e073cf5a", "node_type": "1", "metadata": {}, "hash": "e555ac4a927fe0bf2c91358acf3ddc1bd43ccd2fa7749d369188bda876fffcc2", "class_name": "RelatedNodeInfo"}}, "text": "Based on the literature review, eight heat source models are used for the numerical modeling of LPBF and can be categorized as 1) geometrically modified group (GMG); and, 2) absorptivity profile group (APG). Experiments were carried out to validate the simulation results. All the eight heat source models lead to over $40 \\%$ shallower melt pools compared with the experiments.\n\nIn order to improve the model performance, a novel mathematical\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-15(1)}\n\\end{center}\n\nFig. 17. Ripple-angle $\\theta$ comparison of a track with process parameter $195 \\mathrm{~W}$ and $800 \\mathrm{~mm} / \\mathrm{s}$, (a) experimental result, (b) numerical result.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_0862f05ef1456ffe25f0g-15}\n\\end{center}\n\nFig. 18. Ripple angles $\\theta$ comparison between the experimental results and simulated data for all the stable tracks.\n\nmodel with varied anisotropically enhanced thermal conductivity and varied absorptivity was proposed and applied to the heat transfer simulation with the exponentially decaying heat source (APG4).\n\nThe main conclusions are listed as follows:\n\n\\begin{enumerate}\n  \\item The expressions of varied anisotropically enhanced thermal conductivity and varied absorptivity were linear algebraic equations. Good agreement between the simulation and the experimental results was derived. The averaged error of melt pool width and depth are $2.9 \\%$ and $7.3 \\%$, respectively.\n\n  \\item The proposed heat transfer model has been further validated by the surface features, track stability and ripple angle. For the track stability, the predicted results are in good agreement with the experimental results. In addition, the simulated ripple angles are within the range of experimental results.\n\n\\end{enumerate}\n\n\\section*{Acknowledgments}\nThis work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Federal Economic Development Agency for Southern Ontario (FedDev Ontario) and China Scholarship Council. The authors would also like to thank Jerry Ratthapakdee and Karl Rautenberg for helping in the LPBF setup and printing the samples.\n\n\\section*{Appendix A. Supplementary material}\nSupplementary data associated with this article can be found, in the online version, at \\href{https://doi.org/10.1016/j.optlastec.2018.08.012}{https://doi.org/10.1016/j.optlastec.2018.08.012}.\n\n\\section*{References}\n[1] T. Wohlers, Wohlers Report 2013: Additive Manufacturing and 3D Printing State of the Industry-Annual Worldwide Progress Report, Wohlers Associates, Fort Collins, CO, 2013.\n\n[2] C. Teng, H. Gong, A. Szabo, J.J.S. Dilip, K. 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LeBrun, T. Nakamoto, K. Horikawa, H. Kobayashi, Effect of retained austenite on subsequent thermal processing and resultant mechanical properties of selective laser melted 17-4 PH stainless steel, Mater. Des. 81 (2015) 44-53, \\href{https://doi.org/}{https://doi.org/} 10.1016/j.matdes.2015.05.026.\n\n[45] A.M. Rubenchik, W.E. King, S. Wu, Scaling laws for the additive manufacturing, J. Mater. Process. Technol. (2018), \\href{https://doi.org/10.1016/j.jmatprotec.2018.02}{https://doi.org/10.1016/j.jmatprotec.2018.02}. 034.\n\n[46] S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, Courier Corporation (2013).\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Laser powder bed fusion of a near-eutectic Al-Fe binary alloy: Processing and microstructure }\n\n\n\\author{Xing $\\mathrm{Qi}^{\\mathrm{a}, *}$, Naoki Takata ${ }^{\\mathrm{a}}$, Asuka Suzuki ${ }^{\\mathrm{a}}$, Makoto Kobashi ${ }^{\\mathrm{a}}$, Masaki Kato ${ }^{\\mathrm{b}}$\\\\\n${ }^{a}$ Department of Materials Process Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan\\\\\n${ }^{\\mathrm{b}}$ Aichi Center for Industry and Science Technology, 1267-1 Akiai, Yakusa-cho, Toyota 470-0356, Japan}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nResearch Paper\n\n\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing\n\nAl-Fe binary alloy\n\nProcessing parameters\n\nMicrostructure\n\n$\\mathrm{Al}-\\mathrm{Fe}$ intermetallics\n\n\\section*{A B S T R A C T}\n\\begin{itemize}\n  \\item This study focused on additive manufacturing (AM) of the Al-Fe binary alloy samples with a near-eutectic composition of 2.5 mass $\\%$ Fe using the laser powder bed fusion (LPBF) process. The melt pool depth, relative density, and hardness of LPBF-fabricated Al-2.5Fe alloy samples under different laser power $(P)$ and scan speed $(v)$ conditions were systematically examined.", "start_char_idx": 308396, "end_char_idx": 311275, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "84285a28-daba-4b99-9650-b4139662935a": {"__data__": {"id_": "84285a28-daba-4b99-9650-b4139662935a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3717e075-663c-451f-b091-24cfa71c8f34", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "aae01733e4b77c28db76d327b38b6a69aa78d9a8f51e582d1840b570e3d9f33d", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "f177514d-40d5-4e4f-aa12-299840e0fc86", "node_type": "1", "metadata": {}, "hash": "e08afc9b8706fc99fa3777256b3e9f7088b3c5e94b54d9b934cfe0d17e4a0a0d", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing\n\nAl-Fe binary alloy\n\nProcessing parameters\n\nMicrostructure\n\n$\\mathrm{Al}-\\mathrm{Fe}$ intermetallics\n\n\\section*{A B S T R A C T}\n\\begin{itemize}\n  \\item This study focused on additive manufacturing (AM) of the Al-Fe binary alloy samples with a near-eutectic composition of 2.5 mass $\\%$ Fe using the laser powder bed fusion (LPBF) process. The melt pool depth, relative density, and hardness of LPBF-fabricated Al-2.5Fe alloy samples under different laser power $(P)$ and scan speed $(v)$ conditions were systematically examined. The results provided optimum laser parameter sets $(P=$ $204 \\mathrm{~W}, v \\leq 800 \\mathrm{~mm} \\mathrm{~s}^{-1}$ ) for the fabrication of dense alloy samples with high relative densities $>99 \\%$. Additionally, $P v^{-1 / 2}$, which is based on the deposited energy density model, was found to be a more appropriate parameter for additively manufacturing $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples, and using it to simplify the relative densities of the samples made the determination of a threshold value for the laser parameters required to fabricate dense alloy samples. The microstructural and crystallographic characterization of the LPBF-built Al-2.5Fe alloy samples revealed a characteristic microstructure consisting of multi-scan melt pools that resulted from local melting and rapid solidification owing to laser irradiation during the LPBF process. Furthermore, a number of columnar grains with a mean width of $\\sim 21 \\mu \\mathrm{m}$ elongated along the building direction were also observed in the $\\alpha$ - $\\mathrm{Al}$ matrix. Numerous nano-sized particles of the metastable $\\mathrm{Al}_{6} \\mathrm{Fe}$ intermetallic phase with a mean size $<100 \\mathrm{~nm}$ were finely dispersed in the $\\alpha$-Al matrix. The hardness of the refined microstructure produced by the LPBF process was high at $\\sim 90 \\mathrm{HV}$, which is more than twofold higher than that of conventionally casted alloys that contain the coarsened plate-shaped $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ intermetallic phase in equilibrium with the $\\alpha$-Al matrix.\n\\end{itemize}\n\n\\section*{1. Introduction}\nAluminum (Al) alloys, which are advantageous owing to their low weight, high specific strength, and superior corrosion resistance, have been extensively used in the aerospace and automotive industries. It is generally known that at ambient temperature, $\\mathrm{Al}$ and its alloys show high thermal conductivities $\\left(\\sim 160 \\mathrm{~W} \\mathrm{~m}^{-1} \\mathrm{~K}^{-1}\\right)$, and relatively low specific heat capacities ( $\\sim 0.9 \\mathrm{~J} \\mathrm{~g}^{-1} \\mathrm{~K}^{-1}$ for pure Al). Thus, they are applied in the manufacture of the heat exchangers destined for refrigeration and air conditioning systems, and/or the radiators with applications ranging from air coils to gas furnaces [1,2]. Additionally, the properties of the materials required for the fabrication of heat exchangers include high thermal conductivity, high specific strength, and sufficient formability, which make the fabrication of complex components, such as plate-fin exchangers possible [3]. Commercial purity Al with iron (Fe) as a major impurity or Al-Fe binary alloys are often used in the fabrication of heat exchangers. These Al-Fe based alloys, which have relatively low strengths compared with conventional age-hardenable alloys (e.g. Al-Mg-Si alloys), exhibit high thermal conductivity owing to the limited solubility of $\\mathrm{Fe}(<0.05$ at\\%) in the $\\alpha-\\mathrm{Al}$ (fcc) matrix. Increasing the $\\mathrm{Fe}$ content favors the formation of $\\mathrm{Al}-\\mathrm{Fe}$ intermetallic compounds, such as the $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase in equilibrium with the $\\alpha-\\mathrm{Al}$ (fcc) matrix [4], resulting in an increase in strength.", "start_char_idx": 310669, "end_char_idx": 314527, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "f177514d-40d5-4e4f-aa12-299840e0fc86": {"__data__": {"id_": "f177514d-40d5-4e4f-aa12-299840e0fc86", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "84285a28-daba-4b99-9650-b4139662935a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5ed3088418f6a12bcd8bdef0a03787df3298af7ef3df0ea7cd945b64d3766316", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7098566f-bd32-4b3f-98f2-a2ab57d109d2", "node_type": "1", "metadata": {}, "hash": "c93431cba77c3326221c46e1af37f05a1d1e02d6dbc8daeb3b15f9dbb5988024", "class_name": "RelatedNodeInfo"}}, "text": "Commercial purity Al with iron (Fe) as a major impurity or Al-Fe binary alloys are often used in the fabrication of heat exchangers. These Al-Fe based alloys, which have relatively low strengths compared with conventional age-hardenable alloys (e.g. Al-Mg-Si alloys), exhibit high thermal conductivity owing to the limited solubility of $\\mathrm{Fe}(<0.05$ at\\%) in the $\\alpha-\\mathrm{Al}$ (fcc) matrix. Increasing the $\\mathrm{Fe}$ content favors the formation of $\\mathrm{Al}-\\mathrm{Fe}$ intermetallic compounds, such as the $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase in equilibrium with the $\\alpha-\\mathrm{Al}$ (fcc) matrix [4], resulting in an increase in strength. However, the coarsened $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase with a plate- or needle-shaped morphology, which is often encountered in several Al-Fe based alloys [5], exhibits brittleness [6], which reduces material formability during plasticforming processes, at ambient temperature. This drawback limits the application of these Al-Fe based alloys in the fabrication of the complex-shaped metal parts of heat exchangers and/or radiators.\n\nGenerally, metal additive manufacturing (AM) technologies [7,8] are promising routes for the fabrication of complex-shaped metal components with controllable structures, and one of the most common\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:qi.xing@i.mbox.nagoya-u.ac.jp}{qi.xing@i.mbox.nagoya-u.ac.jp} (X. Qi).\n}\n\nAM processes is laser powder bed fusion (LPBF), which uses laser beam irradiations to melt and fuse metal powder layers successively. The optimization for the processing parameters of the LPBF technique could enable the fabrication of complex geometrical parts, such as plate-fin exchangers using various $\\mathrm{Al}$ alloy powders $[9,10]$. Recently, it has been demonstrated that this technique brings about characteristic microstructures of Al alloy parts [11,12], due to the rapid solidification process that occurs at an extremely high cooling rate as a result of the scanning laser irradiations. This rapid solidification rate might be employed to significantly refine microstructures containing coarsened $\\mathrm{Al}-\\mathrm{Fe}$ intermetallic compounds [13]. The refinement of the Al-Fe intermetallic compounds in the LPBF-fabricated Al-Fe alloys would result in the improvement of not only mechanical properties (strength and ductility) [14] but also corrosion resistance [15]. In order to achieve the manufacturing of Al-Fe alloy heat exchangers with high strength and high thermal conductivity, it is necessary to understand the controlling of the size, morphology, and distribution of the Al-Fe intermetallic phase formed in the $\\alpha$-Al matrix by LPBF processing. However, the LPBF process has not been applied to Al-Fe binary alloys. Therefore, any characteristics of microstructure containing Al-Fe intermetallic phases formed in the LPBF-fabricated Al-Fe alloys have not been identified.\n\nIn the present study, we made an attempt of additive manufacturing for Al-Fe binary alloy samples with a near-eutectic composition of $\\mathrm{Al}-2.5 \\mathrm{Fe}$ (mass\\%) using the LPBF process for understanding the possibility of controlling the size and morphology of Al-Fe intermetallic phases during rapid solidification in the LPBF process. Thereafter, the microstructural and crystallographic features of the LPBF-fabricated $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples were characterized, and the effect of two laser parameters (scan speed and laser power) on their relative density and microhardness were also investigated. The experimental results were used to discuss the optimization of the laser processing parameters that can be employed in the subsequent fabrication of the studied alloy.\n\n\\section*{2. Experimental procedure}\n\\subsection*{2.1. 1 Al-Fe alloy powder}\nThe studied Al-2.5Fe (mass\\%) binary alloy powder with mean particle size $\\sim 38 \\mu \\mathrm{m}$, was produced using gas atomization, and scanning electron microscopy (SEM) images showing its surface morphology and cross-sectional microstructure are presented in Fig. 1. The alloy powder particles were less regularly shaped, whereas some nearly spherical particles existed, asymmetric as well as fine satellite particles were often observed. (Fig.", "start_char_idx": 313857, "end_char_idx": 318188, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7098566f-bd32-4b3f-98f2-a2ab57d109d2": {"__data__": {"id_": "7098566f-bd32-4b3f-98f2-a2ab57d109d2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "f177514d-40d5-4e4f-aa12-299840e0fc86", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6af3986b93869b6327487ed3538c74fb5328ed1e9efe6e9b6f23a3703bc4d95c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5f7c8b84-9aa4-4f0b-afa4-af442a3655f9", "node_type": "1", "metadata": {}, "hash": "01612e3474813dad7ff2fb24e8a51d59bc96cfe44c38d2802ec7800031c8671e", "class_name": "RelatedNodeInfo"}}, "text": "The experimental results were used to discuss the optimization of the laser processing parameters that can be employed in the subsequent fabrication of the studied alloy.\n\n\\section*{2. Experimental procedure}\n\\subsection*{2.1. 1 Al-Fe alloy powder}\nThe studied Al-2.5Fe (mass\\%) binary alloy powder with mean particle size $\\sim 38 \\mu \\mathrm{m}$, was produced using gas atomization, and scanning electron microscopy (SEM) images showing its surface morphology and cross-sectional microstructure are presented in Fig. 1. The alloy powder particles were less regularly shaped, whereas some nearly spherical particles existed, asymmetric as well as fine satellite particles were often observed. (Fig. 1(a)). The image analyses using SEM images provided a quantitative value of 0.69 in the sphericity of studied powder particles [16]. Additionally, the alloy powder particles also showed a cellular microstructure that consisted mainly of the $\\alpha-\\mathrm{Al}$ matrix and fine Al-Fe intermetallic phase (Fig. 1(b)), which corresponded to the solidification microstructure formed by rapid cooling process during gas atomization.\n\nThe chemical compositions of the studied alloy powder and LPBFfabricated samples were measured using inductively coupled plasmaatomic emission spectrometry and inert gas fusion-infrared absorption spectrometry, and the results are presented in Table 1. The proportions of the major elements ( $\\mathrm{Fe}, \\mathrm{Si}$, and $\\mathrm{O}$ ) in the initial powder were almost the same as those in the LPBF-fabricated sample. Although the alloy powder contained trace amounts of $\\mathrm{Si}$ and $\\mathrm{O}$ as impurity, and $\\mathrm{Al}-\\mathrm{Fe}$ binary phase diagram (Fig. 2(a)) indicated a eutectic reaction of liquid (L) $\\rightarrow \\alpha-\\mathrm{Al}+\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ in solidification [4]. In this study, the alloy powder in an alumina tube was melted using high-frequency induction followed by furnace cooling (by cutting off the power source in the furnace) to prepare an as-cast alloy ingot, as schematically illustrated in Fig. 3(d). The cooling rate during solidification measured experimentally using K-type thermocouples was $\\sim 0.3^{\\circ} \\mathrm{C} / \\mathrm{s}$ [17]. The SEM images displaying the microstructure of the prepared alloy ingots are shown in\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-02}\n\nFig. 1. (a) Surface morphology and (b) cross-section of the studied Al-2.5Fe alloy powder particles.\n\nTable 1\n\nMeasured chemical compositions (mass\\%) of initial alloy powders and built samples.\n\n\\begin{center}\n\\begin{tabular}{llllllll}\n\\hline\nElement & $\\mathrm{Cu}$ & $\\mathrm{Fe}$ & $\\mathrm{Si}$ & $\\mathrm{Mn}$ & $\\mathrm{Mg}$ & $\\mathrm{O}$ & $\\mathrm{Al}$ \\\\\n\\hline\npowder & $<0.01$ & 2.55 & 0.03 & $<0.01$ & $<0.01$ & 0.19 & Bal. \\\\\nbuilt samples & - & 2.54 & 0.03 & - & - & 0.20 & Bal. \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nFig. 2(b) and (c). The needle- or plate-like Al-Fe intermetallic phase, with length in the order of a few hundred micrometers, was randomly distributed in the $\\alpha$-Al matrix, which is consistent with previous reports on conventionally casted Al-Fe alloys [5]. The observed intermetallic phase was identified as $\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase by $\\mathrm{X}$-ray diffraction (XRD) analyses, which is described in detail later.\n\n\\subsection*{2.2. Laser powder bed fusion (LPBF) process}\nThe experimental samples were fabricated via the LPBF process using a 3D Systems ProX 200 (3D SYSTEMS, Rock Hill, SC, USA), equipped with a $\\mathrm{Yb}$-fiber laser.", "start_char_idx": 317489, "end_char_idx": 321112, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5f7c8b84-9aa4-4f0b-afa4-af442a3655f9": {"__data__": {"id_": "5f7c8b84-9aa4-4f0b-afa4-af442a3655f9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7098566f-bd32-4b3f-98f2-a2ab57d109d2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "0c6eb4b2d6dff09cb6ec0d69018ef0d382c7366740fa68c8901441e47fd11a02", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "958be8a7-841b-488c-a78d-3e161f65b80a", "node_type": "1", "metadata": {}, "hash": "45493ae97f5e5ccc9cc8c4fbdeadfa47bde21d445a18a40e7f4211dc9fc32a04", "class_name": "RelatedNodeInfo"}}, "text": "2(b) and (c). The needle- or plate-like Al-Fe intermetallic phase, with length in the order of a few hundred micrometers, was randomly distributed in the $\\alpha$-Al matrix, which is consistent with previous reports on conventionally casted Al-Fe alloys [5]. The observed intermetallic phase was identified as $\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase by $\\mathrm{X}$-ray diffraction (XRD) analyses, which is described in detail later.\n\n\\subsection*{2.2. Laser powder bed fusion (LPBF) process}\nThe experimental samples were fabricated via the LPBF process using a 3D Systems ProX 200 (3D SYSTEMS, Rock Hill, SC, USA), equipped with a $\\mathrm{Yb}$-fiber laser. Using the following set of design process parameters: bedded-powder layer thickness $(t), 30 \\mu \\mathrm{m}$; hatch distance between adjacent scanning tracks $(h), 100 \\mu \\mathrm{m}$; laser power $(P)$, $102-204 \\mathrm{~W}$; scan speed $(v), 600-1400 \\mathrm{~mm} \\mathrm{~s}^{-1}$; and laser spot size $(\\sigma)$, $~$ $100 \\mu \\mathrm{m}$, which was calculated by the extent of negatively defocusing (convergent nature) [18] from the focal position of the laser. Twentyfive $15 \\times 15 \\times 10 \\mathrm{~mm}^{3}$ samples were fabricated in a high-purity argon atmosphere to prevent oxidation. The oxygen concentration was monitored inside the process chamber. The concentration was controlled below $500 \\mathrm{ppm}$ in fabricating samples via the LPBF process. The overall appearance of the fabricated samples is shown in Fig. 3(a), while Fig. 3(b) shows the laser conditions applied to fabricate each of the samples. The numbers marked on the samples as shown in Fig. 3(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-03}\n\\end{center}\n\n\\section*{Fe content $/ \\mathrm{wt} \\%$}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-03(1)}\n\\end{center}\n\nFig. 2. (a) Al-Fe binary phase diagram of experimental alloy composition, (b) and (c) SEM images showing the microstructure of the cast Al-2.5Fe alloy ingots.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-04(1)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-04}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-04(4)}\n\\end{center}\n\n(d)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-04(2)}\n\\end{center}\n\nFig. 3. (a) Appearance of experimental samples fabricated under different laser conditions, (b) corresponding scan speed and laser power for the fabricated samples (the numbers in (a) correspond to those in (b)), (c) schematic showing the hexagonal grid laser scanning strategy applied in this experiment, (d) schematic illustration of the sample preparation process.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-04(3)}\n\\end{center}\n\nFig. 4. Variation of the measured relative density of the fabricated Al-2.5Fe samples as a function of applied laser power.\n\ncorresponds to the numbers on the laser power $(P)$-scan speed $(v)$ map shown in Fig. 3(b), while Fig.", "start_char_idx": 320445, "end_char_idx": 323654, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "958be8a7-841b-488c-a78d-3e161f65b80a": {"__data__": {"id_": "958be8a7-841b-488c-a78d-3e161f65b80a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5f7c8b84-9aa4-4f0b-afa4-af442a3655f9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "61bc0df8204cfcb0a2f043f25b7598d36adc967ffa792b3c6dc03c21ad995f74", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c0fcf6a7-98e2-4e0c-bdc4-3d9f908219b9", "node_type": "1", "metadata": {}, "hash": "9b3b0bc30bea0f7b7682f13de0cb7632c831cf1854b3db251a74741e3d92e734", "class_name": "RelatedNodeInfo"}}, "text": "3. (a) Appearance of experimental samples fabricated under different laser conditions, (b) corresponding scan speed and laser power for the fabricated samples (the numbers in (a) correspond to those in (b)), (c) schematic showing the hexagonal grid laser scanning strategy applied in this experiment, (d) schematic illustration of the sample preparation process.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-04(3)}\n\\end{center}\n\nFig. 4. Variation of the measured relative density of the fabricated Al-2.5Fe samples as a function of applied laser power.\n\ncorresponds to the numbers on the laser power $(P)$-scan speed $(v)$ map shown in Fig. 3(b), while Fig. 3(c) schematically illustrates the hexagonal grid laser scanning strategy that was applied in this experiment. The longest diagonals of the regular hexagons were set as $10 \\mathrm{~mm}$, and the laser scanning track was rotated $90^{\\circ}$ between two successive bedded-powder layers. The planes perpendicular and parallel to the building direction were designated $\\mathrm{XY}$ and $\\mathrm{XZ}$, respectively as shown in Fig. 3(c). The preparation process of as-cast samples and LPBF-fabricated samples used in the experiments was schematically illustrated in Fig. 3(d).\n\n\\subsection*{2.3. Characterizations}\nThe densities of the fabricated samples were measured using the Archimedes' method, which provided the densities of the LPBF-fabricated samples (relative density) as a ratio of the density of the as-cast ingots prepared in this study. The cut samples were mounted and polished mechanically. For microstructural observations using optical microscopy, the sample surfaces were etched using a solution of HF in alcohol (5 vol\\%), and to perform SEM, the samples were ion-polished using a JEOL cross-section polisher at $6 \\mathrm{~V}$. Thereafter, microstructures were observed using optical microscopy (NIKON ECLIPSE LV150 N, JAPAN) and SEM (JEOL JSM-6610A and JEOL JSM-7401, JAPAN). Analyses of the crystallographic orientation of the $\\alpha$-Al (fcc) matrix were conducted using electron backscatter diffraction (EBSD) with a step size of $1 \\mu \\mathrm{m}$, while the constituent phases were analyzed using an $\\mathrm{X}$-ray diffraction (XRD) equipment with a $\\mathrm{Cu}$ target at $40 \\mathrm{kV}$ and 40 $\\mathrm{mA}$, and at a scan speed of $1^{\\circ} / \\mathrm{min}$ in continuous mode for $2 \\theta$ angles ranging from $20^{\\circ}$ to $90^{\\circ}$. Thin samples for TEM observations were prepared using a JEOL ion slicer at $6 \\mathrm{~V}$. TEM observations and energydispersive X-ray spectroscopy (EDS) analyses were performed using a JEOL JEM-2100 F at $200 \\mathrm{kV}$. At ambient temperature, the hardness of mounted samples was determined using a Vickers indenter (FUTURETECH CORP., FM-300e) at two different constant loads ( 9.8 and 0.98 N).\n\n\\section*{3. Results}\nThe relative density variation of the samples fabricated under different scan speeds $(v)$, as a function of the applied laser power $(P)$ is shown in Fig. 4. At all the applied scan speeds, the relative density of\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-05}\n\nFig. 5.", "start_char_idx": 322954, "end_char_idx": 326161, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c0fcf6a7-98e2-4e0c-bdc4-3d9f908219b9": {"__data__": {"id_": "c0fcf6a7-98e2-4e0c-bdc4-3d9f908219b9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "958be8a7-841b-488c-a78d-3e161f65b80a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7c65782f5122fb52e37514e1563a51330eb77977a686e64fa7ac9bf139e35075", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2c8e37e7-c145-4e4d-a9e4-426826be499f", "node_type": "1", "metadata": {}, "hash": "13e171501349ffcb4921f87b26b16db3842ea224f109e16692207191601e6960", "class_name": "RelatedNodeInfo"}}, "text": "TEM observations and energydispersive X-ray spectroscopy (EDS) analyses were performed using a JEOL JEM-2100 F at $200 \\mathrm{kV}$. At ambient temperature, the hardness of mounted samples was determined using a Vickers indenter (FUTURETECH CORP., FM-300e) at two different constant loads ( 9.8 and 0.98 N).\n\n\\section*{3. Results}\nThe relative density variation of the samples fabricated under different scan speeds $(v)$, as a function of the applied laser power $(P)$ is shown in Fig. 4. At all the applied scan speeds, the relative density of\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-05}\n\nFig. 5. Optical micrographs showing the cross-section of the fabricated Al-2.5 Fe samples under laser power and scan speeds of (a) $179 \\mathrm{~W}$ and $600 \\mathrm{~mm} \\mathrm{~s}{ }^{-1}$, (b) 204 $\\mathrm{W}$ and $600 \\mathrm{~mm} \\mathrm{~s}^{-1}$, (c) $102 \\mathrm{~W}$ and $800 \\mathrm{~mm} \\mathrm{~s}^{-1}$, and (d) $102 \\mathrm{~W}$ and $1400 \\mathrm{~mm} \\mathrm{~s}^{-1}$, respectively. The small amounts of unmelted powder particles, which suggest that the detachment of powder particles might be responsible for the large number of pores formed during the sample preparation process, remained within the pores in the white dashed circles inserted in (c) and (d).\n\nthe samples increased with increasing laser power. It was also observed that samples with higher relative densities could be fabricated using lower scan speeds. The applied laser parameters of high laser power $(P$ $=204 \\mathrm{~W}$ ) and low scan speed ( $v \\leq 800 \\mathrm{~mm} \\mathrm{~s}^{-1}$ ) achieved to fabricate dense $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples with high relative density values $>99 \\%$. The optical micrographs of the samples fabricated under different laser conditions, observed on the XZ plane, are presented in Fig. 5. In samples fabricated under a laser power of $179 \\mathrm{~W}$ and a scan speed of 600 $\\mathrm{mm} \\mathrm{s}^{-1}$, relatively large irregular-shaped pores with sizes above 50 $\\mu \\mathrm{m}$, which corresponded to \"process-introduced porosity\" [19] resulting from incomplete melting, owing to insufficient supplied energy, were observed in Fig. 5(a), and as shown in Fig. 5(b), the relatively large pores appeared to decrease with increasing laser power. The decrease in pore number was consistent with the increase in the measured relative densities (Fig. 4). In samples fabricated using a low laser power and a high scan speed, a number of irregular-shaped pores that appeared to connect each other were observed as shown in Fig. 5(c) and (d), and unmelted alloy powders, indicated by the dashed circles in Fig. 5(c) and (d), were also observed in some of the pores, owing to an insufficient laser power supply to completely melt the bed powder layer $[9,20]$. Additionally, a number of fine spherical pores were observed in the samples fabricated under a high laser power and a low scan speed, as presented in Fig. 5(a) and (b). The spherical pores could be attributed to the inert gas atmosphere in the process chamber that was employed to prevent oxidation or to the hydrogen that dissolved in the alloy powder degassed during the fusion process [9].\n\nThe optical micrographs (observed on the XZ plane) of the microstructure of the samples fabricated under the following laser parameters: $204 \\mathrm{~W}$ and $600 \\mathrm{~mm} \\mathrm{~s}^{-1}$, and $153 \\mathrm{~W}$ and $1200 \\mathrm{~mm} \\mathrm{~s}^{-1}$, are shown in Fig. 6(a) and (b), respectively, and Fig. 6(c) shows the variation of melt pool depth with the different laser parameters. Two representative optical micrographs (Fig.", "start_char_idx": 325521, "end_char_idx": 329187, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2c8e37e7-c145-4e4d-a9e4-426826be499f": {"__data__": {"id_": "2c8e37e7-c145-4e4d-a9e4-426826be499f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c0fcf6a7-98e2-4e0c-bdc4-3d9f908219b9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "15a30b433218ed77fadf9f92dd64cd2ceccaa4c55b3ec45eebe3345c03a4ebcc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5792ecb1-94d1-4ecf-b103-f5aca6e36d92", "node_type": "1", "metadata": {}, "hash": "7877a7e11aa9e15aef82c26a6b9fd43b34fd9a29d51f61cc7be6c149254f641f", "class_name": "RelatedNodeInfo"}}, "text": "5(a) and (b). The spherical pores could be attributed to the inert gas atmosphere in the process chamber that was employed to prevent oxidation or to the hydrogen that dissolved in the alloy powder degassed during the fusion process [9].\n\nThe optical micrographs (observed on the XZ plane) of the microstructure of the samples fabricated under the following laser parameters: $204 \\mathrm{~W}$ and $600 \\mathrm{~mm} \\mathrm{~s}^{-1}$, and $153 \\mathrm{~W}$ and $1200 \\mathrm{~mm} \\mathrm{~s}^{-1}$, are shown in Fig. 6(a) and (b), respectively, and Fig. 6(c) shows the variation of melt pool depth with the different laser parameters. Two representative optical micrographs (Fig. 6(a) and (b)) showed melt pool morphologies with different depths ranging between $\\sim 60$ and $100 \\mu \\mathrm{m}$, indicating that the melt pool depth changed depending on the laser parameters. Moreover, under the different laser conditions employed in this study, no keyhole-shaped melt pools resulting from the melt pool peak temperature exceeding the boiling and vaporization temperatures of the alloy [21], were observed in the fabricated samples. The summarized melt pool depth data is shown in Fig. 6(c). This provides evidence that melt pool depth increased with increasing laser power $(P)$. The melt pool depth appears less dependent on laser scan speed $(v)$ in comparison with the laser power $(P)$. The tendency is similar to the variation of relative density depending on different laser conditions (Fig. 4).\n\nA summary of the measured Vickers hardness of the fabricated samples is presented in Fig. 7, and the hardness values measured at two different loads of $9.8 \\mathrm{~N}$ (Fig. 7(a)) and $0.98 \\mathrm{~N}$ (Fig. 7(b)) were designated HV1 and HV0.1, respectively. The indentation tests at a $9.8 \\mathrm{~N}$ load were performed on the regions that included pores as shown in Fig. 5, while similar tests at a lower load $(0.98 \\mathrm{~N})$ were conducted on the defect-free regions identified using optical microscopy. The hardness measurements revealed that the HV1 hardness values of the samples (Fig. 7(a)) increased with increasing laser power and decreasing scan speed. At higher laser power values $>179 \\mathrm{~W}$, the HV1 value\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-06}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-06(1)}\n\\end{center}\n\nFig. 6. (a, b) Optical micrographs showing melt pool morphologies of Al-2.5Fe alloy samples fabricated under laser power and scan speeds of (a) $204 \\mathrm{~W}$ and $600 \\mathrm{~mm}$ $\\mathrm{s}^{-1}$ and (b) $153 \\mathrm{~W}$ and $1200 \\mathrm{~mm} \\mathrm{~s}^{-1}$ and (c) variation in melt pool depth of fabricated samples as a function of applied laser power.\n\npractically remained constant at $\\sim 70 \\mathrm{HV}$ and was independent of the scan speed. Additionally, the hardness of the fabricated samples was approximately twofold higher than that of the as-cast ingots prepared in this study (Fig. 2), and the variation of the HV1 values followed the same trend as the measured relative densities, indicating that porosity defects had an unneglectable effect on the hardness of the LPBF-fabricated samples with lower relative densities. Contrarily, hardness values measured at a lower load (HV0.1) only changed slightly with the laser parameters, $P$ and $v$ (Fig. 7(b)), suggesting that the laser parameters have a slight effect on the microstructure of fabricated samples.\n\nThe representative XRD profile of the LPBF-fabricated sample, as well as that of the initial alloy powder and the as-cast alloy ingot, are shown in Fig. 8.", "start_char_idx": 328508, "end_char_idx": 332193, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5792ecb1-94d1-4ecf-b103-f5aca6e36d92": {"__data__": {"id_": "5792ecb1-94d1-4ecf-b103-f5aca6e36d92", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2c8e37e7-c145-4e4d-a9e4-426826be499f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7b75bd34e24af3828f3fca50ee93e16e358b477cda432e33f344ace78c957360", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c074cd78-6a28-43a1-8831-36e859b17f25", "node_type": "1", "metadata": {}, "hash": "e1b33f789c17e4db359f36fb113106bca022e2a2cd7c6792ddbc1072d37417e4", "class_name": "RelatedNodeInfo"}}, "text": "practically remained constant at $\\sim 70 \\mathrm{HV}$ and was independent of the scan speed. Additionally, the hardness of the fabricated samples was approximately twofold higher than that of the as-cast ingots prepared in this study (Fig. 2), and the variation of the HV1 values followed the same trend as the measured relative densities, indicating that porosity defects had an unneglectable effect on the hardness of the LPBF-fabricated samples with lower relative densities. Contrarily, hardness values measured at a lower load (HV0.1) only changed slightly with the laser parameters, $P$ and $v$ (Fig. 7(b)), suggesting that the laser parameters have a slight effect on the microstructure of fabricated samples.\n\nThe representative XRD profile of the LPBF-fabricated sample, as well as that of the initial alloy powder and the as-cast alloy ingot, are shown in Fig. 8. The XRD profiles revealed that $\\alpha$ - $\\mathrm{Al}$ and $\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ constituted the dominant phases of the as-cast alloy ingot [4], indicating that the formation of these thermodynamically stable phases in the as-cast alloy ingot possibly resulted from an equilibrium solidification (Fig. 2(b) and (c)). In LPBF-fabricated samples, there was a considerable change in the diffraction intensities derived from the $\\theta$ $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase. At $2 \\theta$ diffraction angles ranging between $22^{\\circ}$ and $28^{\\circ}$, no reflections derived from $\\theta$ phase were detected, indicating the reduced fraction of $\\theta$ phase in LPBF-fabricated samples. Additionally, a relatively high intensity, which corresponded to a reflection derived from the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase [22], was detected at a $2 \\theta$ diffraction angle of approximately $40^{\\circ}$. Several reflections of $\\theta$ phase detected in the as-cast alloy ingot were found in the LPBF-fabricated samples, whereas their $2 \\theta$ diffraction angles correspond to diffraction intensities derived from lattice planes of both $\\theta$ phase and $\\mathrm{Al}_{6} \\mathrm{Fe}$ phases. These results suggest the metastable $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase might partially form replacing the stable $\\theta$ phase in rapid solidification during the LPBF process. This conclusion is consistent with the XRD profile obtained from the initial alloy powder, which had a fine solidification microstructure (Fig. 1(b)). Furthermore, the LPBF-fabricated sample exhibited $\\alpha$-Al phase-derived reflections at a higher $2 \\theta$ angle compared with the as-cast alloy ingot, indicating a larger $\\alpha$-Al matrix lattice parameter in the LPBF-fabricated samples. Considering the atomic radii of $\\mathrm{Al}$ and $\\mathrm{Fe}$ atoms, this suggests the formation of a solution of $\\mathrm{Fe}$ element in the $\\alpha$-Al matrix [23,24].\n\nIn order to characterize microstructural and crystallographic features of the $\\alpha$-Al matrix in the LPBF-fabricated Al-2.5Fe alloy samples, EBSD analyses were performed on samples with high relative densities ( $>99 \\%$ ) i.e., those fabricated under a laser power and scan speed of\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-07(1)}\n\nFig. 7. Variation of the Vickers hardness of the fabricated alloy samples measured under two different loads: (a) $9.8 \\mathrm{~N}$ and (b) $0.98 \\mathrm{~N}$. The black dash line represents the Vickers hardness of the cast alloy as a comparison.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-07}\n\\end{center}\n\nFig. 8. XRD spectrum of LPBF-fabricated Al-2.5Fe alloy sample (Laser power $(P)=204 \\mathrm{~W}$ and scan speed $(v)=600 \\mathrm{~mm} \\mathrm{~s}^{-1}$ ), initial alloy powder, and ascast alloy ingot.", "start_char_idx": 331319, "end_char_idx": 335093, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c074cd78-6a28-43a1-8831-36e859b17f25": {"__data__": {"id_": "c074cd78-6a28-43a1-8831-36e859b17f25", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5792ecb1-94d1-4ecf-b103-f5aca6e36d92", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "35da2e50bfa409ceef2ea6381e9ba6ac9a20aa31cf0468bc5189316bd2f963ef", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "0549fe52-827f-4c7c-9230-1f9d1e72690d", "node_type": "1", "metadata": {}, "hash": "dc3193ac9feaebb959bea47fccbe7f6264c45aa77f99c0e3e2af9da58cc5cb20", "class_name": "RelatedNodeInfo"}}, "text": "7. Variation of the Vickers hardness of the fabricated alloy samples measured under two different loads: (a) $9.8 \\mathrm{~N}$ and (b) $0.98 \\mathrm{~N}$. The black dash line represents the Vickers hardness of the cast alloy as a comparison.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-07}\n\\end{center}\n\nFig. 8. XRD spectrum of LPBF-fabricated Al-2.5Fe alloy sample (Laser power $(P)=204 \\mathrm{~W}$ and scan speed $(v)=600 \\mathrm{~mm} \\mathrm{~s}^{-1}$ ), initial alloy powder, and ascast alloy ingot.\n\n$204 \\mathrm{~W}$ and $600 \\mathrm{~mm} \\mathrm{~s}^{-1}$, respectively (Fig. 4), and the analyzed results are summarized in Fig. 9. As shown in Fig. 9(a) and (b), even though local fine equiaxed grains were observed, the $\\alpha$-Al matrix microstructure predominantly consisted of large columnar grains with a mean size of approximately $21 \\mu \\mathrm{m}$ (mean width of the high-angle boundaries with misorientations above $15^{\\circ}$ was measured by the linear intercept method), which are surrounded by high angle boundaries with misorientations above $15^{\\circ}$ and are elongated along the building direction. Moreover, a relatively high density of low-angle boundaries was also detected inside the elongated grains (Fig. 9(c)). The low index stereographic projections indicated the absence of any predominant crystallographic texture in the LPBF-fabricated samples (Fig. 9(d)), which is different from the previous study that identified the $<001$ $>$ texture along the building direction in LPBF-fabricated Al-Si-based alloys [25]. Additionally, no obvious microstructural changes were observed around the melt pool boundaries that are clearly visible in the optical micrographs of the fabricated samples (Fig. 6(a)), suggesting that the epitaxial growth originated from pre-existed $\\alpha$-Al grains at the melt pool boundaries during solidification in the LPBF process of the Al-2.5Fe alloy [20].\n\nFig. 10 depicts high-magnification SEM images showing the microstructure observed from different directions i.e., parallel and perpendicular to the building direction (Z) of the sample built under $204 \\mathrm{~W}$ and $600 \\mathrm{~mm} \\mathrm{~s}^{-1}$. A gradient change in microstructure was observed across melt pool boundaries. Fine intermetallic particles (bright contrast) with mean sizes $<100 \\mathrm{~nm}$, were homogeneously distributed inside the melt pools (\"fine zone\" in Fig. 10), whereas the relatively coarse zone, which consisted of relatively coarsened microstructures, was localized around the melt pool boundaries. The observed intermetallic phases appeared to connect with each other, resulting in the formation of a cellular structure in the coarse zone, within which some coarser granular particles could also be observed. These different microstructural morphologies could be attributed to the variation of local cooling rate and its associated heating effect during the LPBF process [26]. In order to identify the fine particles of the intermetallic phase in the LPBF-fabricated Al-2.5Fe alloy, TEM characterizations were performed, and the summarized results are shown in Fig. 11. The TEM bright-field images (Fig. 11(a) and (b)) showed that the fine particles with a size in the order of several tens of nanometers were distributed in the $\\alpha$-Al matrix, while a relatively coarsened local cellar structure was also observed (Fig. 11(a)), and these microstructural morphologies corresponded well to those observed by SEM (Fig. 10). Furthermore, as shown in Fig. 11(b), numerous spherical or granular particles often appeared to connect each other were also observed. A selected area electron diffraction (SAED) pattern (Fig. 11(c)) obtained from the observed region (Fig.", "start_char_idx": 334545, "end_char_idx": 338312, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "0549fe52-827f-4c7c-9230-1f9d1e72690d": {"__data__": {"id_": "0549fe52-827f-4c7c-9230-1f9d1e72690d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c074cd78-6a28-43a1-8831-36e859b17f25", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "afe58af11dbf5e1ec846e5efa9efa6ee9602d6f39a0afcaab989d3978822264f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c08cc662-2a60-411a-9314-e78f68a7a064", "node_type": "1", "metadata": {}, "hash": "32e213618f2c795d12b3059c2d0112be4d6d957609a62cf0e075764ae68de713", "class_name": "RelatedNodeInfo"}}, "text": "In order to identify the fine particles of the intermetallic phase in the LPBF-fabricated Al-2.5Fe alloy, TEM characterizations were performed, and the summarized results are shown in Fig. 11. The TEM bright-field images (Fig. 11(a) and (b)) showed that the fine particles with a size in the order of several tens of nanometers were distributed in the $\\alpha$-Al matrix, while a relatively coarsened local cellar structure was also observed (Fig. 11(a)), and these microstructural morphologies corresponded well to those observed by SEM (Fig. 10). Furthermore, as shown in Fig. 11(b), numerous spherical or granular particles often appeared to connect each other were also observed. A selected area electron diffraction (SAED) pattern (Fig. 11(c)) obtained from the observed region (Fig. 11(b)), indicated a ring diffraction pattern inside several spots derived from the $\\alpha-\\mathrm{Al}$ (fcc) phase that could be corresponded to a reflection from the (222) lattice plane of the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase, which has an orthodromic structure [22], a finding that is consistent with the reflection detected at approximately $42^{\\circ}$ in the $2 \\theta$ diffraction angles in the XRD profile (Fig. 7). These crystallographic analyses revealed numerous nano-sized particles of the metastable $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase distributed in the $\\alpha$-Al matrix. The ring diffraction pattern indicated that the observed $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase particles had a random orientation distribution, suggesting that there was no peculiar orientation relationship between the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase and the $\\alpha$-Al matrix. Scanning-TEM (STEM) images and the corresponding EDS element maps are presented in Fig. 12. The EDS chemical analysis revealed Fe enrichment in the observed fine particles (Fig. 12(d)), confirming the formation of Al-Fe intermetallic particles $\\left(\\mathrm{Al}_{6} \\mathrm{Fe}\\right.