# Comparative accuracy analysis of continuous fiber composite printers: Coextrusion vs. dual-nozzle technology

OCHANA Imi¹,²,a *, DUCOBU François², SPITAELS Laurent², HOMRANI Mohamed Khalil², DEMARBAIX Anthonin¹

¹Science and Technology Research Unit, Haute Ecole Provinciale de Hainaut Condorcet, Square Hierneaux 2, 6000 Charleroi, Belgium

²Machine Design and Production Engineering Lab, Research Institute for Science and Material Engineering, University of Mons, Mons, Belgium

aimi.ochana@condorcet.be

**Keywords:** Continuous Fiber Reinforced, Dimensional Accuracy, 3D Printing

**Abstract.** Material Extrusion (MEX) technology for continuous fiber reinforced thermoplastic composites (CFRTCs) is based on the extrusion of a continuous fiber to create three-dimensional composite objects layer by layer. This technology explores three distinct methods: pre-impregnated filament, dual-nozzle, and coextrusion. The goal of this paper is to compare two printers, one using the dual nozzle technology and another relying on coextrusion. The first printer, Mark Two of Markforged, is based on dual-nozzle technology. The second printer, the Anisoprint Composer A4, stands out for its coextrusion method. Three adaptive Geometrical Benchmark Test Artifacts (GBTA), proposed by Spitaels et al. were fabricated with each printer to determine their dimensional performances. Measurements are taken using a Coordinate Measuring Machine (CMM) Wenzel LH 54. The overall deviation results of the two printers are around the IT14 standard. Deviations for measurements between 1 and 10 mm are greater compared to dimensions exceeding 10 mm, averaging around IT 12. Along the Y-axis, Markforged shows smaller deviations, attributed to its smaller print bed dimension compared to Anisoprint. Additionally, Z-axis deviations are lower than those along other axes, suggesting both printers have better precision in vertical build plate movement compared to print head movement. Notably, significant deviations are observed at the center of the GBTA in comparison to the other three axes (X, Y, and Z) for both printers.

**Introduction**

Additive Manufacturing (AM) processes are defined as technologies capable of "assembling materials to fabricate objects from 3D model data, typically layer by layer, as opposed to subtractive or formative manufacturing methodologies" following the ASTM D638 [1]. Currently, AM processes are a fairly advanced research topic. They have the potential to manufacture parts with complex geometric shapes with minimal material waste [2]. With this method, it is possible to produce parts with a design impossible to achieve by conventional manufacturing methods. This process is becoming increasingly popular and, as a result, is interesting for a wide range of applications such as aerospace, automotive, medicine, and biofabrication [2]. AM relies on several technologies. The one discussed in this article is Material Extrusion (MEX). It is an additive manufacturing method that uses the fusion and extrusion of material to create 3D objects. The process itself is called Fused Deposition Modeling (FDM) and it consists of the creation of a 3D model using computer-aided design software, followed by a slicing step that divides the model into thin layers. At the 3D printer, a filament of thermoplastic material, possibly accompanied by fibers, is heated up and extruded through a movable nozzle. The nozzle deposits the melted material layer by layer, following the coordinates of the 3D model. The extruded material quickly

<figure><img src="image_127.png" /></figure>
# Comparative accuracy analysis of continuous fiber composite printers: Coextrusion vs. dual-nozzle technology

OCHANA Imi¹,²,a *, DUCOBU François², SPITAELS Laurent², HOMRANI Mohamed Khalil², DEMARBAIX Anthonin¹

¹Science and Technology Research Unit, Haute Ecole Provinciale de Hainaut Condorcet, Square Hierneaux 2, 6000 Charleroi, Belgium

²Machine Design and Production Engineering Lab, Research Institute for Science and Material Engineering, University of Mons, Mons, Belgium

aimi.ochana@condorcet.be

**Keywords:** Continuous Fiber Reinforced, Dimensional Accuracy, 3D Printing

**Abstract.** Material Extrusion (MEX) technology for continuous fiber reinforced thermoplastic composites (CFRTCs) is based on the extrusion of a continuous fiber to create three-dimensional composite objects layer by layer. This technology explores three distinct methods: pre-impregnated filament, dual-nozzle, and coextrusion. The goal of this paper is to compare two printers, one using the dual nozzle technology and another relying on coextrusion. The first printer, Mark Two of Markforged, is based on dual-nozzle technology. The second printer, the Anisoprint Composer A4, stands out for its coextrusion method. Three adaptive Geometrical Benchmark Test Artifacts (GBTA), proposed by Spitaels et al. were fabricated with each printer to determine their dimensional performances. Measurements are taken using a Coordinate Measuring Machine (CMM) Wenzel LH 54. The overall deviation results of the two printers are around the IT14 standard. Deviations for measurements between 1 and 10 mm are greater compared to dimensions exceeding 10 mm, averaging around IT 12. Along the Y-axis, Markforged shows smaller deviations, attributed to its smaller print bed dimension compared to Anisoprint. Additionally, Z-axis deviations are lower than those along other axes, suggesting both printers have better precision in vertical build plate movement compared to print head movement. Notably, significant deviations are observed at the center of the GBTA in comparison to the other three axes (X, Y, and Z) for both printers.

**Introduction**

Additive Manufacturing (AM) processes are defined as technologies capable of "assembling materials to fabricate objects from 3D model data, typically layer by layer, as opposed to subtractive or formative manufacturing methodologies" following the ASTM D638 [1]. Currently, AM processes are a fairly advanced research topic. They have the potential to manufacture parts with complex geometric shapes with minimal material waste [2]. With this method, it is possible to produce parts with a design impossible to achieve by conventional manufacturing methods. This process is becoming increasingly popular and, as a result, is interesting for a wide range of applications such as aerospace, automotive, medicine, and biofabrication [2]. AM relies on several technologies. The one discussed in this article is Material Extrusion (MEX). It is an additive manufacturing method that uses the fusion and extrusion of material to create 3D objects. The process itself is called Fused Deposition Modeling (FDM) and it consists of the creation of a 3D model using computer-aided design software, followed by a slicing step that divides the model into thin layers. At the 3D printer, a filament of thermoplastic material, possibly accompanied by fibers, is heated up and extruded through a movable nozzle. The nozzle deposits the melted material layer by layer, following the coordinates of the 3D model. The extruded material quickly

<figure><img src="image_128.png" /></figure>
solidifies, ensuring adhesion with the previous layer or the print bed. This fusion and extrusion process repeats until the complete fabrication of the object. FDM is widely used in 3D printing due to its simplicity, versatility and ability to produce functional parts with different properties. Due to the low strength of pure polymers, it is possible to reinforce them with fibers to enhance their mechanical properties [3].

Materials such as Acrylonitrile butadiene styrene (ABS), Polylactic acid (PLA), and polyamide (PA) are widely used in FDM due to their low melting points, making them particularly suitable for 3D printing. As illustrated in Fig. 1, some polymers can be filled with particles or short fibers, where the addition of fibers increases the strength of the material. Moreover, it is possible to add continuous fibers to these polymers, providing an additional strength. Indeed, a composite material is up to 30 times stronger than plastic [4]. In addition to improve the mechanical properties, the incorporation of carbon fibers provides additional information about the material, such as its electrical and magnetic properties contributing to a more comprehensive understanding of intelligent materials [5]. 3D printing via FDM of this type of material is more complex, as it requires special attention during extrusion to ensure the continuity of the fiber arrangement within the polymer. The continuous fiber and thermoplastic are initially separated, and it is during printing that the two materials are melted together [6].

<figure><img src="image_128.png" /><figcaption>Figure 1: Composites reinforced with fibers (Image used with the permission of Anisoprint) [4].</figcaption></figure>

Various technologies currently exist for extruding the composite material from a 3D printer nozzle in FDM. This paper compares dual-nozzle technology with coextrusion. Concerning dual-nozzle technology, Mark et al. [7] proposed a patented system using two nozzles, the first for depositing thermoplastic material and the second for laying down continuous fibers on the previously deposited polymer layer. Markforged is the brand that commercializes this patented technology. The reinforced polymer offered by Markforged is Onyx, which is composed of PA as the matrix material reinforced with short carbon fibers [8].

Coextrusion technology is a process characterized by the simultaneous extrusion of multiple materials, which may include polymers and reinforcing fibers, through a common nozzle. This method involves two distinct entrances: one for the polymer and another for the continuous fiber. Within the nozzle, the continuous fiber is integrated through the center of the polymer flow. The output from the nozzle yields a composite material tow [8]. Azarov et al. [9] explored the concept of pre-impregnating a fiber tow with a high-performance epoxy thermosetting polymer as a preliminary step. They proposed introducing these pre-impregnated fibers for in situ impregnation within a Fused Filament Fabrication (FFF) nozzle coated with thermoplastic. Adumitroaie et al. [10] explained that this method enables the utilization of the benefits associated with low-viscosity thermosetting polymers for impregnating the fiber tow, while also ensuring compatibility with the high viscosity of thermoplastic polymers in the FFF process. Anisoprint is the brand that developed this system. The reinforced polymer offered by Anisoprint is Smooth PA, which is composed of PA as the matrix material reinforced with short carbon fibers [4].
solidifies, ensuring adhesion with the previous layer or the print bed. This fusion and extrusion process repeats until the complete fabrication of the object. FDM is widely used in 3D printing due to its simplicity, versatility and ability to produce functional parts with different properties. Due to the low strength of pure polymers, it is possible to reinforce them with fibers to enhance their mechanical properties [3].

Materials such as Acrylonitrile butadiene styrene (ABS), Polylactic acid (PLA), and polyamide (PA) are widely used in FDM due to their low melting points, making them particularly suitable for 3D printing. As illustrated in Fig. 1, some polymers can be filled with particles or short fibers, where the addition of fibers increases the strength of the material. Moreover, it is possible to add continuous fibers to these polymers, providing an additional strength. Indeed, a composite material is up to 30 times stronger than plastic [4]. In addition to improve the mechanical properties, the incorporation of carbon fibers provides additional information about the material, such as its electrical and magnetic properties contributing to a more comprehensive understanding of intelligent materials [5]. 3D printing via FDM of this type of material is more complex, as it requires special attention during extrusion to ensure the continuity of the fiber arrangement within the polymer. The continuous fiber and thermoplastic are initially separated, and it is during printing that the two materials are melted together [6].

<figure><img src="image_129.png" /><figcaption>Figure 1: Composites reinforced with fibers (Image used with the permission of Anisoprint) [4].</figcaption></figure>

Various technologies currently exist for extruding the composite material from a 3D printer nozzle in FDM. This paper compares dual-nozzle technology with coextrusion. Concerning dual-nozzle technology, Mark et al. [7] proposed a patented system using two nozzles, the first for depositing thermoplastic material and the second for laying down continuous fibers on the previously deposited polymer layer. Markforged is the brand that commercializes this patented technology. The reinforced polymer offered by Markforged is Onyx, which is composed of PA as the matrix material reinforced with short carbon fibers [8].