$ phase) within the $\\alpha$-Al phase. Note that local oxygen enrichment was observed (Fig. 12(b)), indicating the local presence of nano-scale oxide particles in the LPBF-fabricated Al-Fe alloy. The source of the $\\mathrm{O}$ element was derived from the initial alloy powder (presumably thin oxide layers on the surface of powder particles), as demonstrated by composition analyses (Table 1).\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-08}\n\nFig. 9. (a), (b) EBSD orientation color maps for the $\\alpha$ - $\\mathrm{Al}$ (fcc) matrix in the LBPF-fabricated Al-2.5Fe sample (Laser power $(P)=204 \\mathrm{~W}$ and scan speed $(v)=600 \\mathrm{~mm}$ $\\left.s^{-1}\\right)$. The colors represent the orientations along the building direction $(\\mathrm{Z})$ according to the orientation color key in the unit triangle. The fine line corresponds to a misorientation ( $\\theta$ ) of $1<\\theta<15^{\\circ}$, while the bold lines represent $\\theta>15^{\\circ}$. (c) misorientation angle distribution, and (d) representative pole figure for low indices.\n\n\\section*{4. Discussion}\n\\subsection*{4.1. Processing parameters}\nGiven its role in the minimization or elimination of porosity and fusion voids, which have a detrimental effect on mechanical properties of LPBF-fabricated alloys, relative density is considered to be one of the critical characteristics of LPBF-fabricated samples. The present results revealed that at all scan speeds, relative density increased with increasing laser power (Fig. 4). Thus, the high laser power and low scan speed are appropriate laser parameters for the fabrication of dense Al-2.5Fe alloy samples with high relative densities ( $\\sim 99 \\%)$. However, these fabricated samples had local defects (micron-sized pores) as shown in Fig. 5(b), indicating that the further optimization of the processing parameters is required to eliminate the local defects.", "start_char_idx": 337524, "end_char_idx": 341386, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c08cc662-2a60-411a-9314-e78f68a7a064": {"__data__": {"id_": "c08cc662-2a60-411a-9314-e78f68a7a064", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "0549fe52-827f-4c7c-9230-1f9d1e72690d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cdb989321c0d5153c8079d8b7e5b2931bc3efa70934916f73178094a38b9bf4b", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a9e4b861-5050-4a8a-aeea-3adf11a1c330", "node_type": "1", "metadata": {}, "hash": "b40fcd5af7bbf0ec51bf445b10de7198c046b9a767f18beb1fd01050d7c015a3", "class_name": "RelatedNodeInfo"}}, "text": "(c) misorientation angle distribution, and (d) representative pole figure for low indices.\n\n\\section*{4. Discussion}\n\\subsection*{4.1. Processing parameters}\nGiven its role in the minimization or elimination of porosity and fusion voids, which have a detrimental effect on mechanical properties of LPBF-fabricated alloys, relative density is considered to be one of the critical characteristics of LPBF-fabricated samples. The present results revealed that at all scan speeds, relative density increased with increasing laser power (Fig. 4). Thus, the high laser power and low scan speed are appropriate laser parameters for the fabrication of dense Al-2.5Fe alloy samples with high relative densities ( $\\sim 99 \\%)$. However, these fabricated samples had local defects (micron-sized pores) as shown in Fig. 5(b), indicating that the further optimization of the processing parameters is required to eliminate the local defects.\n\nThe effect of processing parameters on the relative density of LPBFfabricated metals has been extensively investigated [10,27,28], and the following volumetric energy density $(E)$ equation has been widely used to integrate various LPBF processing parameters $[28,29]$.\n\n$E=\\frac{P}{v \\cdot h \\cdot t}$\n\nwhere $P, t, h$, and $v$ represent laser power, powder layer thickness, hatch distance between adjacent laser-scanning tracks, and laser scan speed, respectively. This approach has often demonstrated applicability in the fabrication of fully dense or defect-free alloy samples from various alloy powders using the LPBF process $[28,29]$. However, this model works on the assumption that the heat applied is completely transferred through the thickness of the bedded-powder layers, regardless of the varying laser scan speed. In some cases, the model would be invalid because a variation in scan speed could change the laser-irradiation time of the powder layer, resulting in different effective depths, in which heat can be transferred. In this study, to simplify the measured relative densities associated with the laser parameters, a deposited energy density $(\\Delta H)$ based model, which takes thermal diffusivity into account, was applied. According to this model [30], the ratio of deposited energy density $(\\Delta H)$ to the enthalpy at melting $\\left(h_{\\mathrm{s}}\\right)$ is expressed as:\n\n$\\frac{\\Delta H}{h_{s}}=\\frac{A P}{h_{s} \\sqrt{\\pi D v \\sigma^{3}}}$\n\nwhere $A, D$, and $\\sigma$ represent laser absorptivity, thermal diffusivity, and laser spot size (half-width of Gaussian beam [30]), respectively. The unit of $\\Delta H$ (Joule per unit volume) is the same as that of $E$. This model takes into account the dynamic time period $(\\tau)$ of laser irradiation, which depends on scan speed variation, and $\\tau$ can be approximated as $\\sigma$ $/ v$. Therefore, based on the deposited energy density model, the depth to which heat is transferred into the powder layer changes, resulting in a heat-diffusion depth of $(D \\tau)^{1 / 2}$ and a heat-distributed region with a\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-09}\n\nFig. 10. Representative SEM images showing the microstructure of $\\mathrm{Al}-2.5 \\mathrm{Fe}$ sample built under Laser power $(P)=204 \\mathrm{~W}$ and scan speed $(v)=600 \\mathrm{~mm} \\mathrm{~s}$ ${ }^{-1}$. These images were observed on different planes: (a) XZ and (b) XY.\n\nvolume of $\\pi \\sigma(D \\tau)^{1 / 2}[31,32]$. This model was originally proposed as a simple methodology to predict the laser-weld properties using the laser irradiation at high laser power $(P)$ above $300 \\mathrm{~W}$ under an assumption of a Gaussian beam distribution in the applied laser condition [30]. In recent, the model has also been used to investigate the correlation between a transition from conduction to keyhole melting mode occurring on the locally melted surface of materials in the LPBF process using relatively lower $P$ values ranging from 86 to $366 \\mathrm{~W}$ [31].", "start_char_idx": 340458, "end_char_idx": 344438, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a9e4b861-5050-4a8a-aeea-3adf11a1c330": {"__data__": {"id_": "a9e4b861-5050-4a8a-aeea-3adf11a1c330", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c08cc662-2a60-411a-9314-e78f68a7a064", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "951b9cd405889e466a66f111909bb5ebf51a4ed70f316eec4fb6121d8257b851", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1dd2f821-ab49-47f0-a9e5-9c93740f9fe2", "node_type": "1", "metadata": {}, "hash": "efa602772f6e5b5fbadc693ee6536a04fcfcafb27556bab263b3b137084cceea", "class_name": "RelatedNodeInfo"}}, "text": "These images were observed on different planes: (a) XZ and (b) XY.\n\nvolume of $\\pi \\sigma(D \\tau)^{1 / 2}[31,32]$. This model was originally proposed as a simple methodology to predict the laser-weld properties using the laser irradiation at high laser power $(P)$ above $300 \\mathrm{~W}$ under an assumption of a Gaussian beam distribution in the applied laser condition [30]. In recent, the model has also been used to investigate the correlation between a transition from conduction to keyhole melting mode occurring on the locally melted surface of materials in the LPBF process using relatively lower $P$ values ranging from 86 to $366 \\mathrm{~W}$ [31]. In addition, our previous study demonstrated that $\\Delta H$ provides a threshold value for the laser conditions required to fabricate fully dense samples from maraging steel powder using the LPBF process [32]. As proposed in this study, to optimize the laser parameters, both $E$ and $\\Delta H$ are applied to simplify the effects of laser power and scan speed on relative density.\n\nIn Fig. 13, the variation of melt pool depth as functions of (a) $E$ and (b) $P v^{-1 / 2}$ derived from $\\Delta H$ is presented. In this study, $A, D$, and $h_{s}$ for the Al-2.5Fe alloy powder were fixed, and a constant $\\sigma(\\sim 100 \\mu \\mathrm{m})$ was applied during the LPBF process. Based on Eq. (2), $P v^{-1 / 2}$ was used to simplify $\\Delta H$ associated parameters by removing the constant parameters. It was observed that the melt pool depth increased with both the increasing $E$ and $P v^{-1 / 2}$. A roughly linear relationship between $E$ and melt pool depth could be confirmed under present laser conditions, as shown in Fig. 13(a). However, at $E$ values within the range of $\\sim$ 40-58 Jmm $\\mathrm{Jm}^{-3}$, relatively scattered melt pool depth values were observed. Additionally, Fig. 13(b) showed a stronger linear relationship between $P v^{-1 / 2}$ and melt pool depth based on the experimental results. In order to quantify the degree of linearity of measured melt pool depth\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-09(1)}\n\nFig. 11. (a), (b) TEM bright-field images depicting cellular microstructure around the melt pool boundary as well as the fine particles distributed inside the melt pool in the LPBF-fabricated Al-2.5Fe alloy samples, and (c) corresponding SAED pattern obtained from (b).\n\nwith respect to $E$ or $P v^{-1 / 2}$, the linear regression analysis for the experimental data was conducted. The analyses provided a coefficient of determination $\\left(R^{2}\\right)$ of 0.842 for the linear relationship between melt pool depth and $P v^{-1 / 2}$, which was much higher than that derived from the linear regression analysis of the relationship between the melt pool depth and $E\\left(R^{2}=0.586\\right)$. These results obviously indicate that $P v^{-1 / 2}$, which is based on $\\Delta H$ (taking into account the thermal diffusivity),\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-10}\n\nFig. 12. (a) STEM-high angle annular dark-field (HAADF) image, and (b)-(d) corresponding EDS elemental maps for the fine particles in LPBF-fabricated Al-2.5Fe alloy samples.\n\ncould be a more appropriate parameter that can be used to identify the effects of laser power and scan speed on the melt pool depth of LPBFfabricated $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples.", "start_char_idx": 343779, "end_char_idx": 347200, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1dd2f821-ab49-47f0-a9e5-9c93740f9fe2": {"__data__": {"id_": "1dd2f821-ab49-47f0-a9e5-9c93740f9fe2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a9e4b861-5050-4a8a-aeea-3adf11a1c330", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2229e7bd5e0ffdec246ce0540e00b64e0c540a1fd42b72b67d70a2a1cb149eac", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ab59d640-a91a-49d0-ba25-6e282fd47b39", "node_type": "1", "metadata": {}, "hash": "6fd354134b07a74b5341191990e344549266cf5af2b78f0bb2989f281250cf54", "class_name": "RelatedNodeInfo"}}, "text": "These results obviously indicate that $P v^{-1 / 2}$, which is based on $\\Delta H$ (taking into account the thermal diffusivity),\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-10}\n\nFig. 12. (a) STEM-high angle annular dark-field (HAADF) image, and (b)-(d) corresponding EDS elemental maps for the fine particles in LPBF-fabricated Al-2.5Fe alloy samples.\n\ncould be a more appropriate parameter that can be used to identify the effects of laser power and scan speed on the melt pool depth of LPBFfabricated $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples. Considering the heat-diffusion depth, $(D \\tau)^{1 / 2}$ [31] based on the $\\Delta H$ model, it is supposed that thermal diffusivity could significantly contribute to the measured melt pool depth due to local melting of $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy powder layers by laser irradiations, suggesting that keyhole-mode melting could hardly occur under the applied laser conditions in the LPBF process [31]. The supposition is reasonable agreement with the observed melt pool morphologies (Fig. 5). These results represent the high validity of the $\\Delta H$ model for rationalizing physical phenomena within the melt pools (closely associated with the melt pool depth) formed in the LPBF process.\n\nChanges in relative density as a function of (a) $E$ and (b) $P v^{-1 / 2}$ are presented in Fig. 14. As shown in Fig. 14(a), relative density tended to increase with increasing $E$; however, at the same $E$ values of 42.5 or $56.7 \\mathrm{Jmm}^{-3}$, it tended to be scattered with deviations $>10 \\%$. Conversely, its variation with $P v^{-1 / 2}$ could be approximated using a single curve, which indicated that it increased continuously to values above $98 \\%$ until a $P v^{-1 / 2}$ value of $6.5 \\mathrm{Wmm}^{-1 / 2} \\mathrm{~s}^{1 / 2}$, after which it became almost saturated at $\\sim 99 \\%$. Meanwhile, relative density variation simplified using $P v^{-1 / 2}$ could provide an approximate threshold laser condition to fabricate dense samples with relative densities of $\\sim 99 \\%$, although a certain degree of relative density variation was still observed in the dense samples. Compared with the variation of melt pool depth with $P v^{-1 / 2}$ (Fig. 13(b)), the threshold $P v^{-1 / 2}$ value of $6.5 \\mathrm{Wmm}^{-1 / 2} \\mathrm{~s}^{1 /}$ ${ }^{2}$ was associated with a melt pool depth of $\\sim 75 \\mu \\mathrm{m}$, which represents a melt pool depth that is two- or three-fold larger than the powder layer thickness $(30 \\mu \\mathrm{m})$ is required to fabricate dense samples. These results further support $P v^{-1 / 2}$ as a more appropriate design parameter to optimize laser power and scan speed for fabricating Al-2.5Fe alloy samples via the LPBF process.\n\nThe variation of Vickers hardness as a function of relative density measured at two different loads is shown in Fig. 15(a). HV1 hardness values measured at a higher load $(9.8 \\mathrm{~N})$ tended to increase with the increasing relative density, clearly indicating that the HV1 hardness could be attributed to the porosity level of the as-fabricated samples, given that the HV1 indent size was $\\sim 170 \\mu \\mathrm{m}$, which is comparable with the pore sizes observed in the optical micrographs (Fig. 5). On the other hand, when the relative density was higher than approximately $84 \\%$, HV0.", "start_char_idx": 346614, "end_char_idx": 349980, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ab59d640-a91a-49d0-ba25-6e282fd47b39": {"__data__": {"id_": "ab59d640-a91a-49d0-ba25-6e282fd47b39", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1dd2f821-ab49-47f0-a9e5-9c93740f9fe2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1c6bb810724a65f91db3483e58ec0941be96d9b7cf597b5b78eea0e52ccc9943", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9a255a22-3cb7-43c6-9bd5-939e907cafdb", "node_type": "1", "metadata": {}, "hash": "5f1f09ffbe12883123962eff9cf7aa3152b771950d7770622d8d07f85b59a1b1", "class_name": "RelatedNodeInfo"}}, "text": "These results further support $P v^{-1 / 2}$ as a more appropriate design parameter to optimize laser power and scan speed for fabricating Al-2.5Fe alloy samples via the LPBF process.\n\nThe variation of Vickers hardness as a function of relative density measured at two different loads is shown in Fig. 15(a). HV1 hardness values measured at a higher load $(9.8 \\mathrm{~N})$ tended to increase with the increasing relative density, clearly indicating that the HV1 hardness could be attributed to the porosity level of the as-fabricated samples, given that the HV1 indent size was $\\sim 170 \\mu \\mathrm{m}$, which is comparable with the pore sizes observed in the optical micrographs (Fig. 5). On the other hand, when the relative density was higher than approximately $84 \\%$, HV0. 1 hardness values measured at a lower load $(0.98 \\mathrm{~N})$ were constant at $\\sim 90 \\mathrm{HV}$; however, at low relative densities, it was relatively lower.\\\\\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-11}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_c6c2dc7a9cf3f465b1a9g-11(1)}\n\\end{center}\n\nFig. 13. Variation of the melt pool depth of the LPBF-fabricated Al-2.5Fe alloy samples as a function of (a) Volumetric energy density (E) and (b) $P v^{-1 / 2}$, which is based on deposited energy density $(\\Delta H)$.\n\nIts smaller indent size $(\\sim 42 \\mu \\mathrm{m})$ was indicative of the micron-scale porosity level of the samples. Both HV1 and HV0.1 hardness values could be simplified using $P v^{-1 / 2}$ as shown in Fig. 15(b). The variation of HV1 values as a function of $P v^{-1 / 2}$, which synchronized with the variation of relative density, was approximated using a single curve, (Fig. 14(b)), indicating that using $P v^{-1 / 2}$, conventional Vickers hardness tests can provide threshold laser parameters for the fabrication of dense samples. At $P v^{-1 / 2}$ values above $4 \\mathrm{Wmm}^{-1 / 2} \\mathrm{~s}^{1 / 2}$, the HV0.1 value was almost constant at $\\sim 90 \\mathrm{HV}$, whereas it decreased at $P v^{-1 / 2}$ values $<4 \\mathrm{Wmm}^{-1 / 2} \\mathrm{~s}^{1 / 2}$, suggesting the presence of numerous micronscale pores in the samples built under $P V^{-1 / 2}$ values $<4 \\mathrm{Wmm}^{-1 / 2} \\mathrm{~s}^{1 / 2}$.\n\nThe aforementioned results demonstrated that $P v^{-1 / 2}$, which is based on the $\\Delta H$ model, rather than $E$ should be used to optimize laser parameters ( $P$ and $v$ ) for manufacturing dense $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples. In the present study using fixed processing conditions of hatch distance $(h)$, powder layer thickness $(t)$ and laser spot size $(\\sigma)$ for one material (fixed laser absorptivity, $A$ and thermal diffusivity, $D$ ), the different models contribute to only the power index of scan speed $\\left(v^{-1}\\right.$ or $v^{-1 / 2}$ ). The present result can provide significant insights into the selection of laser conditions for the fabrication of larger-sized samples that can be employed in mechanical and thermal tests, whereas the determined $P v^{-1 / 2}$ threshold value might change depending on other processing\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-11(2)}\n\nFig. 14.", "start_char_idx": 349199, "end_char_idx": 352480, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9a255a22-3cb7-43c6-9bd5-939e907cafdb": {"__data__": {"id_": "9a255a22-3cb7-43c6-9bd5-939e907cafdb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ab59d640-a91a-49d0-ba25-6e282fd47b39", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "48644487e418cb807d89e3e47397f34244c99515326fdfdfe83ade433a86c3e2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6be6e440-6751-4e59-87a7-c10ee09784ec", "node_type": "1", "metadata": {}, "hash": "ac4187965253f42c6cfa134d7af924e9963c57be36230822dc5add1d005e3ec9", "class_name": "RelatedNodeInfo"}}, "text": "In the present study using fixed processing conditions of hatch distance $(h)$, powder layer thickness $(t)$ and laser spot size $(\\sigma)$ for one material (fixed laser absorptivity, $A$ and thermal diffusivity, $D$ ), the different models contribute to only the power index of scan speed $\\left(v^{-1}\\right.$ or $v^{-1 / 2}$ ). The present result can provide significant insights into the selection of laser conditions for the fabrication of larger-sized samples that can be employed in mechanical and thermal tests, whereas the determined $P v^{-1 / 2}$ threshold value might change depending on other processing\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-11(2)}\n\nFig. 14. Variation of the relative density of the LPBF-fabricated Al-2.5Fe alloy samples as a function of (a) Volumetric energy density (E) and (b) $\\mathrm{Pv}^{-1 / 2}$, which is based on deposited energy density $(\\Delta H)$.\n\nparameters, including spot size (beam intensity distribution), hatch distance, and powder layer thickness. It still remains unclear whether the $\\Delta H$ model (using a function of $v^{-1 / 2}$ ) is valid for optimizing laser parameters for fabricating any other materials with different properties of $A, D$, and specific heat. Therefore, to propose more appropriate models that cover all the processing parameters of the LPBF process for various materials, further investigations would be required.\n\n\\subsection*{4.2. Microstructure characterization}\nIn this study, the microstructure of the LPBF-fabricated Al-2.5Fe alloy samples with high relative densities ( $>99 \\%$ ) was systematically characterized. A number of melt pools were observed in the LPBFfabricated $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy (Fig. 6) as well as various $\\mathrm{Al}$ alloys [11,12]. Numerous fine and connected particles of the metastable $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase were observed inside melt pools (Figs. 10-12), whereas relatively coarsened microstructures were observed along melt pool boundaries (Fig. 10). The coarsened region may locally form in solidification at relatively slow growth rates, which facilitates the formation of stable $\\theta$ $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase along the melt pool boundaries. The local formation of $\\theta$ $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase is in agreement with the XRD profile for the LPBF-fabricated sample (Fig. 8). The present microstructural characterizations suggest the formation of multi Al-Fe intermetallic phases in the LPBFfabricated $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples.\n\nThe hardness of the LPBF-fabricated Al-2.5Fe alloy samples was found to be twofold higher than that of the cast alloy ingots (Fig. 7),\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_c6c2dc7a9cf3f465b1a9g-12}\n\nFig. 15. Variation in the Vickers hardness of the LPBF-fabricated Al-2.5Fe alloy samples measured under two different loads ( $9.8 \\mathrm{~N}$ and $0.98 \\mathrm{~N})$ as a function of (a) Relative density, (b) $\\mathrm{Pv}^{-1 / 2}$, which is based on deposited energy density $(\\Delta H)$.\n\nwhich is attributed to the fine particle morphology of the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase. The observed morphology was quite different from that of conventionally casted alloy samples (Fig. 2(b) and (c)). It is generally known that during solidification in conventional casting processes, the liquid phase decomposes into the $\\alpha$ - $\\mathrm{Al}$ and $\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phases via a eutectic reaction in the Al-rich portion of the Al-Fe binary system (Fig. 2(a)), resulting in the formation of the plate-shaped $\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase, which is in equilibrium with the surrounding $\\alpha$-Al matrix (Fig. 2(b) and (c)) [33].", "start_char_idx": 351765, "end_char_idx": 355533, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6be6e440-6751-4e59-87a7-c10ee09784ec": {"__data__": {"id_": "6be6e440-6751-4e59-87a7-c10ee09784ec", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9a255a22-3cb7-43c6-9bd5-939e907cafdb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4746bef4327e81cf13834bb6c02ae2a1847f47b03c84d239be51448d21ed243f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d0e3ee3b-32e2-43fc-80f4-49915ec30211", "node_type": "1", "metadata": {}, "hash": "e3682aa48ab15567841f16bcc1f30b3a3658429731a675e1c7060db1e2f0efb2", "class_name": "RelatedNodeInfo"}}, "text": "which is attributed to the fine particle morphology of the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase. The observed morphology was quite different from that of conventionally casted alloy samples (Fig. 2(b) and (c)). It is generally known that during solidification in conventional casting processes, the liquid phase decomposes into the $\\alpha$ - $\\mathrm{Al}$ and $\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phases via a eutectic reaction in the Al-rich portion of the Al-Fe binary system (Fig. 2(a)), resulting in the formation of the plate-shaped $\\theta-\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase, which is in equilibrium with the surrounding $\\alpha$-Al matrix (Fig. 2(b) and (c)) [33]. Additionally, it has been reported that during solidification at a higher growth rate $\\left(>0.1 \\mathrm{~mm} \\mathrm{~s}^{-1}\\right)$ and a higher temperature gradient ( $>10{ }^{\\circ} \\mathrm{C} / \\mathrm{mm}$ ), the eutectic reaction changes to the decomposition of $\\alpha$ - $\\mathrm{Al}$ and $\\mathrm{Al}_{6} \\mathrm{Fe}$ phases [34]. The product of growth rate $\\left(\\mathrm{mm} \\mathrm{s}^{-1}\\right)$ and temperature gradient $\\left(\\mathrm{Kmm}^{-1}\\right)$ provides the corresponding cooling rate $\\left(\\mathrm{Ks}^{-1}\\right)$, and it is supposed that the eutectic decomposition of the $\\alpha$ - $\\mathrm{Al}$ and $\\mathrm{Al}_{6} \\mathrm{Fe}$ phases may occur at cooling rates $>1 \\mathrm{Ks}^{-1}$. The cooling rate required for the formation of the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase is much lower than that in the LPBF process, which is extremely high $\\left(\\sim 10^{5} \\mathrm{Ks}^{-1}\\right.$ ). This high cooling rate has also been found to be associated with the different phases identified in this study (Fig. 8) i.e., both the LPBF-fabricated $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy sample as well as the initial alloy powder, which has a fine solidification microstructure (Fig. 1(b)) that results from gas atomization. In previously observed eutectic microstructure, the spherical or granular $\\mathrm{Al}_{6} \\mathrm{Fe}$ particles appeared to be somewhat different from the rod-shaped morphology of the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase\\\\\n[35]. The formation of the different $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase morphologies might be related to either different solidification mode at the high cooling rate or a slight decomposition process (transformation to the stable $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ phase) caused by the additional heating effect of the upper powder layers heated by laser irradiation. Such nano-sized $\\mathrm{Al}_{6} \\mathrm{Fe}$ particles have also been observed in rapidly solidified $\\mathrm{Al}-\\mathrm{Fe}$ alloy produced by the twin-roll technique [36]. However, the detailed mechanism still remains unclear. To understand the peculiar fine particle morphology of the $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase in the LPBF-fabricated $\\mathrm{Al}-\\mathrm{Fe}$ alloys, an investigation of the thermal stability of the metastable $\\mathrm{Al}_{6} \\mathrm{Fe}$ phase (and relatively coarsened $\\mathrm{Al}-\\mathrm{Fe}$ intermetallic phases localized along the melt pool boundaries) at elevated temperatures is required. These future investigations could provide useful insights regarding the microstructural control of LPBF-fabricated Al-2.5Fe alloy samples using post-heat treatment processes.\n\n\\section*{5. Conclusions}\nIn this study, the effects of laser power $(P)$ and scan speed $(v)$ on the relative density, melt pool depth, and Vickers hardness of LPBF-fabricated Al-Fe binary alloy samples of near-eutectic composition (Al-2.5 mass $\\% \\mathrm{Fe})$ were investigated. The characterization of the microstructural and crystallographic features of the fabricated alloy samples led to the following conclusions regarding the LPBF process.", "start_char_idx": 354852, "end_char_idx": 358631, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d0e3ee3b-32e2-43fc-80f4-49915ec30211": {"__data__": {"id_": "d0e3ee3b-32e2-43fc-80f4-49915ec30211", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6be6e440-6751-4e59-87a7-c10ee09784ec", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9cb0875714d192b19d489c0351cea977d2a40aeb56d9578ff2a462f8d827722f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9acc7a11-3883-474e-b066-71539eb8d34b", "node_type": "1", "metadata": {}, "hash": "87c1b79a24605baa69a0103a8b23df255ccc04dbbe66f85b8ae0c07ab3e7d5ad", "class_name": "RelatedNodeInfo"}}, "text": "These future investigations could provide useful insights regarding the microstructural control of LPBF-fabricated Al-2.5Fe alloy samples using post-heat treatment processes.\n\n\\section*{5. Conclusions}\nIn this study, the effects of laser power $(P)$ and scan speed $(v)$ on the relative density, melt pool depth, and Vickers hardness of LPBF-fabricated Al-Fe binary alloy samples of near-eutectic composition (Al-2.5 mass $\\% \\mathrm{Fe})$ were investigated. The characterization of the microstructural and crystallographic features of the fabricated alloy samples led to the following conclusions regarding the LPBF process.\n\n(1) The systematic characterization of LPBF-fabricated samples under controlled laser parameters $(P=102-204 \\mathrm{~W}, v=600-1400 \\mathrm{~mm} \\mathrm{~s}$ ${ }^{-1}$ ) provided optimum laser parameter sets $(P=204 \\mathrm{~W}, v \\leq 800$ $\\mathrm{mm} \\mathrm{s}{ }^{-1}$ ) for the fabrication of dense samples with high relative densities $>99 \\%$. The variation of relative density with $P v^{-1 / 2}$, which is based on the deposited energy density model $(\\Delta H)$, could be represented using a single curve, which allowed the identification of a threshold value for the laser parameters required to fabricate dense materials. Thus, compared with the generally used volumetric energy density $(E)$ model, $P v^{-1 / 2}$, could be a more appropriate design parameter for the manufacture of $\\mathrm{Al}-2.5 \\mathrm{Fe}$ alloy samples using the LPBF process.\n\n(2) The LPBF-fabricated Al-2.5Fe alloy samples exhibited a peculiar microstructure, which consisted of multi-scan melt pools that resulted from local melting and rapid solidification, owing to laser irradiation during the LPBF process. In the $\\alpha$-Al matrix, several columnar grains with a mean width of $\\sim 21 \\mu \\mathrm{m}$ were identified. Additionally, numerous nano-scale particles with mean size $<100$ $\\mathrm{nm}$ of the metastable $\\mathrm{Al}_{6} \\mathrm{Fe}$ intermetallic phase were finely dispersed in the $\\alpha$-Al matrix inside the melt pool. No predominant crystallographic texture of $\\alpha$-Al matrix was identified in the LPBFfabricated samples.\n\n(3) The hardness of the refined microstructure resulting from the LPBF process was very high at $\\sim 90 \\mathrm{HV}$, which is more than twofold higher than that of conventionally casted Al-2.5Fe alloy, which has a two-phase microstructure consisting of the coarsened plateshaped $\\mathrm{Al}_{13} \\mathrm{Fe}_{4}$ intermetallic phase and the $\\alpha$-Al matrix. The porosity defects had an unneglectable effect on the hardness of the LPBF-fabricated samples when measured at a higher load of $9.8 \\mathrm{~N}$. Contrarily, hardness values measured at a lower load of $0.98 \\mathrm{~N}$ were almost constant independent of the laser parameters ( $P$ and $v$ ), indicating a slight change in the microstructure of the LPBF-fabricated sample depending on $P$ and $v$.\n\n\\section*{Author Contribution}\nX. Qi: Acquistion of data; analysis and/or interpretation of data; drafting the manuscript; revising the manuscript for important intellectual content.\n\nN. Takata: Conception and design by study; analysis and/or interpretation of data; revising the manuscript for important intellectual\n\n\\section*{content.}\nA. Suzuki: Conception and design by study; revising the manuscript for important intellectual content.\n\nM. Kobashi: Conception and design by study; revising the manuscript for important intellectual content.\n\nM. Kato: Conception and design by study; revising the manuscript for important intellectual content.\n\n\\section*{Declaration of Competing Interest}\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n\\section*{Acknowledgments}\nThe authors are grateful for the alloy powder preparation provided by Dr. Isao Murakami (TOYO ALUMINUM K.K.). The support of \"Knowledge Hub Aichi\", a Priority Research Project of the Aichi Prefectural Government (Japan) was gratefully acknowledged. Xing Qi would also like to acknowledge the fellowship offered by the China Scholarship Council (No.", "start_char_idx": 358006, "end_char_idx": 362188, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9acc7a11-3883-474e-b066-71539eb8d34b": {"__data__": {"id_": "9acc7a11-3883-474e-b066-71539eb8d34b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d0e3ee3b-32e2-43fc-80f4-49915ec30211", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "7c58984348afd7e1651e041b4ea0dd98b4a6d53f0b30fef687c51a952be53337", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "3c4903e7-df8a-487d-b6cc-54247cd0ad00", "node_type": "1", "metadata": {}, "hash": "c5b3bda73e44ecc7d04a63cd899bb260cb7260db39148406148c2755b9689a3c", "class_name": "RelatedNodeInfo"}}, "text": "A. Suzuki: Conception and design by study; revising the manuscript for important intellectual content.\n\nM. Kobashi: Conception and design by study; revising the manuscript for important intellectual content.\n\nM. Kato: Conception and design by study; revising the manuscript for important intellectual content.\n\n\\section*{Declaration of Competing Interest}\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n\\section*{Acknowledgments}\nThe authors are grateful for the alloy powder preparation provided by Dr. Isao Murakami (TOYO ALUMINUM K.K.). The support of \"Knowledge Hub Aichi\", a Priority Research Project of the Aichi Prefectural Government (Japan) was gratefully acknowledged. Xing Qi would also like to acknowledge the fellowship offered by the China Scholarship Council (No. 201806890005), which made his Ph.D. study at Nagoya University possible.\n\n\\section*{References}\n[1] A. Aversa, G. Marchese, A. Saboori, E. Bassini, D. Manfredi, S. Biamino, D. Ugues, P. Fino, M. Lombardi, New aluminum alloys specifically designed for laser powder bed fusion: a review, Materials 12 (2019) 1007.\n\n[2] A. Kawahara, A. Niikura, T. Doko, Development of aluminum alloy fin stock for heat exchangers using twin-roll continuous casting method, Furukawa Rev. 24 (2003) 81-87.\n\n[3] P. Rodriguez, Selection of materials for heat exchangers, HEB 97 (1997) 59-72.\n\n[4] P.J. Black, The structure of $\\mathrm{FeAl}_{3}$, Acta Cryst. 8 (1955) 175-182.\n\n[5] X. Wang, R.G. Guan, R.D.K. Misra, Y. Wang, H.C. Li, Y.Q. Shang, The mechanistic contribution of nanosized $\\mathrm{Al}_{3} \\mathrm{Fe}$ phase on the mechanical properties of $\\mathrm{Al}-\\mathrm{Fe}$ alloy, Mater. Sci. Eng. 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Hono, Microstructure and mechanical properties of bulk nanocrystalline $\\mathrm{Al}-\\mathrm{Fe}$ alloy processed by mechanical alloying and spark plasma sintering, Acta Mater. 57 (2009) 3529-3538.", "start_char_idx": 363882, "end_char_idx": 366641, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8a35bacd-ffc7-42e1-b36a-796b8ad492d5": {"__data__": {"id_": "8a35bacd-ffc7-42e1-b36a-796b8ad492d5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "3c4903e7-df8a-487d-b6cc-54247cd0ad00", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cb8abfe8ca7cd798892a6fb454a3f0d1710ccd23e576f03e922c9d989681f8e2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "4737ec94-4fc1-450d-93c0-94c97f238bb7", "node_type": "1", "metadata": {}, "hash": "8a31cd1c25ca07bdd10bdab6c95828fa6e5b6a5af64ec6eb0aad93bc8623b96b", "class_name": "RelatedNodeInfo"}}, "text": "[21] U.S. Bertoli, A.J. 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Zeng, Microstructure, mechanical properties and strengthening mechanisms of AlCu5MnCdVA aluminum alloy fabricated by selective laser melting, Mater. Sci. Eng. A 759 (2019) 154-166.\n\n[27] T. Kimura, T. Nakamoto, Thermal and mechanical properties of commercial-purity aluminum fabricated using selective laser melting, J. Jpn Inst. Light Metals 66 (2016) 167-173.\n\n[28] H. Gong, K. Rafi, H. Gu, T. Starr, B. Stucker, Analysis of defect generation in Ti-6Al-4V parts made using powder bed fusion additive manufacturing processes, Addit. Manuf. 1-4 (2014) 87-98.\n\n[29] G. Casalino, S.L. Campanelli, N. Contuzzi, A.D. Ludovico, Experimental investigation and statistical optimisation of the selective laser melting process of a maraging steel, Opt. Laser Technol. 65 (2015) 151-1.\n\n[30] D.B. Hann, J. Iammi, J. Folkes, A simple methodology for predicting laser-weld properties from material and laser parameters, J. Phys. Appl. Phys. 44 (2011) 445401.\n\n[31] W.E. King, H.D. Barth, V.M. Castillo, G.F. Gallegos, J.W. Gibbs, D.E. Hahn, C. Kamath, A.M. Rubenchik, Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing, J. Mater. Process. Technol. 214 (2014) 2915-2925.\n\n[32] A. Suzuki, R. Nishida, N. Takata, M. Kobashi, M. Kato, Design of laser parameters for selectively laser melted maraging steel based on deposited energy density, Addit. Manuf. 28 (2019) 160-168.\n\n[33] G.M. Adam, L.M. Hogan, Crystallography of the $\\mathrm{Al}^{-\\mathrm{Al}_{3} \\mathrm{Fe}}$ eutectic, Acta Metall. 23 (1974) 345-354.\n\n[34] Harumi Kosuge, Intermetallic compounds in Al-Fe alloys, J. Jpn Inst. Light Metals 30 (1980) 217-226.\n\n[35] I.R. Hughes, H. Jones, Coupled eutectic growth in Al-Fe alloys, J. Mater. Sci. 11 (1976).\n\n[36] A. Kamio, H. Tezuka, S. Suzuki, T.T.", "start_char_idx": 366086, "end_char_idx": 368853, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "4737ec94-4fc1-450d-93c0-94c97f238bb7": {"__data__": {"id_": "4737ec94-4fc1-450d-93c0-94c97f238bb7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8a35bacd-ffc7-42e1-b36a-796b8ad492d5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "be0d471f6039c2f1a357abaa9454941c4bcad0eabe2a0d68873d8f64ca155f20", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "67b26b8b-a72a-4850-b12c-655ae92e551d", "node_type": "1", "metadata": {}, "hash": "7c2ffdcc503f2c94e62c06455cd2098894bc727d1579c41ac9bd82fadae4c168", "class_name": "RelatedNodeInfo"}}, "text": "Manuf. 28 (2019) 160-168.\n\n[33] G.M. Adam, L.M. Hogan, Crystallography of the $\\mathrm{Al}^{-\\mathrm{Al}_{3} \\mathrm{Fe}}$ eutectic, Acta Metall. 23 (1974) 345-354.\n\n[34] Harumi Kosuge, Intermetallic compounds in Al-Fe alloys, J. Jpn Inst. Light Metals 30 (1980) 217-226.\n\n[35] I.R. Hughes, H. Jones, Coupled eutectic growth in Al-Fe alloys, J. Mater. Sci. 11 (1976).\n\n[36] A. Kamio, H. Tezuka, S. Suzuki, T.T. Long, T. Takahashi, Structure and mechanical properties of rapidly solidified Al-8mass\\%Fe alloys, J. Jpn Inst. Light Metals 37 (1987) 109-118.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Heat source model calibration for thermal analysis of laser powder-bed fusion }\n\n\n\\author{Shahriar Imani Shahabad ${ }^{1} \\cdot$ Zhidong Zhang $^{1} \\cdot$ Ali Keshavarzkermani ${ }^{1} \\cdot$ Usman Ali $^{1} \\cdot$ Yahya Mahmoodkhani $^{1} \\cdot$\\\\\nReza Esmaeilizadeh ${ }^{1} \\cdot$ Ali Bonakdar $^{2} \\cdot$ Ehsan Toyserkani $^{1}$}\n\\date{}\n\n\n\\begin{document}\n\\maketitle\nReceived: 15 November 2019 / Accepted: 27 December 2019 /Published online: 5 January 2020\n\n(C) Springer-Verlag London Ltd., part of Springer Nature 2020\n\n\\begin{abstract}\nLaser powder-bed fusion (LPBF) is one of the mainstream additive manufacturing (AM) processes, which has dominated the metal AM manufacturing market. LPBF has the capability to manufacture complex parts, which pose a manufacturing challenge by conventional methods. In this paper, an efficient numerical-experimental approach has been introduced to calibrate the parameters of a proposed three-dimensional (3D) conical Gaussian moving laser heat source model. For this purpose, several Hastelloy X single tracks are printed with various process parameters. The melt pool depth and width were measured experimentally, and results were used to calibrate and validate the heat source model. An empirical relationship between heat source parameters and laser energy density was also proposed. In addition, temperature gradients and cooling rates around the melt pool were extracted from the numerical model to be used towards microstructure prediction. Estimated microstructure cell spacing, calculated based on predicted cooling rate during solidification, was in good agreement with experimental measurements, indicating the validity of the heat source model.", "start_char_idx": 368443, "end_char_idx": 371167, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "67b26b8b-a72a-4850-b12c-655ae92e551d": {"__data__": {"id_": "67b26b8b-a72a-4850-b12c-655ae92e551d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "4737ec94-4fc1-450d-93c0-94c97f238bb7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "73fa746d5456a1bf4d73d35d1f6355eea2e3f4654da7221e602334e5813e524f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a67f68db-dbe8-40c4-9438-644f27676e14", "node_type": "1", "metadata": {}, "hash": "d3d3f9ac28431568219d70385d5b27e4f38e4e07bae06bdaa9b31b3ab96cf994", "class_name": "RelatedNodeInfo"}}, "text": "LPBF has the capability to manufacture complex parts, which pose a manufacturing challenge by conventional methods. In this paper, an efficient numerical-experimental approach has been introduced to calibrate the parameters of a proposed three-dimensional (3D) conical Gaussian moving laser heat source model. For this purpose, several Hastelloy X single tracks are printed with various process parameters. The melt pool depth and width were measured experimentally, and results were used to calibrate and validate the heat source model. An empirical relationship between heat source parameters and laser energy density was also proposed. In addition, temperature gradients and cooling rates around the melt pool were extracted from the numerical model to be used towards microstructure prediction. Estimated microstructure cell spacing, calculated based on predicted cooling rate during solidification, was in good agreement with experimental measurements, indicating the validity of the heat source model.\n\\end{abstract}\n\nKeywords Laser powder-bed fusion $(\\mathrm{LPBF}) \\cdot$ Additive manufacturing $\\cdot$ Heat source modeling $\\cdot$ Temperature gradient $\\cdot$ Cooling rate\n\n\\section*{Nomenclature}\n$k_{e} \\quad$ Effective thermal conductivity of powder\n\n$k_{g} \\quad$ Thermal conductivity of the continuous gas phase\n\n$k_{s} \\quad$ Thermal conductivity of skeletal solid\n\n$\\varphi \\quad$ The porosity of powder bed\n\n$k_{R} \\quad$ Thermal conductivity part of the powder bed owing to radiation\n\n$\\varnothing \\quad$ The flattened surface fraction of particle in contact with another particle\n\n$B$ Deformation parameter of the particle\n\n$k_{\\text {contact }}$ Contact conductivity between two particles according to the value of $\\varnothing$\n\n$C_{p} \\quad$ Specific heat\n\nEhsan Toyserkani\n\n\\href{mailto:ehsan.toyserkani@uwaterloo.ca}{ehsan.toyserkani@uwaterloo.ca}\n\n1 University of Waterloo, 200 University Avenue West, Waterloo, Ontario N2L 3G1, Canada\n\n2 Siemens Canada Limited, 9545 C\u00f4te-de-Liesse, Montr\u00e9al, Qu\u00e9bec H9P 1A5, Canada\n\n\\begin{center}\n\\begin{tabular}{ll}\n$L$ & Latent heat \\\\\n$\\rho$ & Density \\\\\n$k$ & Thermal conductivity \\\\\n$Q$ & Internal heat generation \\\\\n$h_{c}$ & Heat transfer coefficient \\\\\n$\\varepsilon$ & Emissivity coefficient \\\\\n$\\sigma_{s b}$ & Stefan-Boltzmann coefficient \\\\\n$q_{c}$ & Convective heat dissipation \\\\\n$q_{r}$ & Radiative heat dissipation \\\\\n$I$ & Heat intensity distribution \\\\\n$q_{0}$ & The maximum value of heat intensity \\\\\n$r_{0}$ & The top radius of heat source \\\\\n$r_{d}$ & The bottom radius of heat source \\\\\n$z_{e}$ & Z coordinates of the top surface of heat source \\\\\n$z_{i}$ & Z coordinates of the bottom surface of heat source \\\\\n$H$ & Height of heat source \\\\\n$\\alpha$ & Absorption coefficient \\\\\n$P$ & Laser power \\\\\n$V$ & Scanning speed \\\\\n$T$ & Cooling rate \\\\\n$\\lambda_{1}$ & Primary spacing \\\\\n\\end{tabular}\n\\end{center}\n\n\\section*{1 Introduction}\nAdditive manufacturing (AM) is an emerging technology that is becoming more common in different industries such as aerospace and automotive. This process has gained the advantage of producing complex shapes by importing digital drawing data to the machine [1]. The selective laser melting process, which is named as laser powder-bed fusion (LPBF) by the ASTM standard, produces parts in a layer upon layer fashion. After spreading metal powder on the build plate, a laser heat source selectively melts powder particles and the solidified track forms the shape of desired contours. A new layer of powder is then added to the previous layer and this process is repeated until the final part is fabricated [2].