Coextrusion technology is a process characterized by the simultaneous extrusion of multiple materials, which may include polymers and reinforcing fibers, through a common nozzle. This method involves two distinct entrances: one for the polymer and another for the continuous fiber. Within the nozzle, the continuous fiber is integrated through the center of the polymer flow. The output from the nozzle yields a composite material tow [8]. Azarov et al. [9] explored the concept of pre-impregnating a fiber tow with a high-performance epoxy thermosetting polymer as a preliminary step. They proposed introducing these pre-impregnated fibers for in situ impregnation within a Fused Filament Fabrication (FFF) nozzle coated with thermoplastic. Adumitroaie et al. [10] explained that this method enables the utilization of the benefits associated with low-viscosity thermosetting polymers for impregnating the fiber tow, while also ensuring compatibility with the high viscosity of thermoplastic polymers in the FFF process. Anisoprint is the brand that developed this system. The reinforced polymer offered by Anisoprint is Smooth PA, which is composed of PA as the matrix material reinforced with short carbon fibers [4].
In parallel with the developments in the design of these printers, the assessment of geometric capabilities and uncertainties of a printer is crucial. Therefore, to evaluate them, a Geometric Benchmark Test Artifacts (GBTA) is used to identify printing limitations. Moylan et al. [11] introduced a GBTA model with an extensive measurement range. Spitaels et al. [12] later enhanced Moylan's model by making it adaptive for many printers such as Pollen PAM Series MC, Ultimaker 2+, Ultimaker S3, offering a design covering more than 90% of the available printing area in the printer's X and Y axes [13].

The purpose of this study is to compare two 3D printers in terms of dimensional accuracy. The printers in question are the Mark Two by Markforged, using dual-nozzle technology, and the Composer A4 by Anisoprint, using coextrusion. To achieve this, three Geometric Benchmark Test Artifacts were printed by each printer and subsequently compared. The GBTA model of Spitaels et al. is used to analyze the Composer A4 (Anisoprint) and readjusted for the Mark Two (Markforged), considering its smaller print bed. Markforged uses Onyx as the material for printing GBTAs, while Anisoprint uses Smooth PA for the same purpose.

## Procedure and Materials

The two printers have Cartesian architecture. The first one, Markforged's Mark Two printer, is built on dual-nozzle technology, as illustrated in Fig. 2(a). It enables the printing of thermoplastic with one nozzle and, on a separate head, the printing of continuous fiber using another nozzle. The print bed exhibits dimensions of 320 mm x 132 mm x 154 mm for its X, Y and Z axes. The second one, Anisoprint's Composer A4, stands out for its coextrusion method, as illustrated in Fig. 2(b). The fibers are pre-impregnated with a thermosetting epoxy polymer, creating a filament consisting of 1500 fibers. This filament is then directly impregnated into the nozzle by a thermoplastic material, thus forming the composite material that exits the nozzle. The printer offers a printing volume of 297 mm x 210 mm x 140 mm across its X, Y and Z axes.

<figure><img src="image_129.png" /><figcaption>Figure 2: Technologies of double buses (a) and coextrusion (b) [8].</figcaption></figure>

These two printers serve as the primary tools for this study. Since their capabilities are not fully known, three GBTAs were printed for each printer to assess and compare their dimensional accuracy, providing insights into the anticipated tolerances of the resulting parts. The printing parameters are presented in Table 1. A 50% infill density was chosen to optimize printing time and save material. Despite this percentage reduction, the GBTA retains the necessary characteristics to fulfill its specific function as a measuring component.
In parallel with the developments in the design of these printers, the assessment of geometric capabilities and uncertainties of a printer is crucial. Therefore, to evaluate them, a Geometric Benchmark Test Artifacts (GBTA) is used to identify printing limitations. Moylan et al. [11] introduced a GBTA model with an extensive measurement range. Spitaels et al. [12] later enhanced Moylan's model by making it adaptive for many printers such as Pollen PAM Series MC, Ultimaker 2+, Ultimaker S3, offering a design covering more than 90% of the available printing area in the printer's X and Y axes [13].

The purpose of this study is to compare two 3D printers in terms of dimensional accuracy. The printers in question are the Mark Two by Markforged, using dual-nozzle technology, and the Composer A4 by Anisoprint, using coextrusion. To achieve this, three Geometric Benchmark Test Artifacts were printed by each printer and subsequently compared. The GBTA model of Spitaels et al. is used to analyze the Composer A4 (Anisoprint) and readjusted for the Mark Two (Markforged), considering its smaller print bed. Markforged uses Onyx as the material for printing GBTAs, while Anisoprint uses Smooth PA for the same purpose.

## Procedure and Materials

The two printers have Cartesian architecture. The first one, Markforged's Mark Two printer, is built on dual-nozzle technology, as illustrated in Fig. 2(a). It enables the printing of thermoplastic with one nozzle and, on a separate head, the printing of continuous fiber using another nozzle. The print bed exhibits dimensions of 320 mm x 132 mm x 154 mm for its X, Y and Z axes. The second one, Anisoprint's Composer A4, stands out for its coextrusion method, as illustrated in Fig. 2(b). The fibers are pre-impregnated with a thermosetting epoxy polymer, creating a filament consisting of 1500 fibers. This filament is then directly impregnated into the nozzle by a thermoplastic material, thus forming the composite material that exits the nozzle. The printer offers a printing volume of 297 mm x 210 mm x 140 mm across its X, Y and Z axes.