\n\nIn order to mitigate costs and turnaround time for identifying optimum process parameters and predict the temperature distribution and gradient for further microstructure analysis of printed parts, several numerical analysis methods have been implemented by many researchers [3-5]. Kundakc et al. [6] developed a finite element (FE) model, considering a threedimensional (3D) heat source to predict melt pool geometries and temperature distribution during LPBF. They carried out some experimental tests on Inconel 625 and titanium material for validating their model. Their model was able to predict melt pool shapes within the error range of $11-18 \\%$. Liu et al.", "start_char_idx": 370160, "end_char_idx": 374453, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a67f68db-dbe8-40c4-9438-644f27676e14": {"__data__": {"id_": "a67f68db-dbe8-40c4-9438-644f27676e14", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "67b26b8b-a72a-4850-b12c-655ae92e551d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8c53f7652fec33401f3decede712cfca1dcd8eaac0fd46ce28a59d612cce4fbc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ab7d7d43-eaa2-418a-aafe-bc97b0e3a80f", "node_type": "1", "metadata": {}, "hash": "ed662667cf20e9e079858c4e0a145a23758ea712693208f5a9cecc48dbefac4a", "class_name": "RelatedNodeInfo"}}, "text": "After spreading metal powder on the build plate, a laser heat source selectively melts powder particles and the solidified track forms the shape of desired contours. A new layer of powder is then added to the previous layer and this process is repeated until the final part is fabricated [2].\n\nIn order to mitigate costs and turnaround time for identifying optimum process parameters and predict the temperature distribution and gradient for further microstructure analysis of printed parts, several numerical analysis methods have been implemented by many researchers [3-5]. Kundakc et al. [6] developed a finite element (FE) model, considering a threedimensional (3D) heat source to predict melt pool geometries and temperature distribution during LPBF. They carried out some experimental tests on Inconel 625 and titanium material for validating their model. Their model was able to predict melt pool shapes within the error range of $11-18 \\%$. Liu et al. [7] investigated the LPBF of AlSi10Mg using the FE method for predicting microstructure within the solidified melt pool. They extracted temperature gradient, solidification rate, and cooling rate in order to predict the microstructure behavior of the melt pool. Antony et al. [8] investigated single track formation in LPBF of SS 316 powder on the AISI 316L substrate. They developed an FE model for predicting the temperature distribution in one layer deposited powder. Moreover, the influence of process parameters on melt pool characteristics was studied. Ali et al. [9] proposed a numerical model considering a volumetric heat source model for taking into account heat transfer penetration within the material. They were able to predict the cooling rate, temperature gradient, and residual stress evolution. Their model was validated based on melt pool dimensions extracted experimentally. $\\mathrm{Du}$ et al. [10] implemented a 3D Gaussian heat source in their model for predicting temperature field within LPBF. In addition, the variation of laser absorptivity with temperature was considered. Zhidong et al. [11] carried out a comprehensive study of different volumetric heat source models. They proposed a new model including anisotropically thermal conductivity with a variable laser absorption coefficient. Their predicted results were very close to experimental measurements of melt pool dimensions and surface morphologies of tracks.\n\nMany studies on the LPBF modeling have been conducted. However, the literature lacks detailed procedures on calibrating the heat source models in order to develop a relationship between heat source parameters and melt pool geometries. The authors have previously published a work, in which variable thermal conductivity and absorption factors have been incorporated into the exponentially decaying heat source [11]. In this paper, a conical Gaussian heat source model $[12,13]$ with a varying depth of penetration along with a variable absorption factor has been implemented for modeling the melt pool depth and width of single tracks of Hastelloy $\\mathrm{X}$ during LPBF. Numerical results showed excellent agreement with experimental melt pool geometries based on the varying laser power and scanning speed. In addition, temperature gradients and cooling rates due to their critical role in microstructure analysis such as predicting cell size are also extracted from the numerical results.\n\n\\section*{2 Experimental approach}\nIn this study, a commercially gas-atomized Hastelloy $\\mathrm{X}$ powder (Table 1), provided from EOS GmbH was utilized with a D10, D50, and D90 of $15.5 \\mu \\mathrm{m}, 29.3 \\mu \\mathrm{m}$, and $46.4 \\mu \\mathrm{m}$, respectively. Hastelloy X (nickel-based superalloy) has several applications in manufacturing gas turbine combustion systems due to its good creep resistance, tensile strength, and ductility at high temperatures [13]. A Zeiss ULTRA plus Scanning Electron Microscopy (SEM) (Carl Zeiss Microscopy GmbH, Jena, Germany) was used to capture the powder distribution (Fig. 1).\n\nSingle tracks of Hastelloy $\\mathrm{X}$ were produced using an EOS M290 (EOS GmbH, Krailling, Germany) machine with a laser spot size of $100 \\mu \\mathrm{m}$. The laser of this system is a Ytterbium fiber laser with a wavelength of $1060 \\mathrm{~nm}$.", "start_char_idx": 373494, "end_char_idx": 377774, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ab7d7d43-eaa2-418a-aafe-bc97b0e3a80f": {"__data__": {"id_": "ab7d7d43-eaa2-418a-aafe-bc97b0e3a80f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a67f68db-dbe8-40c4-9438-644f27676e14", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a0d5e9a0cfcbab84e630cbddd99d394d471d894ca1178feac675565cfdecf769", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "522dbe19-b359-4434-948c-5ddf4fafe7e3", "node_type": "1", "metadata": {}, "hash": "86906131d2340bf8b38f3ca0f960dfbe51a897cc021a8c7834e3370b253631a5", "class_name": "RelatedNodeInfo"}}, "text": "Hastelloy X (nickel-based superalloy) has several applications in manufacturing gas turbine combustion systems due to its good creep resistance, tensile strength, and ductility at high temperatures [13]. A Zeiss ULTRA plus Scanning Electron Microscopy (SEM) (Carl Zeiss Microscopy GmbH, Jena, Germany) was used to capture the powder distribution (Fig. 1).\n\nSingle tracks of Hastelloy $\\mathrm{X}$ were produced using an EOS M290 (EOS GmbH, Krailling, Germany) machine with a laser spot size of $100 \\mu \\mathrm{m}$. The laser of this system is a Ytterbium fiber laser with a wavelength of $1060 \\mathrm{~nm}$. Initially, substrates with dimensions of $25 \\times 18.5 \\times 5 \\mathrm{~mm}$ were printed from the same material (Hastelloy $\\mathrm{X}$ ) by using the default EOS process parameters (laser power $195 \\mathrm{~W}$, scanning speed $1150 \\mathrm{~mm} / \\mathrm{s}$ with hatch distance of $90 \\mu \\mathrm{m}$ ). Then, an additional layer thickness of powder was spread on top of the printed substrate to manufacture the single tracks with specified process parameters. For this study, various process parameters such as laser power and laser scanning speed were considered. The range of laser power and scanning speed are listed in (Table 2) which are used for validation of the numerical model. Figure 2 shows the produced single tracks\n\nTable 1 Chemical composition (in wt\\%) of Hastelloy X powder [14]\n\n\\begin{center}\n\\begin{tabular}{llllllllllll}\n\\hline\n$\\mathrm{Ti}$ & $\\mathrm{Al}$ & $\\mathrm{Cu}$ & $\\mathrm{Mn}$ & $\\mathrm{Si}$ & $\\mathrm{C}$ & $\\mathrm{Co}$ & $\\mathrm{W}$ & $\\mathrm{Mo}$ & $\\mathrm{Fe}$ & $\\mathrm{Cr}$ & $\\mathrm{Ni}$ \\\\\n\\hline\n$<0.15$ & $<0.5$ & $<0.5$ & $<1$ & $<1$ & $<0.1$ & $1.5 \\pm 1$ & $0.6 \\pm 0.4$ & $9 \\pm 1$ & $18.5 \\pm 1.5$ & $21.75 \\pm 1.25$ & Balance \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-03}\n\\end{center}\n\nFig. 1 SEM image of Hastelloy X powder\n\nat different process parameters. The distance between every single track was $2.5 \\mathrm{~mm}$. Then, the printed specimens were removed from the build plate and cut perpendicular to single tracks using a Buehler ISOMET 1000 (Buehler, IL, USA) precision cutter with $5 \\mathrm{~mm}$ distance from the side of samples. Afterward, the specimens were mounted and polished before etching with a Glyceregia solution [15]. Finally, in order to measure the single tracks melt pool geometries, a Keyence VK-X250 confocal laser microscope (Keyence Corporation, Osaka, Japan) was used.", "start_char_idx": 377165, "end_char_idx": 379727, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "522dbe19-b359-4434-948c-5ddf4fafe7e3": {"__data__": {"id_": "522dbe19-b359-4434-948c-5ddf4fafe7e3", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ab7d7d43-eaa2-418a-aafe-bc97b0e3a80f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "de680dbe297e084b95666b742065010525b5d286e5d76278e315399376b7f152", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "38565926-c2b0-494a-8e2a-0669cc77a642", "node_type": "1", "metadata": {}, "hash": "2fd660e73ccd99eda2b02c6aaae43aa0aa9687926b1c3595126f4b92e44d4398", "class_name": "RelatedNodeInfo"}}, "text": "1 SEM image of Hastelloy X powder\n\nat different process parameters. The distance between every single track was $2.5 \\mathrm{~mm}$. Then, the printed specimens were removed from the build plate and cut perpendicular to single tracks using a Buehler ISOMET 1000 (Buehler, IL, USA) precision cutter with $5 \\mathrm{~mm}$ distance from the side of samples. Afterward, the specimens were mounted and polished before etching with a Glyceregia solution [15]. Finally, in order to measure the single tracks melt pool geometries, a Keyence VK-X250 confocal laser microscope (Keyence Corporation, Osaka, Japan) was used. In addition, a TESCAN VEGA 3 SEM (TESCAN, Brno, Czech Republic) was used for validating the cooling rate extracted from the numerical results based on cell spacing.\\\\\nTable 2 Process parameters used for a single track\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nProcess parameters & Values \\\\\n\\hline\nLaser power $(\\mathrm{W})$ & $150-200-250$ \\\\\nScanning speed $(\\mathrm{mm} / \\mathrm{s})$ & $800-1000-1200-1300$ \\\\\nLaser spot diameter $(\\mu \\mathrm{m})$ & 100 \\\\\nLayer thickness $(\\mu \\mathrm{m})$ & 20 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\n\\section*{3 Finite element modeling}\n\\subsection*{3.1 Model geometry and material properties}\nThe commercial software COMSOL Multiphysics ${ }^{\\circledR}$ was utilized to predict the melt pool dimensions, cooling rate, and temperature gradient during LPBF of Hastelloy X samples. In order to capture melt pool geometries in the microscale model, a substrate domain of $1 \\times 1 \\times 0.5 \\mathrm{~mm}$ was modeled. A powder layer of a thickness of $0.02 \\mathrm{~mm}$ was also applied on top of the substrate (Fig. 3). Finer tetrahedral mesh size $(20 \\mu \\mathrm{m})$ was implemented in regions close to the laser-material interaction zone for reducing computational cost as shown in Fig. 3.\n\nThe properties of Hastelloy X material (Fig. 4) for bulk and powder were assigned to the respective domains. The thermal conductivity of powder material is derived using Eq. (1) [6]:\n\n$\\frac{k_{e}}{k_{g}}=(1-\\sqrt{1-\\varphi})\\left(1+\\frac{\\varphi k_{R}}{k_{g}}\\right)+\\sqrt{1-\\varphi}\\left\\{(1-\\varnothing)\\left[\\frac{2}{1-\\frac{B k_{g}}{k_{s}}}\\left(\\frac{B}{\\left(1-\\frac{B k_{g}}{k_{s}}\\right)^{2}}\\left(1-\\frac{k_{g}}{k_{s}}\\right) \\operatorname{Ln} \\frac{k_{s}}{B k_{g}}-\\frac{B+1}{2}-\\frac{B-1}{1-\\frac{B k_{g}}{k_{s}}}\\right)+\\frac{k_{R}}{k_{g}}\\right]+\\varnothing \\frac{k_{\\text {Contact }}}{k_{g}}\\right\\}$\n\nwhere $k_{e}$ is the effective thermal conductivity of powder bed, $k_{g}$ is the thermal conductivity of the gas, $k_{s}$ is the thermal conductivity of solid, $\\varphi$ is the experimentally measured porosity of the powder bed (52\\%) [16], $k_{R}$ is the thermal conductivity of the powder bed due to radiation, $\\varnothing$ is the flattened surface fraction between particles, $B$ is the deformation parameter of the particle, and $k_{\\text {contact }}$ can be derived from Eq. (2) [17]:\n\n$k_{\\text {contact }}=18 \\varnothing k_{s} \\quad$ if $\\varnothing<3 \\times 10^{-4} \\quad k_{\\text {contact }} \\approx k_{\\mathrm{s}} \\quad$ if $\\varnothing>0.01$\\\\\nAs shown in Fig.", "start_char_idx": 379116, "end_char_idx": 382257, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "38565926-c2b0-494a-8e2a-0669cc77a642": {"__data__": {"id_": "38565926-c2b0-494a-8e2a-0669cc77a642", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "522dbe19-b359-4434-948c-5ddf4fafe7e3", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "322c1110f3932bc7019b0fe8e4ce94a1adc704b237f8111422894916b98b7b98", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "99e3df50-b0df-4aba-8ee2-5ddc21a001b6", "node_type": "1", "metadata": {}, "hash": "48261dea2e7f37a77ccacc2466e53b322f10fc0686f546fc6706590b2a288256", "class_name": "RelatedNodeInfo"}}, "text": "(2) [17]:\n\n$k_{\\text {contact }}=18 \\varnothing k_{s} \\quad$ if $\\varnothing<3 \\times 10^{-4} \\quad k_{\\text {contact }} \\approx k_{\\mathrm{s}} \\quad$ if $\\varnothing>0.01$\\\\\nAs shown in Fig. 4 (a), the plot depicts that there is a huge difference between the thermal conductivity of powder and bulk material and the thermal conductivity of the powder is approximately $1 \\%$ of bulk material.\n\nIn addition, Fig. 4 (b) demonstrates the difference between the density of bulk and powder material which can be calculated based on the porosity of powder bed using (Eq. (3)).\n\n$\\rho_{\\text {powder }}=(1-\\varphi) \\rho_{\\text {bulk }}$\n\nIn order to consider phase change from solid to liquid, apparent heat capacity method [18] is implemented (Eq. (4)):\n\n$C_{p}=\\left\\{\\begin{array}{ccccc}C_{p, \\text { sensible }} & \\text { if } & T<T_{m}-0.5 \\Delta T_{m} & \\text { or } & T>T_{m}+0.5 \\Delta T_{m} \\\\ C_{p, \\text { modified }}= & C_{p, \\text { sensible }}+\\frac{L}{\\Delta T_{m}} & \\text { if } & T_{m}-0.5 \\Delta T_{m}<T<T_{m}+0.5 \\Delta T_{m}\\end{array}\\right\\}$\n\nFig. 2 a Produced single tracks on printed substrates. b Schematic of printed single tracks and the substrate\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-04(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-04}\n\\end{center}\n\n(b) where $T_{m}$ is the melting temperature which is considered as the center point between solidus and liquidus temperature. $\\Delta T_{m}$ is the temperature difference between liquidus and solidus temperature and $L$ is the latent heat of fusion. As shown in Fig. 4 (c), in this method, the latent heat of fusion is compensated with increasing the specific heat between solidus and liquidus such that the extra heat absorbed by the material in this interval is equal to the latent heat of fusion. Therefore, within those ranges of temperatures, the specific heat will be increasing dramatically.\n\nIt needs to be mentioned that for simplicity and acceleration of computation, it is assumed that the absorption coefficient is not affected by phase change.\n\n\\subsection*{3.2 Governing equation and boundary conditions}\nGoverning equation of heat transfer can be described as [11]:\n\n$\\rho C_{p} \\frac{\\partial T}{\\partial t}=\\frac{\\partial}{\\partial x}\\left(k_{x} \\frac{\\partial T}{\\partial x}\\right)+\\frac{\\partial}{\\partial y}\\left(k_{y} \\frac{\\partial T}{\\partial y}\\right)+\\frac{\\partial}{\\partial z}\\left(k_{z} \\frac{\\partial T}{\\partial z}\\right)+Q$\n\nwhere $\\rho, C_{p}, k_{x}, k_{y}, k_{z}, T$, and $Q$ are the density of the material $\\left(\\mathrm{kg} / \\mathrm{m}^{3}\\right)$, specific heat $(\\mathrm{J} / \\mathrm{kgK})$, thermal conductivity $(\\mathrm{W} / \\mathrm{mK})$ of $x, y$, and $z$ directions, temperature $(\\mathrm{K})$ and internal heat generation $\\left(\\mathrm{W} / \\mathrm{m}^{3}\\right)$, respectively.\n\nIn terms of boundary conditions, the convective heat transfer with the ambient environment based on Newton's law was considered on all open surfaces (Eq. (6)).", "start_char_idx": 382066, "end_char_idx": 385143, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "99e3df50-b0df-4aba-8ee2-5ddc21a001b6": {"__data__": {"id_": "99e3df50-b0df-4aba-8ee2-5ddc21a001b6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "38565926-c2b0-494a-8e2a-0669cc77a642", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ec4294193d5eba08b327ef94b2f555175f78359becdc665928fc13cff9208df2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "38e6df23-84ff-4abf-9692-1a4d15b2b5a9", "node_type": "1", "metadata": {}, "hash": "d2b56284b0f6d72341fd2811aeb2210c9dc9326d301225e82525c409bb0e3859", "class_name": "RelatedNodeInfo"}}, "text": "In terms of boundary conditions, the convective heat transfer with the ambient environment based on Newton's law was considered on all open surfaces (Eq. (6)).\n\n$q_{c}=h_{c}\\left(T_{\\text {ext }}-T\\right)$\\\\\nAbove, $q_{c}$ is the heat dissipation, $h_{c}$ is the heat transfer coefficient $\\left(\\mathrm{W} / \\mathrm{m}^{2} \\mathrm{~K}\\right), T_{\\text {ext }}$ is the geometry temperature, and $T$ is the ambient temperature (293 K).\n\nIn addition, the radiative heat transfer from the top surface of the geometry domain was applied (Eq. (7)). The bottom surface of the geometry domain was set as the ambient temperature (293 K).\n\n$q_{r}=\\sigma_{s b} \\varepsilon\\left(T_{\\text {ext }}{ }^{4}-T^{4}\\right)$\n\nAbove, $\\sigma_{s b}$ is the Stefan-Boltzmann coefficient $\\left(\\mathrm{W} / \\mathrm{m}^{2} \\mathrm{~K}^{4}\\right)$ and $\\varepsilon$ is the emissivity coefficient.\n\n\\subsection*{3.3 Heat source model calibration}\n\\subsection*{3.3.1 Heat source model}\nA moving heat source with a conical Gaussian shape was applied for predicting the melt pool dimensions and temperature distributions (Fig. 5). The conical Gaussian heat source is described as [11]:\n\n$I(x, y, z)=q_{0} \\cdot \\exp \\left(-2 \\frac{x^{2}+y^{2}}{r_{0}^{2}}\\right)$\n\n$r_{0}(z)=r_{e}+\\frac{z}{H}\\left(r_{e}-r_{i}\\right)$\n\nwhere $I(x, y, z), q_{0}, r_{e}$, and $r_{i}$ are the heat intensity distribution, the maximum value of heat intensity, and radius on top and bottom of the heat source profile, respectively.\\\\\nFig. 3 Simulated single-track model geometry and mesh\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-04(2)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-05(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-05(3)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-05}\n\\end{center}\n\n(c)\n\nFig. 4 Thermo-physical properties of bulk and powder material. a Thermal conductivity. b Density. c Specific heat\n\nBased on the thermal energy conservation (Eq. (10)):\n\n$\\alpha . P=\\int_{-H}^{0} \\int_{-\\infty}^{\\infty} \\int_{-\\infty}^{\\infty} q_{0} \\cdot \\exp \\left(-2 \\frac{x^{2}+y^{2}}{r_{0}^{2}}\\right) d x d y d z$\n\nwhere and $P$ are the laser beam absorptivity and laser power respectively.\n\n$q_{0}$ is derived from Eq. (10) and can be calculated Eq. (11):\n\n$q_{0}=\\frac{6 \\alpha \\cdot P}{\\pi H\\left(r_{e}^{2}+r_{e} r_{i}+r_{i}^{2}\\right)}$\n\nwhere $H$ is the height of the conical Gaussian heat source.\n\nBy substituting $q_{0}$ in Eq. (8) by Eq. (11), the final equation of the intensity distribution can be derived as follows (Eq. (12)):\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-05(2)}\n\\end{center}\n\nFig.", "start_char_idx": 384984, "end_char_idx": 387823, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "38e6df23-84ff-4abf-9692-1a4d15b2b5a9": {"__data__": {"id_": "38e6df23-84ff-4abf-9692-1a4d15b2b5a9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "99e3df50-b0df-4aba-8ee2-5ddc21a001b6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1b2a73fad1090198c5ecb6a08140d315431ff00277e77f1f046dc9499b93e2b3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "039ed095-e5d8-4e76-9121-f38127c3a4e2", "node_type": "1", "metadata": {}, "hash": "3104e060952f5333bc8c0f700995c85c1bdc09e9943c8291a65a88e008ff520d", "class_name": "RelatedNodeInfo"}}, "text": "$q_{0}$ is derived from Eq. (10) and can be calculated Eq. (11):\n\n$q_{0}=\\frac{6 \\alpha \\cdot P}{\\pi H\\left(r_{e}^{2}+r_{e} r_{i}+r_{i}^{2}\\right)}$\n\nwhere $H$ is the height of the conical Gaussian heat source.\n\nBy substituting $q_{0}$ in Eq. (8) by Eq. (11), the final equation of the intensity distribution can be derived as follows (Eq. (12)):\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-05(2)}\n\\end{center}\n\nFig. 5 Conical Gaussian volumetric heat source $I(x, y, z)=\\frac{6 \\alpha \\cdot P}{\\pi H\\left(r_{e}^{2}+r_{e} r_{i}+r_{i}^{2}\\right)} \\cdot \\exp \\left(-2 \\frac{x^{2}+y^{2}}{r_{0}^{2}}\\right)$\n\nwhere $H$ is the height of the conical Gaussian heat source.\n\nThe internal heat generated as a result of the heat input and losses is plugged into Eq. 5.\n\n\\subsection*{3.3.2 Calibration procedure}\nIn order to calibrate the numerical model, the heat source parameters such as height $(H)$ and absorption coefficient $(\\alpha)$ are altered to minimize the error between the experimental and simulated melt pool dimensions. Since the upper radius of the conical Gaussian heat source $\\left(r_{e}\\right)$ is the radius of laser spot size $(50 \\mu \\mathrm{m})$, the bottom radius of the heat source has a limited range to be varied. In addition, based on Eq. (11) and the calibration iteration, it is found that a lower radius of heat source $r_{i}$ does not have a significant influence on the melt pool depth where it has a slight effect on melt pool width, so it has been fixed in the chosen value $(30 \\mu \\mathrm{m})$. It is also noted that the height of the conical Gaussian heat source $(H)$ is the most important parameter and numerical results show that as the height of the heat source is increased, the width of the melt pool decreases. In order to compensate for the reduction in melt pool width, the absorption coefficient has been modified for acquiring more accurate melt pool shapes. It is realized that the absorption coefficient has a significant effect on the melt pool width and depth at the same time.\n\nFigure 6 demonstrates a flow chart of the procedure implemented for calibrating heat source model, where $W_{e x}, W_{\\text {sim }}$, $D_{e x}$, and $D_{\\text {sim }}$ are the experimental melt pool width, predicted melt pool width, experimental melt pool depth, and predicted melt pool depth, respectively. The maximum acceptable deviation of model predictions for the melt pool width and height is identified as $\\varepsilon_{1}$ and $\\varepsilon_{2}$ respectively. As the flow chart shows, in the first step, the initial values of the height of the heat source and absorption coefficient are selected and based on those values numerical simulation was carried out. Due to the complexity of the laser powder-bed fusion process,\n\nFig. 6 Flow chart showing the calibration procedure for the heat source\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-06}\n\\end{center}\n\nresearchers use a lot of underlying assumptions to capture the model accurately $[19,20]$. As a result, numerical results have some deviations from experimental and the current studies show a $\\pm 30 \\%$ as a fair and acceptable range [21,22]. By comparing the experimental and numerical results of melt pool depth and width, the values of the absorption coefficient and height of heat source are modified such that the difference between the numerical with experimental ones is within an acceptable range.\n\n\\section*{4 Results and discussion}\n\\subsection*{4.1 Experimental measurements of the melt pool, calibration, and validation results}\nBased on Section 3.3, the heat source model was calibrated using the power and scanning speed values listed in Table 2.\n\nValidation of the melt pool dimensions with experimental measurements is done in such a way that melt pool depth and width below the powder layer are compared with experimental results $[6,11]$.", "start_char_idx": 387363, "end_char_idx": 391297, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "039ed095-e5d8-4e76-9121-f38127c3a4e2": {"__data__": {"id_": "039ed095-e5d8-4e76-9121-f38127c3a4e2", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "38e6df23-84ff-4abf-9692-1a4d15b2b5a9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "11f1b246333989d033bdbc4ad5d38d7a7df54139f22e4efc1709af12768408ca", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fcd12280-1770-4699-bc80-26f7d50131ab", "node_type": "1", "metadata": {}, "hash": "0fcb8ac2391134c591b11acb2806a0f85d763615398acf175a8fa6442f05e6f2", "class_name": "RelatedNodeInfo"}}, "text": "As a result, numerical results have some deviations from experimental and the current studies show a $\\pm 30 \\%$ as a fair and acceptable range [21,22]. By comparing the experimental and numerical results of melt pool depth and width, the values of the absorption coefficient and height of heat source are modified such that the difference between the numerical with experimental ones is within an acceptable range.\n\n\\section*{4 Results and discussion}\n\\subsection*{4.1 Experimental measurements of the melt pool, calibration, and validation results}\nBased on Section 3.3, the heat source model was calibrated using the power and scanning speed values listed in Table 2.\n\nValidation of the melt pool dimensions with experimental measurements is done in such a way that melt pool depth and width below the powder layer are compared with experimental results $[6,11]$. Evaporation and shrinkage of the powder layer are ignored due to modeling complexities.\n\nFigure 7 illustrates that the experimentally measured melt pool geometries are in good agreement with the numerical results. The average percentage differences between the simulation results and experimental ones for the melt pool depth and width are $13 \\%$ and $6 \\%$, respectively.\n\nThe melt pool dimensions can be represented as a function of deposited energy density for various process parameters based on the findings in [23]. It has been reported that the absorbed energy density has a relationship with the ratio of the laser power to the root square of scanning speed $\\left(\\frac{P}{\\sqrt{V}}\\right)$, where $P$ is the laser power and $V$ is the scanning speed [11].\n\nIt is realized that the absorption coefficient and height of conical Gaussian heat source has a linear relationship with the $\\frac{P}{\\sqrt{V}}$. The physical reason behind this is due to the fact that as the energy density increases, melt pool depth becomes larger due to higher heat penetration to the powder-bed. On the other hand, by increasing the energy density, the material tends to absorb more energy [24]. Therefore, the absorption coefficient and the height of conical Gaussian heat source should be adapted based on the $\\frac{P}{\\sqrt{V}}$. As a result, a higher $\\frac{P}{\\sqrt{V}}$ will cause a higher absorption coefficient and a larger height of the conical Gaussian heat source.\n\nEmpirical equations (Eqs. (13) and (14)) show the relationship between the $\\frac{P}{\\sqrt{V}}$, height of conical Gaussian heat source and absorption coefficient which were derived based on the calibration of the heat source with experimental results. It should be mentioned that this empirical equation would be valid for the energy density within the range of 4.74 to 7.90 $(\\mathrm{W} / \\sqrt{\\mathrm{mm} / \\mathrm{s}})$ which falls within the conduction mode of the melt pool and ensures near full dense parts.\n\n$\\alpha=a_{1} \\frac{P}{\\sqrt{V}}+b_{1}$\n\n$H=a_{2} \\frac{P}{\\sqrt{V}}+b_{2}$\n\nwhere $P[W], V\\left[\\frac{\\mathrm{mm}}{\\mathrm{s}}\\right], H[\\mu \\mathrm{m}]$ and are the laser power, scanning speed, the height of the conical Gaussian heat source and the absorption coefficient, respectively. In addition, $a_{1}, a_{2}, b_{1}$,\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e4cf3633ae941c3dd044g-07(2)}\n\n(a)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e4cf3633ae941c3dd044g-07(1)}\n\n(b)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e4cf3633ae941c3dd044g-07}\n\n(c)\n\nFig. 7 Experimental and numerical results of melt pool geometries with various process parameters.", "start_char_idx": 390431, "end_char_idx": 393985, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fcd12280-1770-4699-bc80-26f7d50131ab": {"__data__": {"id_": "fcd12280-1770-4699-bc80-26f7d50131ab", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "039ed095-e5d8-4e76-9121-f38127c3a4e2", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8719e7016551f814952c9f199ddb1aea230d8216eba54694037866174a4d3d15", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "5ccd6ba0-3b13-4f1b-835b-c24878f441ff", "node_type": "1", "metadata": {}, "hash": "378d31b6a716d50134a499f35e70af81f14515e7668a97784fd94c2a880bcc75", "class_name": "RelatedNodeInfo"}}, "text": "In addition, $a_{1}, a_{2}, b_{1}$,\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e4cf3633ae941c3dd044g-07(2)}\n\n(a)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e4cf3633ae941c3dd044g-07(1)}\n\n(b)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_e4cf3633ae941c3dd044g-07}\n\n(c)\n\nFig. 7 Experimental and numerical results of melt pool geometries with various process parameters. a Power: 150 W. b Power: 200 W. c Power: 250 W\n\nTable 3 The coefficient in the empirical equation for deriving absorption coefficient and height of heat source\n\n\\begin{center}\n\\begin{tabular}{llll}\n\\hline\n$a_{1}$ & $b_{1}$ & $a_{2}$ & $b_{2}$ \\\\\n\\hline\n0.126 & -0.297 & 15.82 & -24.99 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nand $b_{2}$ are parameters which will be established by experimental results (Table 3).\n\nThe porosity of the powder and the convection heat transfer of the melt pool have a significant increase in heat penetration to the powder bed. By doing the calibration procedure the height of the conical Gaussian heat source have been found to be in the range of 50 to $100 \\mu \\mathrm{m}$ for the energy density range of 4.74 to $7.90(\\mathrm{~W} / \\sqrt{\\mathrm{mm} / \\mathrm{s}})$.\n\n\\subsection*{4.2 Effect of process parameters on melt pool dimensions}\nExperimental single tracks with the various range of laser scanning speeds and power were printed, cross-sectioned and polished to measure the melt pool depth and width.\n\nThe results show that by increasing the laser power from $150 \\mathrm{~W}$ to $250 \\mathrm{~W}$ while keeping other process parameters constant, the depth and width of the melt pool will also elevate, whereas increasing the scanning speed from 800 to $1300 \\mathrm{~mm} / \\mathrm{s}$ will cause a decrease in the melt pool dimensions. Figure 8 (a) shows that with the increasing laser power from $150 \\mathrm{~W}$ to $250 \\mathrm{~W}$, the depth and width of the melt pool will increase from 26 to $82 \\mu \\mathrm{m}$ and 88 to $129 \\mu \\mathrm{m}$, respectively. Figure 8 (b) demonstrates the effect of scanning speed on melt pool dimensions. With increasing scanning speed from 800 to $1300 \\mathrm{~mm} / \\mathrm{s}$, the melt pool depth and width will decrease from 72 to $34 \\mu \\mathrm{m}$ and 127 to $90 \\mu \\mathrm{m}$, respectively. This phenomenon happens due to a changing energy density, which is fluxing into the material. Therefore, as mentioned previously, higher laser power and a lower scanning speed will result in a higher energy density, which is absorbed by the material;\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-08(1)}\n\\end{center}\n\nFig. 9 Influence of energy density on melt pool depth and width\n\nconsequently, the melt pool geometries including the melt pool depth and width will be increasing. The same scenario will also happen when a lower energy density is given to the material. Therefore, a lower $\\frac{P}{\\sqrt{V}}$ will cause smaller melt pool dimensions. Figure 9 shows the effect of $\\frac{P}{\\sqrt{V}}$ on the melt pool dimensions. It is found that increasing the $\\frac{P}{\\sqrt{V}}$ from 4.74 to 7.9 $(\\mathrm{W} / \\sqrt{\\mathrm{mm} / \\mathrm{s}})$, the melt pool depth and width will increase from 26 to $82 \\mu \\mathrm{m}$ and 88 to $129 \\mu \\mathrm{m}$, respectively.\n\nExperimental results demonstrate that increasing scanning speed from 800 to $1300 \\mathrm{~mm} / \\mathrm{s}$ will lead to a reduction in the melt pool depth by $52 \\%$.", "start_char_idx": 393571, "end_char_idx": 397052, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "5ccd6ba0-3b13-4f1b-835b-c24878f441ff": {"__data__": {"id_": "5ccd6ba0-3b13-4f1b-835b-c24878f441ff", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fcd12280-1770-4699-bc80-26f7d50131ab", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "668e4f112174e6518480eb29acf80292d5e7cdc238fd035c233fb4e5ccac53c0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9bfaf6f9-5fa7-449b-b76c-cc6ff962cd3c", "node_type": "1", "metadata": {}, "hash": "562a0363e38a8b5772d3d65de03758c204fc6d7ff57ea73f42a64545ec8c5f39", "class_name": "RelatedNodeInfo"}}, "text": "The same scenario will also happen when a lower energy density is given to the material. Therefore, a lower $\\frac{P}{\\sqrt{V}}$ will cause smaller melt pool dimensions. Figure 9 shows the effect of $\\frac{P}{\\sqrt{V}}$ on the melt pool dimensions. It is found that increasing the $\\frac{P}{\\sqrt{V}}$ from 4.74 to 7.9 $(\\mathrm{W} / \\sqrt{\\mathrm{mm} / \\mathrm{s}})$, the melt pool depth and width will increase from 26 to $82 \\mu \\mathrm{m}$ and 88 to $129 \\mu \\mathrm{m}$, respectively.\n\nExperimental results demonstrate that increasing scanning speed from 800 to $1300 \\mathrm{~mm} / \\mathrm{s}$ will lead to a reduction in the melt pool depth by $52 \\%$. On the other hand, decreasing the laser power from $250[\\mathrm{~W}]$ to 150 [W] causes a reduction in the melt pool depth up to $68 \\%$. Therefore, it can be concluded that the laser power has a stronger influence on the melt pool dimensions compared to the laser scanning speed [25].\n\n\\subsection*{4.3 Temperature distribution}\nIn order to derive temperature distribution along the $X$ - and $Y$ axis of the melt pool, two paths have been identified on the top\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-08}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-08(2)}\n\\end{center}\n\n(b)\n\nFig. 8 a Effect of laser power on melt pool depth and width. b Effect of scanning speed on melt pool depth and width\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-09(2)}\n\\end{center}\n\nFig. 10 Top view of moving laser heat source with identifying two paths along with $\\mathrm{X}$ and $\\mathrm{Y}$ directions\n\nof the powder surface where the laser heat source is applied (Fig. 10). Figure 11 demonstrates the effect of different scanning speed on the temperature distribution. By increasing the scanning speed from 1000 to $1600 \\mathrm{~mm} / \\mathrm{s}$, the laser energy input to the material will be decreased, which results in decreasing the peak temperatures. On the other hand, the temperature distribution in the $\\mathrm{X}$ direction illustrates that the maximum temperature occurs in the melt pool front. In addition, the temperature distribution along $Y$-axis clearly shows the Gaussian distribution of laser heat source.\n\n\\subsection*{4.4 Temperature gradient}\nDue to the fast solidification within LPBF [26], the temperature gradient and cooling rates play a crucial role in predicting the microstructure, grain orientation, and growth within the melt pool. In order to extract temperature history from the numerical results, several points were set in the $z$-axis from the top of the powder layer towards the bulk material at $5 \\mu \\mathrm{m}$ intervals as shown in Fig. 12.\n\nFor obtaining temperature gradient within the melt pool at the specific time from $20 \\mu \\mathrm{m}$ under the surface of powder $(Z=20 \\mu \\mathrm{m})$ to $150 \\mu \\mathrm{m}$ below the surface, the temperature distributions along the $\\mathrm{Z}$ direction for different scanning speeds are extracted. Figure 13 (a) shows that the temperature will drop from the powder to the bulk material due to the higher thermal conductivity of the bulk region compared to the powder material. Moreover, the heat source is decaying linearly along the $\\mathrm{Z}$ direction. The results show that a higher scanning speed leads to a reduction in the temperature gradient within the melt pool. This could be due to providing less energy density input to the material so that the peak transient temperature will decrease. As a result, the temperature difference from the top to the bottom surface will be decreasing which means that by increasing the scanning speed, the temperature gradient will be reduced.", "start_char_idx": 396393, "end_char_idx": 400170, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9bfaf6f9-5fa7-449b-b76c-cc6ff962cd3c": {"__data__": {"id_": "9bfaf6f9-5fa7-449b-b76c-cc6ff962cd3c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "5ccd6ba0-3b13-4f1b-835b-c24878f441ff", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3abcc26be61902d9a76a63dc166ab42da5f7043e977ba25944c78208f5d41f4c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ba7b83ce-1225-4d69-b2d1-79a620d520c8", "node_type": "1", "metadata": {}, "hash": "edf342011011cb352ee3573451ac67bc97eea70e4eb121fb25690e8d2bf2b700", "class_name": "RelatedNodeInfo"}}, "text": "Figure 13 (a) shows that the temperature will drop from the powder to the bulk material due to the higher thermal conductivity of the bulk region compared to the powder material. Moreover, the heat source is decaying linearly along the $\\mathrm{Z}$ direction. The results show that a higher scanning speed leads to a reduction in the temperature gradient within the melt pool. This could be due to providing less energy density input to the material so that the peak transient temperature will decrease. As a result, the temperature difference from the top to the bottom surface will be decreasing which means that by increasing the scanning speed, the temperature gradient will be reduced. In addition, it has been found that the maximum temperature gradient for different scanning speeds, $1000 \\mathrm{~mm} / \\mathrm{s}, 1200 \\mathrm{~mm} / \\mathrm{s}, 1600 \\mathrm{~mm} / \\mathrm{s}$ is $69 \\mathrm{~K} / \\mu \\mathrm{m}, 63 \\mathrm{~K} / \\mu \\mathrm{m}$, and $52 \\mathrm{~K} / \\mu \\mathrm{m}$, respectively, which has occurred at $52 \\mu \\mathrm{m}$ below the powder surface, close to the interface of solid and liquid phase within the melt pool (Fig. 13 (b)).\n\n\\subsection*{4.5 Cooling rate}\nFigure 14 shows the effect of laser scanning speed on the transient temperature corresponding to different points within the melt pool. Increasing the scanning speed leads to the less amount of energy density that fluxes to the material. Therefore, peak temperatures will be decreasing by increasing the scanning speed. On the other hand, by moving down from the powder to the bulk material along the $\\mathrm{Z}$ direction, the temperature peak will be reduced. This is happening firstly because the conical Gaussian heat source is decaying linearly\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-09(1)}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-09}\n\\end{center}\n\n(b)\n\nFig. 11 Effect of laser scanning speed on temperature distribution $\\mathbf{a}$ along $\\mathrm{X}$ direction and $\\mathbf{b}$ along the $\\mathrm{Y}$ direction\n\nFig. 12 Probes along melt pool depth and model predicted the temperature distribution in melt pool cross-section normal to the laser movement direction\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-10(2)}\n\\end{center}\n\nalong the $\\mathrm{Z}$ direction. Secondly, moving from the powder to the bulk material, the heat conductivity will increase drastically such that heat will dissipate more in the bulk regions, which causes the cooling rate to increase. Figure 14 depicts slope changing when the temperature is below the melting point due to the phase change. In addition, the cooling rate has been derived from different points, which are located within the melt pool and the effect of laser power on the cooling rate is investigated (Fig. 15). It has been found that by increasing the laser power, the cooling rate will be increased. It is attributed to the fact that as the laser power is increased, a higher energy density is given to the material so that the peak transient temperature will be increasing. Therefore, the maximum cooling rate will be increased due to drastically decreasing temperatures. The results illustrate that the maximum cooling rate for a different range of laser power, $150 \\mathrm{~W}, 200 \\mathrm{~W}$, and $250 \\mathrm{~W}$ is $1.7 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}, 2.5 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}$, and $3.1 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}$ which occurs at the top surface of melt pool $(Z=20 \\mu \\mathrm{m})$.", "start_char_idx": 399480, "end_char_idx": 403124, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ba7b83ce-1225-4d69-b2d1-79a620d520c8": {"__data__": {"id_": "ba7b83ce-1225-4d69-b2d1-79a620d520c8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9bfaf6f9-5fa7-449b-b76c-cc6ff962cd3c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "153d2d8381c702c7a587476735e8a08c5b6b63cf17abe54dd33e9b2eb385a9c0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "750c3112-6959-4ecd-a0d8-906f3544bdef", "node_type": "1", "metadata": {}, "hash": "29ffe99a36675e560bb1a9682bb8badfd670f0c320ca5fbbde7ab1f27e1aca4b", "class_name": "RelatedNodeInfo"}}, "text": "It is attributed to the fact that as the laser power is increased, a higher energy density is given to the material so that the peak transient temperature will be increasing. Therefore, the maximum cooling rate will be increased due to drastically decreasing temperatures. The results illustrate that the maximum cooling rate for a different range of laser power, $150 \\mathrm{~W}, 200 \\mathrm{~W}$, and $250 \\mathrm{~W}$ is $1.7 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}, 2.5 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}$, and $3.1 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}$ which occurs at the top surface of melt pool $(Z=20 \\mu \\mathrm{m})$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-10}\n\\end{center}\n\n(a)\n\n\\subsection*{4.6 Experimental validation of cooling rate and predicting primary dendrite spacing}\nFigure 16 (a) displays the simulated melt pool temperature distribution of a produced single track using the laser power of $200 \\mathrm{~W}$, the scan speed of $1000 \\mathrm{~mm} / \\mathrm{s}$, and the layer thickness of $20 \\mu \\mathrm{m}$ with four points located in the middle of the melt pool with different depths from the surface of the substrate. Figure 16 (b, c) shows low and high magnification SEM images from a cross-sectioned single track. The cellular structure of the solidified material is also shown in Fig. 16 (c) where primary cell spacing was measured to be around $320 \\mathrm{~nm}$. These fine features in the microstructure are a result of the rapid solidification of molten metal during LPBF [27-29]. It is well known that higher cooling rates significantly reduce the feature size of the solidified microstructure. Here in the LPBF, both the high-temperature gradient and solidification rate result in outstandingly high cooling rates $[27,30]$.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-10(1)}\n\\end{center}\n\n(b)\n\nFig. 13 a Temperature distribution along build direction. b Temperature gradient within the melt pool\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-11}\n\\end{center}\n\nFig. 14 The model-predicted temperature history of probes from powder to the bulk region with fixed laser power of $150 \\mathrm{~W}$ and different laser scanning speed of $1000 \\mathrm{~mm} / \\mathrm{s}, 1200 \\mathrm{~mm} / \\mathrm{s}$, and $1600 \\mathrm{~mm} / \\mathrm{s}$\n\nPrimary spacing $\\left(\\lambda_{1}\\right)$ of either cells or dendrites in the microstructure of Ni-base superalloys is directly related to the cooling rate with an empirical Eq. (15) reported by [30]:\n\n$\\lambda_{1}=97(\\dot{T})^{-0.36}$\n\nwhere $\\dot{T}$ is the cooling rate of the interface of solid/liquid during solidification. Considering the average $\\lambda_{1}$ to be around $0.32 \\mu \\mathrm{m}$ (Fig. 16 (c)), the cooling rate can be calculated $\\left(\\sim 7.82 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}\\right)$. On the other hand, a maximum value for the cooling rate related to the probe in the same location of the melt pool has been calculated to be around $\\sim 8.82 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}$ which is very close to the calculated cooling rate with an estimated dendrite spacing of $0.32 \\mu \\mathrm{m}$. A detailed effect of energy density on primary dendrite spacing is demonstrated in Fig. 17. It is found that simulation results are very close to experimental ones for different process parameters and predict\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-11(1)}\n\\end{center}\n\nFig.", "start_char_idx": 402491, "end_char_idx": 406053, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "750c3112-6959-4ecd-a0d8-906f3544bdef": {"__data__": {"id_": "750c3112-6959-4ecd-a0d8-906f3544bdef", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ba7b83ce-1225-4d69-b2d1-79a620d520c8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b1f5bed3ce9be0192e68aeeb733dfd9803aa2be58648fc726845f7f82ca9fa83", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a6aeeeab-5985-461a-ab42-7c93dc84dbb4", "node_type": "1", "metadata": {}, "hash": "3e7c5aeb886793bc97e3219b9c30cbda29a8f43c27b3b1b706be83b8fe13d1fe", "class_name": "RelatedNodeInfo"}}, "text": "On the other hand, a maximum value for the cooling rate related to the probe in the same location of the melt pool has been calculated to be around $\\sim 8.82 \\times 10^{6} \\mathrm{~K} / \\mathrm{s}$ which is very close to the calculated cooling rate with an estimated dendrite spacing of $0.32 \\mu \\mathrm{m}$. A detailed effect of energy density on primary dendrite spacing is demonstrated in Fig. 17. It is found that simulation results are very close to experimental ones for different process parameters and predict\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-11(1)}\n\\end{center}\n\nFig. 15 Model-predicted cooling rate for different probes within melt pool with fixed scanning speed $1000 \\mathrm{~mm} / \\mathrm{s}$ and varying laser power of $150 \\mathrm{~W}, 200 \\mathrm{~W}$, and $250 \\mathrm{~W}$ dendrite spacing accurately. Increasing the energy density leads to higher cooling rates which cause smaller primary dendrite spacing. Since the SEM images extracted from each grain may be observed from the projection of the image derived from different cutting planes, there were some variations of primary dendrite spacing for each specimen. However, the simulation results were within the range of experimental results.\n\nSensitivity analysis on heat source parameter and absorption coefficient is done for confirming the fact that selecting the most optimum parameters for the Conical Gaussian heat source and absorption coefficient results in a more accurate prediction of cooling rate and cell space. These results confirm the strength and accuracy of the model.\n\nThe sensitivity plot for various heat source parameters on the cooling rate with a fixed process parameter of laser power of $150 \\mathrm{~W}$ and scanning speed of $1000 \\mathrm{~mm} / \\mathrm{s}$ at the interface of solidus and liquidus $(Z=40 \\mu \\mathrm{m})$ is shown in Fig. 18. It clearly shows that with implementing a height of $50 \\mu \\mathrm{m}$ and the absorption coefficient of 0.3 , the cooling rate is $8.7 \\times 10^{6} \\mathrm{~K} /$ $\\mathrm{s}$ which is comparable to the experimental results derived from Eq. (15). On the other hand, changing the height or the absorption coefficient results in larger errors. Therefore, it can be concluded that by implementing the calibrated heat source model, the numerical results will predict the microstructure within the melt pool more precisely.\n\n\\section*{5 Conclusions}\nIn this work, experimental and numerical investigations of single tracks of Hastelloy X made by LPBF were carried out and the melt pool dimensional features were measured experimentally. The main conclusions can be summarized as follows:\n\n\\begin{enumerate}\n  \\item Based on the experimental results, the heat source model was calibrated and the proposal empirical equations show the relationship between the energy density $\\left(\\alpha=a_{1} \\frac{P}{\\sqrt{V}}+b_{1}, H=a_{2} \\frac{P}{\\sqrt{V}}+b_{2}\\right)$, the height of the heat source and the absorption coefficient. However, these empirical equations are only valid for the specific range of energy density which provides conduction mode of the melt pool.\n\n  \\item The simulated results for the melt pool dimensions show a good agreement with the experimental data. The percentage difference between the simulated and experimental melt pool depth and width results is around $13 \\%$ and $6 \\%$, respectively.\n\n\\end{enumerate}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-12}\n\\end{center}\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-12(3)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-12(1)}\n\\end{center}\n\n(c)\n\nFig. 16 a Simulated temperature distribution in the melt pool area, $\\mathbf{b}$ low magnification, and $\\mathbf{c}$ high magnification SEM image from a cross-section of single track deposited by laser power of $200 \\mathrm{~W}$ and scanning speed of $1000 \\mathrm{~mm} / \\mathrm{s}$\n\nFig.", "start_char_idx": 405420, "end_char_idx": 409478, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a6aeeeab-5985-461a-ab42-7c93dc84dbb4": {"__data__": {"id_": "a6aeeeab-5985-461a-ab42-7c93dc84dbb4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "750c3112-6959-4ecd-a0d8-906f3544bdef", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "2b042e35874c0a0fe98e1ba901e9e8db4a2f72d9d4e1ce8f125da08e3c6e67ec", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fcba859d-fe9e-4652-8622-4ed6113d1ab4", "node_type": "1", "metadata": {}, "hash": "455404f644ea9890da3dfc338ada53b04f328384c46ac8241283db3449f3b4a2", "class_name": "RelatedNodeInfo"}}, "text": "16 a Simulated temperature distribution in the melt pool area, $\\mathbf{b}$ low magnification, and $\\mathbf{c}$ high magnification SEM image from a cross-section of single track deposited by laser power of $200 \\mathrm{~W}$ and scanning speed of $1000 \\mathrm{~mm} / \\mathrm{s}$\n\nFig. 17 Effect of energy density on the primary dendrite spacing\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-12(2)}\n\\end{center}\n\n\\begin{enumerate}\n  \\setcounter{enumi}{2}\n  \\item The influence of laser power and scanning speed on the melt pool depth and width was investigated. By decreasing the laser power from $250 \\mathrm{~W}$ to $150 \\mathrm{~W}$ in fixed\n\\end{enumerate}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_e4cf3633ae941c3dd044g-12(4)}\n\\end{center}\n\nFig. 18 Sensitivity plot of heat source parameter on cooling rate with a laser power of $150 \\mathrm{~W}$ and scanning speed of $1000 \\mathrm{~mm} / \\mathrm{s}$ scanning speed $(1000 \\mathrm{~mm} / \\mathrm{s})$, the melt pool depth and width decrease $68 \\%$ ( 82 to $26 \\mu \\mathrm{m}$ ) and $32 \\%$ (129 to $88 \\mu \\mathrm{m}$ ), respectively. On the other hand, by increasing the laser scanning speed from 800 to $1300 \\mathrm{~mm} / \\mathrm{s}$ in fixed laser power $(200 \\mathrm{~W})$, the melt pool depth and width reduce $53 \\%$ ( 72 to $34 \\mu \\mathrm{m}$ ) and 29\\% (127 to $90 \\mu \\mathrm{m}$ ), respectively. It is concluded that the effect of laser power on the melt pool geometry is more dominant than the scanning speed.\n\n\\begin{enumerate}\n  \\setcounter{enumi}{3}\n  \\item It is found that the cooling rate increases with increasing laser power. The results illustrate that the maximum cooling rate is $3.1 \\times 10^{7} \\mathrm{~K} / \\mathrm{s}$ corresponding to a laser power of $250 \\mathrm{~W}$ which occurs at the top surface of the melt pool.\n\n  \\item On the other hand, with increasing the scanning speed, the temperature gradient decreases significantly. Moreover, the maximum temperature gradient $69 \\mathrm{~K} / \\mu \\mathrm{m}$ is achieved by implementing the scanning speed of $1000 \\mathrm{~mm} / \\mathrm{s}$ which occurs at $52 \\mu \\mathrm{m}$ below the powder surface, close to the interface of solid and liquid phase within the melt pool.\n\n  \\item The effect of energy density on the primary cell spacing is also studied and numerical results of cooling rates validated with experimental results. The results show that dendrite cell spacing decreased from 0.365 to $0.330 \\mu \\mathrm{m}$ by increasing energy density from 4.74 to 7.22 $(W / \\sqrt{m m / s})$.\n\n  \\item The sensitivity analysis is also carried out which indicates that by implementing the calibrated heat source model, the cooling rate and estimated primary dendrite spacing are predicted more precisely.\n\n\\end{enumerate}\n\nAcknowledgments The authors would like to appreciate the Federal Economic Development Agency for Southern Ontario (FedDev Ontario), Natural Sciences and Engineering Research Council of Canada (NSERC), and Siemens Canada Limited, for supporting financially. In addition, special thanks to Jerry Ratthapakdee and Karl Rautenberg for assisting in preparing the LPBF setup and printing the samples, National Research Council Canada (NRC) and Adhitan Rani Kasinathan for their contributions to the LPBF modeling.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item Stavropoulos P, Foteinopoulos P (2018) Modelling of additive manufacturing processes: a review and classi fi cation. Manuf Rev 2\n\n  \\item Fayazfar $\\mathrm{H}$ et al (2018) A critical review of powder-based additive manufacturing of ferrous alloys: process parameters, microstructure and mechanical properties.", "start_char_idx": 409194, "end_char_idx": 412890, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fcba859d-fe9e-4652-8622-4ed6113d1ab4": {"__data__": {"id_": "fcba859d-fe9e-4652-8622-4ed6113d1ab4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a6aeeeab-5985-461a-ab42-7c93dc84dbb4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4e3a82e969d189c2d22331ed87d39468f2d458ff1f25767f06a3d2213a986e60", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "6442fbd3-6e94-48d1-8875-e1eb9cdd3c5d", "node_type": "1", "metadata": {}, "hash": "8eae8a82f9770bfdcf18e2ce46c2aaaa3cb614e6cb47f9938e4ddf760d9adb6c", "class_name": "RelatedNodeInfo"}}, "text": "\\end{enumerate}\n\nAcknowledgments The authors would like to appreciate the Federal Economic Development Agency for Southern Ontario (FedDev Ontario), Natural Sciences and Engineering Research Council of Canada (NSERC), and Siemens Canada Limited, for supporting financially. In addition, special thanks to Jerry Ratthapakdee and Karl Rautenberg for assisting in preparing the LPBF setup and printing the samples, National Research Council Canada (NRC) and Adhitan Rani Kasinathan for their contributions to the LPBF modeling.\n\n\\section*{References}\n\\begin{enumerate}\n  \\item Stavropoulos P, Foteinopoulos P (2018) Modelling of additive manufacturing processes: a review and classi fi cation. Manuf Rev 2\n\n  \\item Fayazfar $\\mathrm{H}$ et al (2018) A critical review of powder-based additive manufacturing of ferrous alloys: process parameters, microstructure and mechanical properties. Mater Des 144:98-128\n\n  \\item Chiumenti M et al (2017) Numerical modelling and experimental validation in selective laser melting. Addit Manuf 18:171-185\n\n  \\item Luo C, Qiu J, Yan Y, Yang J, Uher C, Tang X (2018) Finite element analysis of temperature and stress fields during the selective laser melting process of thermoelectric SnTe. J Mater Process Technol 261(June):74-85\n\n  \\item Peng $\\mathrm{H}$ et al (2018) Fast prediction of thermal distortion in metal powder bed fusion additive manufacturing: part 2 , a quasi-static thermo-mechanical model. Addit Manuf 22(2010):869-882\n\n  \\item Kundakc E et al (2018) Thermal and molten pool model in selective laser melting process of Inconel 625. Int J Adv Manuf Technol\n\n  \\item Liu S, Zhu H, Peng G, Yin J, Zeng X (2018) Microstructure prediction of selective laser melting AlSi10Mg using finite element analysis. Mater Des 142:319-328\n\n  \\item Antony K, Arivazhagan N, Senthilkumaran K (2014) Numerical and experimental investigations on laser melting of stainless steel 316L metal powders. J Manuf Process 16(3):345-355\n\n  \\item H. Ali, H. Ghadbeigi, and K. Mumtaz, \"Residual stress development in selective laser-melted Ti6A14V: a parametric thermal modelling approach\" 2018\n\n  \\item Du Y, You X, Qiao F, Guo L, Liu Z (2019) A model for predicting the temperature field during selective laser melting. Results Phys 12(November 2018):52-60\n\n  \\item Zhang $\\mathrm{Z}$ et al (2019) 3-dimensional heat transfer modeling for laser powder-bed fusion additive manufacturing with volumetric heat sources based on varied thermal conductivity and absorptivity. Opt Laser Technol 109:297-312\n\n  \\item Wu CS, Wang HG, Zhang YM (2006) A new heat source model for keyhole plasma arc welding in FEM analysis of the temperature profile. Weld J 85(12):284\n\n  \\item Bonakdar A, Molavi-Zarandi M, Chamanfar A, Jahazi M, Firoozrai A, Morin E (2017) Finite element modeling of the electron beam welding of Inconel-713LC gas turbine blades. J Manuf Process 26: 339-354\n\n  \\item EOS GmbH - Electro Optical Systems (2015) Material data sheet EOS NickelAlloy HX Material data sheet Technical data\n\n  \\item Esmaeilizadeh R, Ali U, Keshavarzkermani A, Mahmoodkhani Y, Marzbanrad E, Toyserkani E (2019) On the effect of spatter particles distribution on the quality of Hastelloy X parts made by laser powder-bed fusion additive manufacturing. J Manuf Process 37(November 2018):11-20\n\n  \\item Ali U et al (2018) On the measurement of relative powder-bed compaction density in powder-bed additive manufacturing processes. J Mater Des\n\n  \\item Sih SS, Barlow JW (2004) The prediction of the emissivity and thermal conductivity of powder beds.", "start_char_idx": 412006, "end_char_idx": 415559, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "6442fbd3-6e94-48d1-8875-e1eb9cdd3c5d": {"__data__": {"id_": "6442fbd3-6e94-48d1-8875-e1eb9cdd3c5d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fcba859d-fe9e-4652-8622-4ed6113d1ab4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "97ea7db48b1b7cb4268a4fc3901878ca14ddf7d658d570e51064c3953ddaa4a6", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "500f9f93-0b40-49f9-99ac-4ea93ed7bd4a", "node_type": "1", "metadata": {}, "hash": "3d7a46ccea7ee779897e4ff6def03e022502c2c6217ade49f53f76d43066b54c", "class_name": "RelatedNodeInfo"}}, "text": "J Manuf Process 26: 339-354\n\n  \\item EOS GmbH - Electro Optical Systems (2015) Material data sheet EOS NickelAlloy HX Material data sheet Technical data\n\n  \\item Esmaeilizadeh R, Ali U, Keshavarzkermani A, Mahmoodkhani Y, Marzbanrad E, Toyserkani E (2019) On the effect of spatter particles distribution on the quality of Hastelloy X parts made by laser powder-bed fusion additive manufacturing. J Manuf Process 37(November 2018):11-20\n\n  \\item Ali U et al (2018) On the measurement of relative powder-bed compaction density in powder-bed additive manufacturing processes. J Mater Des\n\n  \\item Sih SS, Barlow JW (2004) The prediction of the emissivity and thermal conductivity of powder beds. Part Sci Technol 22(4):427440\n\n  \\item Promoppatum P, Yao S, Pistorius PC, Rollett AD (2017) A comprehensive comparison of the analytical and numerical prediction of the thermal history and solidification microstructure of Inconel 718 products made by laser powder-bed fusion. Engineering 3(5):685694\n\n  \\item Huang W, Zhang Y (2019) Finite element simulation of thermal behavior in single-track multiple-layers thin wall without-support during selective laser melting. J Manuf Process 42(April):139-148\n\n  \\item Luo C, Qiu J, Yan Y, Yang J, Uher C, Tang X (2018) Finite element analysis of temperature and stress fields during the selective laser melting process of thermoelectric SnTe. J Mater Process Technol 261(February):74-85\n\n  \\item Gouge M, Michaleris P (2017) Thermo-mechanical modeling of additive manufacturing, 1st edn. Elsevier Inc.\n\n  \\item Kreith F, Manglik RM, Bohn MS (2012) Principles of heat transfer. Cengage Learning\n\n  \\item King WE et al (2014) Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J Mater Process Technol 214(12):2915-2925\n\n  \\item Trapp J, Rubenchik AM, Guss G, Matthews MJ (2017) In situ absorptivity measurements of metallic powders during laser powder-bed fusion additive manufacturing. Appl Mater Today 9: 341-349\n\n  \\item Keshavarzkermani A et al (2019) An investigation into the effect of process parameters on melt pool geometry, cell spacing, and grain refinement during laser powder bed fusion. Opt Laser Technol 116(January):83-91\n\n  \\item Acharya R, Sharon JA, Staroselsky A (2017) Prediction of microstructure in laser powder bed fusion process. Acta Mater 124:360371\n\n  \\item Darvish K, Chen ZW, Phan MAL, Pasang T (2018) Materials characterization selective laser melting of $\\mathrm{Co}-29 \\mathrm{Cr}-6 \\mathrm{Mo}$ alloy with laser power 180-360 W: cellular growth, intercellular spacing and the related thermal condition. Mater Charact 135(November 2017): 183-191\n\n  \\item Kurz W, Trivedi R (1994) Rapid solidification processing and microstructure formation. 17:46-51\n\n  \\item S. Kou, Welding metallurgy. 2002\n\n  \\item Harrison NJ, Todd I, Mumtaz K (2015) Reduction of microcracking in nickel superalloys processed by selective laser melting: a fundamental alloy design approach. Acta Mater 94:59-68\n\n\\end{enumerate}\n\nPublisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.", "start_char_idx": 414867, "end_char_idx": 418014, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "500f9f93-0b40-49f9-99ac-4ea93ed7bd4a": {"__data__": {"id_": "500f9f93-0b40-49f9-99ac-4ea93ed7bd4a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "6442fbd3-6e94-48d1-8875-e1eb9cdd3c5d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6e833c50858a1a4f61086aa29e206c355bc15a8b1135a01335948b0c37e69e89", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2fc8a964-d607-4705-b094-9ffd9889d38a", "node_type": "1", "metadata": {}, "hash": "9cd4e5e8684b90579a246f308308b2fb537e925624ad9991ad3339229976b46c", "class_name": "RelatedNodeInfo"}}, "text": "Mater Charact 135(November 2017): 183-191\n\n  \\item Kurz W, Trivedi R (1994) Rapid solidification processing and microstructure formation. 17:46-51\n\n  \\item S. Kou, Welding metallurgy. 2002\n\n  \\item Harrison NJ, Todd I, Mumtaz K (2015) Reduction of microcracking in nickel superalloys processed by selective laser melting: a fundamental alloy design approach. Acta Mater 94:59-68\n\n\\end{enumerate}\n\nPublisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\\usepackage{bbold}\n\n\\title{Using machine learning to identify in-situ melt pool signatures indicative of flaw formation in a laser powder bed fusion additive manufacturing process }\n\n\n\\author{Luke Scime*, Jack Beuth\\\\\nNextManufacturing Center, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh PA 15213, United States}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\nFull Length Article\n\n\n\n\\section*{A R T I C L E I N F O}\n\\section*{Keywords:}\nAdditive manufacturing\n\nMelt pool-scale flaws\n\nComputer vision\n\nMachine learning\n\nIn-situ process monitoring\n\n\\begin{abstract}\nA B S T R A C T Because many of the most important defects in Laser Powder Bed Fusion (L-PBF) occur at the size and timescales of the melt pool itself, the development of methodologies for monitoring the melt pool is critical. This works examines the possibility of in-situ detection of keyholing porosity and balling instabilities. Specifically, a visiblelight high speed camera with a fixed field of view is used to study the morphology of L-PBF melt pools in the Inconel 718 material system. A scale-invariant description of melt pool morphology is constructed using Computer Vision techniques and unsupervised Machine Learning is used to differentiate between observed melt pools. By observing melt pools produced across process space, in-situ signatures are identified which may indicate flaws such as those observed ex-situ. This linkage of ex-situ and in-situ morphology enabled the use of supervised Machine Learning to classify melt pools observed (with the high speed camera) during fusion of nonbulk geometries such as overhangs.\n\\end{abstract}\n\n\\section*{1. Introduction}\nIn order for Additively Manufactured (AM) components to be used for safety-critical applications in industries such as aerospace, biomedical, energy, automotive, and tooling [1-3], a greater degree of part quality assurance must first be achieved. A key approach for achieving this goal is the integration of closed-loop control schema into the AM processes [4].", "start_char_idx": 417482, "end_char_idx": 421103, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "2fc8a964-d607-4705-b094-9ffd9889d38a": {"__data__": {"id_": "2fc8a964-d607-4705-b094-9ffd9889d38a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "500f9f93-0b40-49f9-99ac-4ea93ed7bd4a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "35b642c7e2417c12d859dff06728304923f26eb077b89930e5b0ab19359f1c32", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9d1ea3c8-736e-4636-a899-1d08ad11456b", "node_type": "1", "metadata": {}, "hash": "a5db7459af459025628a0775e1503a84350d5ee7459c19e558576c2ffff0c9a0", "class_name": "RelatedNodeInfo"}}, "text": "A scale-invariant description of melt pool morphology is constructed using Computer Vision techniques and unsupervised Machine Learning is used to differentiate between observed melt pools. By observing melt pools produced across process space, in-situ signatures are identified which may indicate flaws such as those observed ex-situ. This linkage of ex-situ and in-situ morphology enabled the use of supervised Machine Learning to classify melt pools observed (with the high speed camera) during fusion of nonbulk geometries such as overhangs.\n\\end{abstract}\n\n\\section*{1. Introduction}\nIn order for Additively Manufactured (AM) components to be used for safety-critical applications in industries such as aerospace, biomedical, energy, automotive, and tooling [1-3], a greater degree of part quality assurance must first be achieved. A key approach for achieving this goal is the integration of closed-loop control schema into the AM processes [4]. Monitoring efforts for the Powder Bed Fusion (PBF) and Direct Energy Deposition (DED) AM processes have variously focused on detecting macro-scale flaws (e.g. part delamination and residual stress-induced warping) [5,6], detecting micro-scale flaws (e.g. porosity), measuring temperature fields and histories [5,6], measuring shielding gas quality [7], and understanding melt pool dynamics [5,6].\n\nIn Laser PBF (L-PBF), a shallow layer of metal powder is deposited over a build plate or existing powder bed. After the layer is deposited a laser beam selectively exposes (melts) the powder bed in the shape of a 2D slice of the desired 3D part. This process is repeated throughout the \"build\" until the entire part is complete. A schematic representation of an EOS M290 L-PBF machine (EOS GmbH, Germany) [8] is shown in Fig. 1.\n\nDefects common in L-PBF such as porosity formed by the keyholing mechanism [9] and the surface tension-related balling phenomenon $[10,11]$ are on the same size scale as the melt pool and occur along the melt tracks themselves. For these reasons, the authors consider in-situ monitoring of the melt pool itself to be critical for ensuring part quality. This view is also shared by many in the AM community, and a substantial body of work now exists relating to the observation of melt pools in L-PBF and DED AM processes using high speed visible-light and thermal imaging. Much of the existing work has focused on monitoring the dimensions of the melt pool. For example, Tan et al. [12] measured melt pool dimensions in a welding process using a coaxially aligned high speed camera and Heigel et al. [13] measured melt pool length in L-PBF using a high speed thermal camera. Impressively, Clijsters et al. [14] developed a real-time system capable of measuring the in-situ melt pool dimensions for an L-PBF process and similar systems are now in use by several L-PBF machine manufacturers [15,16]. Fisher et al. [17] worked to correlate temperature information (collected using a visiblelight camera) with melt pool dimensions in an L-PBF process.\n\nQualitative and quantitative observation of L-PBF melt pool dynamics has been performed by Gunenthiram et al. [18], Criales et al. [19], and Bertoli et al. [20] although none of these groups sought to directly detect defect formation. Alternate but related sensor modalities have also been used to investigate the melt pool. For example, spectrographic imaging of the vapor plume has been utilized to detect processing defects in the LENS process by Nassar et al. [21]. While Islam et al. [22] attempted to use a combination of a high speed pyrometer and a high speed camera to detect balling via observation of the temperature profile of the melt pool and the surrounding area.\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:lscime@andrew.cmu.edu}{lscime@andrew.cmu.edu} (L. Scime).\n}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-02}\n\\end{center}\n\nFig. 1. A schematic representation of an EOS M290 machine. The arrows indicate the direction that the schematic components will move immediately following the lasing of the current layer.", "start_char_idx": 420152, "end_char_idx": 424317, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9d1ea3c8-736e-4636-a899-1d08ad11456b": {"__data__": {"id_": "9d1ea3c8-736e-4636-a899-1d08ad11456b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "2fc8a964-d607-4705-b094-9ffd9889d38a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "75fd1daa73e1c655c558ff8af507541de5c933d78c88a3a2178efba3c331db6f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "78eec70a-557a-4bb2-a81a-b7115ce0cc77", "node_type": "1", "metadata": {}, "hash": "0a297b56fb0b53cdaf8000708b2b96162bbda2590572cb84fff942d892097711", "class_name": "RelatedNodeInfo"}}, "text": "[21]. While Islam et al. [22] attempted to use a combination of a high speed pyrometer and a high speed camera to detect balling via observation of the temperature profile of the melt pool and the surrounding area.\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:lscime@andrew.cmu.edu}{lscime@andrew.cmu.edu} (L. Scime).\n}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-02}\n\\end{center}\n\nFig. 1. A schematic representation of an EOS M290 machine. The arrows indicate the direction that the schematic components will move immediately following the lasing of the current layer.\n\nOf most relevance, some work has also applied traditional statistical analysis methods and rudimentary Machine Learning (ML) and Computer Vision (CV) techniques to the task of defect detection. Luo et al. [23] leveraged a Neural Network to identify the correlation between process parameters and keyhole formation in laser beam welding using data collected from a high speed camera. Grasso et al. [24] detected off-nominal melting via statistical comparisons between the pixel-wise trans-layer emitted light intensity profiles. Repossini et al. [25] and Grasso et al. [26] correlated traditional statistical descriptors of spatter (e.g. number and size of spatter particles) and the vapor plume (e.g. emission intensity) with processing parameters (three different energy densities), laser beam scan direction, and catastrophic flaw formation in L-PBF processes. Khanzadeh et al. $[27,28]$ presented a method for detecting porosity in the LENS DED process by autonomously clustering different melt pool morphologies, where the morphologies are defined by a radial function that traces the melt pool boundary as detected by a thermal camera. Finally, recent work by Zhang et al. [29] has demonstrated the ability of ML, operating on both simple statistical descriptors and those generated by a Convolutional Neural Network, to differentiate between L-PBF melt pools produced using three different processing parameters.\n\nThe melt pool monitoring approaches reported in the literature have a number of critical limitations: First and foremost, few focus on in-situ flaw detection and many of those that do operate on DED AM processes. In DED, the beam travel velocities are approximately one order of magnitude slower than those used in L-PBF and the melt pool dimensions are approximately one order of magnitude larger than those found in $\\mathrm{L}-$ PBF $[30,31]$ - overall DED is a much more conducive environment for insitu melt pool monitoring than L-PBF. While Khanzadeh et al. [27,28] utilized unsupervised ML to differentiate between LENS melt pool morphologies, the chosen descriptor of melt pool shape was neither scale invariant nor capable of incorporating information about the spatter or vapor plume. While statistical learning was used by Repossini et al. [25] and Grasso et al. [26] to characterize spatter and the vapor plume, the work ignored the morphology of the melt pool itself and relied on segmentation rather than more advanced CV feature extraction techniques. Additionally, the work of Grasso et al. [24] requires either comparisons between data collected at different layers or a \"clean\" signal from a successful build of the same geometry - limiting its applicability to many situations. Finally, none of the work in the literature leverages knowledge of process space to enable the use of supervised ML techniques for melt pool classification and none seek to differentiate between flaw types (i.e. prior work focuses only on detecting \"off-nominal\" melt pools as opposed to specific defect generation mechanisms).\n\nIn this work, a high speed, off-axis, visible-light camera with a fixed Field of View is used to image Inconel 718 (In718) melt pools in a commercially-available L-PBF process. In-situ melt pool morphology is studied and classified using CV and ML techniques in order to identify in-situ flaw formation signatures. It is worth noting that the high speed camera system used in this work detects the thermal emissions from both the melt pool as well as any hot material in the surrounding region [32]. Therefore the in-situ data are not well predicted by existing simulations - motivating the usage of CV and ML techniques to describe these data.", "start_char_idx": 423645, "end_char_idx": 428009, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "78eec70a-557a-4bb2-a81a-b7115ce0cc77": {"__data__": {"id_": "78eec70a-557a-4bb2-a81a-b7115ce0cc77", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9d1ea3c8-736e-4636-a899-1d08ad11456b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5e6ec6476fa284e786aff7a732c9c5801b0ad5d790542f6be3215403c3d9de30", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7efa3959-b53a-42e4-8dca-352c2c80d44a", "node_type": "1", "metadata": {}, "hash": "d1bed586effc1cfeea41356748ebbb67c84fc9e08537b4c17e96e73906570139", "class_name": "RelatedNodeInfo"}}, "text": "Finally, none of the work in the literature leverages knowledge of process space to enable the use of supervised ML techniques for melt pool classification and none seek to differentiate between flaw types (i.e. prior work focuses only on detecting \"off-nominal\" melt pools as opposed to specific defect generation mechanisms).\n\nIn this work, a high speed, off-axis, visible-light camera with a fixed Field of View is used to image Inconel 718 (In718) melt pools in a commercially-available L-PBF process. In-situ melt pool morphology is studied and classified using CV and ML techniques in order to identify in-situ flaw formation signatures. It is worth noting that the high speed camera system used in this work detects the thermal emissions from both the melt pool as well as any hot material in the surrounding region [32]. Therefore the in-situ data are not well predicted by existing simulations - motivating the usage of CV and ML techniques to describe these data. Because the melt pool size often does not correlate to ex-situ flaws, a scale-agnostic description of melt pool morphology is created by applying the Bag-of-Words (or Keypoints) [33] ML technique to features extracted using SIFT (Scale Invariant Feature Transforms) [34]. The presented description of melt pool morphology explicitly incorporates information regarding the shape of the melt pool itself, the vapor plume, and spatter in order to improve differentiation between in-situ morphologies. Acquiring ground-truth information about in-situ melt pool morphology in a commercially-available L-PBF system is extremely non-trivial. Therefore, ex-situ melt pool morphology data previously collected by the authors [35], combined with fundamental knowledge of process space [36], are used to bridge the gap between unsupervised and supervised ML. This novel, human-in-the-loop, ML approach enables not only the identification of similar and dissimilar melt pool morphologies, but also the preliminary classification of melt pools based on observed in-situ flaw signatures. Specifically, the presented ML methodology is capable of classifying melt pool morphologies into four categories: desirable, balling, under-melting, and keyholing porosity which are defined in [35].\n\nFurthermore, while prior work [37] demonstrates that process parameters can be chosen to reduce the likelihood of melt pool-scale defects, the approach is not easily extensible to non-bulk geometries. In other words, even if process parameters are chosen to reside within a desirable processing window based on bulk data, defects may still occur during the printing of certain geometries such as unsupported overhangs [38]. As a result, the only way to assure machine users that melt pool-scale flaws are not occurring is through the implementation of insitu process monitoring or prohibitively-expensive ex-situ testing [39]. To address this issue, the high speed camera is used to collect data during the printing of a test artifact containing an unsupported overhang. The imaged melt pools are then analyzed using the trained ML methodology. The Additive Manufacturing terminology used herein complies as closely as possible with ISO/ASTM 52900:2015 [40].\n\n\\section*{2. Experimental procedure and methods}\n\\subsection*{2.1. Programming environment}\nUnless otherwise noted, all software was developed within the MATLAB R2016a or R2017a environments. The above MATLAB versions also included the following add-on packages: the Image Processing Toolbox and the Statistics Toolbox.\n\n\\subsection*{2.2. High speed camera}\nThe in-situ melt pool images analyzed in this work were captured by a one megapixel Photron FASTCAM Mini AX200 high speed camera mounted to the EOS M290 at CMU's NextManufacturing Center, the setup for which is described in [41]. Visible light collected by the camera sensor originates as thermal emissions ${ }^{1}$ from the melt pool and surrounding material which is also at an elevated temperature. The\n\\footnotetext{${ }^{1}$ As discussed in [[41]], \"this implies that the true melt pool boundaries are unknown when viewing the melt pool images.\" Further characterization of the system is explored by Fisher et al. [[32]] which enables the estimation of melt pool size under certain conditions. Nonetheless, the inability to precisely identify the true melt pool boundary is not a hindrance to the presented study of melt pool morphology.\n}\nhigh melt pool temperatures for the In718 alloy allow for sufficient emission in the visible spectrum for the use of a visible-light camera to be practical.\n\nData are recorded on an onboard 16 GB circular RAM buffer.", "start_char_idx": 427036, "end_char_idx": 431664, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7efa3959-b53a-42e4-8dca-352c2c80d44a": {"__data__": {"id_": "7efa3959-b53a-42e4-8dca-352c2c80d44a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "78eec70a-557a-4bb2-a81a-b7115ce0cc77", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ad54690e36c828b4ab4a7e213861d02c5d766ab0be06c4840fc0b88ede88efa0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d2c2e01a-1ce6-42f8-b7fa-9d8a10a69cbe", "node_type": "1", "metadata": {}, "hash": "97e41ed8da7483c4c88453f1272c5ff0964544c08abb8a94e37660ab9f855835", "class_name": "RelatedNodeInfo"}}, "text": "Visible light collected by the camera sensor originates as thermal emissions ${ }^{1}$ from the melt pool and surrounding material which is also at an elevated temperature. The\n\\footnotetext{${ }^{1}$ As discussed in [[41]], \"this implies that the true melt pool boundaries are unknown when viewing the melt pool images.\" Further characterization of the system is explored by Fisher et al. [[32]] which enables the estimation of melt pool size under certain conditions. Nonetheless, the inability to precisely identify the true melt pool boundary is not a hindrance to the presented study of melt pool morphology.\n}\nhigh melt pool temperatures for the In718 alloy allow for sufficient emission in the visible spectrum for the use of a visible-light camera to be practical.\n\nData are recorded on an onboard 16 GB circular RAM buffer. For the experiments presented in this chapter, camera recording was triggered either manually by the authors or automatically by the Photron PFV software package [42] based on the sudden increase in brightness corresponding to a melt pool entering the Field of View (FoV). \"The optical train that is used in this work provides a maximum field of view of $6.35 \\mathrm{~mm} \\times 6.35 \\mathrm{~mm}$, with each pixel covering a $6.2 \\mu \\mathrm{m} \\times 6.2 \\mu \\mathrm{m}$ area. The resolving power of the system is approximately 50 line-pairs per millimeter as determined by visual inspection of a negative 1951 USAF resolution test target supplied by Thorlabs\" [41].\n\n\\subsection*{2.3. Camera calibration procedure}\nThe location of the available chamber viewport [41] necessitates that the high speed camera be mounted such that its axis is not parallel to the normal vector of the build plate ( $z$-axis). The resulting distortion is compensated for by applying an affine warp [43] to the image such that a rectangular object in the initial image will appear truly rectangular in the final image. In order to determine the appropriate Homography matrix, a rectangular fiducial exposed using the nominal EOS parameters was imaged using both the high speed camera (Fig. 2) and an Alicona Infinite-Focus optical microscope (Fig. 3). Specifically, the four interior corners of the fiducial were used to map the high speed camera image to the \"true\" dimensions as measured from the microscope image. As expected, the camera distortion was minimal, given the relatively small FoV and shallow camera angle (relative to the $z$-axis).\n\nThe frame rate of the high speed camera was chosen a priori to be $6400 \\mathrm{fps}$ - the maximum frame rate for which the entire FoV (1024 pixels $\\times 1024$ pixels) can be captured. At this frame capture rate the 16 GB RAM buffer on the high speed camera can record data for approximately $1.7 \\mathrm{~s}$. An exposure time of $5.00 \\mu \\mathrm{s}$ was chosen based on visual observation of melt pools produced using four different power and velocity combinations spanning the process space of interest. Specifically, melt pools produced using PV \\#1 (nominal EOS parameters), PV \\#19 (high energy density regime), PV \\#6 (low energy density regime), and PV \\#36 (balling regime) were imaged at multiple exposure times (see Table 1). The exposure time was chosen such that the low energy density melt pool was visible while the vapor plume of high energy density melt pool did not completely obscure the melt pool itself. During a $5.00 \\mu \\mathrm{s}$ exposure time a melt pool traveling at the maximum tested velocity of $1400 \\mathrm{~mm} / \\mathrm{s}$ will travel $7 \\mu \\mathrm{m}$, or approximately one pixel; therefore motion blur can be considered negligible under these conditions. At a frame rate of $6400 \\mathrm{fps}$ the melt pool will travel between $30 \\mu \\mathrm{m}$ and $220 \\mu \\mathrm{m}$ (over the range of beam velocities tested) between camera frames. These inter-frame travel distances are comparable to the length of the melt pool [35].\n\n\\subsection*{2.4. Coaxial melt pool transformation}\nThe high speed camera configuration described above provides a stationary FoV; as a result, the melt pool data are collected in an Eulerian frame of reference. This increases the difficulty of comparing data between melt pool images, and for this reason a Lagrangian frame of reference is preferred.", "start_char_idx": 430832, "end_char_idx": 435118, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d2c2e01a-1ce6-42f8-b7fa-9d8a10a69cbe": {"__data__": {"id_": "d2c2e01a-1ce6-42f8-b7fa-9d8a10a69cbe", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7efa3959-b53a-42e4-8dca-352c2c80d44a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "852b0fdc44dde0bf6ce8b4de235ac521deabe858387bed4c1a63a3d6c331daee", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "595cc06a-5938-4e56-99ed-346deae39129", "node_type": "1", "metadata": {}, "hash": "faaba7e447edbe6da36df67ba7f473e56ad663a666cc5829485f3cd86a8b1fbd", "class_name": "RelatedNodeInfo"}}, "text": "At a frame rate of $6400 \\mathrm{fps}$ the melt pool will travel between $30 \\mu \\mathrm{m}$ and $220 \\mu \\mathrm{m}$ (over the range of beam velocities tested) between camera frames. These inter-frame travel distances are comparable to the length of the melt pool [35].\n\n\\subsection*{2.4. Coaxial melt pool transformation}\nThe high speed camera configuration described above provides a stationary FoV; as a result, the melt pool data are collected in an Eulerian frame of reference. This increases the difficulty of comparing data between melt pool images, and for this reason a Lagrangian frame of reference is preferred. While this can be accomplished via a coaxially-aligned optical configuration as demonstrated by Clijsters et al. [14] and Lane et al. [44], such an implementation is extremely nontrivial for an AM machine user that is not also an AM machine manufacturer. Therefore, in this work, the software solution reported by Scime et al. [41] is used to transform the high speed camera images into data analogous that which is collected in a coaxially-aligned configuration.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-03}\n\\end{center}\n\nFig. 2. The rectangular fiducial as imaged by the high speed camera.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-03(1)}\n\\end{center}\n\nFig. 3. The rectangular fiducial as imaged by the Alicona Infinite-Focus microscope.\n\n\\subsection*{2.5. Collection of ex-situ process data}\nPrior work by the authors [35] studied the morphological behavior of In718 melt pools in the EOS M290 L-PBF process. As is discussed in Section 3.6, this ex-situ information is critical for the study of in-situ melt pool morphology and training of the presented ML algorithm. For this reason, the results presented in [35] are summarized in Fig. 4. Note that the morphology of the melt pools produced by each of the 36 process parameter combinations (Table 1) was categorized as producing one or more of five different types of melt pools: desirable, balling, severe keyholing, keyholing porosity, or under-melting using both qualitative and quantitative measures.\n\n\"Specifically, balling melt pools were defined as those exhibiting the characteristic balling morphology. Processing parameters were considered to produce severely keyholed melt pools if the average aspect ratio (defined as the depth over the half-width) was greater than 2.5. If any of the melt pool cross-sections for a given power and velocity combination showed examples of keyholing porosity, that process parameter combination was categorized as producing keyholing porosity. Process parameter combinations producing melt pools with average depths less than the powder layer thickness of $70 \\mu \\mathrm{m}$ were considered to\n\nTable 1\n\nProcess parameter combinations used for each 1LSB melt track on the EOS M290 L-PBF machine.", "start_char_idx": 434495, "end_char_idx": 437407, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "595cc06a-5938-4e56-99ed-346deae39129": {"__data__": {"id_": "595cc06a-5938-4e56-99ed-346deae39129", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d2c2e01a-1ce6-42f8-b7fa-9d8a10a69cbe", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5748837b2d6ff93375717f8dd8ec658c4bf844d981ca73d5fbde2eea2151a238", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ac302b32-d929-4c4c-95ea-cc80c2a20f60", "node_type": "1", "metadata": {}, "hash": "d249e8c16d82424d88058fbac7a9e6636560cde11404f61148eeb507e6c71e4f", "class_name": "RelatedNodeInfo"}}, "text": "\"Specifically, balling melt pools were defined as those exhibiting the characteristic balling morphology. Processing parameters were considered to produce severely keyholed melt pools if the average aspect ratio (defined as the depth over the half-width) was greater than 2.5. If any of the melt pool cross-sections for a given power and velocity combination showed examples of keyholing porosity, that process parameter combination was categorized as producing keyholing porosity. Process parameter combinations producing melt pools with average depths less than the powder layer thickness of $70 \\mu \\mathrm{m}$ were considered to\n\nTable 1\n\nProcess parameter combinations used for each 1LSB melt track on the EOS M290 L-PBF machine.\n\n\\begin{center}\n\\begin{tabular}{|c|c|c|}\n\\hline\nSample (PV) Number & Beam Power (W) & Beam Velocity $(\\mathrm{mm} / \\mathrm{s})$ \\\\\n\\hline\n(EOS Nominal) 1 & 285 & 960 \\\\\n\\hline\n2 & 100 & 200 \\\\\n\\hline\n3 & 100 & 400 \\\\\n\\hline\n4 & 100 & 600 \\\\\n\\hline\n5 & 100 & 800 \\\\\n\\hline\n6 & 100 & 1000 \\\\\n\\hline\n7 & 150 & 200 \\\\\n\\hline\n8 & 150 & 400 \\\\\n\\hline\n9 & 150 & 600 \\\\\n\\hline\n10 & 150 & 800 \\\\\n\\hline\n11 & 150 & 1000 \\\\\n\\hline\n12 & 150 & 1200 \\\\\n\\hline\n13 & 200 & 200 \\\\\n\\hline\n14 & 200 & 400 \\\\\n\\hline\n15 & 200 & 600 \\\\\n\\hline\n16 & 200 & 800 \\\\\n\\hline\n17 & 200 & 1000 \\\\\n\\hline\n18 & 200 & 1200 \\\\\n\\hline\n19 & 250 & 200 \\\\\n\\hline\n20 & 250 & 400 \\\\\n\\hline\n21 & 250 & 600 \\\\\n\\hline\n22 & 250 & 800 \\\\\n\\hline\n23 & 250 & 1000 \\\\\n\\hline\n24 & 250 & 1200 \\\\\n\\hline\n25 & 250 & 1400 \\\\\n\\hline\n26 & 300 & 400 \\\\\n\\hline\n27 & 300 & 600 \\\\\n\\hline\n28 & 300 & 800 \\\\\n\\hline\n29 & 300 & 1000 \\\\\n\\hline\n30 & 300 & 1200 \\\\\n\\hline\n31 & 300 & 1400 \\\\\n\\hline\n32 & 370 & 400 \\\\\n\\hline\n33 & 370 & 800 \\\\\n\\hline\n34 & 370 & 1000 \\\\\n\\hline\n35 & 370 & 1200 \\\\\n\\hline\n36 & 370 & 1400 \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nbe under-melting. Finally, any melt pools not otherwise categorized were considered to be desirable\" [35].