<figure><img src="image_130.png" /><figcaption>Figure 2: Technologies of double buses (a) and coextrusion (b) [8].</figcaption></figure>

These two printers serve as the primary tools for this study. Since their capabilities are not fully known, three GBTAs were printed for each printer to assess and compare their dimensional accuracy, providing insights into the anticipated tolerances of the resulting parts. The printing parameters are presented in Table 1. A 50% infill density was chosen to optimize printing time and save material. Despite this percentage reduction, the GBTA retains the necessary characteristics to fulfill its specific function as a measuring component.
<table><caption>Table 1: Printing parameters of printers Mark Two (Markforged) and Composer A4 (Anisoprint)</caption><thead><tr><th></th><th>Mark Two (Markforged)</th><th>Composer A4 (Anisoprint)</th></tr></thead><tbody><tr><td>Printing Time (h)</td><td>11h39</td><td>23h41</td></tr><tr><td>Infill Density [%]</td><td>50</td><td>50</td></tr><tr><td>Number of total layers</td><td>516</td><td>267</td></tr><tr><td>Layer thickness [mm]</td><td>0,050</td><td>0,100</td></tr><tr><td>FFF nozzle diameter [mm]</td><td>0,4</td><td>0,4</td></tr><tr><td>Build plate temperature [°C]</td><td>Not heated</td><td>60</td></tr><tr><td>Max nozzle temperature [°C]</td><td>275</td><td>270</td></tr></tbody></table>

Firstly, the size of the GBTA is selected to be compatible with the dimensions of each printer's build volume. As illustrated in Fig. 3, the GBTA size is smaller for the Mark Two printer than for the Composer A4, owing to the smaller dimensions of its print bed. Additionally, the GBTA is designed to facilitate the evaluation of the maximum surface of the build platform and enable the assessment of spatial repeatability. Indeed, the relative coverage of the build platform along the Y-axis is defined by Eq. 1.

$$Y_{\text{GBTA}}/Y_{\text{Build plate}} \qquad (1)$$

Y<sub>GBTA</sub> represents the length of the GBTA along the Y-axis, while Y<sub>Build plate</sub> corresponds to the length of the build plate of the printer. Eq. 2 is the practical application of Eq. 1 by taking the Markforged printer as an example.

$$120.8/132 = 91.5\% \qquad (2)$$

The result obtained in Eq. 2 shows that the GBTA tests 91.5% of the Markforged printer's build plate along the Y-axis. It is worth noting that the chosen value of 120.8 mm, rather than the extreme possible dimension of 132 mm, is due to the necessity of incorporating a brim for enhanced adherence during the printing process. Evaluating the majority surface of the build platform is crucial as the precision of positioning devices can vary significantly between the center and corners [14]. However, it is important to highlight that the entire build plate has not been tested due to its rectangular shape, while the GBTA has a square shape.

Secondly, since the GBTA is intended to assess dimensional and geometric accuracy, it incorporates various features. These elements come in different sizes to cover the dimensional ranges specified in ISO286-1:1988 [15]. Indeed, to guarantee the proper functioning of a part, its dimensions must be between two limits defining the dimensional variation authorized in manufacturing, commonly called "tolerance". In the context of this study, all dimensions fall within the range of 1 to 174 mm and the IT range from 10 to 15. Simple geometric shapes such as cylinders, cubes, and planes are chosen to simplify the measurement process during analysis [16]. Dedicated orientation and position must be given to the features to relate the measured deviations directly to the cartesian axes of the machine and enable measurements using conventional measuring means, such as a Coordinate Measuring Machine (CMM) [11].
<table><caption>Table 1: Printing parameters of printers Mark Two (Markforged) and Composer A4 (Anisoprint)</caption><thead><tr><th></th><th>Mark Two (Markforged)</th><th>Composer A4 (Anisoprint)</th></tr></thead><tbody><tr><td>Printing Time (h)</td><td>11h39</td><td>23h41</td></tr><tr><td>Infill Density [%]</td><td>50</td><td>50</td></tr><tr><td>Number of total layers</td><td>516</td><td>267</td></tr><tr><td>Layer thickness [mm]</td><td>0,050</td><td>0,100</td></tr><tr><td>FFF nozzle diameter [mm]</td><td>0,4</td><td>0,4</td></tr><tr><td>Build plate temperature [°C]</td><td>Not heated</td><td>60</td></tr><tr><td>Max nozzle temperature [°C]</td><td>275</td><td>270</td></tr></tbody></table>

Firstly, the size of the GBTA is selected to be compatible with the dimensions of each printer's build volume. As illustrated in Fig. 3, the GBTA size is smaller for the Mark Two printer than for the Composer A4, owing to the smaller dimensions of its print bed. Additionally, the GBTA is designed to facilitate the evaluation of the maximum surface of the build platform and enable the assessment of spatial repeatability. Indeed, the relative coverage of the build platform along the Y-axis is defined by Eq. 1.

$$Y_{\text{GBTA}}/Y_{\text{Build plate}} \qquad (1)$$

Y<sub>GBTA</sub> represents the length of the GBTA along the Y-axis, while Y<sub>Build plate</sub> corresponds to the length of the build plate of the printer. Eq. 2 is the practical application of Eq. 1 by taking the Markforged printer as an example.

$$120.8/132 = 91.5\% \qquad (2)$$

The result obtained in Eq. 2 shows that the GBTA tests 91.5% of the Markforged printer's build plate along the Y-axis. It is worth noting that the chosen value of 120.8 mm, rather than the extreme possible dimension of 132 mm, is due to the necessity of incorporating a brim for enhanced adherence during the printing process. Evaluating the majority surface of the build platform is crucial as the precision of positioning devices can vary significantly between the center and corners [14]. However, it is important to highlight that the entire build plate has not been tested due to its rectangular shape, while the GBTA has a square shape.