\n\n\\subsection*{2.6. Collection of in-situ training data}\nAs described in Section 2.2, the high speed camera is only able to image a single, fixed FoV; therefore in-situ data collection during the experiments reviewed in Section 2.5 could not be performed. Therefore, the 36 process parameter combinations enumerated in Table 1 were exposed within the FoV of the high speed camera. Specifically, for each parameter combination, a set of $10 \\mathrm{~mm}$ long single bead melt tracks were exposed within a rectangular region of size $10 \\mathrm{~mm} \\times 20 \\mathrm{~mm}$. Each melt track was separated by a hatch spacing of $500 \\mu \\mathrm{m}$ and adjacent melt tracks were not exposed subsequently i.e. at least $140 \\mathrm{~ms}$ elapsed between the exposures of adjacent melt tracks. As in [35], the chamber preheat was $80{ }^{\\circ} \\mathrm{C}$, the nominal ${ }^{2}$ beam diameter was $100 \\mu \\mathrm{m}$, and the nominal powder layer thickness was $40 \\mu \\mathrm{m}$ (resulting in an approximately $70 \\mu \\mathrm{m}$ effective layer thickness [35]).", "start_char_idx": 436673, "end_char_idx": 439662, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ac302b32-d929-4c4c-95ea-cc80c2a20f60": {"__data__": {"id_": "ac302b32-d929-4c4c-95ea-cc80c2a20f60", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "595cc06a-5938-4e56-99ed-346deae39129", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "5c4bc2e350d81cbace2da4188e990b54f2996a407295c25758fc6c23191dbf45", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bb7a6fa3-02d6-4cc3-bec2-81c1a4ab3709", "node_type": "1", "metadata": {}, "hash": "0f8bcce1d67e5c824fb24f3b939acdab47d8874b9ff2af6dd35616d8b58793ee", "class_name": "RelatedNodeInfo"}}, "text": "Specifically, for each parameter combination, a set of $10 \\mathrm{~mm}$ long single bead melt tracks were exposed within a rectangular region of size $10 \\mathrm{~mm} \\times 20 \\mathrm{~mm}$. Each melt track was separated by a hatch spacing of $500 \\mu \\mathrm{m}$ and adjacent melt tracks were not exposed subsequently i.e. at least $140 \\mathrm{~ms}$ elapsed between the exposures of adjacent melt tracks. As in [35], the chamber preheat was $80{ }^{\\circ} \\mathrm{C}$, the nominal ${ }^{2}$ beam diameter was $100 \\mu \\mathrm{m}$, and the nominal powder layer thickness was $40 \\mu \\mathrm{m}$ (resulting in an approximately $70 \\mu \\mathrm{m}$ effective layer thickness [35]).\n\nAfter the exposure of the single bead melt tracks for a given parameter combination, the rectangular region was re-exposed (without the addition of another powder layer) using the EOS nominal parameters (PV \\#1) and the nominal hatch spacing of $110 \\mu \\mathrm{m}$. Then, an additional 11 layers of material were built using the EOS nominal parameters such that each set of single bead melt tracks were vertically separated by a $440 \\mu \\mathrm{m}$ tall block of nominally-processed material. Vertical separation was implemented to ensure that the observed melt pool morphologies\n\\footnotetext{${ }^{2}$ The D86 beam diameter was measured to be approximately $90 \\mu \\mathrm{m}$ during the machine maintenance temporally closest to the reported experiments.\n}\n\nwere not influenced by an interaction with porosity (or other defects) left behind by previously tested process parameter combinations. The initial set of single bead melt tracks were separated from the sub-size build plate ${ }^{3}$ by approximately $1 \\mathrm{~mm}$ of nominally-processed material. Fig. 5 shows a Computer Aided Design (CAD) rendering of the experiment and Fig. 6 shows the as-built block of material.\n\nThe $10 \\mathrm{~mm}$ length of each single bead melt track was chosen such that the melt pool was always a minimum of $2 \\mathrm{~mm}$ away from the end of the melt track while it was in view of the camera. More discussion of steady state melt pool lengths and the appropriate hatch spacing is available in [35]. The vertical buffer distance between sets of single bead melt tracks was informed by the maximum expected melt pool depth $^{4}$ of $175 \\mu \\mathrm{m}$ reported in [35]. To support robust training of the ML methodology, a substantial amount of training data are required - a minimum of 500 camera frames for each of the 36 power and velocity combinations was deemed sufficient for this task based on prior ML work by the authors [45]. Additional details regarding the design of this experiment can be found in [46].\n\nThe number of frames of training data collected for a single process parameter combination ranged from 504 to 1394 . A total of 24,385 frames of usable data were collected across 29 of the 36 process parameter combinations. Data from four of the parameter combinations in the low energy density regime ( $\\mathrm{PV} \\# 5, \\# 6, \\# 12$, and $\\# 18$ ) were not collected as the apparent melt pool size (brightness) was too small to automatically trigger the high speed camera's recording feature. Data from a further three parameter combinations (PV \\#27, 28, and \\#29) were inadvertently recorded using an incorrect exposure time and were therefore not used for training.\n\n\\subsection*{2.7. Non-bulk geometry (unsupported overhang)}\nThis experiment was designed to investigate melt pool behavior during the fusion of an unsupported overhang. Specially, the goal was to observe any melt pool morphological changes triggered by the differing thermal conditions present due to the low thermal conductivity of the unfused powder [47,48] below the overhang. As shown in Fig. 7, the camera's FoV is centered on an overhang spanning a gap of $5 \\mathrm{~mm}$. To decrease the turnaround time between the experiments, a channel was milled into several of the sub-size plates - thereby reducing the build time and allowing additional test artifacts to be fabricated in the event of a build or data capture failure.", "start_char_idx": 438981, "end_char_idx": 443086, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bb7a6fa3-02d6-4cc3-bec2-81c1a4ab3709": {"__data__": {"id_": "bb7a6fa3-02d6-4cc3-bec2-81c1a4ab3709", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ac302b32-d929-4c4c-95ea-cc80c2a20f60", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "531fdf2b5e31a38b799a963d41101c37755e5e62109449c4ac48460aa367b33f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "43a2ba86-bbd6-4f6d-91b4-4ac3a308ea50", "node_type": "1", "metadata": {}, "hash": "108498b674beb317b5ec8f02f6738273ff20102a179593b1d7202d7a41f3f6b7", "class_name": "RelatedNodeInfo"}}, "text": "Data from a further three parameter combinations (PV \\#27, 28, and \\#29) were inadvertently recorded using an incorrect exposure time and were therefore not used for training.\n\n\\subsection*{2.7. Non-bulk geometry (unsupported overhang)}\nThis experiment was designed to investigate melt pool behavior during the fusion of an unsupported overhang. Specially, the goal was to observe any melt pool morphological changes triggered by the differing thermal conditions present due to the low thermal conductivity of the unfused powder [47,48] below the overhang. As shown in Fig. 7, the camera's FoV is centered on an overhang spanning a gap of $5 \\mathrm{~mm}$. To decrease the turnaround time between the experiments, a channel was milled into several of the sub-size plates - thereby reducing the build time and allowing additional test artifacts to be fabricated in the event of a build or data capture failure. Pads $160 \\mu \\mathrm{m}$ in height were built using nominal parameters (PV \\#1) and a hatch spacing of $110 \\mu \\mathrm{m}$ on either side of the pre-cut channel in order to ensure appropriate bonding between the overhanging layers of interest and the sub-size plate.\n\nData were collected for a total of 5 layers spanning the channel. The first observed layer was exposed directly on top of a bed of unfused powder while the fifth layer was exposed on top of (nominally) $160 \\mu \\mathrm{m}$ of fused material. The overhang test artifact was exposed with the EOS nominal parameters (PV \\#1) and a hatch spacing of $110 \\mu \\mathrm{m}$. As in the previous experiments, the chamber preheat was $80^{\\circ} \\mathrm{C}$, the nominal beam diameter was $100 \\mu \\mathrm{m}$, and the nominal powder layer thickness was $40 \\mu \\mathrm{m}$. Fig. 8 shows the as-built test artifact after completion of the build. Over the course of this build, approximately 1500 frames of data were collected for each of the five overhanging layers.\n\\footnotetext{${ }^{3}$ A sub-size low-carbon steel plate (McMaster-Carr P/N: 1388K311) mounted to a modified EOS build plate was used to decrease the turnaround time between the sequence of experiments.\n\n${ }^{4}$ The buffer depth was chosen based on the maximum predicted melt pool depth of $175 \\mu \\mathrm{m}$ and the depths reported by Narra [[67]]. The maximum measured depth of any melt pool was $600 \\mu \\mathrm{m}$. This only barely exceeds the sum of the vertical separation depth $(440 \\mu \\mathrm{m})$ and the penetration depth of the melt pools produced with the nominal parameters $(150 \\mu \\mathrm{m})$.\n}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-05(4)}\n\\end{center}\n\nFig. 4. Process space annotated with the ex-situ melt pool morphologies as determined by analysis of the 1LSB crosssections. The annotations indicate the percentage of melt pool cross-sections which had either keyholing porosity or exhibited the balling morphology. For reference, the EOS nominal parameter combination is indicated and two lines of constant melt pool geometry are overlaid. Note that this figure an caption were original reported by the authors in [35], but is reproduced here for clarity.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-05(1)}\n\\end{center}\n\nFig. 5. A CAD rendering of the rectangular exposure region built up over many sets of single bead melt tracks and separation layers. Note the FoV of the high speed camera.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-05}\n\\end{center}\n\nFig. 6. The as-built material deposited over the course of the in-situ data collection process.\n\n\\section*{3. Theory}\n\\subsection*{3.1. Overview}\nFundamentally, all ML algorithms operate by extracting features from a set of training data provided by a human [49]. The extracted features are then analyzed: their frequencies in the training data are quantified and their similarities and differences are described [33].", "start_char_idx": 442177, "end_char_idx": 446155, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "43a2ba86-bbd6-4f6d-91b4-4ac3a308ea50": {"__data__": {"id_": "43a2ba86-bbd6-4f6d-91b4-4ac3a308ea50", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bb7a6fa3-02d6-4cc3-bec2-81c1a4ab3709", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c0f6ff26989be76de84a80cb99e6593a08c9eed39b352d24c12f5ea9bff664b2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bfa33da3-94e9-42c5-a482-82f6f245f66d", "node_type": "1", "metadata": {}, "hash": "c61e052621b1f5e05921d0ad1e841d7cb497caccd93538e17890be560c4a7432", "class_name": "RelatedNodeInfo"}}, "text": "5. A CAD rendering of the rectangular exposure region built up over many sets of single bead melt tracks and separation layers. Note the FoV of the high speed camera.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-05}\n\\end{center}\n\nFig. 6. The as-built material deposited over the course of the in-situ data collection process.\n\n\\section*{3. Theory}\n\\subsection*{3.1. Overview}\nFundamentally, all ML algorithms operate by extracting features from a set of training data provided by a human [49]. The extracted features are then analyzed: their frequencies in the training data are quantified and their similarities and differences are described [33]. In the case of Deep Learning, the algorithm will actually design its own optimized set of feature extraction tools, as opposed to only using the tools provided by the human programmer [49]. Once the feature extraction system is robust, a model for describing the input data (based on its features) is created [49]. Features are extracted from any new data (i.e. data a user wishes to analyze) and are input into the model allowing the algorithm to make a decision (e.g. whether or not a process anomaly is present) that is informed by the knowledge contained within the training database.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-05(3)}\n\\end{center}\n\nFig. 7. A CAD rendering of the completed overhang test artifact. Note the FoV of the high speed camera.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-05(2)}\n\\end{center}\n\nFig. 8. The as-built test artifact deposited over the course of the in-situ data collection process.\n\nThe ML methodology presented in this section is an application of a widely-used ML technique, known as Bag of Words (or Keypoints) (BoW) [33], often applied to CV problems. In this implementation, the training data consist of frames of data captured by the high speed camera during the experiment described in Section 2.6 and transformed such that the melt pool appears to be in a Lagrangian (coaxial) reference frame (Section 2.4). The only human-applied \"ground-truth\" labels associated with the training data are the process parameter combinations used to produce each observed melt pool. While the BoW technique can be applied to multiple feature types, the authors chose to use SIFT features for their ability to be agnostic to scale information. The potential for scale agnosticism is considered by the authors to be critical, as melt pool size often does not correlate to ex-situ flaws. For example, two different process parameter combinations may produce melt pools with similar widths, however their morphologies could be radically different with one melt pool considered desirable and the other prone to generating keyholing porosity [35]. This section is intended to provide an overview of this methodology along with relevant ML and CV theory. Fig. 9 is a flowchart of this ML methodology and is referred to extensively throughout this section.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-06}\n\\end{center}\n\nFig. 9. Flowchart of the implementation of the BoW ML technique discussed in this section. Steps (a) through (f) depict the feature extraction process, step (g) shows a representation of the fingerprints used to describe the melt pool morphologies, steps (h) and (i) depict the linkage of in-situ and ex-situ results, and steps (j) and (k) show the training of the classification algorithm and its usage on new data. The representative micrographs shown in step (i) were collected during [35].\n\n\\subsection*{3.2. Selection of the training data}\nTraining data were collected as described in Section 2.6 - the high speed camera was used to image melt pools produced using a total of 29 different process parameter combinations spanning the EOS M290 process space. Unlike in prior work [45], the morphology of each training image is not labeled with a \"ground truth\" classification by the authors. Such an action is impossible as the correlations between the insitu appearance of a melt pool and ex-situ outcomes are not known.", "start_char_idx": 445464, "end_char_idx": 449657, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bfa33da3-94e9-42c5-a482-82f6f245f66d": {"__data__": {"id_": "bfa33da3-94e9-42c5-a482-82f6f245f66d", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "43a2ba86-bbd6-4f6d-91b4-4ac3a308ea50", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ea7ebe723f32b6923786598c161a9c78912a4b3070cf7c6e00bea8489b3016b3", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "571f98c0-cdc5-4664-8aa4-5b0ce6ea56e6", "node_type": "1", "metadata": {}, "hash": "d4e7c75835cdfd8f65877ccf12ba426f17cc65f5609852bbcea1098169cb30b5", "class_name": "RelatedNodeInfo"}}, "text": "The representative micrographs shown in step (i) were collected during [35].\n\n\\subsection*{3.2. Selection of the training data}\nTraining data were collected as described in Section 2.6 - the high speed camera was used to image melt pools produced using a total of 29 different process parameter combinations spanning the EOS M290 process space. Unlike in prior work [45], the morphology of each training image is not labeled with a \"ground truth\" classification by the authors. Such an action is impossible as the correlations between the insitu appearance of a melt pool and ex-situ outcomes are not known. Indeed, this challenge necessitated the development of the ex-situ database reported in [35] and the identification of linkages between the in-situ and ex-situ melt pool morphologies is a primary goal of the current work. The labels associated with each training melt pool image only indicate the process parameter combination used to generate the corresponding melt pool. The final training database is composed of a total of 24,385 coaxially-transformed melt pool images labeled with their associated process parameters.\n\n\\subsection*{3.3. Scale Invariant Feature Transform (SIFT)}\nThis implementation of the BoW ML technique extracts features using the SIFT algorithm. SIFT features, as their name (Scale Invariant Feature Transform) might suggest, are considered robust even when the objects of interest in an image (or across images) may be of varying sizes. First developed by Lowe [34], they are commonly used when it is an object's overall shape that is of interest. Interestingly, this is not SIFT's first foray into the AM community as DeCost et al. [50] have used SIFT to classify metal powders for AM applications and a conceptually-similar feature known as DAISY has been used by Jacobsm\u00fchlen et al. [51] to detect super-elevation.\n\nSIFT features characterize the gradient field surrounding each pixel in an image. In this work, gradient orientations within a 2 pixels $\\times 2$ pixels window are considered. That is, a coaxially-transformed melt pool image is broken into non-overlapping windows (Fig. 9b), each containing 4 pixels. The gradient orientations are grouped into nine, unsigned bins, e.g. one of the bins encompasses all gradients with the following orientations: $0^{\\circ}-20^{\\circ}$ and $180^{\\circ}-200^{\\circ}$. Observe that the output of this process is an image with a spatial resolution that has been reduced by a factor of two in each direction. While it is common practice to only calculate SIFT features at interest points (a.k.a. keypoints) in an image [52], in this implementation, a dense field of SIFT features is calculated at every strong edge. Where a \"strong edge\" is defined as any pixel at which the magnitude of the gradient is at least $10 \\%$ of the magnitude of the strongest gradient in the image. Fig. 11 shows a visualization of the SIFT descriptors applied to the coaxially-transformed melt pool image shown in Fig. 10.\n\n\\subsection*{3.4. Histogram of Oriented Gradients (HOG)}\nSIFT features are traditionally considered highly specific, that is, they have a dimensionality equal to the number of orientation bins (i.e. nine) with values in each dimension spanning a subset ${ }^{5}$ of $\\mathbb{R}$. For this reason, SIFT algorithms are often used for template matching applications [52] and less often for classification. A variety of techniques are available to artificially reduce the specificity ${ }^{6}$ of the SIFT features. For this work, specificity reduction was accomplished using an\n\\footnotetext{${ }^{5}$ Only numbers of the set $\\mathbb{Z}[0, W] / W$ are possible, where $W$ is the window size (i.e. four pixels).\n\n${ }^{6}$ A simple method for specificity reduction is rounding a given value to a set number of digits after the decimal point. For example, reducing the $\\mathbb{R}$ space to the subspace of $\\mathbb{Z} / 10$ would eliminate the distinction between the values 42.14 and 42.13 .\n}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-07}\n\\end{center}\n\nFig. 10. An example false-color and coaxially-transformed image of a melt pool produced using PV \\#36.", "start_char_idx": 449050, "end_char_idx": 453237, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "571f98c0-cdc5-4664-8aa4-5b0ce6ea56e6": {"__data__": {"id_": "571f98c0-cdc5-4664-8aa4-5b0ce6ea56e6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bfa33da3-94e9-42c5-a482-82f6f245f66d", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a8a58fb342ddaba993fbdfe14589b91b4248b8861cd9975e2d428b591cbecdf4", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ddb04fac-d8cb-491b-88ac-ec96c7dff778", "node_type": "1", "metadata": {}, "hash": "5c7c6cf7b6f38ee09caf2eeca7a70c4565e644a9ea4a3dae41a840e8ffc2c19d", "class_name": "RelatedNodeInfo"}}, "text": "For this work, specificity reduction was accomplished using an\n\\footnotetext{${ }^{5}$ Only numbers of the set $\\mathbb{Z}[0, W] / W$ are possible, where $W$ is the window size (i.e. four pixels).\n\n${ }^{6}$ A simple method for specificity reduction is rounding a given value to a set number of digits after the decimal point. For example, reducing the $\\mathbb{R}$ space to the subspace of $\\mathbb{Z} / 10$ would eliminate the distinction between the values 42.14 and 42.13 .\n}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-07}\n\\end{center}\n\nFig. 10. An example false-color and coaxially-transformed image of a melt pool produced using PV \\#36.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-07(1)}\n\\end{center}\n\nFig. 11. The SIFT features extracted from the melt pool shown in Fig. 10. This visualization of the SIFT features was generated using a MATLAB script written by Dollar [53].\n\nunsupervised clustering approach.\n\nIn order to utilize a pre-existing high-dimensional clustering method, the SIFT features were first converted into a standard vectorized format known as Histogram of Oriented Gradients (HOG) [54] (Fig. 9c). Specifically, the number of gradients within the SIFT window falling into each orientation bin is counted and stored in the corresponding element in the HOG vector (i.e. for nine orientation bins the HOG vector will be nine elements long). The values in each element of the HOG vector are then normalized such that they range in magnitude from $\\mathbb{R}[0,1]$. SIFT features (and their HOG equivalents) were collected from all of the melt pool images in the training database. Note that these features were extracted from each training image under three different contrast adjustments which are further discussed in the following subsection. Note that no subsampling of the training data is performed, i.e. all of the extracted SIFT features are included in the training process.\\\\\nOnce collected, HOG vectors with similar values in each element (i.e. vectors that describe a similar gradient field) are grouped together using a standard k-means unsupervised clustering algorithm [55], represented by Fig. 9d. For this work, cluster initialization was performed using random seeding, with preference given to a uniform spacing between clusters. During development of this ML methodology, the requested number of clusters was varied between 25 and 200; satisfactory performance was achieved with 50 clusters. Each cluster is represented by a mean HOG vector. The 50 mean HOG vectors are commonly referred to as visual words, and are stored in a dictionary, represented by Fig. 9e.\n\nAfter the dictionary is constructed, each HOG vector in each training image can be matched to the closest (pair-wise distance [56]) visual word in the dictionary (Fig. 9f). Note that this operation has reduced the set of possible values of the SIFT features to the set $\\mathbb{Z}[1,50]$. For each training image, the percentage of SIFT features matched to each visual word is calculated. This information can be represented by a histogram of size $1 \\times 50$ (Fig. 9g). These histograms are referred to as fingerprints. Ideally, melt pools with similar in-situ appearances will have similar fingerprints, while melt pools with dissimilar appearances will have dissimilar fingerprints. The observant reader may have noticed that in addition to the loss of scale information (desired), the method presented above also loses information about the relative spatial positions of the SIFT features (not desired). To mitigate this side-effect, the spatial relationships are partially represented by a multi-modality histogram which is detailed in the following subsection.\n\n\\subsection*{3.5. Multi-modality representation of melt pool morphology}\nWhile each melt pool could potentially be represented by a single histogram of visual word occurrences (as is the case for each image patch in [45]), such a representation was found to provide relatively poor differentiation between certain in-situ melt pool appearances. To improve differentiation, additional information contained within the original melt pool images was incorporated into the melt pool morphology representation by appending multiple histograms of visual word occurrences (Fig.", "start_char_idx": 452549, "end_char_idx": 456887, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ddb04fac-d8cb-491b-88ac-ec96c7dff778": {"__data__": {"id_": "ddb04fac-d8cb-491b-88ac-ec96c7dff778", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "571f98c0-cdc5-4664-8aa4-5b0ce6ea56e6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4de576b9c3d224bec7b62183b60dfc68c57140e44d9c27ef44be61cd7cb30ffb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "59854dc0-fa89-48ef-a37e-a3d9ec6b44d4", "node_type": "1", "metadata": {}, "hash": "30f7786104af2d997e7957033e07c1f810caf7c072ee5d515b2936983e1390f6", "class_name": "RelatedNodeInfo"}}, "text": "Ideally, melt pools with similar in-situ appearances will have similar fingerprints, while melt pools with dissimilar appearances will have dissimilar fingerprints. The observant reader may have noticed that in addition to the loss of scale information (desired), the method presented above also loses information about the relative spatial positions of the SIFT features (not desired). To mitigate this side-effect, the spatial relationships are partially represented by a multi-modality histogram which is detailed in the following subsection.\n\n\\subsection*{3.5. Multi-modality representation of melt pool morphology}\nWhile each melt pool could potentially be represented by a single histogram of visual word occurrences (as is the case for each image patch in [45]), such a representation was found to provide relatively poor differentiation between certain in-situ melt pool appearances. To improve differentiation, additional information contained within the original melt pool images was incorporated into the melt pool morphology representation by appending multiple histograms of visual word occurrences (Fig. 9g); where the calculation of each histogram was preceded by a different set of pre-processing operations performed on the original (coaxially-transformed) melt pool image.\n\nAs noted in Section 2.2, the information of interest in each melt pool image spans a wide dynamic range. In order to capture gradient fields across this dynamic range, three different contrast adjustments [57] are applied to each melt pool image in the training database. Specifically, the pixel-wise data in each image are scaled using gamma values ${ }^{7}$ of 1 (no change), 0.75 (decreased contrast), and 10 (increased contrast). Physically, decreasing the contrast allows gradient fields to be captured for the lower temperature (strictly, lower emitting) regions of the image while increasing the contrast emphasizes the gradient fields in the higher temperature (strictly, higher emitting) regions of the image. In other words, the diffuse vapor plume and colder spatter particles may be more visible in the lower contrast image, while only the melt pool body and the hottest spatter particles will be visible in the high contrast image. Note that this difference in \"visibility\" is also dependent upon the gradient magnitude threshold used to define a \"strong edge\" (Section 3.3).\n\nRecall that the fingerprint presented in the previous subsection contains no information about the relative spatial configuration of the SIFT features. In order to preserve some of this spatial information, each of the three contrast-adjusted melt pool images is segmented into three different components. First, the spatter is isolated using the same connected-components algorithm described in [41]. Then the main melt\n\\footnotetext{${ }^{7}$ The pixel-wise scaling is accomplished using a non-linear function of the form: $I_{\\text {out }}=I_{i n}^{\\Gamma}$, where $I_{\\text {in }}$ is the original value of the pixel, $I_{\\text {out }}$ is the adjusted value of the pixel, and the shape of the curve is defined by $\\Gamma[[57]]$.\n}\nno contrast adjustment\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-08}\n\\end{center}\n\nFig. 12. False-color and coaxially-transformed images of a melt pool produced using PV \\#1. The top row shows the melt pool image after three different contrast adjustments. The middle row shows each contrast-adjusted image segmented into spatter, the nose region, and the tail region. The bottom row shows a visualization of the SIFT features generated using a MATLAB script written by Dollar [53]. pool body (i.e. everything that is not considered spatter) is separated into the \"tail\" region and the \"nose\" region. These two regions are delineated by the line perpendicular to the $\\xi$-axis (parallel to the direction of melt pool travel) at the point of maximum melt pool width. This process, shown schematically in Fig. 12, produces nine distinct fingerprints (calculated as described in Section 3.4) for each training image. All nine fingerprints are combined (appended) to form the final multi-modality representation of the melt pool which is of size $1 \\times 450$. Note that programmatically all of the SIFT features are first calculated across the entirety of each contrast-adjusted melt pool image before segmentation in order to avoid the creation of artifacts at the boundaries of the segmented images.\n\nWhile the choice of the three segmentation regions (spatter, nose, and tail) is informed by knowledge of melt pool dynamics (e.g.", "start_char_idx": 455770, "end_char_idx": 460365, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "59854dc0-fa89-48ef-a37e-a3d9ec6b44d4": {"__data__": {"id_": "59854dc0-fa89-48ef-a37e-a3d9ec6b44d4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ddb04fac-d8cb-491b-88ac-ec96c7dff778", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ff704e552510a643489c535aad91da4e5497c40ae4ba0722a4caa50e6252af65", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "23f93cd9-dc3c-4128-952c-79c4eabafcab", "node_type": "1", "metadata": {}, "hash": "ae18b52d07ce23573b1ff9dea53569718190a98cb8c924fc04a28c1f7620807e", "class_name": "RelatedNodeInfo"}}, "text": "These two regions are delineated by the line perpendicular to the $\\xi$-axis (parallel to the direction of melt pool travel) at the point of maximum melt pool width. This process, shown schematically in Fig. 12, produces nine distinct fingerprints (calculated as described in Section 3.4) for each training image. All nine fingerprints are combined (appended) to form the final multi-modality representation of the melt pool which is of size $1 \\times 450$. Note that programmatically all of the SIFT features are first calculated across the entirety of each contrast-adjusted melt pool image before segmentation in order to avoid the creation of artifacts at the boundaries of the segmented images.\n\nWhile the choice of the three segmentation regions (spatter, nose, and tail) is informed by knowledge of melt pool dynamics (e.g. that spatter is likely to occur when a deep keyhole is present [25] and balling affects the morphology of the tail [11,58]), the choices of the exact contrast adjustments, SIFT window size, and number of visual words, are less informed. Therefore the authors suspect that an improved representation of the in-situ melt pool appearance could be developed through the use of Deep Learning techniques [49].\n\n\\subsection*{3.6. Training}\nAs observed previously, the ground-truths in this work are not known a priori. That is, the authors do not know what groupings are appropriate to describe the in-situ melt pool morphologies; much less which specific in-situ melt pool appearances should correspond to each label. When confronting an \"unsupervised\" ML task, it is often useful to visualize the locations of the final feature vectors (in this case the fingerprints) of each training datum in feature space. Because feature space is typically high-dimensional (in this case 450D) direct visualization is not possible and a low-dimensional approximation of feature space must be used instead. A common algorithm for constructing this low-dimensional approximation is t-SNE (t-distributed Stochastic Neighbor Embedding) [59]. In a low-dimensional t-SNE visualization the relative distances between the feature vectors are preserved (albeit non-linearly), however the absolute distances between data and their relative positions are lost [59]. In other words, fingerprints that are close in 450D space will be close in t-SNE 2D space and fingerprints that are far apart in 450D space will be far apart in t-SNE 2D space, but no other conclusions about their relative distribution can be inferred. For this reason, $t$-SNE visualizations are often used to identify natural clusters of high-dimensional feature vectors [59]. Fig. 13 shows a t-SNE visualization of the 24,385 training fingerprints in which each datum has been color-coded using the only label available - the dominant ex-situ morphological characteristics for the given parameter combination reported in [35].\n\nPerhaps unsurprisingly, the above t-SNE visualization is not particularly illuminating. For example, fingerprints of melt pools produced using desirable process parameters overlap extensively with fingerprints of melt pools produced using balling and keyholing porosity process parameters. As discussed in [35], many of the ex-situ flaws such as keyholing porosity and balling are periodic in nature, therefore it is to be expected that each process parameter combination will produce a range of in-situ melt pool morphologies.\n\nA far more effective approach is to visualize the regions in process space for which a given set of fingerprints appear. In order to accomplish this, \"sets\" of similar fingerprints must first be identified and delineated. Grouping of similar fingerprints was performed using a standard kmeans unsupervised clustering algorithm [55], represented by Fig. 9h. For this work, cluster initialization was performed using random seeding, with preference given to a uniform spacing between clusters. Ideally, the number of requested clusters could be informed by the $t-$ SNE visualization in Fig. 13, unfortunately, very few distinct clusters are evident. Instead, many of the melt pool fingerprints appear to exist on a continuum. Therefore, a total of 30 clusters were requested; while this value is somewhat arbitrary, poor differentiation between in-situ melt pool appearances was observed when fewer than 20 clusters were delineated while additional meaningful differentiations did not appear when more than approximately 30 clusters were delineated. Cluster seeding is repeated 10 times to reduce the chance of the algorithm converging to a poor solution; e.g. a shallow local minimum instead of a global, or at least a deeper local, minimum.\n\nFig.", "start_char_idx": 459535, "end_char_idx": 464210, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "23f93cd9-dc3c-4128-952c-79c4eabafcab": {"__data__": {"id_": "23f93cd9-dc3c-4128-952c-79c4eabafcab", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "59854dc0-fa89-48ef-a37e-a3d9ec6b44d4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cb61b0752fe3040fc3613a81b8457aebb60c4dd2a0cd455c240c2f4aeb2e8206", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d342b2f1-e3ea-4814-b89a-0d992e80f0ac", "node_type": "1", "metadata": {}, "hash": "ea1ab4bead477ab27f68247c6997d59a0d1f17a04cfd1cf02d84b0c5a7ea84a5", "class_name": "RelatedNodeInfo"}}, "text": "9h. For this work, cluster initialization was performed using random seeding, with preference given to a uniform spacing between clusters. Ideally, the number of requested clusters could be informed by the $t-$ SNE visualization in Fig. 13, unfortunately, very few distinct clusters are evident. Instead, many of the melt pool fingerprints appear to exist on a continuum. Therefore, a total of 30 clusters were requested; while this value is somewhat arbitrary, poor differentiation between in-situ melt pool appearances was observed when fewer than 20 clusters were delineated while additional meaningful differentiations did not appear when more than approximately 30 clusters were delineated. Cluster seeding is repeated 10 times to reduce the chance of the algorithm converging to a poor solution; e.g. a shallow local minimum instead of a global, or at least a deeper local, minimum.\n\nFig. 14 shows the percentage of training melt pools at each of the 29 process parameter combinations with fingerprints belonging to one of the 30 clusters. Observe that this set (cluster) of fingerprints is far more prevalent in the keyholing porosity regime than elsewhere in process space. Therefore this set of fingerprints (i.e. this in-situ melt pool appearance) can be linked to keyholing porosity. This linkage process (Fig. 9i) is performed by a human and is repeated for all 30 sets\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-09}\n\\end{center}\n\n(clusters) of fingerprints. Over the course of this work it was observed that no clusters of fingerprints could be associated with only the severe keyholing region of process space, implying that the depth of the keyhole-mode melting vapor cavity does not have a controlling influence on the in-situ appearance of the melt pool. Furthermore, it was observed that a side-effect of the multi-modality fingerprint histogram is the occurrence of clusters of fingerprints with locations in high-dimensional space that are driven primarily by the morphology of the spatter, which is not necessarily correlated with any ex-situ flaws observed in [35]. Clusters of this type were labeled spatter are discussed in more detail in Section 4.1.\n\nOnce unsupervised ML techniques have been used to understand and label the in-situ appearances of the training melt pools, supervised ML techniques can be employed to classify melt pools not included in the training database. It is extremely important to note that any classifications based on this approach are not tied directly to ex-situ outcomes. In other words, even if a melt pool is classified as keyholing porosity it cannot be concluded that keyholing porosity was indeed generated by that melt pool - even within some degree of uncertainty.\\\\\nFig. 13. A t-SNE visualization of all of the training fingerprints with each datum colorcoded according to the dominate ex-situ morphology of melt pools produced using the same process parameter combination. While t-SNE visualizations are sometimes presented with axes, they have been removed from this figure as neither their magnitudes nor their relative values carry any physical meaning. The t-SNE algorithm was executed with a perplexity of 75 while all other parameters were set to their default value [59] and no dimensionality reduction using Principle Component Analysis was implemented.\\\\\nInstead, such a classification only indicates that a given melt pool has an in-situ fingerprint which is similar to fingerprints found most prevalently (or ideally, exclusively) in the keyholing porosity regime of process space.\n\nClassification of the melt pool morphologies (i.e. the 450 element fingerprints) is performed using a multi-class Support Vector Machine (SVM) [60,61] which is shown graphically in Fig. 9j. In its original formulation, an SVM is a binary classifier capable of distinguishing between only two different classes [61]. During training an SVM learns a hyperplane which bisects the high-dimensional feature space such that all of the feature vectors belonging to one class lie on a different side of the hyperplane than all of the feature vectors belonging to the other class (with the minimum error possible) [61]. A variety of methods are available to apply SVMs to non-binary (i.e. multi-class) classification problems. Perhaps the simplest such method converts a multi-class problem into a set of binary classification problems such that binary classifiers can be trained to distinguish between each class and \"all of the other classes\" [62]. The multiple binary classifiers can then be combined to form the multi-class SVM.", "start_char_idx": 463316, "end_char_idx": 467943, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d342b2f1-e3ea-4814-b89a-0d992e80f0ac": {"__data__": {"id_": "d342b2f1-e3ea-4814-b89a-0d992e80f0ac", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "23f93cd9-dc3c-4128-952c-79c4eabafcab", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e3274abd9e73c004ff1c181e3892740bb23bec1e19facc4a267fa9e1d66667e1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "38ac53ef-328c-4031-8cd9-4454d0db7de8", "node_type": "1", "metadata": {}, "hash": "73b0c105fbfab0954bbb19de6dcd5fe5702db012d9aa503b6fcfa5fda2adaeaa", "class_name": "RelatedNodeInfo"}}, "text": "9j. In its original formulation, an SVM is a binary classifier capable of distinguishing between only two different classes [61]. During training an SVM learns a hyperplane which bisects the high-dimensional feature space such that all of the feature vectors belonging to one class lie on a different side of the hyperplane than all of the feature vectors belonging to the other class (with the minimum error possible) [61]. A variety of methods are available to apply SVMs to non-binary (i.e. multi-class) classification problems. Perhaps the simplest such method converts a multi-class problem into a set of binary classification problems such that binary classifiers can be trained to distinguish between each class and \"all of the other classes\" [62]. The multiple binary classifiers can then be combined to form the multi-class SVM. All of the training parameters\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-09(1)}\n\\end{center}\n\nFig. 14. A heat map showing the prevalence of a given set (cluster) of melt pool fingerprints across process space. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with fingerprints belonging to the given cluster. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6).\\\\\nfor the multi-class SVM were set to the default values listed in [60].\n\n\\subsection*{3.7. Melt pool classification and performance of the ML methodology}\nOnce the training of the ML methodology is complete, previously \"unseen\" melt pool images captured during the overhang experiment (Section 2.7) can be classified as one of five melt pool types: desirable, balling, under-melting, keyholing porosity, or spatter (Fig. 9k). After coaxial transformation If each camera frame, the multi-modality fingerprint is calculated (Sections 3.3-3.5) and classified by the trained SVM (Section 3.6). The results of these classifications are presented in Section 4.2.\n\nThe classification process requires approximately $0.4 \\mathrm{~s}$ per frame on a single Intel ${ }^{\\circledR} \\mathrm{i} 7-6700 \\mathrm{~K} 4.00 \\mathrm{GHz}$ processor. It is important to note that in the absence of ground-truth labels, quantifying the overall performance of the presented ML methodology is not possible. However, 10fold cross-validation $[63,64]$ was performed during training of the multi-class SVM and reported a classification accuracy of $85.1 \\%$. In other words, the hyperplanes learned by the SVM are able to properly delineate the fingerprints contained within the training database according to the labels applied in Section 3.6 with an accuracy of $85.1 \\%$. It is important to note that this measure of classification accuracy is not an indicator of overall algorithm performance; it is only reported to demonstrate that the use of an SVM (as opposed to another classifier) is reasonable for this dataset.\n\n\\section*{4. Results}\n\\subsection*{4.1. Melt pool morphologies across process space}\nThe prevalence of a particular in-situ melt pool appearance throughout process space can be visualized by considering the cluster assignments at each tested process parameter combination. In other words, for each parameter combination imaged during training, a certain percentage of the captured melt pool frames will belong to a given set (cluster) of fingerprints described in Section 3.6. For the remainder of this document, a set of similar fingerprints is referred to as a morphology.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-10(1)}\n\\end{center}\n\nFig. 15. A heat map showing the prevalence of melt pool morphologies associated with desirable ex-situ outcomes. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with desirable morphologies. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6). Refer to Fig.", "start_char_idx": 467106, "end_char_idx": 471340, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "38ac53ef-328c-4031-8cd9-4454d0db7de8": {"__data__": {"id_": "38ac53ef-328c-4031-8cd9-4454d0db7de8", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d342b2f1-e3ea-4814-b89a-0d992e80f0ac", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9cc60936166b1d49905db85dfee92e0982f70b086c6426bbbdfd1b962a0e9f2e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "8ab71292-ee47-4835-9bba-9ba2d7d2baf6", "node_type": "1", "metadata": {}, "hash": "448bc589fed67e83aa4aa410a4466c3ffa617d03a8755b067cf85612176617e1", "class_name": "RelatedNodeInfo"}}, "text": "For the remainder of this document, a set of similar fingerprints is referred to as a morphology.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-10(1)}\n\\end{center}\n\nFig. 15. A heat map showing the prevalence of melt pool morphologies associated with desirable ex-situ outcomes. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with desirable morphologies. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6). Refer to Fig. 4 for explanation of the overlaid ex-situ data.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_552cb8e3f1f233ad179cg-10}\n\nFig. 16. A selection of false-color melt pool images captured by the high speed camera. All three melt pools have fingerprints associated with desirable ex-situ outcomes.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-10(2)}\n\\end{center}\n\nFig. 17. A heat map showing the prevalence of melt pool morphologies associated with balling. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with desirable morphologies. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6). Refer to Fig. 4 for explanation of the overlaid ex-situ data.\n\nWhile the example heat map shown in Section 3.6 (Fig. 14) contains information about only one of the morphologies, Figs. 15, 17, 19, 21, and 23 show the percentage of training melt pools (at each process parameter combination) belonging to the morphologies associated with a given ex-situ morphology. Also as in Section 3.6, the ex-situ morphology results are overlaid on top the heat map.\n\nFig. 15, for example, shows the distribution of the six melt pool morphologies (i.e. six sets of similar fingerprints) associated with desirable outcomes. Observe that the desirable morphologies are most prevalent in the \"center\" of studied processing space - away from the high energy density, low energy density, and balling regimes. In the training dataset, $76 \\%$ of the melt pools produced using the EOS nominal PV \\#1 parameters ( $285 \\mathrm{~W}, 960 \\mathrm{~mm} / \\mathrm{s}$ ) had fingerprints associated with desirable outcomes. More strictly, $76 \\%$ of these melt pools had fingerprints belonging to one of the six clusters associated with desirable outcomes. Fig. 15 shows several examples of desirable melt pools.\n\nFig. 17 shows the distribution of the single melt pool morphology associated with balling. Observe that the balling morphology is most prevalent in the high beam power and high beam velocity regime of\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-11(1)}\n\\end{center}\n\nFig. 18. A selection of false-color melt pool images captured by the high speed camera. All three melt pools have fingerprints associated with balling. Note the balling instabilities visible just behind the melt pool tail in the left and center images.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-11(3)}\n\\end{center}\n\nFig. 19. A heat map showing the prevalence of melt pool morphologies associated with under-melting. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with desirable morphologies. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6). Refer to Fig. 4 for explanation of the overlaid ex-situ data.\n\nprocess space. Fig.", "start_char_idx": 470652, "end_char_idx": 474600, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "8ab71292-ee47-4835-9bba-9ba2d7d2baf6": {"__data__": {"id_": "8ab71292-ee47-4835-9bba-9ba2d7d2baf6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "38ac53ef-328c-4031-8cd9-4454d0db7de8", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cf68fdc24bbe1957abdab32c33a4d69f8fb97f3d850c8c7e8a48c7bbdc9aed60", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e54a347a-9c10-4ead-af4f-41e2f887d1f4", "node_type": "1", "metadata": {}, "hash": "c69b4082ab40d17e8d3f4698ded977448a7555d6c373eb4ec64220f3f4944f15", "class_name": "RelatedNodeInfo"}}, "text": "All three melt pools have fingerprints associated with balling. Note the balling instabilities visible just behind the melt pool tail in the left and center images.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-11(3)}\n\\end{center}\n\nFig. 19. A heat map showing the prevalence of melt pool morphologies associated with under-melting. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with desirable morphologies. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6). Refer to Fig. 4 for explanation of the overlaid ex-situ data.\n\nprocess space. Fig. 18 shows several examples of balling melt pools. In general, the balling melt pools are more elongated than the desirable melt pools (this difference is expected as discussed in [35]). In some of the high speed images (Fig. 18) the balling instability itself is visible as small circle separated from the main melt pool body and located directly behind the melt pool tail.\n\nFig. 19 shows the distribution of the two melt pool morphologies associated with under-melting. Observe that the under-melting morphologies are most prevalent in the low beam power regime of process space. Interestingly, these morphologies extend well into the regions of process space producing melt pools with depths greater than the $70 \\mu$ m effective powder layer thickness. As noted in Section 2.6, in-situ data were not successfully collected for much of the under-melting region; more in-situ data may allow for a more robust understanding of morphologies associated with under-melting. Fig. 20 shows several examples of undermelting melt pools. In general, under-melting melt pools exhibit a \"fragmented\" appearance composed of multiple irregular bodies of\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_552cb8e3f1f233ad179cg-11(2)}\n\nFig. 20. A selection of false-color melt pool images captured by the high speed camera. All three melt pools have fingerprints associated with under-melting.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-11}\n\\end{center}\n\nFig. 21. A heat map showing the prevalence of melt pool morphologies associated with keyholing porosity. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with desirable morphologies. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6). Refer to Fig. 4 for explanation of the overlaid ex-situ data.\n\ncomparatively similar size.\n\nFig. 21 shows the distribution of the three melt pool morphologies associated with keyholing porosity. Observe that the keyholing porosity morphologies are most prevalent in the low beam velocity regime of process space - particularly at higher beam powers. Interestingly, no insitu morphologies could be associated with the severe keyholing melt pools discussed in Section 2.5 and [35]. This suggests that the keyholing porosity morphologies are detectable due to the instability, and not the depth, of the vapor cavity present during keyhole-mode melting [65]. Fig. 22 shows several examples of keyholing porosity melt pools. In general, keyholing porosity melt pools are more radially symmetric and less elongated than either desirable or balling melt pools.\n\nFig. 23 shows the distribution of the eighteen melt pool morphologies associated with spatter. Strictly, spatter is not a melt pool morphology identified by the ex-situ analysis presented in [35]. Indeed, its appearance as unique in-situ morphologies is an artifact of the multimodality melt pool representation discussed in Section 3.5.", "start_char_idx": 473789, "end_char_idx": 477748, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e54a347a-9c10-4ead-af4f-41e2f887d1f4": {"__data__": {"id_": "e54a347a-9c10-4ead-af4f-41e2f887d1f4", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "8ab71292-ee47-4835-9bba-9ba2d7d2baf6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b3b5cc8a0e75bab548b9fbc4c587e463b72511bca6d31f7250a95f2f440b7b8e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "20768a7c-8655-406a-9d82-7a2138b1f1ed", "node_type": "1", "metadata": {}, "hash": "da4c791ad666fbd933555d1b25bf4f9d665e8e46cb0c6feaa85535719d6e54e4", "class_name": "RelatedNodeInfo"}}, "text": "Interestingly, no insitu morphologies could be associated with the severe keyholing melt pools discussed in Section 2.5 and [35]. This suggests that the keyholing porosity morphologies are detectable due to the instability, and not the depth, of the vapor cavity present during keyhole-mode melting [65]. Fig. 22 shows several examples of keyholing porosity melt pools. In general, keyholing porosity melt pools are more radially symmetric and less elongated than either desirable or balling melt pools.\n\nFig. 23 shows the distribution of the eighteen melt pool morphologies associated with spatter. Strictly, spatter is not a melt pool morphology identified by the ex-situ analysis presented in [35]. Indeed, its appearance as unique in-situ morphologies is an artifact of the multimodality melt pool representation discussed in Section 3.5. While independent calculation of a spatter fingerprint was observed to improve overall classification performance, it occasionally allows the morphology of the spatter to \"overpower\" information about the shape of the melt pool itself - resulting in the aforementioned spatter\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-12}\n\\end{center}\n\nFig. 22. A selection of false-color melt pool images captured by the high speed camera. All three melt pools have fingerprints associated with keyholing porosity.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-12(3)}\n\\end{center}\n\nFig. 23. A heat map showing the prevalence of melt pool morphologies associated with spatter. Values within the text boxes indicate the percentage of training melt pools (at each process parameter combination) with desirable morphologies. The ex-situ morphology information from [35] is overlaid on top of the heat map. In-situ data were not collected for the seven parameter combinations (circles) without an associated text box (see Section 2.6). Refer to Fig. 4 for explanation of the overlaid ex-situ data.\n\nmorphologies. In general, spatter appears least frequently in the region of process space associated with desirable melt pool morphologies. Fig. 24 shows several examples spatter melt pools. Observe that the melt pool bodies exhibit dramatically different melt pool morphologies while the primary commonality between the selected images is the presence of spatter.\n\nFinally, Fig. 25 shows the occurrence of the various melt pool morphologies for several selected process parameter combinations. As hypothesized in [35], every process parameter combination produces melt pools with a range of in-situ appearances. For example, even the parameter combination producing the most keyholing porosity melt pools (PV \\#19) also produces melt pools with desirable morphologies in $21 \\%$ of frames.\n\n\\subsection*{4.2. Non-bulk geometry (unsupported overhang)}\nFig. 26 reports the melt pool morphology classifications during fusion of the first layer of a $5.0 \\mathrm{~mm}$ wide unsupported overhang. Recall that in the first layer of an overhang there is no fused material below the melt pool, only unfused powder. Data were collected from multiple\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_552cb8e3f1f233ad179cg-12(2)}\n\nFig. 24. A selection of false-color melt pool images captured by the high speed camera. All three melt pools have fingerprints associated with spatter.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-12(1)}\n\\end{center}\n\nFig. 25. The melt pool morphologies produced by four different process parmeter combinations in the training database. PV \\#1 is the EOS nominal parameter combination. PV \\#36 produced the largest percentage of balling melt pools. PV \\#4 produced the largest percentage of under-melting melt pools. PV \\#19 produced the largest percentage of keyholing porosity melt pools.\n\nadjacent melt tracks as the layer was fused. Each data bar reports the classifications for all of the melt pools that are certain distance across the width of the overhang; data are binned in increments of approximately $500 \\mu \\mathrm{m}$. The edges of the overhang are indicated by the vertical dashed lines.", "start_char_idx": 476906, "end_char_idx": 481094, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "20768a7c-8655-406a-9d82-7a2138b1f1ed": {"__data__": {"id_": "20768a7c-8655-406a-9d82-7a2138b1f1ed", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e54a347a-9c10-4ead-af4f-41e2f887d1f4", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "dfda09bc3941d0434160b41cac26b1f0c8702565c699c1226e569b2ad3dc3313", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "436309d8-572e-45fa-b0bd-dedf9742e4c9", "node_type": "1", "metadata": {}, "hash": "2fb7326abc53d675b1eea3e3007220f558f15f33a82c2f0312d1502ed12da444", "class_name": "RelatedNodeInfo"}}, "text": "\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-12(1)}\n\\end{center}\n\nFig. 25. The melt pool morphologies produced by four different process parmeter combinations in the training database. PV \\#1 is the EOS nominal parameter combination. PV \\#36 produced the largest percentage of balling melt pools. PV \\#4 produced the largest percentage of under-melting melt pools. PV \\#19 produced the largest percentage of keyholing porosity melt pools.\n\nadjacent melt tracks as the layer was fused. Each data bar reports the classifications for all of the melt pools that are certain distance across the width of the overhang; data are binned in increments of approximately $500 \\mu \\mathrm{m}$. The edges of the overhang are indicated by the vertical dashed lines. Note that the left-most and right-most data bars report data corresponding to melt pools beyond the extents of the overhang, i.e. those melt pools are, at least partially, on top of fused material. Data were collected for melt pools traveling in both directions across the overhang with each classification average based on between 60 and 129 frames of data. It is readily apparent that the melt pools transition from primarily desirable to primarily keyholing porosity as the melt pool travels from the edge of the overhang to its center. A symmetric transition back to desirable classifications occurs as the melt pool exits the overhang region and returns to previously-fused material. This behavior is fully expected as the low thermal conductivity [47,48] of the unfused powder is expected to result in a much deeper and more unstable keyhole vapor pocket than is otherwise produced by the EOS nominal process parameter combination ( $\\mathrm{PV} \\# 1$ ).\n\nFig. 27 reports the melt pool morphology classifications during fusion of the first five layers of a $5.0 \\mathrm{~mm}$ wide unsupported overhang. For the first three to four layers, the observed melt pool behavior is similar to that discussed above. That is, a substantial percentage of the melt pools transition from desirable to keyholing porosity as they pass over the unsupported overhang. Note that the upper bar plot is a simplified\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_552cb8e3f1f233ad179cg-13}\n\\end{center}\n\nFig. 26. Melt pool morphology classifications across the $5.0 \\mathrm{~mm}$ width of the first layer of an unsupported overhang. Each data bar bins classifications in $500 \\mu \\mathrm{m}$ increments along the melt tracks spanning the width of the overhang. The extents of the overhang are indicated by the vertical dashed lines.The values in parantheses indicate the number of melt pool classifications included in the corresponding bin. The indicated positive $x$-axis corresponds to the global coordinate system used throughout this thesis.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_552cb8e3f1f233ad179cg-13(1)}\n\nFig. 27. Melt pool morphology classifications across the $5.0 \\mathrm{~mm}$ width of the first five layers of an unsupported overhang. Each data bar bins classifications in $500 \\mu \\mathrm{m}$ increments along the melt tracks spanning the width of the overhang. The extents of the overhang are indicated by the vertical dashed lines. The indicated positive $x$ axis corresponds to the global coordinate system used throughout this thesis.\n\nduplicate of the plot shown above in Fig. 26. As expected, the melt pools spanning the overhang are increasingly classified as desirable as subsequent layers are built. In other words, the morphology of the melt pools improves as the test artifact approaches bulk geometry. Indeed, by the fifth layer melt pool behavior in the center of the overhang is quite similar to melt pool behavior near the edges.\n\n\\section*{5. Conclusions}\nIn this work, In718 L-PBF melt pools were imaged using a high speed, visible-light camera with a fixed FoV. High speed camera data collected from across process space were analyzed using contemporary\\\\\nCV feature extraction methods and unsupervised ML techniques. These data were then used to link in-situ melt pool morphologies to the ex-situ melt pool morphologies and processing defects previously reported by the authors in [35].", "start_char_idx": 480301, "end_char_idx": 484542, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "436309d8-572e-45fa-b0bd-dedf9742e4c9": {"__data__": {"id_": "436309d8-572e-45fa-b0bd-dedf9742e4c9", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "20768a7c-8655-406a-9d82-7a2138b1f1ed", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "e59d6771438a58c3c42df351720ca3fac6d1919dd40d6db54834a4127d328d0f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "56e3501c-e336-447b-8f88-961220197818", "node_type": "1", "metadata": {}, "hash": "73d5f593ca2823e364baffb0dfe42bab3ac6df43850fd62b1a64d713e6d0c978", "class_name": "RelatedNodeInfo"}}, "text": "duplicate of the plot shown above in Fig. 26. As expected, the melt pools spanning the overhang are increasingly classified as desirable as subsequent layers are built. In other words, the morphology of the melt pools improves as the test artifact approaches bulk geometry. Indeed, by the fifth layer melt pool behavior in the center of the overhang is quite similar to melt pool behavior near the edges.\n\n\\section*{5. Conclusions}\nIn this work, In718 L-PBF melt pools were imaged using a high speed, visible-light camera with a fixed FoV. High speed camera data collected from across process space were analyzed using contemporary\\\\\nCV feature extraction methods and unsupervised ML techniques. These data were then used to link in-situ melt pool morphologies to the ex-situ melt pool morphologies and processing defects previously reported by the authors in [35]. These linkages allowed for the identification of potential in-situ flaw formation signatures and the training of a melt pool classification algorithm.\n\nFeature extraction was performed using SIFT and the BoW ML technique - resulting in a scale-invariant representation of the in-situ melt pool morphology. The need for scale-invariance is well demonstrated by Fig. 16, in which melt pools of dissimilar size are linked to similar ex-situ outcomes. In order to compensate for the loss of spatial information during feature extraction as well as the large dynamic range\\\\\nof the input images, the final fingerprint describing melt pool morphology is composed of nine different segments. Each segment describes the gradient fields under different contrast adjustments and in different regions of the melt pool. While effective at differentiating between melt pools of differing in-situ appearances, many of the parameters controlling the architecture of the final morphology descriptor remain un-optimized; Deep Learning techniques may be well suited for developing an even more robust representation of in-situ melt pool morphology.\n\nSeveral in-situ melt pool appearances were successfully linked to the ex-situ melt pool types identified in [35] and reviewed Section 2.5: (1) A set of in-situ morphologies were found to occur almost exclusively at keyholing porosity parameter combinations (Fig. 21). (2) Conversely, no in-situ morphologies were found to be associated with severe keyholing. (3) A set of in-situ morphologies were found to occur more frequently in the balling region of process space (Fig. 17). (4) Interestingly, the set of in-situ morphologies most closely linked to under-melting extended well throughout the low power regime of process space (Fig. 19). (5) Several melt pool morphologies were associated with desirable ex-situ outcomes (Fig. 15). (6) As discussed in Section 3.6, an additional set of morphologies were associated with the presence of spatter, as opposed to a specific ex-situ outcome (Fig. 23). The periodic nature of many of the flaws was observed in-situ, as each process parameter combination produced melt pools with fingerprints associated with a range of ex-situ morphologies. Using a unique approach, the associations determined via unsupervised learning were used as the inputs for a supervised learning technique; thereby enabling the classification of melt pools not studied during training.\n\nSpecifically, melt pools were imaged during the printing of an unsupported overhang. Significant morphological changes were observed as the melt pools traveled away from the bulk region and across the overhang (Fig. 26). After the overhang reached a thickness exceeding the nominal depth of the melt pool, the in-situ morphological behavior approached that observed in the bulk (Fig. 27). The authors intend to utilize the presented methodology to study melt pool behavior of other non-bulk geometries such as contours and the edges of stripes [66] in the near future.\n\nIt is worth reiterating that any classifications based on the presented approach are not tied directly to ex-situ outcomes. In other words, even if a melt pool is classified as keyholing porosity it cannot be concluded that keyholing porosity was indeed generated by that melt pool - even within some degree of uncertainty. Instead, such a classification only indicates that a given melt pool has an in-situ fingerprint which is similar to fingerprints found most prevalently in the keyholing porosity regime of process space. In order to improve the fidelity of the classification methodology, ground truth information is required to link each frame of in-situ training data to specific instances of flaws observed ex-situ.", "start_char_idx": 483677, "end_char_idx": 488277, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "56e3501c-e336-447b-8f88-961220197818": {"__data__": {"id_": "56e3501c-e336-447b-8f88-961220197818", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "436309d8-572e-45fa-b0bd-dedf9742e4c9", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c8b553f447ada94155cf9584e5a68b00f45126c7d20c4d9036a32013450d09b0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "69ffe2d3-920c-4eb4-a2db-48f0f9091210", "node_type": "1", "metadata": {}, "hash": "e185ad727b6caea19e16a5c8086af567415ad18c01c7a51eb1398d75646a7da8", "class_name": "RelatedNodeInfo"}}, "text": "27). The authors intend to utilize the presented methodology to study melt pool behavior of other non-bulk geometries such as contours and the edges of stripes [66] in the near future.\n\nIt is worth reiterating that any classifications based on the presented approach are not tied directly to ex-situ outcomes. In other words, even if a melt pool is classified as keyholing porosity it cannot be concluded that keyholing porosity was indeed generated by that melt pool - even within some degree of uncertainty. Instead, such a classification only indicates that a given melt pool has an in-situ fingerprint which is similar to fingerprints found most prevalently in the keyholing porosity regime of process space. In order to improve the fidelity of the classification methodology, ground truth information is required to link each frame of in-situ training data to specific instances of flaws observed ex-situ. Finally, it is worth noting that while implementing the presented melt pool classification algorithm in a real-time scenario is beyond the current capabilities of the authors, ${ }^{8}$ extremely high speed calculation of simple melt pool descriptors (e.g. melt pool size) has been demonstrated in the literature [14].\n\n\\section*{Acknowledgements}\nThe authors would like to thank Dr. Brian Fisher (CMU) for lending their significant expertise with the high speed camera to help with the determination of appropriate camera settings. The authors would also like to thank Dr. Sneha Prabha Narra (CMU) for preliminary ex-situ\n\\footnotetext{${ }^{8}$ At 6,400 fps and a resolution of 1024 pixels $\\times 1024$ pixels a high speed camera would produce approximately $13 \\mathrm{~Gb}$ of data per second. As a result, over the course of a relatively short, 24 hour L-PBF build, on the order of 1000 $\\mathrm{Tb}$ of data would be generated. Such a data burden is currently unmanageable both in terms of data storage capacity as well as data transmission times.\n}\n\nIn718 melt pool data which were used to plan these experiments. Funding for this work was provided by CMU's Manufacturing Futures Initiative (internal grant number 062900.005.105.100020.01) and the purchase of the high speed camera and associated optics was supported by a Carnegie Institute of Technology Dean's Equipment Grant, FY 2016.\n\n\\section*{References}\n[1] K.M. Taminger, R.A. Hafley, Electron beam freeform fabrication for cost effective near-net shape manufacturing, NATO/RTOAVT-139 Spec. Metting Cost Eff. Manuf via Net Shape Process, (2006).\n\n[2] T. Wohlers, T. Caffrey, Wohlers Report, Fort Collins, CO, 2011.\n\n[3] C.A. Giffi, B. Gangula, P. Illinda, 3D Opportunity for the Automotive Industry: Additive Manufacturing Hits the Road, (2014) \\href{http://dupress.com/articles/}{http://dupress.com/articles/} additive-manufacturing-3d-opportunity-in-automotive/.\n\n[4] D. Bourell, M. Leu, D. Rosen, Roadmap for additive manufacturing: identifying the future of freeform processing, Solid Free. Fabr. Proc. (2009) (Accessed 23 May 2017), \\href{http://wohlersassociates.com/roadmap2009A.pdf}{http://wohlersassociates.com/roadmap2009A.pdf}.\n\n[5] M. Grasso, B.M. Colosimo, Process defects and in situ monitoring methods in metal powder bed fusion: a review, Meas. Sci. Technol. 28 (2017) 044005, , \\href{https://doi}{https://doi}. org/10.1088/1361-6501/aa5c4f.\n\n[6] S.K. Everton, M. Hirsch, P. Stravroulakis, R.K. Leach, A.T. Clare, Review of in-situ process monitoring and in-situ metrology for metal additive manufacturing, JMADE. 95 (2016) 431-445, \\href{https://doi.org/10.1016/j.matdes.2016.01.099}{https://doi.org/10.1016/j.matdes.2016.01.099}.\n\n[7] T.G. Spears, S.A.", "start_char_idx": 487367, "end_char_idx": 491015, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "69ffe2d3-920c-4eb4-a2db-48f0f9091210": {"__data__": {"id_": "69ffe2d3-920c-4eb4-a2db-48f0f9091210", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "56e3501c-e336-447b-8f88-961220197818", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "6f613258d9a86ccca203b266b51237baa994da4765497af3e98b36d616c3fc08", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "25c8d19a-0b6d-4111-8915-97ece8ca054f", "node_type": "1", "metadata": {}, "hash": "c918f4c71b664e6491378816b89876c66594256e6e31f7fcb3b96cbde7e834a7", "class_name": "RelatedNodeInfo"}}, "text": "Colosimo, Process defects and in situ monitoring methods in metal powder bed fusion: a review, Meas. Sci. Technol. 28 (2017) 044005, , \\href{https://doi}{https://doi}. org/10.1088/1361-6501/aa5c4f.\n\n[6] S.K. Everton, M. Hirsch, P. Stravroulakis, R.K. Leach, A.T. Clare, Review of in-situ process monitoring and in-situ metrology for metal additive manufacturing, JMADE. 95 (2016) 431-445, \\href{https://doi.org/10.1016/j.matdes.2016.01.099}{https://doi.org/10.1016/j.matdes.2016.01.099}.\n\n[7] T.G. Spears, S.A. Gold, In-process sensing in selective laser melting (SLM) additive manufacturing, Integr. Mater. Manuf. Innov. 5 (2016) 1-25, \\href{https://doi.org/10}{https://doi.org/10}. 1186/s40192-016-0045-4.\n\n[8] EOS GmbH, EOS M 290 Data Sheet, (2017) (Accessed 20 January 2018), https:// \\href{http://cdn0.scrvt.com/eos/413c861f2843b377/51d966b8b31d/EOS_System_Data_Sheet_}{cdn0.scrvt.com/eos/413c861f2843b377/51d966b8b31d/EOS\\_System\\_Data\\_Sheet\\_} EOS\\_M\\_290\\_EN\\_V6\\_Web.pdf.\n\n[9] H. Gong, K. Rafi, H. Gu, T. Starr, B. 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Anam, J.J.S.", "start_char_idx": 503332, "end_char_idx": 506117, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "61898987-3818-4e4d-92db-38fa3e2f5c2f": {"__data__": {"id_": "61898987-3818-4e4d-92db-38fa3e2f5c2f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "36850e0e-63ee-454d-b668-8dc56cc05833", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "c3de2ff60a61aa2331d62448e19f7554150bd8dfde2979b7f84ec84a22fca7a8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fbed3d5c-44f4-45b0-a992-17c4df432026", "node_type": "1", "metadata": {}, "hash": "c5b1f74b82bbf10a8ab4c8cbd16da3ef8d39dc6b906742d1f89e40737fcec3a4", "class_name": "RelatedNodeInfo"}}, "text": "[65] C. 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Narra, Melt Pool Geometry and Microstructure Control Across Alloys in Metal Based Additive Manufacturing Processes, Carnegie Mellon University, 2017.\n\n\\begin{itemize}\n  \\item \n\\end{itemize}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\DeclareUnicodeCharacter{2020}{$\\dagger$}\n\n\\begin{document}\n\\section*{3D PRINTING}\n\\section*{Keyhole threshold and morphology in laser melting revealed by ultrahigh-speed $x$-ray imaging}\n\\begin{abstract}\nRoss Cunningham ${ }^{1 *}$, Cang Zhao ${ }^{2 *}$, Niranjan Parab ${ }^{2}$, Christopher Kantzos ${ }^{1}$, Joseph Pauza', Kamel Fezzaa ${ }^{2}$, Tao Sun ${ }^{2}$, Anthony D. Rollett ${ }^{1}+$\\\\\nWe used ultrahigh-speed synchrotron x-ray imaging to quantify the phenomenon of vapor depressions (also known as keyholes) during laser melting of metals as practiced in additive manufacturing. Although expected from welding and inferred from postmortem cross sections of fusion zones, the direct visualization of the keyhole morphology and dynamics with high-energy $x$-rays shows that (i) keyholes are present across the range of power and scanning velocity used in laser powder bed fusion; (ii) there is a well-defined threshold from conduction mode to keyhole based on laser power density; and (iii) the transition follows the sequence of vaporization, depression of the liquid surface, instability, and then deep keyhole formation. These and other aspects provide a physical basis for three-dimensional printing in laser powder bed machines.", "start_char_idx": 505792, "end_char_idx": 508857, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fbed3d5c-44f4-45b0-a992-17c4df432026": {"__data__": {"id_": "fbed3d5c-44f4-45b0-a992-17c4df432026", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "61898987-3818-4e4d-92db-38fa3e2f5c2f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8313a7027e24790b8ac14ad302bc101c6f138f3913c7276d290644b327f629e9", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "07dc24ab-0926-4ecb-aadc-ad487128893c", "node_type": "1", "metadata": {}, "hash": "e417c1c57ca87c0be5dec254c6f7c81e868e33dbbbe79a892ccce69570f473bf", "class_name": "RelatedNodeInfo"}}, "text": "Although expected from welding and inferred from postmortem cross sections of fusion zones, the direct visualization of the keyhole morphology and dynamics with high-energy $x$-rays shows that (i) keyholes are present across the range of power and scanning velocity used in laser powder bed fusion; (ii) there is a well-defined threshold from conduction mode to keyhole based on laser power density; and (iii) the transition follows the sequence of vaporization, depression of the liquid surface, instability, and then deep keyhole formation. These and other aspects provide a physical basis for three-dimensional printing in laser powder bed machines.\n\\end{abstract}\n\n$1 /$ etal additive manufacturing (AM) describes a family of technologies that fabricate complex metallic three-dimensional (3D) parts directly from a digital model. Laser powder bed fusion (LPBF) is common in metal AM and utilizes a scanning laser to melt parallel lines on the order of $100 \\mu \\mathrm{m}$ wide in each successive layer of powder to develop the desired solid part in 3D. High energy densities at high laser power and low scanning velocity result in a transition in the melt pool shape from shallow and semicircular (conduction mode) to deep and narrow (keyhole mode). The keyhole mode in 3D printing is known to be associated with excessive porosity. The resulting large pores degrade the fatigue life of the part by acting as crack initiators (1). A keyhole is a vapor-filled depression well known in welding and is associated with the onset of vaporization of the liquid metal $(2-4)$ at a critical power density. Our current understanding of keyhole formation is based on indirect cross-sectional measurements of melt pools after freezing combined with occasional videography of the top surface of the melt pool and vapor hole. The importance of the power density under the illuminated spot was understood, but the literature favored a powerlaw relation between penetration and power, taking beam width into account (5).\n\nWe used an ultrahigh-speed synchrotron x-ray imaging technique to visualize the development of the melt pool and vapor depression (i.e., keyhole) in solid Ti-6Al-4V under both the stationary beam and scanning beam modes. The synchrotron-\n\\footnotetext{${ }^{1}$ Department of Materials Science and Engineering Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA, USA. ${ }^{2}$ X-ray Science Division, Argonne National Laboratory, 9700 S Cass Ave, Lemont, IL, USA. *These authors contributed equally to this work. \u2020Corresponding author. Email: \\href{mailto:rollett@andrew.cmu.edu}{rollett@andrew.cmu.edu}\n}\n\nbased AM instrumentation and technique development were reported previously by this team and others (6-10). With high spatial (i.e., $2 \\mu \\mathrm{m}$ ) and temporal (i.e., 50 to $400 \\mathrm{kHz}$ ) resolutions afforded by the hard $x$-ray synchrotron facility and the state-of-the-art beamline instruments at Argonne National Laboratory's Advanced Photon Source (APS), we demonstrated that vapor depressions exist under essentially all conditions relevant to LPBF and that the size and shape of such depressions vary in a systematic fashion. This relation contradicts the commonly held belief that the transition from conduction to keyhole mode coincides with the point at which the porosity and high-aspect-ratio melt pools appear. Moreover, strong similarities between laser drilling and the keyholing regime of a moving beam are evident. The presence of a layer of powder results in only a second-order effect. Above all, our high-resolution visualization data reveal the transition kinetics from conduction to keyhole modes at a well-defined threshold power density and support quantitative relationships between drilling rate, keyhole depression depth, front wall angle of the keyhole, and excess power density.\n\nDuring the evolution of the melt pool and vapor depression under stationary illumination, we found five distinct regimes of behavior: (i) melting, (ii) vapor depression formation and growth, (iii) vapor depression instability, (iv) keyhole formation and growth, and (v) melt pool shape change (Fig. 1 and movie S1) (11). Soon after we turned the laser on, the metal began to melt, and a solid-liquid interface was visible owing to the $\\mathrm{x}$-ray absorption contrast (Fig. 1A). Once the surface temperature neared the boiling point, localized vaporization formed a depression from the recoil pressure (Fig. 1B) (12).", "start_char_idx": 508205, "end_char_idx": 512676, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "07dc24ab-0926-4ecb-aadc-ad487128893c": {"__data__": {"id_": "07dc24ab-0926-4ecb-aadc-ad487128893c", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fbed3d5c-44f4-45b0-a992-17c4df432026", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "ccf7aae65991d1bde6914ff16795514f3970285bf77d10a253b481e1a1f62ae1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "09bf9d67-d3fe-4584-adf4-1ebb98c7daf7", "node_type": "1", "metadata": {}, "hash": "f274f861fb48f4049c2a762d2938e21a92a9a4e32d8f5987a5fef43f9084f75f", "class_name": "RelatedNodeInfo"}}, "text": "Above all, our high-resolution visualization data reveal the transition kinetics from conduction to keyhole modes at a well-defined threshold power density and support quantitative relationships between drilling rate, keyhole depression depth, front wall angle of the keyhole, and excess power density.\n\nDuring the evolution of the melt pool and vapor depression under stationary illumination, we found five distinct regimes of behavior: (i) melting, (ii) vapor depression formation and growth, (iii) vapor depression instability, (iv) keyhole formation and growth, and (v) melt pool shape change (Fig. 1 and movie S1) (11). Soon after we turned the laser on, the metal began to melt, and a solid-liquid interface was visible owing to the $\\mathrm{x}$-ray absorption contrast (Fig. 1A). Once the surface temperature neared the boiling point, localized vaporization formed a depression from the recoil pressure (Fig. 1B) (12). The pressure pushed liquid up and out of the depression (13), which grew at a constant rate until it began to fluctuate (Fig. 1C). Shortly thereafter, the vapor depression transitioned from shallow and semicircular to a deep, conical depression (Fig. 1D). After this transition, the vapor depression penetrated rapidly through the melt pool, suggesting substantial displacement of liquid from the region at the center of the spot. The vapor depression then penetrated at a much faster rate into the material, and the liquid-vapor interface fluctuated strongly (Fig. 1, $\\mathrm{E}$ to $\\mathrm{H}$ ). After the vapor depression fluctuation, the melt pool soon changed from a quasisemicircular shape to a bimodal shape with a bowl on top and a spike in the middle at the bottom (Fig. 1, I and J). We observed two different melt pool shapes (Fig. 1, E and J), which resolves previous uncertainty about the transition from conduction to keyhole mode (14).\n\nWe measured the maximum depth of the vapor depression for each frame as a function of spot size $D$ and applied laser power (Fig. 2, A and B). We found a clear transition over $\\sim 5 \\mu \\mathrm{s}$ that separated the slow growth of the melt pool through conduction alone and the regime of rapid penetration and keyhole formation. The time leading to this transition decreased nonlinearly with power for a given spot size. We also observed that the drill rate (i.e., slope of depth versus time) in the keyhole regime increased with power. The occurrence of substantial fluctuations as the keyhole forms means that measuring an accurate drill rate is subject to error depending on the duration of the measurement. To mitigate this, we determined the drill rate from both the entire data for each experiment and just the portion of the curve between the transition and the onset of substantial fluctuations. To compare two spot sizes, we calculated the average power density as $\\rho=\\frac{2 P}{\\pi D^{2}}$, where $P$ is the laser power. We ignored laser absorptivity, as we assumed it to be constant across each experiment because we did not vary the material, so $\\rho$ is applied power density. Often, a material-dependent critical power density is defined, over which the keyhole mode is active, on the order of $0.5 \\mathrm{MW} / \\mathrm{cm}^{2}(3,15,16)$. The drill rate in the keyhole regime for our experiments followed approximately a linear relation with power density after the threshold of $\\sim 0.4 \\mathrm{MW} / \\mathrm{cm}^{2}$ (Fig. 2C), consistent with previous estimates $(3,15,16)$.\n\nWe analyzed the morphology and dimension of the melt pool and found that the depth-towidth aspect ratio of the melt pool increased with time, with two distinct transitions (fig. S2) (11). The first transition occurred almost simultaneously with the beginning of fluctuations in the vapor depression, after which the increase in aspect ratio accelerated. The second transition occurred when the aspect ratio reached a value close to 0.5 (this number varies with laser power). After this transition, the increase of aspect ratio slowed. We defined the first transition as the vapor depression transition and the second as the melt pool transition. This multistep transition from hemispherical melt pool (i.e., conduction mode) through smooth\\\\\ndepression and instability to developed sharp keyhole stands in contrast to previous analyses that had to rely on indirect information from cross sections of solidified weld pools.", "start_char_idx": 511751, "end_char_idx": 516155, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "09bf9d67-d3fe-4584-adf4-1ebb98c7daf7": {"__data__": {"id_": "09bf9d67-d3fe-4584-adf4-1ebb98c7daf7", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "07dc24ab-0926-4ecb-aadc-ad487128893c", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d67ef91cac9f71f180523058529b9a6bdf165f6ce1eb62d6443a8d4c288aa25c", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "e1dd9e13-a6ac-4371-8a83-cfe9399d3f00", "node_type": "1", "metadata": {}, "hash": "c133fdb762f83ddf206ecd04f8fceae8e0e8101f38876eb599a08c2625a573fb", "class_name": "RelatedNodeInfo"}}, "text": "2C), consistent with previous estimates $(3,15,16)$.\n\nWe analyzed the morphology and dimension of the melt pool and found that the depth-towidth aspect ratio of the melt pool increased with time, with two distinct transitions (fig. S2) (11). The first transition occurred almost simultaneously with the beginning of fluctuations in the vapor depression, after which the increase in aspect ratio accelerated. The second transition occurred when the aspect ratio reached a value close to 0.5 (this number varies with laser power). After this transition, the increase of aspect ratio slowed. We defined the first transition as the vapor depression transition and the second as the melt pool transition. This multistep transition from hemispherical melt pool (i.e., conduction mode) through smooth\\\\\ndepression and instability to developed sharp keyhole stands in contrast to previous analyses that had to rely on indirect information from cross sections of solidified weld pools.\n\nUnderstanding the boundaries of the process window for metal AM is of critical importance to repeatedly producing parts without defects. We directly observed and identified the conditions at which the transitions detected in the stationary beam experiment take place, as well as the subsequent morphological changes of the vapor depression as a function of processing parameters. The two main process parameters for both laser welding and AM are laser power and velocity, i.e., P-V space (17). Unlike the stationary beam experiments, which showed similar behavior at different powers, the morphologies of the moving beam vapor depressions vary widely across $\\mathrm{P}-\\mathrm{V}$ space (Fig. $3 \\mathrm{~A}$ and movies S2 to S6) (11). Counter to the commonly drawn keyhole boundary in $\\mathrm{P}-\\mathrm{V}$ space, nearly all combinations of power and velocity exhibited a substantial vapor depression, although only those in the traditional keyhole region (i.e., high power and low velocity) displayed the characteristic deep and narrow depression for which keyholing was named and which is characteristic of deep penetration welds at a much coarser scale. By combining the stationary and scanning beam experiments, we found that only the P-V space below the blue dashed line in Fig. 3A is in the conduction domain, whereas all the space above the red dashed line is in the keyhole domain. The high-power and low-velocity zone in the $\\mathrm{P}-\\mathrm{V}$ space is known as the unstable keyhole zone. The tendency of spherical pores to occur (fig. S9) in this zone may be related to keyholes that have too high of an aspect ratio, for which the front wall angle may be a proxy for the stability of the bottom of the keyhole (11).\n\nWe measured the vapor depression depths as a function of laser power and velocity for laser spot sizes of 95 and $140 \\mu \\mathrm{m}$ (Fig. 3, B and C). The error bar of each datum point for these measurements, and in other plots to be discussed, represents the standard deviation of more than 30 individual measurement results. We found a highly linear depth versus power relation for most scanning velocities. As the velocity increased, the slope of the curves decreased slowly, although we found some overlap in the curves for 700 to $900 \\mathrm{~mm} / \\mathrm{s}$ (Fig. 3B), possibly because of some slight variation in laser spot size between experiments. We also found some exceptions at high-power regions in the cases of low to medium velocities, i.e., 400 to $900 \\mathrm{~mm} / \\mathrm{s}$. The outliers have a \"J\" shape morphology (Fig. 3A), in which a tail formed that trailed behind the vapor depression but was not directly under the laser illumination. When we adjusted this value to the depth of the depression that was directly under the keyhole opening and laser illumination, the values move back toward a linear relation. We also did experiments on samples in the presence of powder and observed a similar trend of keyhole morphology variation (fig. S4) (11).\n\nFull-field predictions of the morphology and dynamic behavior using multiphysics simulations have been conducted by Tan $e t$ al. (18) and Khairallah et al. (19), among some others (20). However, these simulations are extremely computationally expensive and difficult to scale. Our experiments allow for a simplified approach for predicting the vapor depression size and shape. The portion of the vapor depression lying directly under the laser beam formed a nearly straight (in projection) liquid-vapor interface with\n\n\\section*{Fig. 1.", "start_char_idx": 515179, "end_char_idx": 519713, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "e1dd9e13-a6ac-4371-8a83-cfe9399d3f00": {"__data__": {"id_": "e1dd9e13-a6ac-4371-8a83-cfe9399d3f00", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "09bf9d67-d3fe-4584-adf4-1ebb98c7daf7", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "1dafa3cf1772d6a6ad3c20c6bc208c5a5c0ee613bed4e6e32fde8c7f4d646287", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "bea4e271-8543-4b5f-9c60-9f4200b2eddd", "node_type": "1", "metadata": {}, "hash": "532b4885518e2275e0e5a1b097f3455df2411ecabc4cf29971f29331e3c30a69", "class_name": "RelatedNodeInfo"}}, "text": "When we adjusted this value to the depth of the depression that was directly under the keyhole opening and laser illumination, the values move back toward a linear relation. We also did experiments on samples in the presence of powder and observed a similar trend of keyhole morphology variation (fig. S4) (11).