Secondly, since the GBTA is intended to assess dimensional and geometric accuracy, it incorporates various features. These elements come in different sizes to cover the dimensional ranges specified in ISO286-1:1988 [15]. Indeed, to guarantee the proper functioning of a part, its dimensions must be between two limits defining the dimensional variation authorized in manufacturing, commonly called "tolerance". In the context of this study, all dimensions fall within the range of 1 to 174 mm and the IT range from 10 to 15. Simple geometric shapes such as cylinders, cubes, and planes are chosen to simplify the measurement process during analysis [16]. Dedicated orientation and position must be given to the features to relate the measured deviations directly to the cartesian axes of the machine and enable measurements using conventional measuring means, such as a Coordinate Measuring Machine (CMM) [11].
<figure><img src="image_130.png" /><figcaption>Figure 3: GBTA of Markforged (a) and GBTA of Anisoprint (b).</figcaption></figure>

The CMM used to measure these GBTAs is a Wenzel LH 54. The measurement uncertainty of the machine for the X and Y axes is determined by Eq. 3 while for the Z axis, it is determined by Eq. 4.

$$3 + L/300 \qquad (3)$$

$$3.5 + L/300 \qquad (4)$$

The unit of uncertainty is micrometers, and the unit of the measured length L is in millimeters. The machine's resolution is 0.1 µm. There are 348 dimensional measurements for a single small GBTA, as depicted in Fig. 3(a), resulting in a total of 1044 measurements for the three GBTAs. Additionally, there are 395 dimensional measurements for the larger one in Fig. 3(b), totaling 1185 measurements. These measurements are grouped by zones on the GBTA. More specifically, there are measurements taken at the center of the GBTA, as illustrated in Fig. 4, measurements related to the three axes X, Y, and Z, and finally, the "other" measurement category which corresponds to the features relying on more than one axis, as a cylinder for example.

<figure><img src="image_131.png" /><figcaption>Figure 4: Center of GBTA</figcaption></figure>
<figure><img src="image_131.png" /><figcaption>Figure 3: GBTA of Markforged (a) and GBTA of Anisoprint (b).</figcaption></figure>

The CMM used to measure these GBTAs is a Wenzel LH 54. The measurement uncertainty of the machine for the X and Y axes is determined by Eq. 3 while for the Z axis, it is determined by Eq. 4.

$$3 + L/300 \qquad (3)$$

$$3.5 + L/300 \qquad (4)$$

The unit of uncertainty is micrometers, and the unit of the measured length L is in millimeters. The machine's resolution is 0.1 µm. There are 348 dimensional measurements for a single small GBTA, as depicted in Fig. 3(a), resulting in a total of 1044 measurements for the three GBTAs. Additionally, there are 395 dimensional measurements for the larger one in Fig. 3(b), totaling 1185 measurements. These measurements are grouped by zones on the GBTA. More specifically, there are measurements taken at the center of the GBTA, as illustrated in Fig. 4, measurements related to the three axes X, Y, and Z, and finally, the "other" measurement category which corresponds to the features relying on more than one axis, as a cylinder for example.

<figure><img src="image_132.png" /><figcaption>Figure 4: Center of GBTA</figcaption></figure>
## Results and Interpretations

The results of the 3D printers from Markforged and Anisoprint discussed below address dimensional deviations of the studied features on the GBTA. The following two graphs, depicted in Fig. 5 and Fig. 6, focus on the tolerance intervals of the printers according to ISO 286-1 standards [15]. The maximum authorized values of the number of tolerance units for an IT is represented by the horizontal green bars. Therefore, if a measurement, with its error bars, is under a green horizontal bar, it means that it satisfies this IT. Each measurement has an associated error bar which indicates the repeatability of the printer. Indeed, the wider they are, the less repeatable the printer is. Regarding the y-axis of the graphs, it is important to note that they do not directly represent deviations but rather serve as an intermediate calculation. This is the reason why the y-axis is not explicitly represented. A detailed explanation of how this variable has been defined and measured is provided by Spitaels et al. [13]. For each of the graphs, the notation PA (polyamide) is used to refer to Smooth PA and Onyx and MKF represent the Markforged printer, while ANI is used for the Anisoprint printer.

The graph shown in Fig. 5 represents the tolerance intervals of ISO classes for dimensions ranging from 1 to 30 mm. In general, measurements are below the IT 14 standard. However, a notable exception concerns measurements between 6 and 10 mm at the center of the GBTA illustrated in Fig. 4 for Anisoprint, revealing significant deviations of up to IT 15. This issue does not appear to affect the Markforged. When visually inspecting the GBTA printed by Anisoprint and those printed by Markforged, it is noticeable that, within the central cylinder (Fig. 4), there are material residues and a surface condition that is not as clean as the GBTA printed by Markforged. This can be attributed to the fact that the layer thickness specified in Table 1 is twice as small for Markforged as compared to Anisoprint.

More specifically, when analyzing measurements between 1 and 10 mm at the center of the GBTA, significant deviations are observed (depicted by the blue bars) reaching IT15. On the other hand, for measurements from 10 mm and above, at the center of the GBTA, deviations are considerably lower, around IT 12. This suggests that, for all measurements related to the center of GBTA, both printers are more accurate in printing at the center of the print bed for objects with dimensions of 10 mm or more. Below this value, deviations are larger.

A cross-sectional observation of all measurements between 1 and 30 mm reveals that, for both printers, deviations along the X-axis (represented by the orange bars) are on average higher than deviations along the other two axes. This observation highlights a specific trend in deviations along the X-axis, indicating lower dimensional performances for features aligned with X-axis compared to the other axes. This observation can be attributed to the fact that, during printing, the printer nozzle, whether for Markforged or Anisoprint, covers a longer distance along the X-axis compared to the Y and Z axes. Indeed, the largest dimension of the build platform corresponds to the X-axis.
## Results and Interpretations

The results of the 3D printers from Markforged and Anisoprint discussed below address dimensional deviations of the studied features on the GBTA. The following two graphs, depicted in Fig. 5 and Fig. 6, focus on the tolerance intervals of the printers according to ISO 286-1 standards [15]. The maximum authorized values of the number of tolerance units for an IT is represented by the horizontal green bars. Therefore, if a measurement, with its error bars, is under a green horizontal bar, it means that it satisfies this IT. Each measurement has an associated error bar which indicates the repeatability of the printer. Indeed, the wider they are, the less repeatable the printer is. Regarding the y-axis of the graphs, it is important to note that they do not directly represent deviations but rather serve as an intermediate calculation. This is the reason why the y-axis is not explicitly represented. A detailed explanation of how this variable has been defined and measured is provided by Spitaels et al. [13]. For each of the graphs, the notation PA (polyamide) is used to refer to Smooth PA and Onyx and MKF represent the Markforged printer, while ANI is used for the Anisoprint printer.

The graph shown in Fig. 5 represents the tolerance intervals of ISO classes for dimensions ranging from 1 to 30 mm. In general, measurements are below the IT 14 standard. However, a notable exception concerns measurements between 6 and 10 mm at the center of the GBTA illustrated in Fig. 4 for Anisoprint, revealing significant deviations of up to IT 15. This issue does not appear to affect the Markforged. When visually inspecting the GBTA printed by Anisoprint and those printed by Markforged, it is noticeable that, within the central cylinder (Fig. 4), there are material residues and a surface condition that is not as clean as the GBTA printed by Markforged. This can be attributed to the fact that the layer thickness specified in Table 1 is twice as small for Markforged as compared to Anisoprint.

More specifically, when analyzing measurements between 1 and 10 mm at the center of the GBTA, significant deviations are observed (depicted by the blue bars) reaching IT15. On the other hand, for measurements from 10 mm and above, at the center of the GBTA, deviations are considerably lower, around IT 12. This suggests that, for all measurements related to the center of GBTA, both printers are more accurate in printing at the center of the print bed for objects with dimensions of 10 mm or more. Below this value, deviations are larger.

A cross-sectional observation of all measurements between 1 and 30 mm reveals that, for both printers, deviations along the X-axis (represented by the orange bars) are on average higher than deviations along the other two axes. This observation highlights a specific trend in deviations along the X-axis, indicating lower dimensional performances for features aligned with X-axis compared to the other axes. This observation can be attributed to the fact that, during printing, the printer nozzle, whether for Markforged or Anisoprint, covers a longer distance along the X-axis compared to the Y and Z axes. Indeed, the largest dimension of the build platform corresponds to the X-axis.
<figure><img src="image_132.png" /><figcaption>Figure 5: IT of printers Markforged (MKF) and Anisoprint (ANI) for ISO classes 1 to 30 mm</figcaption></figure>

The diagram presented in Fig. 6 represents the tolerance intervals of ISO classes for dimensions ranging from 30 to 250 mm. It is noteworthy that there are no deviations for the Z-axis in this graph, as there are no measurements on GBTAs with dimensions exceeding 30 mm. Furthermore, there are no results for measurements between 180 and 250 for the Markforged, as the maximum dimension of its GBTA is limited to 120.8 mm.

Overall, it is observed that the deviations from the Anisoprint printer are generally smaller than those from Markforged. Globally, for both printers, the deviations do not exceed IT 13, except for deviations for measurements between 80 and 120 mm. A detailed analysis reveals that these deviations, illustrated by the blue bars in the graph in Fig. 6, correspond to distances between the planes representing the walls of the GBTA, as shown in Fig. 7.
<figure><img src="image_133.png" /><figcaption>Figure 5: IT of printers Markforged (MKF) and Anisoprint (ANI) for ISO classes 1 to 30 mm</figcaption></figure>

The diagram presented in Fig. 6 represents the tolerance intervals of ISO classes for dimensions ranging from 30 to 250 mm. It is noteworthy that there are no deviations for the Z-axis in this graph, as there are no measurements on GBTAs with dimensions exceeding 30 mm. Furthermore, there are no results for measurements between 180 and 250 for the Markforged, as the maximum dimension of its GBTA is limited to 120.8 mm.

Overall, it is observed that the deviations from the Anisoprint printer are generally smaller than those from Markforged. Globally, for both printers, the deviations do not exceed IT 13, except for deviations for measurements between 80 and 120 mm. A detailed analysis reveals that these deviations, illustrated by the blue bars in the graph in Fig. 6, correspond to distances between the planes representing the walls of the GBTA, as shown in Fig. 7.
<figure><img src="image_133.png" /><figcaption>Figure 6: IT of printers Markforged (MKF) and Anisoprint (ANI) for ISO classes 30 to 250 mm</figcaption></figure>

<figure><img src="image_134.png" /><figcaption>Figure 7: Walls of the Anisoprint's GBTA</figcaption></figure>

The results indicate greater printing precision for Anisoprint, with deviations below IT 10, while for Markforged, the average is close to IT 12.

Regarding measurements between 30 and 80 mm, the highest deviations are observed in relation to the X-axis. However, when the measurements are higher, between 80 and 120 mm, the trend reverses. Deviations along the Y-axis then become more significant than those along the X-axis.

Furthermore, when examining both graphs (Fig. 5 and 6) on a global scale, we observe that deviations in measurements along the Y-axis are smaller for the Markforged printer than for the Anisoprint. This can be explained by the fact that the dimensions along the Y-axis of the Markforged print bed (132 mm) are smaller than those of the Anisoprint bed (210 mm). This
<figure><img src="image_134.png" /><figcaption>Figure 6: IT of printers Markforged (MKF) and Anisoprint (ANI) for ISO classes 30 to 250 mm</figcaption></figure>

<figure><img src="image_135.png" /><figcaption>Figure 7: Walls of the Anisoprint's GBTA</figcaption></figure>

The results indicate greater printing precision for Anisoprint, with deviations below IT 10, while for Markforged, the average is close to IT 12.

Regarding measurements between 30 and 80 mm, the highest deviations are observed in relation to the X-axis. However, when the measurements are higher, between 80 and 120 mm, the trend reverses. Deviations along the Y-axis then become more significant than those along the X-axis.