\n\nFull-field predictions of the morphology and dynamic behavior using multiphysics simulations have been conducted by Tan $e t$ al. (18) and Khairallah et al. (19), among some others (20). However, these simulations are extremely computationally expensive and difficult to scale. Our experiments allow for a simplified approach for predicting the vapor depression size and shape. The portion of the vapor depression lying directly under the laser beam formed a nearly straight (in projection) liquid-vapor interface with\n\n\\section*{Fig. 1. Evolutions of melt pool and vapor depression under stationary laser}\n illumination. (A) Initial formation of a melt pool.(B) Formation of a small, stable vapor depression. (C) Steady growth of the vapor depression. (D) Instabilities form in the vapor depression. ( $\\mathbf{E}$ and $\\mathbf{F}$ ) Rapid change in the vapor depression shape. ( $\\mathbf{G}$ and $\\mathbf{H}$ ) Periodic fluctuation of the vapor\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_87c231f4210d1b60569eg-2(1)}\\\\\ndepression. (I and $\\mathbf{J}$ ) Change of the melt pool shape from quasisemicircular to bimodal with a bowl on top and a spike in the middle at the bottom. The sample is a Ti-6Al-4V bare plate. The laser spot size is\n\n$140 \\mu \\mathrm{m}$, and the laser power is $156 \\mathrm{~W}$. The images have been backgroundcorrected by the image collected before the laser illumination. The shape of the melt pool is marked with a red shade in (E) and (J).\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_87c231f4210d1b60569eg-2}\n\nFig. 2. Keyhole drilling under stationary laser illumination.\n\n(A and B) Penetration depth of vapor depression over time at different powers for a spot size of 95 and $140 \\mu \\mathrm{m}$, respectively. The transition occurs at approximately the same vapor depression depth for a given spot size, with the smaller spot size having a shallower critical depth. (C) Drill rate of the laser as a function of power density after the transition. The black dashed line is the linear fitting to the prefluctuation drill rates.\\\\\nan inclination angle (Fig. 4A and many other keyhole images in Fig. 3A) that is straightforward to measure with the $\\mathrm{x}$-ray imaging technique.\n\nFabbro et al. suggested a simple model for determining the front wall angle and penetration depth, excluding the influence of multiple reflections and angular dependence of absorption (21). In this model, the front keyhole wall angle is simply determined by $\\tan \\theta=\\frac{V_{\\mathrm{d}}}{V_{\\mathrm{w}}}$, where $V_{\\mathrm{w}}$ is the laser beam velocity, and $V_{\\mathrm{d}}(\\rho)$ is the drill rate of a stationary laser for a given power density ( $\\rho$ ) on a flat surface, comparable to the stationary beam measurements performed in this experiment. After this, and assuming a beam of equal intensity, the penetration depth $(d)$ is immediately obtained as $D \\cdot \\tan \\theta$.\n\nUsing the power density-dependent drilling rate (line fit in Fig. 2C), we calculated the front wall angle as a function of power density and beam velocity (Fig. 4C). Despite ignoring a number of other variables that account for more complicated simulations, such as the angular dependence of absorption or the effect of multiple reflections (22), this simple relation evidently captures the trends in the variation of the front wall angle with power density. Moreover, the relation holds over a wide range of power and velocity and at substantially higher velocity and smaller keyholes than encountered in welding. In terms of conditions relevant to $\\mathrm{AM}$, the good fit suggests that the front wall angle is mostly dependent on the ratio of the beam velocity and drill rate, with negligible influence of secondary reflections.\n\nAfter this, we estimated the keyhole depth from the front wall angle.", "start_char_idx": 518863, "end_char_idx": 523020, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "bea4e271-8543-4b5f-9c60-9f4200b2eddd": {"__data__": {"id_": "bea4e271-8543-4b5f-9c60-9f4200b2eddd", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "e1dd9e13-a6ac-4371-8a83-cfe9399d3f00", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "37c709b58becabcd4a06c83a1b01132cafdd94476f47494c56c56388bd1f2645", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "73bc5492-5ba6-463c-a702-64bd2e8db09f", "node_type": "1", "metadata": {}, "hash": "0ce6d73abbbe371856a144e37b0726111a3ddd5fd18c45a1a6fb172fed414c32", "class_name": "RelatedNodeInfo"}}, "text": "Using the power density-dependent drilling rate (line fit in Fig. 2C), we calculated the front wall angle as a function of power density and beam velocity (Fig. 4C). Despite ignoring a number of other variables that account for more complicated simulations, such as the angular dependence of absorption or the effect of multiple reflections (22), this simple relation evidently captures the trends in the variation of the front wall angle with power density. Moreover, the relation holds over a wide range of power and velocity and at substantially higher velocity and smaller keyholes than encountered in welding. In terms of conditions relevant to $\\mathrm{AM}$, the good fit suggests that the front wall angle is mostly dependent on the ratio of the beam velocity and drill rate, with negligible influence of secondary reflections.\n\nAfter this, we estimated the keyhole depth from the front wall angle. This model clearly captured the behavior of the keyhole depth as a function of processing parameters (Fig. 3, B and C), but using the full beam sizes of 95 and $140 \\mu \\mathrm{m}$ overestimated the depths by a factor of about 2. The model assumes a top-hat distribution of power instead of the Gaussian distribution of our power source that concentrated the power at the center of the beam. To compensate for this, we used the critical depression widths of $\\sim 50$ and $\\sim 100 \\mu \\mathrm{m}$ that we measured at the top of the vapor depression in the $x$-ray images under stationary laser illumination for the $95-$ and $140-\\mu \\mathrm{m}$ beam widths, respectively. This correction resulted in a very good model fit to our entire dataset (Fig. 4D), validating our simplified approach for estimating keyhole depth and front wall angle. We did experiments on powder bed samples and also different materials. We found that the presence of powder induced more fluctuation of the keyhole (particularly rear wall morphology) compared with bare plate, but the trends are otherwise the same (see figs. S5 and S7), and this relation between the keyhole depth and front wall angle is independent of material (fig. S8) (11).\n\nThe linear variation in keyhole depth with power and tangent of the front keyhole wall angle above a well-defined threshold in power density means that users of laser powder bed printers have a reproducible process on which to base predictions. The dependence on power\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_87c231f4210d1b60569eg-3}\n\nFig. 3. Keyhole morphologies across P-V space. (A) Tableau of representative radiographs in P-V space of Ti-6Al-4V bare plate for a laser spot size of $95 \\mu \\mathrm{m}$, showing the variation in vapor depression size and morphology. The vapor depression and melt pool transitions, measured in the stationary beam experiment (Fig. 2A and fig. S2) (11), are marked with blue and red dashed lines, respectively. (B and C) Vapor depression depth as a function of laser power at different scanning velocities for laser spot sizes of $95 \\mu \\mathrm{m}$ (B) and $140 \\mu \\mathrm{m}$ (C). Error bars indicate SD.\n\ndensity points out the importance of the focus conditions or spot size, which is a parameter that most machines do not permit to be altered and that is subject to drift over time. Published process maps (23) commonly show an upper limit in power with a line that corresponds to a constant front wall angle. Apart from mechanisms, the ability of ultrahigh-speed $x$-ray imaging to define the physical mechanisms of limits for viable operation in process space will be important for qualification of this technology. Also, the existence of keyholes for the entire gamut of currently typical values of power and scan velocity in LPBF means that\n\nFig. 4. Relationships between keyhole depth, front wall angle, and laser power density.\n\n(A) Representative $x$-ray image of the vapor depression in a Ti-6Al-4V bare plate, labeling the depression zone depth, $d$, and the front keyhole wall angle, $\\theta$. (B) Schematic of keyhole depth and front keyhole wall angle, adapted from Fabbro et al.", "start_char_idx": 522115, "end_char_idx": 526196, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "73bc5492-5ba6-463c-a702-64bd2e8db09f": {"__data__": {"id_": "73bc5492-5ba6-463c-a702-64bd2e8db09f", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "bea4e271-8543-4b5f-9c60-9f4200b2eddd", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b9eedcae52bece9220d17e35897604c671c10e88bf43ff08d8460366d8a9e0ef", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "56a37a74-dd56-44f9-bd2e-354ef113d08b", "node_type": "1", "metadata": {}, "hash": "252c9e3840fc0e6a62c8f285cadf0d428b1a79820524ff37c6d400516f2651e8", "class_name": "RelatedNodeInfo"}}, "text": "Published process maps (23) commonly show an upper limit in power with a line that corresponds to a constant front wall angle. Apart from mechanisms, the ability of ultrahigh-speed $x$-ray imaging to define the physical mechanisms of limits for viable operation in process space will be important for qualification of this technology. Also, the existence of keyholes for the entire gamut of currently typical values of power and scan velocity in LPBF means that\n\nFig. 4. Relationships between keyhole depth, front wall angle, and laser power density.\n\n(A) Representative $x$-ray image of the vapor depression in a Ti-6Al-4V bare plate, labeling the depression zone depth, $d$, and the front keyhole wall angle, $\\theta$. (B) Schematic of keyhole depth and front keyhole wall angle, adapted from Fabbro et al.\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_87c231f4210d1b60569eg-4(1)}\n\\end{center}\n\nB\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_87c231f4210d1b60569eg-4}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_87c231f4210d1b60569eg-4(3)}\n\\end{center}\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_87c231f4210d1b60569eg-4(2)}\n\\end{center}\n\n(21). (C) Comparison of the front keyhole wall angles between theoretical predictions (dashed and dash-dotted lines) and experimental measurements (open and solid symbols) for selected beam velocities with spot sizes of 95 and $140 \\mu \\mathrm{m}$.\n\n(D) Keyhole depth $95-\\mu \\mathrm{m}$ laser spot size. Two equivalent plots are shown in figs. S5 and $\\mathrm{S} 7$, which reveal that adding powder on top of the plate has only a small effect (11). Error bars indicate SD.\n\nusers should be aware that the effective heat source is not at all well described by the prototypical moving point as commonly expressed by the Rosenthal equation (24), and the transition from conduction mode at low power levels to keyholing helps to explain the strong variations in effective absorptivity as a function of power density that have been documented (25-28).\n\n\\section*{REFERENCES AND NOTES}\n\\begin{enumerate}\n  \\item R. Cunningham, S. P. Narra, C. Montgomery, J. Beuth, A. Rollett, JOM 69, 479-484 (2017).\n\n  \\item E. Metzbower, Metall. Trans. B 24, 875-880 (1993)\n\n  \\item J. Elmer, W. Giedt, T. Eagar, Weld. J. 69, 167s-175s (1990).\n\n  \\item A. Poueyo-Verwaerde, B. Dabezies, R. Fabbro, in Laser Materials Processing: Industrial and Microelectronics Applications, E. Beyer et al., Eds. (International Society for Optics and Photonics, 1994), vol. 2207, pp. 175-185.\n\n  \\item D. Swift-Hook, A. Gick, Weld. J. 52, 492s-499s (1973).\n\n  \\item C. Zhao et al., Sci. Rep. 7, 3602 (2017).\n\n  \\item Q. Guo et al., Acta Mater. 151, 169-180 (2018)\n\n  \\item N. D. Parab et al., J. Synchrotron Radiat. 25, 1467-1477 (2018).\n\n  \\item N. P. Calta et al., Rev. Sci. Instrum. 89, 055101 (2018)\n\n  \\item C. L. A. Leung et al., Nat. Commun. 9, 1355 (2018).\n\n  \\item Materials, methods, and additional data are available as supplementary materials.\n\n  \\item K. Hirano, R. Fabbro, M. Muller, J. Phys. D Appl. Phys. 44 , 435402 (2011).", "start_char_idx": 525388, "end_char_idx": 528531, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "56a37a74-dd56-44f9-bd2e-354ef113d08b": {"__data__": {"id_": "56a37a74-dd56-44f9-bd2e-354ef113d08b", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "73bc5492-5ba6-463c-a702-64bd2e8db09f", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "d83341594a9c670a47d3c2415c5b83e49eb986fc3ad3ff1992b6d12eb8f23897", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ed7667c0-b983-4cc2-8720-476a894a83d5", "node_type": "1", "metadata": {}, "hash": "0333dfa073d49d38a9f5285ca0d2ceaf6f2bd6cd815ceaf02d834c5e37f25111", "class_name": "RelatedNodeInfo"}}, "text": "\\item C. Zhao et al., Sci. Rep. 7, 3602 (2017).\n\n  \\item Q. Guo et al., Acta Mater. 151, 169-180 (2018)\n\n  \\item N. D. Parab et al., J. Synchrotron Radiat. 25, 1467-1477 (2018).\n\n  \\item N. P. Calta et al., Rev. Sci. Instrum. 89, 055101 (2018)\n\n  \\item C. L. A. Leung et al., Nat. Commun. 9, 1355 (2018).\n\n  \\item Materials, methods, and additional data are available as supplementary materials.\n\n  \\item K. Hirano, R. Fabbro, M. Muller, J. Phys. D Appl. Phys. 44 , 435402 (2011).\n\n  \\item S. Basu, T. DebRoy, J. Appl. Phys. 72, 3317-3322 (1992).\n\n  \\item E. Assuncao, S. Williams, D. Yapp, Opt. Lasers Eng. 50, 823-828 (2012)\n\n  \\item R. Rai, J. Elmer, T. Palmer, T. DebRoy, J. Phys. D Appl. Phys. 40, 5753-5766 (2007).\n\n  \\item T. DebRoy, S. A. David, Rev. Mod. Phys. 67, 85-112 (1995)\n\n  \\item A. Vasinonta, J. L. Beuth, M. L. Griffith, J. Manuf. Sci. Eng. 123 , 615-622 (2001)\n\n  \\item W. Tan, Y. C. Shin, J. Phys. D Appl. Phys. 47, 345501 (2014).\n\n  \\item S. A. Khairallah, A. T. Anderson, A. Rubenchik, W. E. King, Acta Mater. 108, 36-45 (2016).\n\n  \\item M. Dal, R. Fabbro, Opt. Laser Technol. 78, 2-14 (2016).\n\n  \\item R. Fabbro, K. Chouf, J. Appl. Phys. 87, 4075-4083 (2000)\n\n  \\item A. Matsunawa, V. Semak, J. Phys. D Appl. Phys. 30, 798-809 (1997).\n\n  \\item J. L. Beuth et al., in Solid Freeform Fabrication Proceeding (University of Texas at Austin, 2013), pp. 655-665.\n\n  \\item D. Rosenthal, Weld. J. 20, 220-234 (1941).\n\n  \\item J. Trapp, A. M. Rubenchik, G. Guss, M. J. Matthews, Appl. Mater. Today 9, 341-349 (2017).\n\n  \\item Y. Kizaki, H. Azuma, S. Yamazaki, H. Sugimoto, S. Takagi, Jpn. J. Appl. Phys. 32, 205-212 (1993).\n\n  \\item C. Kamath, B. El-dasher, G. F. Gallegos, W. E. King, A. Sisto, Int. J. Adv. Manuf. Technol. 74, 65-78 (2014).\n\n  \\item T. Childs, C. Hauser, Proc. Inst. Mech. Eng. B 219, 379-384 (2005).\n\n\\end{enumerate}\n\n\\section*{ACKNOWLEDGMENTS}\nThis research used resources of the APS, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory (contract no. DEAC02-06CH11357). We acknowledge J. Elmer and R. Fabbro for fruitful discussions, and we thank A. Deriy at the APS for technical support of the beamline experiments. Funding: The work was supported by the Department of Defense, Office of Economic Adjustment (grant no. ST1605-17-02, M. Gilroy, CTO and Program Director).", "start_char_idx": 528051, "end_char_idx": 530443, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ed7667c0-b983-4cc2-8720-476a894a83d5": {"__data__": {"id_": "ed7667c0-b983-4cc2-8720-476a894a83d5", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "56a37a74-dd56-44f9-bd2e-354ef113d08b", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "9f5de610f1626818685e50bb21f414b1ce6bfd7b8978698a15bfa577f5f39aeb", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fbe160b4-e1a9-4eed-9bd4-c25bad0d5ba1", "node_type": "1", "metadata": {}, "hash": "ee81b20233cd5524509171d3d48ecc38cb72fa3f2c8295db382a6438f2f61419", "class_name": "RelatedNodeInfo"}}, "text": "Manuf. Technol. 74, 65-78 (2014).\n\n  \\item T. Childs, C. Hauser, Proc. Inst. Mech. Eng. B 219, 379-384 (2005).\n\n\\end{enumerate}\n\n\\section*{ACKNOWLEDGMENTS}\nThis research used resources of the APS, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory (contract no. DEAC02-06CH11357). We acknowledge J. Elmer and R. Fabbro for fruitful discussions, and we thank A. Deriy at the APS for technical support of the beamline experiments. Funding: The work was supported by the Department of Defense, Office of Economic Adjustment (grant no. ST1605-17-02, M. Gilroy, CTO and Program Director). The work was also supported by the Laboratory Directed Research and Development (LDRD) funding from Argonne National Laboratory, provided by the Director, Office of Science, of the U.S. DOE (contract no. DE-AC02-06CH11357); the National Nuclear Security Administration of the U.S. DOE (contract no. DE-NA0002918); and the National Aeronautics and Space Administration (grant no. NNX17AD03G). Author contributions: R.C. and C.Z. performed the majority of the experiments with assistance from T.S., N.P., C.K., J.P., and A.D.R.. A.D.R. advised R.C. in the course of his doctoral program. T.S., C.Z., K.F., and N.P. conceived and built the apparatus for ultrahigh-speed $x$-ray imaging of laser melting. R.C. and C.Z. performed the image processing and data analysis with help from all authors. The manuscript was written by R.C., C.Z., T.S., and A.D.R. All authors revised and commented on the manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: All data needed to evaluate our conclusions are provided in the manuscript or the supplementary materials.\n\n\\section*{SUPPLEMENTARY MATERIALS}\n\\href{http://www.sciencemag.org/content/363/6429/849/suppl/DC1}{www.sciencemag.org/content/363/6429/849/suppl/DC1} Materials and Methods\n\nSupplementary Text\n\nFigs. $\\mathrm{S} 1$ to $\\mathrm{Sg}$\n\nReferences $(29,30)$\n\nMovies S1 to S14\n\n18 September 2018; accepted 23 January 2019 10.1126/science.aav4687\n\n\\section*{Science}\n\\section*{Keyhole threshold and morphology in laser melting revealed by ultrahigh-speed x-ray imaging}\nRoss Cunningham, Cang Zhao, Niranjan Parab, Christopher Kantzos, Joseph Pauza, Kamel Fezzaa, Tao Sun and Anthony D. Rollett\n\nScience 363 (6429), 849-852.\n\nDOI: $10.1126 /$ science.aav4687\n\nThe key to keyhole formation\n\nThe formation of keyholes, or vapor-filled depressions, during laser welding presents a large problem for additive manufacturing. Cunningham et al. used high-speed x-ray imaging to take a detailed look at keyhole formation in a titanium alloy. They found a simplified relationship between operational parameters and keyhole shape, which may allow for the prevention of pore formation going forward.\n\nScience, this issue p. 849 \\href{http://science.sciencemag.org/content/363/6429/849#BIBL}{http://science.sciencemag.org/content/363/6429/849\\#BIBL}\n\nPERMISSIONS \\href{http://www.sciencemag.org/help/reprints-and-permissions}{http://www.sciencemag.org/help/reprints-and-permissions}", "start_char_idx": 529775, "end_char_idx": 532916, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fbe160b4-e1a9-4eed-9bd4-c25bad0d5ba1": {"__data__": {"id_": "fbe160b4-e1a9-4eed-9bd4-c25bad0d5ba1", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ed7667c0-b983-4cc2-8720-476a894a83d5", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "8e17b252694d373ea219610fecc1b330fddeedabcd92a05f8e6e91ed3b1a8545", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "ab7cda7c-5a35-463b-8944-f4fb96b2d0ee", "node_type": "1", "metadata": {}, "hash": "490080dc7c923df07bf484a3a08c50a3bb56cf0a1c12f6b455c68e2076cf3e77", "class_name": "RelatedNodeInfo"}}, "text": "DOI: $10.1126 /$ science.aav4687\n\nThe key to keyhole formation\n\nThe formation of keyholes, or vapor-filled depressions, during laser welding presents a large problem for additive manufacturing. Cunningham et al. used high-speed x-ray imaging to take a detailed look at keyhole formation in a titanium alloy. They found a simplified relationship between operational parameters and keyhole shape, which may allow for the prevention of pore formation going forward.\n\nScience, this issue p. 849 \\href{http://science.sciencemag.org/content/363/6429/849#BIBL}{http://science.sciencemag.org/content/363/6429/849\\#BIBL}\n\nPERMISSIONS \\href{http://www.sciencemag.org/help/reprints-and-permissions}{http://www.sciencemag.org/help/reprints-and-permissions}\n\n\n\\end{document}\r\n\\documentclass[10pt]{article}\n\\usepackage[utf8]{inputenc}\n\\usepackage[T1]{fontenc}\n\\usepackage{amsmath}\n\\usepackage{amsfonts}\n\\usepackage{amssymb}\n\\usepackage[version=4]{mhchem}\n\\usepackage{stmaryrd}\n\\usepackage{hyperref}\n\\hypersetup{colorlinks=true, linkcolor=blue, filecolor=magenta, urlcolor=cyan,}\n\\urlstyle{same}\n\\usepackage{graphicx}\n\\usepackage[export]{adjustbox}\n\\graphicspath{ {./images/} }\n\n\\title{Determining processing behaviour of pure $\\mathrm{Cu}$ in laser powder bed fusion using direct micro-calorimetry }\n\n\n\\author{Leonidas Gargalis ${ }^{\\mathrm{a}, *}$, Jianchao $\\mathrm{Ye}^{\\mathrm{c}}$, Maria Strantza ${ }^{\\mathrm{c}}$, Alexander Rubenchik ${ }^{\\mathrm{c}}$,\\\\\nJames W. Murray ${ }^{b}$, Adam T. Clare ${ }^{b}$, Ian A. Ashcroft ${ }^{a}$, Richard Hague ${ }^{a}$, Manyalibo J. Matthews ${ }^{c}$\\\\\n${ }^{\\text {a }}$ Centre for Additive Manufacturing (CfAM), Faculty of Engineering, University of Nottingham, Nottingham, NG8 1BB, UK\\\\\n${ }^{\\mathrm{b}}$ Advanced Manufacturing, Faculty of Engineering, University of Nottingham, NG7 2RD, UK\\\\\n${ }^{\\mathrm{c}}$ Lawrence Livermore National Laboratory (LLNL), 7000 East Avenue, Livermore, CA94550, USA}\n\\date{}\n\n\n%New command to display footnote whose markers will always be hidden\n\\let\\svthefootnote\\thefootnote\n\\newcommand\\blfootnotetext[1]{%\n  \\let\\thefootnote\\relax\\footnote{#1}%\n  \\addtocounter{footnote}{-1}%\n  \\let\\thefootnote\\svthefootnote%\n}\n\n%Overriding the \\footnotetext command to hide the marker if its value is `0`\n\\let\\svfootnotetext\\footnotetext\n\\renewcommand\\footnotetext[2][?]{%\n  \\if\\relax#1\\relax%\n    \\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n  \\else%\n    \\if?#1\\ifnum\\value{footnote}=0\\blfootnotetext{#2}\\else\\svfootnotetext{#2}\\fi%\n    \\else\\svfootnotetext[#1]{#2}\\fi%\n  \\fi\n}\n\n\\begin{document}\n\\maketitle\n\n\n\\section*{A R T C L E I N F O}\nAssociate Editor: R Mishra\n\n\\section*{Keywords:}\nAbsorptivity\n\nDirect micro-calorimetry\n\nCopper\n\nLaser powder bed fusion\n\nAdditive manufacturing\n\nInfrared laser diode\n\n\\begin{abstract}\nA B S T R A C T Copper is challenging to process by laser powder bed fusion (LPBF) given its high reflectivity at common infrared laser diode wavelengths and high thermal conductivity.", "start_char_idx": 532172, "end_char_idx": 535172, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "ab7cda7c-5a35-463b-8944-f4fb96b2d0ee": {"__data__": {"id_": "ab7cda7c-5a35-463b-8944-f4fb96b2d0ee", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fbe160b4-e1a9-4eed-9bd4-c25bad0d5ba1", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "07810ec9391e64e2a986436c062bb89bab9853a68c4915a0ba5e1bfc01162937", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "07127146-e5be-4eba-a07e-c4cff0a1c287", "node_type": "1", "metadata": {}, "hash": "766762a2afd257fa1091bd77c2519e24618f94f23bfefd438e976d070e596cd1", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{A R T C L E I N F O}\nAssociate Editor: R Mishra\n\n\\section*{Keywords:}\nAbsorptivity\n\nDirect micro-calorimetry\n\nCopper\n\nLaser powder bed fusion\n\nAdditive manufacturing\n\nInfrared laser diode\n\n\\begin{abstract}\nA B S T R A C T Copper is challenging to process by laser powder bed fusion (LPBF) given its high reflectivity at common infrared laser diode wavelengths and high thermal conductivity. Successful deposition of copper in a predictable and repeatable fashion relies on understanding the development of the keyhole melting regime, as well as heating, melting, boiling and vapour formation behaviour when interacting with a laser beam within an LPBF environment. In this study, in situ optical absorptivity measurements are used to clarify the complex physics of the laser material interaction. Absorptivity of laser energy is measured using direct micro-calorimetry and compared to melt pool depth in correlation to processing parameters. The measured absorptivity for a $100 \\mu \\mathrm{m}$ layer thickness of powder was found to be approximately four times higher than that of the bare polished discs. It was also shown that high laser power above $500 \\mathrm{~W}$ and scan speed up to $150 \\mathrm{~mm} / \\mathrm{s}$ are appropriate for effective melting of the powder layer, with these parameters overcoming the threshold required to achieve keyhole melting. This is explained by multiple reflections withing the powder particles and the lower thermal conductivity of packed powder in comparison to bare discs. Melt pool formation was found to be highly unstable and an explosive behavior was observed when in the keyhole regime, caused by high fluctuations in absorptivity values. This work demonstrates calorimetry can be used to monitor melting behaviour in a real-time fashion during processing for this challenging to proces material, thereby avoiding unnecessary parametric optimisation. In addition, the parametric window for optimum processing revealed here can inform future work.\n\\end{abstract}\n\n\\section*{1. Introduction}\nCopper and copper alloys are extensively used as functional materials in electronic devices and heat exchangers owing to their excellent electrical and thermal properties (Davis, 2001). The increasing demand for functional circuits, electronics, heat sinks and high-performance devices with superior electrical and thermal properties has led to recent advances in the manufacture of copper and copper alloy parts via AM processes. Laser Powder Bed Fusion (LPBF) for pure copper was studied by Ikeshoji et al. (2017) who used a thermoviewer to compare melt pool dimensions with estimated values. Direct Metal Laser Sintering (DMLS) of copper on ferrous and non-ferrous substrates was investigated by Pogson et al. (2003) and Electron Beam Melting (EBM) was used by Frigola et al. (2014) to produce fully dense copper components with complex geometries. However, as pointed out in the review of\\\\\nAuwal et al. (2018) on laser beam welding of copper alloys, some critical challenges remain for the manufacture of high-density copper parts via LPBF. These include excessive oxidation and the requirement for high power lasers that are not of standard wavelengths, due to high thermal losses. Moreover, low laser radiation absorption and the formation of an unstable melt pool with standard IR lasers hinder the stability and quality of the process as shown by Hess et al. (2011). Owing to its high thermal conductivity, copper facilitates rapid heat transport away from the melt pool resulting in partial melting and poor interlayer adhesion. Samples produced with conventional LPBF machines (200-400 W laser power) typically feature a low average density, depending on the laser system source. Lykov et al. (2016) used a $200 \\mathrm{~W} \\mathrm{CO}_{2}$ laser to process copper resulting in a density of $88 \\%$ whereas (Silbernagel et al. 2019) used a $200 \\mathrm{~W}$, Yb-fiber laser and produced samples with a density between $83-88 \\%$. This poor densification is related to the low absorption\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:leonidas.gargalis@nottingham.ac.uk}{leonidas.gargalis@nottingham.ac.uk} (L. Gargalis).\n}\nof infrared radiation during LPBF of copper due to the wavelength dependency of the absorption coefficient (McVey et al., 2007).", "start_char_idx": 534772, "end_char_idx": 539142, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "07127146-e5be-4eba-a07e-c4cff0a1c287": {"__data__": {"id_": "07127146-e5be-4eba-a07e-c4cff0a1c287", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "ab7cda7c-5a35-463b-8944-f4fb96b2d0ee", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "22f62f33b9c5afa45cd06d3d294f0a1c18364e8940e8dea82730206ac806b5b8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "fbc17f4a-95be-4085-8c2a-9b2dc9a75705", "node_type": "1", "metadata": {}, "hash": "0b7f84b2f950b64d62a7e065f9354724d1acfdc468b9d8ebb30440f4cfce9d4e", "class_name": "RelatedNodeInfo"}}, "text": "Lykov et al. (2016) used a $200 \\mathrm{~W} \\mathrm{CO}_{2}$ laser to process copper resulting in a density of $88 \\%$ whereas (Silbernagel et al. 2019) used a $200 \\mathrm{~W}$, Yb-fiber laser and produced samples with a density between $83-88 \\%$. This poor densification is related to the low absorption\n\\footnotetext{\\begin{itemize}\n  \\item Corresponding author.\n\\end{itemize}\n\nE-mail address: \\href{mailto:leonidas.gargalis@nottingham.ac.uk}{leonidas.gargalis@nottingham.ac.uk} (L. Gargalis).\n}\nof infrared radiation during LPBF of copper due to the wavelength dependency of the absorption coefficient (McVey et al., 2007). In the work of (Colopi et al., 2018) copper was processed with a $1 \\mathrm{~kW}$ single mode fiber laser in order to produce high density parts ( $>97 \\%$ ). Kaiser et al. (2018) used a $1 \\mathrm{~kW} 515 \\mathrm{~nm}$ (green) continuous wave laser to weld copper joints and presented the benefits in terms of melt pool stability and weld quality. However, as shown by Jadhav et al. (2019a), overcoming this issue by simply increasing the laser power to $1 \\mathrm{~kW}$ and above is not normally an option, given the lack of access to commercial systems at such high-power levels, as well as the vulnerability of the optics (i.e. mirrors) to high powered lasers.\n\nSolid copper has very low absorptivity at the infrared wavelengths $(\\sim 1070 \\mathrm{~nm})$ commonly used in LPBF, absorbing only up to $5 \\%$ of the incoming thermal energy when in flat solid form and up to $15 \\%$ of the laser energy when in powder form as shown by Wang et al. (2000). This is to be compared with $\\sim 30$ and $\\sim 60 \\%$ absorptivity values for common structural alloys in flat solid or powder form respectively as shown by Ye et al. (2019). An increase in absorptivity for copper can be achieved with shorter laser wavelengths, due to an increase in intraband electronic transitions. Liebl et al. (2014) showed that when the laser wavelength is reduced (typically using blue/green lasers), copper absorptivity increases significantly; at wavelengths below $532 \\mathrm{~nm}$ (green spectrum) it can reach maximum values close to $40 \\%$ as presented by Engler et al. (2011). Engler compared experimentally green and IR laser radiation in continuous laser welding of copper.\n\nIn the work of Rubenchik et al. (2015) the authors calculated, using ray-trace modelling and simulations, the absorption of laser light by metal powders and investigated the dependence of absorption on powder content and beam size. It was found that the absorption is significantly increased relative to its flat-surface value by multiple scattering (reflections of the IR laser beam between powder particles) and this effect is especially important for highly reflective materials such as copper. That means that the absorption value is strongly affected by the size distribution of the powder spheres and their geometrical arrangement. For a laser wavelength of $1070 \\mathrm{~nm}$, incident angle of $0^{\\circ}$ and a flat clean surface the absorptivity of copper is $\\mathrm{A}=0.028$ whereas for powder layers, the absorptivity value is increased to $\\mathrm{A} \\approx 0.12-0.17$.\n\nBoley et al. (2017) demonstrated that absorptivity of metallic powders is dependent on numerous parameters, including powder layer thickness, particle size and distribution and powder surface morphology; Tolochko et al. (2000) showed that absorptivity is also affected by the temperature of the substrate and by laser scanning parameters such as laser power. Measuring absorptivity in LPBF is complex because the material undergoes continuous dynamic surface morphology fluctuations. In addition, several physical effects take place during laser-matter interaction, for example, multiple light reflections, energy loss by material euation and ablation, absorption and refraction of light by the vapour jet formed as shown in the experimental work by Ly et al. (2017).", "start_char_idx": 538514, "end_char_idx": 542465, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "fbc17f4a-95be-4085-8c2a-9b2dc9a75705": {"__data__": {"id_": "fbc17f4a-95be-4085-8c2a-9b2dc9a75705", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "07127146-e5be-4eba-a07e-c4cff0a1c287", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "01a8bdf34f515c003902334c9f500b956e299e56bf1f2df40f9ad1097a0af4c1", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9db2e909-790f-4f4f-be57-f358ba20eb90", "node_type": "1", "metadata": {}, "hash": "4919df220c4540f718df1cc44320e5109aabc1b12f5cd341ea151f2d48efea9f", "class_name": "RelatedNodeInfo"}}, "text": "Boley et al. (2017) demonstrated that absorptivity of metallic powders is dependent on numerous parameters, including powder layer thickness, particle size and distribution and powder surface morphology; Tolochko et al. (2000) showed that absorptivity is also affected by the temperature of the substrate and by laser scanning parameters such as laser power. Measuring absorptivity in LPBF is complex because the material undergoes continuous dynamic surface morphology fluctuations. In addition, several physical effects take place during laser-matter interaction, for example, multiple light reflections, energy loss by material euation and ablation, absorption and refraction of light by the vapour jet formed as shown in the experimental work by Ly et al. (2017). At high laser energy densities, when the vapour recoil pressure is sufficient to form a deep depression in the melt pool (i.e., the keyhole welding regime), light interacts with the keyhole walls at steep angles and with the ejected vapours. A fraction of the net absorbed energy is lost via evaporative cooling and part of the laser light is directly absorbed in the vapour plume. On the other hand, multiple reflections in the melt pool vapour depression under keyhole conditions causes a net $2-3 \\times$ increase in absorbed energy making the process more efficient and potentially more stable.\n\nThere is therefore a need to measure the effective absorptivity of pure copper under conditions similar to the LPBF process, focusing only on the energy absorbed by the substrate. An experimental method to directly measure the absorptivity using a micro-calorimetry setup was developed, validated and used previously by Trapp et al. (2017). Trapp, measured the absorptivity of various materials and concluded that absorptivity values can vary greatly and differ from estimated values found in the literature. However, the results were in good agreement with a finite element simulation for LPBF which involved laser beam interaction with the melt pool through ray tracing analysis developed by Matthews et al. (2019). A similar setup, designed to minimise thermal losses and equipped with an IR pyrometer was shown recently in the work of Clare et al. (2020), where carbon nanotubes were used to modify the chemistry of aluminium and enhance its absorptivity.\n\nThe role of powder chemistry on absorption in terms of oxygen content (thin oxide layer formed onto the powder particles) is significant. As shown in Jadhav et al. (2019b) the oxides can greatly increase absorption. The authors intentionally modified the surface of copper powder by heat treatment to form a surface oxide layer (105 nm) featuring a mixture of $\\mathrm{Cu} 2 \\mathrm{O}$ and $\\mathrm{CuO}$. The optical absorption was improved from $32 \\%$ to $58 \\%$ for a $1080 \\mathrm{~nm}$ fiber laser wavelength. Coating the copper powder particle surface with metallic or oxide coatings, which are less reflective than copper, can significantly improve the copper laser beam absorptivity. However, oxides can precipitate in copper reducing its thermal and electrical conductivity, leading to oxide inclusions and poor weld quality.\n\nIn this work, a systematic study is performed in which the fundamental melting and conduction/keyhole behaviour of copper powder on a copper substrate system, are assessed. This is achieved through analysis of the absorptivity of the laser during processing, as well as an investigation of the key process parameters of scan speed and laser power. The cross-sectional features of the single tracks are analysed to understand the processing behaviour in the context of the conduction and keyhole melting regimes. High frame-rate video recording and optical metallography are used to support the identification of conduction and keyhole welding regimes and offer new insights into the energy coupling of copper as a function of laser parameters. Such a fundamental study has not yet been performed on copper, a key material for thermal and electrical applications.\n\n\\section*{2. Material and methods}\n\\subsection*{2.1. Materials}\nHigh chemically pure copper powder $(\\mathrm{HCP} \\mathrm{Cu})$ feedstock was used in this study, made by nitrogen gas atomisation, with a purity of 99.9 w.t. $\\%$, and an apparent density of $4.80 \\mathrm{~g} / \\mathrm{cm}^{3}$ (ISO3923/1) (ECKA Granules GmbH Germany). A Hitachi High-Technologies Corp. (Japan) TM3030 scanning electron microscope (SEM) at $15 \\mathrm{kV}$ was used for surface and cross-sectional analysis.", "start_char_idx": 541698, "end_char_idx": 546218, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9db2e909-790f-4f4f-be57-f358ba20eb90": {"__data__": {"id_": "9db2e909-790f-4f4f-be57-f358ba20eb90", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "fbc17f4a-95be-4085-8c2a-9b2dc9a75705", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "acaba757500a6027b56c2d6b244ecdf1b974ae676eda2a8a173afda58135d5bc", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "9f8c3c07-3452-45ad-a5af-094d794f8a63", "node_type": "1", "metadata": {}, "hash": "8e665a5a6b5f79a66816ede8f04155882a406a4c9484f9a2f6f2828f783b9390", "class_name": "RelatedNodeInfo"}}, "text": "Such a fundamental study has not yet been performed on copper, a key material for thermal and electrical applications.\n\n\\section*{2. Material and methods}\n\\subsection*{2.1. Materials}\nHigh chemically pure copper powder $(\\mathrm{HCP} \\mathrm{Cu})$ feedstock was used in this study, made by nitrogen gas atomisation, with a purity of 99.9 w.t. $\\%$, and an apparent density of $4.80 \\mathrm{~g} / \\mathrm{cm}^{3}$ (ISO3923/1) (ECKA Granules GmbH Germany). A Hitachi High-Technologies Corp. (Japan) TM3030 scanning electron microscope (SEM) at $15 \\mathrm{kV}$ was used for surface and cross-sectional analysis. Energy dispersive X-ray (EDX) spectroscopy at the same voltage was used for elemental composition analysis. The powder contained traces of phosphorus ( $<0.05$ w.t. \\%) and oxygen ( $<$ 0.04 w.t. \\%). Powder particle morphology and size distributions are critical factors in developing LPBF process parameters and a stable melting regime. Particle morphology images and Particle size distribution data (PSD) are shown in Fig. 1.\n\nThe powder had a spherical shape with many small particles forming satellites on the larger particles. Powder size distribution was measured with a Mastersizer3000 (Malvern Instruments Ltd. (UK)). The median particle size distribution value (D50) was $38.0 \\mu \\mathrm{m}$ and the values of D10 and D90 were 17.2 and $65.3 \\mu \\mathrm{m}$ respectively. Copper foils supplied from Goodfellow Ltd. UK, with a thickness of $500 \\mu \\mathrm{m}$ were EDM cut into $1 \\mathrm{~cm}$ diameter plates for the absorptivity measurements. Two copper substrate preparations were used: bare substrate 500 grit polished, and the same substrate with a $100 \\mu \\mathrm{m}$ layer of powder. Acetone was used to clean the substrates prior to experiments. After laser processing and removal of excess powder, the build plates were imaged with the use of a VR-3200 wide-area 3D Measurement System (Keyence Corporation). The substrates with the single tracks were cut perpendicular to the track length direction using a slow speed diamond saw (Model 65001, South Bay Technologies) and mounted in epoxy resin for cross-sectional analysis. Metallographic polishing was performed down to a $1 \\mu \\mathrm{m}$ diamond finish and samples were then etched using a 3:1 vol mixture of $\\mathrm{HCl}$ and HNO3 to reveal the microstructure and melt pools. Imaging of melt pool depth and width was performed using an optical microscope\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-03(2)}\n\\end{center}\n\nFig. 1. SEM image of copper powder and particle size distribution data with D10, D50 and D90 values z.\n\n(Olympus STM6 measuring microscope).\n\n\\subsection*{2.2. Experimental method}\n\\subsection*{2.2.1. Laser processing}\nThe LPBF experiments were performed with the use of an in-house at LLNL built LPBF-AM machine equipped with a $600 \\mathrm{~W} \\mathrm{Yb}, 1070 \\mathrm{~nm}$\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-03(1)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-03}\n\\end{center}\n\nFig. 2. (a) Open-architecture LPBF system, (b) build chamber with micro-calorimetry apparatus and welded thermocouples on the rear side of the substrate disc. Temperature measurement curves are also shown. Solid lines are the temperature responses of the two welded thermocouples for a copper substrate disc and dashed lines are the exponential decay fitting using data ranging from $20 \\mathrm{~s}$ to $50 \\mathrm{~s}$ after laser scan.", "start_char_idx": 545609, "end_char_idx": 549201, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "9f8c3c07-3452-45ad-a5af-094d794f8a63": {"__data__": {"id_": "9f8c3c07-3452-45ad-a5af-094d794f8a63", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9db2e909-790f-4f4f-be57-f358ba20eb90", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "86609a6aae49e6f67cdb683a47a986eaad8e06ac11308850845016004e727cb2", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "b9c04e51-bede-478c-a2a9-d5a68aa7f486", "node_type": "1", "metadata": {}, "hash": "bdba815425a0403ce47dc9235c48d46115b58842b71733f583653172b7c7d517", "class_name": "RelatedNodeInfo"}}, "text": "2. (a) Open-architecture LPBF system, (b) build chamber with micro-calorimetry apparatus and welded thermocouples on the rear side of the substrate disc. Temperature measurement curves are also shown. Solid lines are the temperature responses of the two welded thermocouples for a copper substrate disc and dashed lines are the exponential decay fitting using data ranging from $20 \\mathrm{~s}$ to $50 \\mathrm{~s}$ after laser scan. The temperature time curve was measured for a total time of $60 \\mathrm{~s}$ with a measurement frequency of $20 \\mathrm{~Hz}$.\\\\\ncontinuous wave fiber laser. The beam was focused using a $450 \\mathrm{~mm}$ focal length lens to a nearly Gaussian shape with a 1/e ${ }^{2}$ diameter of $45 \\pm$ $5 \\mu \\mathrm{m}$ and scanned using $\\mathrm{x}-\\mathrm{y}$ galvanometer scanning mirrors. The optical system was designed to simulate that of a typical commercial SLM machine. The experiments were performed in a custom-built chamber supplied with protective argon gas to ensure an inert atmosphere. The flow rate of argon was set to a fixed value of 2100 and $700 \\mathrm{~cm}^{3} / \\mathrm{min}$ for the bare discs and the powder samples, respectively. Copper powder was manually spread using a razor blade as a $100 \\mu \\mathrm{m}$ thick single layer on circular pure copper discs. The overall uncertainty during the experiments was calculated at $8 \\%$. A powder layer thickness of $100 \\mu \\mathrm{m}$ was chosen as the average powder size restricted smaller homogeneous layers. Powder layer height was controlled via a threaded stage on which the substrate was mounted and was calibrated using a plane height gauge. A series of $5 \\mathrm{~mm}$ long single tracks was produced by varying laser power and scan speed. Processing parameters were narrowed down, targeting melting conditions in the vicinity of the keyholemode welding regime by reaching the maximum output power of the laser (540 W due to losses of $60 \\mathrm{~W}$ in the optical setup), on bare copper substrate discs and discs coated with powder. Laser powers of 400, 450, 500 and $540 \\mathrm{~W}$, and scan speeds from 25 to $1000 \\mathrm{~mm} / \\mathrm{s}$ were used, resulting in linear energy density values between $0.36-21.6 \\mathrm{~J} / \\mathrm{mm}$. These parameters were chosen after preliminary experimentation and consideration of the literature, and represent practical parameters that are likely to be used for a range of highly reflective materials. The experimental setup illustrating the open architecture and laser calorimetry apparatus is shown in Fig. 2.\n\n\\subsection*{2.2.2. Calorimetry approach}\nTwo type $\\mathrm{K}$ thermocouple probes, with bare wires of $76 \\mu \\mathrm{m}$ diameter each were spot welded to the backside of the copper substrate discs (see Fig. 2(b)). This enabled the absorbed energy in the substrate to be measured whilst excluding the energy absorbed by metal vapour and energy that is reflected or removed by evaporation. The incident laser power varied from $400 \\mathrm{~W}$ up to the maximum of $540 \\mathrm{~W}$. In order to avoid the inertial effects of the scanning mirrors, the scanning distance was set to $10 \\mathrm{~mm}$ and the laser was turned on after $5 \\mathrm{~mm}$ of travelling distance and turned off at the end of the track. Temperature was recorded just before the laser irradiation for a duration of $120 \\mathrm{~s}$. A description of the extrapolation of absorptivity data in this system is also described in Trapp et al. (2017). An exponential decay function was fitted to temperature data of each thermocouple for $t>t_{1}$ and temperature was extrapolated to time $\\mathrm{t}_{0}$ corresponding to the time the tracks were created, as shown in Fig. 2(b).