Furthermore, when examining both graphs (Fig. 5 and 6) on a global scale, we observe that deviations in measurements along the Y-axis are smaller for the Markforged printer than for the Anisoprint. This can be explained by the fact that the dimensions along the Y-axis of the Markforged print bed (132 mm) are smaller than those of the Anisoprint bed (210 mm). This
implies that the print head of the Markforged has to travel a shorter distance than that of the Anisoprint. Besides, the deviations along the Z-axis are lower compared to deviations along the other axes. This suggests that both printers exhibit better precision regarding the vertical movement of their build plate compared to the movement of the print head. An essential consideration is the impact of the actuators utilized for movements in the X and Y directions, implemented through a belt-driven transmission with a guiding system. Concerning the Z-axis, a trapezoidal screw is employed to facilitate the movement of the print bed. Indeed, the amount of play in the movement of the print head and the build plate may vary depending on the specific printer.

## Conclusions

In conclusion, this study systematically compared two Material Extrusion (MEX) technologies, specifically dual-nozzle and coextrusion, employed in 3D printers. The Markforged Mark Two, using dual-nozzle technology, was compared with the Anisoprint Composer A4, distinguished for its coextrusion method. Three Adaptive Geometrical Benchmark Test Artifacts (GBTA) were fabricated with each printer, and their dimensional performances were evaluated.

The results generally indicate that for both printers, dimensional performances are on average around IT 14. For measurements between 1 and 10 mm, the deviations are larger compared to those for dimensions greater than 10 mm, which on average are around IT 12.

Along the Y-axis, the Markforged exhibits smaller deviations in measurements that can be explained that it has a smaller print bed dimension along the Y-axis compared to Anisoprint.

Further analysis reveals that the Markforged printer demonstrates superior precision for smaller dimensions ranging from 1 to 30 mm, while the Anisoprint excels in precision for larger dimensions between 30 and 250 mm. Regarding precision along the Z-axis, both printers exhibit the same level of accuracy. Besides, the deviations along the Z-axis are lower compared to deviations along the other axes. This suggests that both printers exhibit better precision regarding the vertical movement of their build plate compared to the movement of the print head.

A notable observation highlighted significant deviations at the center of the GBTA concerning the other three axes (X, Y, and Z) for both printers. This comprehensive comparison sheds light on the dimensional and capabilities of dual-nozzle and coextrusion technologies, providing valuable insights for applications in continuous fiber reinforced thermoplastic composites (CFRTCs) and guiding future advancements in 3D printing technology.

Looking forward, exploring the incorporation of carbon fiber into the fabrication of the GBTA could lead to new research possibilities. Conducting a similar study with carbon fiber-reinforced prints would allow for an assessment of the impact of this advanced material on dimensional accuracy and overall performance. This perspective is particularly relevant as carbon fiber is known for its strength and lightweight properties, making it a promising candidate for enhancing the capabilities of 3D printing technologies.

## Acknowledgements

The authors would like to thank Région Wallonne for supporting this research as part of the SKYWIN ICOM2C3D research project under grant 8820.

## References

[1] ASTM D638, "Standard Test Method for Tensile Properties of Plastics 1". https://doi.org/10.1520/D0638-14

[2] U. M. Dilberoglu, B. Gharehpapagh, U. Yaman, and M. Dolen, "The Role of Additive Manufacturing in the Era of Industry 4.0," *Procedia Manuf*, vol. 11, pp. 545-554, 2017. https://doi.org/10.1016/j.promfg.2017.07.148
implies that the print head of the Markforged has to travel a shorter distance than that of the Anisoprint. Besides, the deviations along the Z-axis are lower compared to deviations along the other axes. This suggests that both printers exhibit better precision regarding the vertical movement of their build plate compared to the movement of the print head. An essential consideration is the impact of the actuators utilized for movements in the X and Y directions, implemented through a belt-driven transmission with a guiding system. Concerning the Z-axis, a trapezoidal screw is employed to facilitate the movement of the print bed. Indeed, the amount of play in the movement of the print head and the build plate may vary depending on the specific printer.

## Conclusions

In conclusion, this study systematically compared two Material Extrusion (MEX) technologies, specifically dual-nozzle and coextrusion, employed in 3D printers. The Markforged Mark Two, using dual-nozzle technology, was compared with the Anisoprint Composer A4, distinguished for its coextrusion method. Three Adaptive Geometrical Benchmark Test Artifacts (GBTA) were fabricated with each printer, and their dimensional performances were evaluated.

The results generally indicate that for both printers, dimensional performances are on average around IT 14. For measurements between 1 and 10 mm, the deviations are larger compared to those for dimensions greater than 10 mm, which on average are around IT 12.

Along the Y-axis, the Markforged exhibits smaller deviations in measurements that can be explained that it has a smaller print bed dimension along the Y-axis compared to Anisoprint.

Further analysis reveals that the Markforged printer demonstrates superior precision for smaller dimensions ranging from 1 to 30 mm, while the Anisoprint excels in precision for larger dimensions between 30 and 250 mm. Regarding precision along the Z-axis, both printers exhibit the same level of accuracy. Besides, the deviations along the Z-axis are lower compared to deviations along the other axes. This suggests that both printers exhibit better precision regarding the vertical movement of their build plate compared to the movement of the print head.

A notable observation highlighted significant deviations at the center of the GBTA concerning the other three axes (X, Y, and Z) for both printers. This comprehensive comparison sheds light on the dimensional and capabilities of dual-nozzle and coextrusion technologies, providing valuable insights for applications in continuous fiber reinforced thermoplastic composites (CFRTCs) and guiding future advancements in 3D printing technology.

Looking forward, exploring the incorporation of carbon fiber into the fabrication of the GBTA could lead to new research possibilities. Conducting a similar study with carbon fiber-reinforced prints would allow for an assessment of the impact of this advanced material on dimensional accuracy and overall performance. This perspective is particularly relevant as carbon fiber is known for its strength and lightweight properties, making it a promising candidate for enhancing the capabilities of 3D printing technologies.