\n\nThis procedure was chosen to compensate for temperature losses before equilibration of temperature over the disc. These losses are primarily caused by radiation and convection. Heat lost through the thin thermocouple wires and the low conductivity sample holder is considered negligible. The total time of energy deposition is in the millisecond range, much shorter then the temperature equilibration time.", "start_char_idx": 548769, "end_char_idx": 552905, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "b9c04e51-bede-478c-a2a9-d5a68aa7f486": {"__data__": {"id_": "b9c04e51-bede-478c-a2a9-d5a68aa7f486", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "9f8c3c07-3452-45ad-a5af-094d794f8a63", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3e64baf9ef58ab9ec8f11b068c93dcaedf00c5eda3c0884f9cd2bea1ee6c4d92", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "810454c3-84cb-4af8-aec4-eb83c485adfb", "node_type": "1", "metadata": {}, "hash": "837f729d952244711d03ee35b456684e1850016f78d410fbfa4f82a1b654235b", "class_name": "RelatedNodeInfo"}}, "text": "Temperature was recorded just before the laser irradiation for a duration of $120 \\mathrm{~s}$. A description of the extrapolation of absorptivity data in this system is also described in Trapp et al. (2017). An exponential decay function was fitted to temperature data of each thermocouple for $t>t_{1}$ and temperature was extrapolated to time $\\mathrm{t}_{0}$ corresponding to the time the tracks were created, as shown in Fig. 2(b).\n\nThis procedure was chosen to compensate for temperature losses before equilibration of temperature over the disc. These losses are primarily caused by radiation and convection. Heat lost through the thin thermocouple wires and the low conductivity sample holder is considered negligible. The total time of energy deposition is in the millisecond range, much shorter then the temperature equilibration time. Assuming a known disc temperature increase, the effective absorptivity can be calculated by dividing the energy necessary to uniformly heat the specimen from starting temperature $T_{0}$ to end temperature $T_{1}(E H)$ by the energy input due to the laser irradiation (EL):\n\nAbsorptivity $=\\frac{\\text { Energy Out }}{\\text { Energy In }}=\\int_{T_{0}}^{T_{1}} \\frac{m C_{p}(T) d T}{l / v P}$\n\n$T(t)=T_{0}+\\left(T_{1}-T_{0}\\right) e^{-t / \\tau}$.\n\nIn Eq. (1), $\\mathrm{m}$ is the mass of the disc including the powder layer (if applicable), $\\mathrm{P}$ is the nominal laser power (W), $v$ the scanning speed $(\\mathrm{mm} / \\mathrm{s})$ and $l$ the total length of the laser track ( $5 \\mathrm{~mm}$ for a single track line). The exponential decay time constant in Eq. (2) is $\\tau$. Eq. (2) fits to the cooling section of the raw temperature profile. The intersection of this curve with the time the laser is turned on is $T_{1}$ with the starting tempera- ture of the disc being $\\mathrm{T}_{0}$. The temperature-dependent heat capacity over the temperature range measured $\\left(25<\\mathrm{T}<150{ }^{\\circ} \\mathrm{C}\\right)$ is given by the function $C_{p}(T)=C_{p, 0}(1+T)$ with $C_{p, 0}$ and other physical properties of copper are shown in Table 1.\n\n\\section*{3. Results}\n\\subsection*{3.1. Track morphology}\nSingle tracks were produced using the parameters listed in Section 2.2, i.e. $400,450,500$ and $540 \\mathrm{~W}$, with scan speed ranging from 25 to $1000 \\mathrm{~mm} / \\mathrm{s}$. Tracks were produced on the two substrate types; substrate with $100 \\mu \\mathrm{m}$ layer thickness powder and polished bare substrate. Fig. 3 shows optical images and height maps for tracks produced at 400 and $500 \\mathrm{~W}$ with increasing scan speed, on substrates with $100 \\mu \\mathrm{m}$ layer thickness copper powder.\n\nA clear difference in track quality and morphology between the two power parameters can be seen. The $500 \\mathrm{~W}$ tracks are generally more homogenous and continuous, indicating a more stable welding regime at the higher laser power. It is also observed that the width, height, and denudation zone of tracks, at both $400 \\mathrm{~W}$ and $500 \\mathrm{~W}$, reduces with increasing speed. Moreover, in the case of the $500 \\mathrm{~W}$ tracks, there is a clear change in melting behaviour between $50 \\mathrm{~mm} / \\mathrm{s}$ and $150 \\mathrm{~mm} / \\mathrm{s}$ whereby at $150 \\mathrm{~mm} / \\mathrm{s}$ and above, homogeneous tracks are produced. Morphological irregularities, either in the form of balling or accumulation of material causing an increase in height of the tracks, are represented as red spots on the height maps.\n\nTo further characterise track morphology, track width and height measurements for $400 \\mathrm{~W}$ and $500 \\mathrm{~W}$ tracks for bare substrates and substrates with the $100 \\mu \\mathrm{m}$ copper layer are shown in Fig. 4.", "start_char_idx": 552061, "end_char_idx": 555802, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "810454c3-84cb-4af8-aec4-eb83c485adfb": {"__data__": {"id_": "810454c3-84cb-4af8-aec4-eb83c485adfb", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "b9c04e51-bede-478c-a2a9-d5a68aa7f486", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a59ab99581be1cdac5cb71a4807295834f778dfcdff165a435c89eb9f6a80ca8", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "d4121ee5-82b2-4610-82d9-88d235b0c591", "node_type": "1", "metadata": {}, "hash": "67c5fdb28c2eeb920b2580c1747af933154d0133dbdaddda211169348b6e9cc8", "class_name": "RelatedNodeInfo"}}, "text": "Moreover, in the case of the $500 \\mathrm{~W}$ tracks, there is a clear change in melting behaviour between $50 \\mathrm{~mm} / \\mathrm{s}$ and $150 \\mathrm{~mm} / \\mathrm{s}$ whereby at $150 \\mathrm{~mm} / \\mathrm{s}$ and above, homogeneous tracks are produced. Morphological irregularities, either in the form of balling or accumulation of material causing an increase in height of the tracks, are represented as red spots on the height maps.\n\nTo further characterise track morphology, track width and height measurements for $400 \\mathrm{~W}$ and $500 \\mathrm{~W}$ tracks for bare substrates and substrates with the $100 \\mu \\mathrm{m}$ copper layer are shown in Fig. 4. The width and height of the tracks was measured for all tracks, with an average of six measurements along each track.\n\nIn the case of the substrates with the copper powder layer, there was a trend of decreasing width with increasing scan speed. This trend was particularly strong with $400 \\mathrm{~W}$ power. It is also noted that the 400 and $500 \\mathrm{~W}$ widths coincide at higher scan speeds. For the bare plate, no significant trend of track width evolution with scan speed was observed. Under all scenarios, the track widths of the substrate with a powder layer were significantly larger than in the case of the bare substrate, a result that was expected due to the higher powder absorptivity. In the case of bare copper plate, the track width values are low. High conductivity of copper with ultra fast cooling rates is likely to cause selfquenching thus increasing the value of energy input required to fully melt and consolidate the material. The copper disc reflects most of the laser radiation and only a small amount of energy is absorbed and then transformed into thermal energy. On the other hand, the thermal conductivity of powder is lower, hence it may retain a higher fraction of heat leading to melting and spreading out, effectively increasing the width of the laser track.\n\nTrack heights in the case of the powder layer were, as expected, much higher than those of the bare substrates. As is the case for the widths, there was no trend of track heights for the bare substrates with increasing scan speed. However, for the powder layer, a trend of\n\nTable 1\n\nPhysical properties of copper, $\\rho, \\mathrm{C}_{\\mathrm{p}}, \\mathrm{k}$ and $\\mathrm{D}$ correspond to room temperature values as previously shown in Davis (2001).\n\n\\begin{center}\n\\begin{tabular}{ll}\n\\hline\nProperty & Value and Units \\\\\n\\hline\nAbsorptivity, $A$ & 0.05 \\\\\nDensity, $\\rho$ & $8.96 \\mathrm{~g} / \\mathrm{cm}^{3}$ \\\\\nSpecific heat capacity, $C_{p, o}$ & $384.6 \\mathrm{~J} /(\\mathrm{kg} \\mathrm{K})$ \\\\\nMelting point, $T_{m}$ & $1358 \\mathrm{~K}$ \\\\\nThermal conductivity, $k$ & $399 \\mathrm{~W} /(\\mathrm{m} \\mathrm{K})$ \\\\\nLatent Heat of Fusion & $205 \\mathrm{~J} / \\mathrm{g}$ \\\\\nLatent Heat of Evaporation & $4796 \\mathrm{~J} / \\mathrm{g}$ \\\\\nThermal diffusivity, $D$ & $1.11 \\times 10^{-4} \\mathrm{~m}^{2} / \\mathrm{s}$ \\\\\n\\hline\n\\end{tabular}\n\\end{center}\n\nPowder - $400 \\mathrm{~W} \\quad$ Scan speed (mm/s) Powder - $500 \\mathrm{~W}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_407a3fd0a98d50eaf53dg-05(3)}\n\nSubstrate - $500 \\mathrm{~W}$\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_407a3fd0a98d50eaf53dg-05}\n\nFig. 3. (a) and (c) Optical micrographs and (b) and (d) height maps for single tracks of $100 \\mu \\mathrm{m}$ layer thickness copper powder on copper substrates using $400 \\mathrm{~W}$ and $500 \\mathrm{~W}$ laser powers respectively, at increasing scan speeds.", "start_char_idx": 555130, "end_char_idx": 558708, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "d4121ee5-82b2-4610-82d9-88d235b0c591": {"__data__": {"id_": "d4121ee5-82b2-4610-82d9-88d235b0c591", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "810454c3-84cb-4af8-aec4-eb83c485adfb", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "a45c99a7901315809e0a1a6e4fdac9a29bd4930bef8f228b7f07d6c72cbfa637", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "a0b90ba5-53ad-4ad5-b4e5-588548ef2a13", "node_type": "1", "metadata": {}, "hash": "5a0ad543e0083c83a484c9dc72e71f59e424126527f511b257dc1e5843e105f6", "class_name": "RelatedNodeInfo"}}, "text": "3. (a) and (c) Optical micrographs and (b) and (d) height maps for single tracks of $100 \\mu \\mathrm{m}$ layer thickness copper powder on copper substrates using $400 \\mathrm{~W}$ and $500 \\mathrm{~W}$ laser powers respectively, at increasing scan speeds. Optical micrograph (e) and height map (f) for single tracks on bare copper substrate using $500 \\mathrm{~W}$ laser power at increasing scan speeds. Note the height scales vary between powder coated and bare substrates.\n\n(a)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-05(2)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-05(1)}\n\\end{center}\n\nFig. 4. (a) Widths and (b) heights of single tracks of copper powder on copper and bare copper substrates processed at increasing scan speeds, at $400 \\mathrm{~W}$ and $500 \\mathrm{~W}$. The error bars in both cases correspond to the standard deviation of the data across 7 measurements and sampled along each $10 \\mathrm{~mm}$ track.\\\\\nincreasing track height from 50 to $200 \\mathrm{~mm} / \\mathrm{s}$ scan speeds was seen, after which track height remained relatively constant.\n\n\\subsection*{3.2. Track cross-sections}\nIn order to elucidate the melting behaviour further, cross-sections of tracks were analysed by SEM. Micrographs of key cross-sections at 400 $\\mathrm{W}$ and $500 \\mathrm{~W}$ for tracks with copper powder layers are shown in Fig. 5. A significant difference in melting behaviour between $400 \\mathrm{~W}$ and $500 \\mathrm{~W}$ can be seen in the case of the tracks in the copper powder. At $400 \\mathrm{~W}$ (Fig. 5 (a), (b)), no penetrating melt pool could be seen irrespective of the scan speed, and at higher speeds, almost no bonding occurred. Moreover, at $\\mathrm{P}=400 \\mathrm{~W}$, the powder is partially melted, but the substrate is still intact. When the laser power is increased to $500 \\mathrm{~W}$, a transition to the keyhole regime can be observed (Fig. 5 (c)). The formation of keyholes with depth being independent from scan speed is shown. High scan speed increases the probability of defects, both for 400 and $500 \\mathrm{~W}$. Lower scan speed means more time for voids to be closed. It is worth mentioning that the microstructure of the melted copper is similar to that of bulk virgin copper. As a result, it is difficult to define details of the keyhole structure and our discussion will be mainly qualitative.\n\nFig. 6 (a-e) shows the melt pool evolution at the maximum laser power of $540 \\mathrm{~W}$ with increasing scanning speed for bare copper substrates. In Fig. 6 a) oxides are identified with white arrows. Oxide particles were observed after cross sectioning and polishing the samples leading to the assumption that oxides were formed during metallographic preparation. Deep penetration keyholing is seen, with melt pools reaching a depth of $400 \\mu \\mathrm{m}$. The depth is independent of scan speed, though some variation in the shape of the melt pools can be explained by the instability of the laser-matter interaction.", "start_char_idx": 558453, "end_char_idx": 561538, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "a0b90ba5-53ad-4ad5-b4e5-588548ef2a13": {"__data__": {"id_": "a0b90ba5-53ad-4ad5-b4e5-588548ef2a13", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "d4121ee5-82b2-4610-82d9-88d235b0c591", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "55eab71663353b20690394a72c8a50fef250a3ddd38b9bd9254cbe32688a441f", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "75fc19c6-727d-4638-867b-077d2b43b8aa", "node_type": "1", "metadata": {}, "hash": "95f1191bf81ebe0b1d313061931ecab375b139b200a09a694baec5357287d16a", "class_name": "RelatedNodeInfo"}}, "text": "It is worth mentioning that the microstructure of the melted copper is similar to that of bulk virgin copper. As a result, it is difficult to define details of the keyhole structure and our discussion will be mainly qualitative.\n\nFig. 6 (a-e) shows the melt pool evolution at the maximum laser power of $540 \\mathrm{~W}$ with increasing scanning speed for bare copper substrates. In Fig. 6 a) oxides are identified with white arrows. Oxide particles were observed after cross sectioning and polishing the samples leading to the assumption that oxides were formed during metallographic preparation. Deep penetration keyholing is seen, with melt pools reaching a depth of $400 \\mu \\mathrm{m}$. The depth is independent of scan speed, though some variation in the shape of the melt pools can be explained by the instability of the laser-matter interaction. Overall, it is clear that a number of distinct profiles can be identified that are\n\n(a)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_407a3fd0a98d50eaf53dg-06}\n\n(b)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_407a3fd0a98d50eaf53dg-06(3)}\n\n\\section*{$500 \\mathrm{~W}$}\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-06(1)}\n\\end{center}\n\n(c)\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_407a3fd0a98d50eaf53dg-06(2)}\n\nFig. 5. SEM and optical micrographs of (a) polished and (b) etched cross-sections of tracks made using a layer of copper powder on copper substrates at $400 \\mathrm{~W}$ and (c) $500 \\mathrm{~W}$.\\\\\n\\includegraphics[max width=\\textwidth, center]{2024_03_10_407a3fd0a98d50eaf53dg-07(1)}\n\nFig. 6. SEM images in back-scatter mode showing the evolution of a deep melt pool for $540 \\mathrm{~W}$ laser power in the transition regime from conduction to keyholing for bare copper substrates with increasing scan speed; From Figure a) to e) scan speed increases with intervals of $100 \\mathrm{~mm} / \\mathrm{s}$ and the dashed white lines show the melt pool boundaries; note the difference in scale size at the last micrograph.\n\ndetermined by the melting regime: heating, melting and transition from conduction to keyhole. These melting regimes are critical in determining the overall stability and behaviour of the LPBF process.\n\nMelt pool characteristics for $540 \\mathrm{~W}$ at $100 \\mathrm{~mm} / \\mathrm{s}$ are more consistent with a keyhole melting regime, given the higher aspect ratio melt pool, as opposed to the wider and shallower elliptical type melt pool seen at $500 \\mathrm{~mm} / \\mathrm{s}$. In the keyhole laser melting regime, the recoil pressure overcomes the surface tension causing a deep and narrow melt pool depression to form.\n\n\\subsection*{3.3. In situ absorptivity measurements}\nFig. 7 shows the effect of laser power at different scan speeds on absorptivity for bare plates and plates with a powder layer. In the case of the bare substrate, absorptivity values start at 0.05 and remain at this value until the laser power reaches $350 \\mathrm{~W}$. Above this laser power, a steep increase in absorptivity can be seen, indicating the fast transition from solid to liquid (i.e transition from conduction to a state that supports keyhole formation). It must be noted that, consistent with Fig. 4, scan speed does not have a significant impact on the absorptivity of copper. As presented in (Rubenchik et al., 2018) materials featuring high thermal conductivity are prone to keyhole depression and they are much more dependent on laser power than scan speed.\n\nFor the powder layer, this same trend is followed, however the initial absorptivity is notably higher at 0.2 and gradually increases, reaching 0.53 at the maximum laser power of $540 \\mathrm{~W}$.\n\n\\section*{4. Discussion}\n\\subsection*{4.1.", "start_char_idx": 560685, "end_char_idx": 564458, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "75fc19c6-727d-4638-867b-077d2b43b8aa": {"__data__": {"id_": "75fc19c6-727d-4638-867b-077d2b43b8aa", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "a0b90ba5-53ad-4ad5-b4e5-588548ef2a13", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "492e791a90475ba7609678e99fab3e6b0cbe6ad8489027db61109d8514305b46", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c78562c1-9277-4924-8ce0-beb80901677a", "node_type": "1", "metadata": {}, "hash": "f1053ffde0028cd155e8a17dec7edc9afe597ac65dc5879a26b4dc3a44567788", "class_name": "RelatedNodeInfo"}}, "text": "Above this laser power, a steep increase in absorptivity can be seen, indicating the fast transition from solid to liquid (i.e transition from conduction to a state that supports keyhole formation). It must be noted that, consistent with Fig. 4, scan speed does not have a significant impact on the absorptivity of copper. As presented in (Rubenchik et al., 2018) materials featuring high thermal conductivity are prone to keyhole depression and they are much more dependent on laser power than scan speed.\n\nFor the powder layer, this same trend is followed, however the initial absorptivity is notably higher at 0.2 and gradually increases, reaching 0.53 at the maximum laser power of $540 \\mathrm{~W}$.\n\n\\section*{4. Discussion}\n\\subsection*{4.1. Melting behaviour and absorptivity}\nEnergy absorption in LPBF is a complex process, which includes the\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-07}\n\\end{center}\n\nFig. 7. Effect of laser power on absorptivity, for bare plate at 25, 50 and 100 $\\mathrm{mm} / \\mathrm{s}$ scan speed and for a copper powder layer at $100 \\mathrm{~mm} / \\mathrm{s}$ scan speed ( $45 \\mu \\mathrm{m}$ $1 / \\mathrm{e}^{2}$ beam diameter).\n\neffects of temperature on absorptivity, laser irradiation interaction with the deformed melt surface, multiple light reflections, energy loss by material evaporation and ablation, absorption and refraction of light by the vapour. This work has used in-situ calorimetry-based absorptivity measurements of copper for the first time to provide a better understanding of its melting behaviour and dependence on typical processing parameters used in LPBF. In addition, this approach can be used to evaluate the different melting regimes (conduction vs keyhole) and to narrow down the process parameter window when deploying new LPBF systems. As will be discussed in subsequent sections in detail, a universal\\\\\nfunction of normalised enthalpy can guide parameter optimisation by taking the ratio of the deposited laser energy density to the material's melting enthalpy as shown by Ye et al. (2019). Normalised enthalpy effectively unifies the laser and material parameters for both laser absorptivity and melt pool geometries and will be used to support the following discussion.\n\nMelting behaviour was found to vary substantially with process parameters. Fig. 4 the melt pool width standard deviation is observed to generally decrease with increasing scan speed for $\\mathrm{P}=400 \\mathrm{~W}$ with a powder layer. This reduction in standard deviation, and implied reduction in melt pool fluctuation, is indicative of a more stable melting regime at higher scan speeds. The increase in width variation for the 400 $\\mathrm{W}$ tracks in powder may be explained by the entrainment-denudation phenomenon. This is where partially sintered or unmelted particles adhere to the sides of the scan tracks, causing irregularities in the track morphology as demonstrated by Matthews et al. (2017). However at 500 $\\mathrm{W}$, standard deviation of the height and width data, shows a weaker dependence on scan speed than for the $400 \\mathrm{~W}$ cases. At $500 \\mathrm{~W}$, the copper is in the key hole regime, with evaporation and partial metal ejection; in this regime, melt stretching due to the wetting is less pronounced. This suggests that the transition between stable and unstable melting is between 400 and $500 \\mathrm{~W}$ laser power. At both powers, the widths and heights of tracks, and their standard deviations, on the bare substrates show no clear trend with increasing scan speed.\n\nWhen powder is deposited on a substrate, the powder characteristics (porosity and particle size distribution changes from point to point. The resulting fluctuations of absorptivity can be one of the factors driving the observed track instability. The powder absorptivity is 4-5 times (for copper) higher than that for bulk material. As a result it is possible to have a regime where the laser power is high enough to melt the powder, but not sufficient to melt the substrate (Fig. 5(a)). Even at $400 \\mathrm{~W}$ the melt evolves under the effect of surface tension and this evolution can be longer than dwell time. In this situation the track parameters have scan speed dependence (see Fig. 4).", "start_char_idx": 563710, "end_char_idx": 568008, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c78562c1-9277-4924-8ce0-beb80901677a": {"__data__": {"id_": "c78562c1-9277-4924-8ce0-beb80901677a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "75fc19c6-727d-4638-867b-077d2b43b8aa", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3a0dfb81157da259dace4ebb021a050a80449284d52fd953c53025d223386ff0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1ded0a30-77e2-465f-9ade-e85bf8913436", "node_type": "1", "metadata": {}, "hash": "91d537a1a8c2f3ad650649c74850d5ab754e987b3104206dd00a3f62e217329c", "class_name": "RelatedNodeInfo"}}, "text": "At both powers, the widths and heights of tracks, and their standard deviations, on the bare substrates show no clear trend with increasing scan speed.\n\nWhen powder is deposited on a substrate, the powder characteristics (porosity and particle size distribution changes from point to point. The resulting fluctuations of absorptivity can be one of the factors driving the observed track instability. The powder absorptivity is 4-5 times (for copper) higher than that for bulk material. As a result it is possible to have a regime where the laser power is high enough to melt the powder, but not sufficient to melt the substrate (Fig. 5(a)). Even at $400 \\mathrm{~W}$ the melt evolves under the effect of surface tension and this evolution can be longer than dwell time. In this situation the track parameters have scan speed dependence (see Fig. 4). It has been shown that melted powder starts to wet the surface of the substrate after $\\sim 100 \\mu \\mathrm{s}$, at a corresponding scan speed $\\sim 400 \\mathrm{~mm} / \\mathrm{sec}$. For higher speeds, a balling effect, yielding a rough surface with low adhesion is to be expected. For a slow scan speed of $\\sim 100 \\mathrm{~mm} / \\mathrm{s}$, wetting results in the stretching of the melt across the track, providing good adhesion to the substrate, but decreasing melt height. This pattern corresponds to the experimental data in Fig. 4.\n\nThe absorptivity results in Fig. 7 support these findings. The presence of powder increases the effective absorptivity at all processing parameters. Critically, there is a clear increase in measured absorptivity from 350 to $540 \\mathrm{~W}$ in the case of the powder sample, up to a maximum of $\\sim 0.5$. This is in contrast to the case of the bare substrate, whereby until $450 \\mathrm{~W}$, absorptivity remains low, after which it rapidly increases. This behaviour is explained by multiple reflections and scattering of the laser beam in when interacting with the powder. For example, it has been shown previously that for high reflectivity materials, such as silver and gold, powder absorptivity can be increased by a factor of 4-7 in comparison to a flat surface, owing to the numerous reflections before effective absorption as stated by Rubenchik et al. (2015). This is in contrast to low reflectivity materials, such as stainless steel and titanium, for which this factor is only 1.5-2. The absorptivity behaviour of copper is different to that seen with stainless steel and Ti-6Al-4 V, where the powder melting results in a noticeable initial drop in absorptivity followed by an increase to $0.6-0.7$ due to keyhole formation. This drop in absorptivity, followed by a rapid increase is expected in stainless steel powders where the powder initially forms a melt pool, and the measured absorptivity matches closely to that of the bare substrate. Trapp et al. (2017) observed this trend at both low (100 mm/s) and high (1500 $\\mathrm{mm} / \\mathrm{s}$ ) scan speeds in the case of stainless steel. However, it is significant that in our results there was no observed sharp decrease in absorptivity values at any particular point.\n\nThe scan speed dependence of track width for the powder sample may be related to slow melt motion due to the surface tension mentioned earlier, and it is consistent with the observation that the width of tracks greatly exceed the beam diameter (up to 15 times at low scanning speeds). However, another contribution to instability could arise from the relative length scales of the laser beam and powder particles. In order to drive high temperatures to achieve melting for a fixed maximum laser power we a tightly focused laser beam that was approximately the same size as the average powder particle was used. This results in fluctuations of absorptivity during the scan such that when the laser beam interacts with a larger copper particle, the resulting absorptivity is low and close to the absorptivity of the bare copper substrate. However, when the laser beam scatters between powder particles, absorptivity increases abruptly. As such, the fluctuations of absorptivity during scanning can result in fluctuations of the track structure. For a laser power of $500 \\mathrm{~W}$ a transition to the key hole regime was observed.", "start_char_idx": 567159, "end_char_idx": 571421, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1ded0a30-77e2-465f-9ade-e85bf8913436": {"__data__": {"id_": "1ded0a30-77e2-465f-9ade-e85bf8913436", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c78562c1-9277-4924-8ce0-beb80901677a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "432f045eb78d2c709d148d4562fc3ca339d96afea3bf85ce4bd23a26e9fffaf0", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "eed3fcf9-dad5-46bb-b98b-c4c736614576", "node_type": "1", "metadata": {}, "hash": "69601e8df655e52e94685e347f545ac9e21639e108a54f1cf588b0a0de77a3bb", "class_name": "RelatedNodeInfo"}}, "text": "However, another contribution to instability could arise from the relative length scales of the laser beam and powder particles. In order to drive high temperatures to achieve melting for a fixed maximum laser power we a tightly focused laser beam that was approximately the same size as the average powder particle was used. This results in fluctuations of absorptivity during the scan such that when the laser beam interacts with a larger copper particle, the resulting absorptivity is low and close to the absorptivity of the bare copper substrate. However, when the laser beam scatters between powder particles, absorptivity increases abruptly. As such, the fluctuations of absorptivity during scanning can result in fluctuations of the track structure. For a laser power of $500 \\mathrm{~W}$ a transition to the key hole regime was observed. It is important to note that the transition is very sharp as there is no substrate melting at $400 \\mathrm{~W}$ (in comparison to over $100 \\mu \\mathrm{m}$ deep depressions at $500 \\mathrm{~W}$ ). This pattern is different from keyhole growth in other materials (e.g. Ti6Al4V, stainless steels and nickel superalloys) as presented by Ye et al. (2019), where keyhole depth grows gradually (linearly) with laser power. This key difference in behaviour can be explained by the following; In the case of copper, the absorptivity of the laser light jumps rapidly, by 1.5 times, at the melting point, and thermal conductivity drops by 2.4 times. As a result, just after the laser heats material to a temperature above the melting point, there is a sharp temperature increase up to the boiling point, resulting in a sharp transition to the keyhole regime.\n\n\\subsection*{4.2. Absorptivity scaling behaviour}\nIn order to obtain a comparative picture of the melt pool formation behaviour in copper, the bare plate absorptivity of a range of materials should be considered. In the study of Ye et al. (2019) that focused on alloy systems with thermal diffusivities lower than copper (e.g. stainless steel, Ti-6Al-4 V and Inconel 625), it was found that the absorptivity is mainly dependent on two independent dimensionless parameters namely normalised enthalpy $\\beta$ and normalised diffusion length $L_{t h}^{*}$. These parameters take into account both material properties and laser processing parameters, and they can be calculated using Eqs. (3) and (4) respectively.\n\n$\\beta=\\frac{A_{m} P}{\\pi H_{m} \\sqrt{D a^{3} u}}$\n\n$L_{t h}^{*}=\\sqrt{\\frac{D}{a u}}$\n\nFor a given material with low thermal diffusivity, the transverse thermal diffusion is of minor importance as the increase of melt pool depth or depression depth is driven by vapour recoil pressure and Marangoni shear flow. In the work of Campanelli et al. (2014) it was found that the melt pool depth and absorptivity scale with $\\beta L^{*}{ }_{t h}$, which leads to a simplified surface energy density dependence $\\left(\\propto P u^{-1}\\right)$. Thus, for low thermal diffusion materials, the effect of thermal diffusivity will tend to cancel out through the counter-dependence of $\\beta$ and $L^{*} t h$ on $D$. When this scaling is applied to copper, as shown in Fig. 8(a), the plots for different scan speeds become further separated. This is because the above scaling relationship is not applicable for high thermally conducting materials such as copper, where the melt pool depth is strongly influenced by thermal diffusion. For example, when comparing the thermal diffusion time, $\\tau_{\\text {th, }}$, for a $50 \\mu \\mathrm{m}$ laser spot, copper thermal diffusion times are in the order of $\\mu$ s while steel, inconel and titanium are in the order of 100 's of $\\mu \\mathrm{s}$. This can be compared to an effective scan laser dwell time of $\\sim 100 \\mu \\mathrm{s}$ for $\\mathrm{v}=500 \\mathrm{~mm} / \\mathrm{s}$. When the absorptivity is plotted against the original 'bare' form of normalised enthalpy $\\beta$ similar to the work of Hann et al.", "start_char_idx": 570575, "end_char_idx": 574530, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "eed3fcf9-dad5-46bb-b98b-c4c736614576": {"__data__": {"id_": "eed3fcf9-dad5-46bb-b98b-c4c736614576", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "1ded0a30-77e2-465f-9ade-e85bf8913436", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "97d1c60e0e7494c7e6d2dfc6ed9804044aeac432eedec086d0f72870af5a8a04", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "c0b8bd6b-4c77-4ce1-b0de-1a56d92bfbc6", "node_type": "1", "metadata": {}, "hash": "59e955a5ba261727f41e6defcfd9446ac95e6f25027fdaa32b815ecde2e92a16", "class_name": "RelatedNodeInfo"}}, "text": "8(a), the plots for different scan speeds become further separated. This is because the above scaling relationship is not applicable for high thermally conducting materials such as copper, where the melt pool depth is strongly influenced by thermal diffusion. For example, when comparing the thermal diffusion time, $\\tau_{\\text {th, }}$, for a $50 \\mu \\mathrm{m}$ laser spot, copper thermal diffusion times are in the order of $\\mu$ s while steel, inconel and titanium are in the order of 100 's of $\\mu \\mathrm{s}$. This can be compared to an effective scan laser dwell time of $\\sim 100 \\mu \\mathrm{s}$ for $\\mathrm{v}=500 \\mathrm{~mm} / \\mathrm{s}$. When the absorptivity is plotted against the original 'bare' form of normalised enthalpy $\\beta$ similar to the work of Hann et al. (2011), which scales as $P u^{-0.5}$, the plots follow\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-09(1)}\n\\end{center}\n\n(c)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-09(2)}\n\\end{center}\n\n(b)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-09(3)}\n\\end{center}\n\n(d)\n\n\\begin{center}\n\\includegraphics[max width=\\textwidth]{2024_03_10_407a3fd0a98d50eaf53dg-09}\n\\end{center}\n\nFig. 8. Laser absorptivity as functions of the power of normalized enthalpy and normalized thermal diffusion length $\\beta L^{*}$ th where 'ref' refers to data taken from Ye et al. (2019) (a), the normalized enthalpy $\\beta$ (b), the ratio of normalized enthalpy and normalized thermal diffusion length $\\beta / L^{*}$ th $(c)$, and $\\beta / L^{*}$ th $u^{0.18}$ (d).\n\na more unified behaviour, however, the threshold for absorptivity jump is still broadly separated (see Fig. 8(b)). Instead, the scanning speed dependency is less significant due to high thermal diffusivity and short diffusion times. In fact, in deriving the normalised enthalpy from laser scan parameters, if one replaces the effective laser dwell time $(a / u)$ with $\\tau_{\\mathrm{th}}$, the resulting form is $\\beta^{\\prime}=\\frac{A P}{\\pi H_{m} D a}=\\beta / L_{t h}^{*}$, which cancels out the effect of scanning speed $\\left(\\propto p u^{-0}\\right)$. For a fixed material and laser spot size, this scaling is mainly dependent on power as shown Figs. 7 and 8(c). The increased overlapping of the plots proves that the laser absorptivity of copper is less dependent on scanning speed and is consistent with the observation that $L_{t h}^{*}>1$ for the temperature distribution around melt pool. For the best fit, the scaling exponent of absorptivity of copper bare plate vs scanning speed is found to be -0.18 (Fig. 8(d)). Note that the powder case is still separated from the bare plate cases due to the effect of the lower thermal conductivity of the loosely packed powder layer.\n\n\\section*{5. Conclusions}\nLaser calorimetry has been shown as a useful method for revealing melting mechanisms of copper and advancing understanding of material-process-property relationships otherwise difficult to identify. The main findings of this research can be summarised as the following:\n\n\\begin{itemize}\n  \\item The absorptivity of copper powder is approximately four times higher than for the bare material reaching a value of approximately 0.5 .\n  \\item The difference in absorptivity of copper between solid and liquid state is between 6-8\\%.\n  \\item The presence of copper powder reduces the critical energy density thershold required to sufficiently melt material during laser interaction. The powder layer can be melted at a more stable and consistent manner when compared to the bare disc.\n  \\item It was also demonstrated that melted layer quality and adhesion can be controlled by manipulation of scanning speed.", "start_char_idx": 573745, "end_char_idx": 577516, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "c0b8bd6b-4c77-4ce1-b0de-1a56d92bfbc6": {"__data__": {"id_": "c0b8bd6b-4c77-4ce1-b0de-1a56d92bfbc6", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "eed3fcf9-dad5-46bb-b98b-c4c736614576", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "b6e9b09c104dd9c7f119846d0ec4533a5e8bc09be0e1e580b926cfac802e6874", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "7b27fec8-0c3b-45e5-b664-3567e1e7b84a", "node_type": "1", "metadata": {}, "hash": "46b0650c51a476bcdc2755af9a80e13ce0257876a4418038a313c955efe4450e", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{5. Conclusions}\nLaser calorimetry has been shown as a useful method for revealing melting mechanisms of copper and advancing understanding of material-process-property relationships otherwise difficult to identify. The main findings of this research can be summarised as the following:\n\n\\begin{itemize}\n  \\item The absorptivity of copper powder is approximately four times higher than for the bare material reaching a value of approximately 0.5 .\n  \\item The difference in absorptivity of copper between solid and liquid state is between 6-8\\%.\n  \\item The presence of copper powder reduces the critical energy density thershold required to sufficiently melt material during laser interaction. The powder layer can be melted at a more stable and consistent manner when compared to the bare disc.\n  \\item It was also demonstrated that melted layer quality and adhesion can be controlled by manipulation of scanning speed.\n  \\item The onset of increasing absorptivity is shifted to higher power for increased scan speed.\n  \\item From an additive manufacturing perspective, higher laser power and powder layer improves the process efficiency by increasing the effective absorptivity. This was attributed to the lower thermal conductivity of the loosely packed powder. However, even at full power $540 \\mathrm{~W}$, the energy delivered was insufficient to create a stable keyhole melting regime for bare plate and powder. An explosive behavior and sudden changes in absorptivity even when in the keyhole regime were noticed in the melt pool.\n\\end{itemize}\n\nIn conclusion, the findings can be used as guidelines for parameter optimisation of copper and copper alloys in LPBF additive manufacturing. The work has also demonstrated that calorimetry can be used a practical method for performing on-line monitoring of process behaviour during LPBF. The presented results regarding the various relationships between absorptivity and processing parameters may also be useful as a reference for LPBF of Copper, and of theoretical value for further research.\n\n\\section*{CRediT authorship contribution statement}\nLeonidas Gargalis: Data curation, Conceptualization, Writing original draft, Visualization, Investigation, Formal analysis. Jianchao Ye: Data curation, Writing - original draft, Investigation, Formal analysis. Maria Strantza: Data curation, Writing - original draft, Investigation. Alexander Rubenchik: Data curation, Writing - original draft, Investigation. James W. Murray: Writing - review \\& editing, Data curation. Adam T. Clare: Writing - review \\& editing. Ian A. Ashcroft: Writing - review \\& editing. Richard Hague: Supervision, Funding acquisition, Writing - review \\& editing. Manyalibo J. Matthews:\n\nSupervision, Project administration, Funding acquisition, Writing - review \\& editing.\n\n\\section*{Declaration of Competing Interest}\nThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\n\n\\section*{Acknowledgements}\nThe authors would like to thank Tien T. Roehling, Gabe Guss and Michael Crumb Fredrick for their valuable contribution to the experiments. This work was performed under the auspices of the U.S Department of Energy, by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. This research was funded by the Laboratory Directed Research and Development Program at LLNL under project tracking code 18-ERD-003. Leonidas Gargalis received funding by the INNOVATIVE doctoral program. The INNOVATIVE program is partially funded by the Marie Curie Initial Training Networks (ITN) action (project number 665468) and partially by the Institute for Aerospace Technology (IAT) at the University of Nottingham.\n\n\\section*{References}\nAuwal, S.T., Ramesh, S., Yusof, F., Manladan, S.M., 2018. A review on laser beam welding of copper alloys. Int. J. Adv. Manuf. Technol. 97, 1071-1098. \\href{https://doi}{https://doi}. org/10.1007/s00170-018-2030-x.\n\nBoley, C.D., Khairallah, S.A., Rubenchik, A.M., 2017. Calculation of laser absorption by metal powders in additive manufacturing. In: Additive Manufacturing Handbook: Product Development for the Defense Industry, 54, pp. 507-517. \\href{https://doi.org/}{https://doi.org/} 10.1201/9781315119106.", "start_char_idx": 576586, "end_char_idx": 580890, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "7b27fec8-0c3b-45e5-b664-3567e1e7b84a": {"__data__": {"id_": "7b27fec8-0c3b-45e5-b664-3567e1e7b84a", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "c0b8bd6b-4c77-4ce1-b0de-1a56d92bfbc6", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "3843c18003b8794039144e8e45b0271a04053532d2b126295a7b9169dd3d00db", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "1a4a9f63-fa95-48fb-932c-9bb587997270", "node_type": "1", "metadata": {}, "hash": "0bbd09c3b46533fcd2616d3456a316aa9cc75094827adf132404490f7ecf7124", "class_name": "RelatedNodeInfo"}}, "text": "\\section*{References}\nAuwal, S.T., Ramesh, S., Yusof, F., Manladan, S.M., 2018. A review on laser beam welding of copper alloys. Int. J. Adv. Manuf. Technol. 97, 1071-1098. \\href{https://doi}{https://doi}. org/10.1007/s00170-018-2030-x.\n\nBoley, C.D., Khairallah, S.A., Rubenchik, A.M., 2017. Calculation of laser absorption by metal powders in additive manufacturing. In: Additive Manufacturing Handbook: Product Development for the Defense Industry, 54, pp. 507-517. \\href{https://doi.org/}{https://doi.org/} 10.1201/9781315119106.\n\nCampanelli, S.L., Casalino, G., Contuzzi, N., Angelastro, A., Ludovico, A.D., 2014. Analysis of the molten/solidified zone in selective laser melted parts. In: Dorsch, F. (Ed.), Proceedings of SPIE -The International Society for Optical Engineering, p. 8963. \\href{https://doi.org/10.1117/12.2042170}{https://doi.org/10.1117/12.2042170}, 896311.\n\nClare, A.T., Reynolds, W.J., Murray, J.W., Aboulkhair, N.T., Simonelli, M., Hardy, M., Grant, D.M., Tuck, C., 2020. 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Selective laser melting of pure copper.", "start_char_idx": 580358, "end_char_idx": 583044, "text_template": "{metadata_str}\n\n{content}", "metadata_template": "{key}: {value}", "metadata_seperator": "\n", "class_name": "TextNode"}, "__type__": "1"}, "1a4a9f63-fa95-48fb-932c-9bb587997270": {"__data__": {"id_": "1a4a9f63-fa95-48fb-932c-9bb587997270", "embedding": null, "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "excluded_embed_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "excluded_llm_metadata_keys": ["file_name", "file_type", "file_size", "creation_date", "last_modified_date", "last_accessed_date"], "relationships": {"1": {"node_id": "eb69a6e3-7620-40c8-96dc-7dfad8125b3a", "node_type": "4", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "cc9c466d3687de282227e2ac99ac1b8477c7d440b3ec565ef0b9bbf82a105a60", "class_name": "RelatedNodeInfo"}, "2": {"node_id": "7b27fec8-0c3b-45e5-b664-3567e1e7b84a", "node_type": "1", "metadata": {"file_path": "/home/achuthchandrasekhar/Documents/AMGPT/advanced_rag_code/rag_docs_final_review_tex_merged/merged_18_to_36.txt", "file_name": "merged_18_to_36.txt", "file_type": "text/plain", "file_size": 587897, "creation_date": "2024-07-10", "last_modified_date": "2024-07-10"}, "hash": "4f4324e2fc26e233a3d9aed6791ba4339026469c85c88b3bdc9985730a59ed8e", "class_name": "RelatedNodeInfo"}, "3": {"node_id": "2129fbe9-e755-42ba-b8bc-8e2f3582218d", "node_type": "1", "metadata": {}, "hash": "8c7c57f57315c417e6d4de66275cfbe51cff5ead992f1eb20b0de9b9f1a7e92f", "class_name": "RelatedNodeInfo"}}, "text": "445401. J. Phys. D Appl. Phys. 44, 44-54.\\\\\nHess, A., Schuster, R., Heider, A., Weber, R., Graf, T., 2011. Continuous wave laser welding of copper with combined beams at wavelengths of $1030 \\mathrm{~nm}$ and of $515 \\mathrm{~nm}$. Phys. Procedia 12, 88-94. \\href{https://doi.org/10.1016/j.phpro.2011.03.012}{https://doi.org/10.1016/j.phpro.2011.03.012}.\n\nIkeshoji, T.-T., Nakamura, K., Yonehara, M., Imai, K., Kyogoku, H., 2017. Selective laser melting of pure copper. Jom 3-7. \\href{https://doi.org/10.1007/s11837-017-2695-x}{https://doi.org/10.1007/s11837-017-2695-x}.\n\nJadhav, S.D., Dadbakhsh, S., Goossens, L., Kruth, J.P., Van Humbeeck, J., Vanmeensel, K., 2019a. Influence of selective laser melting process parameters on texture evolution in pure copper. J. Mater. Process. 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Metal vapor micro-jet controls material redistribution in laser powder bed fusion additive manufacturing. Sci. Rep. 7, 1-12. \\href{https://doi.org/10.1038/s41598-017-04237-z}{https://doi.org/10.1038/s41598-017-04237-z}.\n\nLykov, P.A., Safonov, E.V., Akhmedianov, A.M., 2016. Selective laser melting of copper. Mater. Sci. Forum 843, 284-288. \\href{https://doi.org/10.4028/www.scientific.net/}{https://doi.org/10.4028/www.scientific.net/} MSF.843.284.\n\nMatthews, M.J., Guss, G., Khairallah, S.A., Rubenchik, A.M., Depond, P.J., King, W.E., 2017. Denudation of metal powder layers in laser powder-bed fusion processes. 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