## Acknowledgements

The authors would like to thank Région Wallonne for supporting this research as part of the SKYWIN ICOM2C3D research project under grant 8820.

## References

[1] ASTM D638, "Standard Test Method for Tensile Properties of Plastics 1". https://doi.org/10.1520/D0638-14

[2] U. M. Dilberoglu, B. Gharehpapagh, U. Yaman, and M. Dolen, "The Role of Additive Manufacturing in the Era of Industry 4.0," *Procedia Manuf*, vol. 11, pp. 545-554, 2017. https://doi.org/10.1016/j.promfg.2017.07.148
[3] F. N. Chaudhry, S. I. Butt, A. Mubashar, A. Bin Naveed, S. H. Imran, and Z. Faping, "Effect of carbon fibre on reinforcement of thermoplastics using FDM and RSM," *Journal of Thermoplastic Composite Materials*, vol. 35, no. 3, pp. 352-374, Mar. 2022. https://doi.org/10.1177/0892705719886891

[4] Read on https://anisoprint.com/ the 28 th October 2023.

[5] A. Demarbaix, I. Ochana, J. Levrie, I. Coutinho, S. S. Cunha, and M. Moonens, "Additively Manufactured Multifunctional Composite Parts with the Help of Coextrusion Continuous Carbon Fiber: Study of Feasibility to Print Self-Sensing without Doped Raw Material," *Journal of Composites Science*, vol. 7, no. 9, Sep. 2023. https://doi.org/10.3390/jcs7090355

[6] Maria Inês Santos Silva, "Non-Destructive Testing for Polymer Matrix Composites produced by Additive Manufacturing," Jul. 2020.

[7] G. T. Mark, R. B. Woodruff, A. L. Parangi, D. S. Benhaim, and B. Tsu Sklaroff, "Multiaxis fiber reinforcement for 3D printing," 2016.

[8] C. Pandelidi, S. Bateman, S. Piegert, R. Hoehner, I. Kelbassa, and M. Brandt, "The technology of continuous fibre-reinforced polymers: a review on extrusion additive manufacturing methods," *The International Journal of Advanced Manufacturing Technology*, 2021. https://doi.org/10.1007/s00170-021-06837-6

[9] A. V. Azarov et al., "Development of a two-matrix composite material fabricated by 3D printing," *Polymer Science - Series D*, vol. 10, no. 1, pp. 87-90, Jan. 2017. https://doi.org/10.1134/S1995421217010026

[10] A. Adumitroaie, F. Antonov, A. Khaziev, A. Azarov, M. Golubev, and V. V. Vasiliev, "Novel continuous fiber bi-matrix composite 3-D printing technology," *Materials*, vol. 12, no. 18, Sep. 2019. https://doi.org/10.3390/ma12183011

[11] S. Moylan, J. Slotwinski, A. Cooke, K. Jurrens, and M. A. Donmez, "An additive manufacturing test artifact," *J Res Natl Inst Stand Technol*, vol. 119, pp. 429-459, 2014. https://doi.org/10.6028/jres.119.017

[12] L. Spitaels, E. Rivière-Lorphèvre, A. Demarbaix, V. Thielens, and F. Ducobu, "Dimensional and geometrical performance assessment of two FDM printers using a benchmark artifact," 2021.

[13] L. Spitaels, E. Rivière-Lorphèvre, A. Demarbaix, and F. Ducobu, "Adaptive benchmarking design for additive manufacturing processes," *Meas Sci Technol*, vol. 33, no. 6, Jun. 2022. https://doi.org/10.1088/1361-6501/ac5877

[14] L. Rebaioli and I. Fassi, "A review on benchmark artifacts for evaluating the geometrical performance of additive manufacturing processes," *International Journal of Advanced Manufacturing Technology*, vol. 93, no. 5-8, pp. 2571-2598, Nov. 2017. https://doi.org/10.1007/s00170-017-0570-0

[15] International Organization for Standardization 1988 ISO 286-1.

[16] M. A. de Pastre, S. C. Toguem Tagne, and N. Anwer, "Test artefacts for additive manufacturing: A design methodology review," *CIRP Journal of Manufacturing Science and Technology*, vol. 31. Elsevier Ltd, pp. 14-24, Nov. 01, 2020. doi: 10.1016/j.cirpj.2020.09.008
[3] F. N. Chaudhry, S. I. Butt, A. Mubashar, A. Bin Naveed, S. H. Imran, and Z. Faping, “Effect of carbon fibre on reinforcement of thermoplastics using FDM and RSM,” *Journal of Thermoplastic Composite Materials*, vol. 35, no. 3, pp. 352–374, Mar. 2022. https://doi.org/10.1177/0892705719886891

[4] Read on https://anisoprint.com/ the 28 th October 2023.

[5] A. Demarbaix, I. Ochana, J. Levrie, I. Coutinho, S. S. Cunha, and M. Moonens, “Additively Manufactured Multifunctional Composite Parts with the Help of Coextrusion Continuous Carbon Fiber: Study of Feasibility to Print Self-Sensing without Doped Raw Material,” *Journal of Composites Science*, vol. 7, no. 9, Sep. 2023. https://doi.org/10.3390/jcs7090355

[6] Maria Inês Santos Silva, “Non-Destructive Testing for Polymer Matrix Composites produced by Additive Manufacturing,” Jul. 2020.

[7] G. T. Mark, R. B. Woodruff, A. L. Parangi, D. S. Benhaim, and B. Tsu Sklaroff, “Multiaxis fiber reinforcement for 3D printing,” 2016.

[8] C. Pandelidi, S. Bateman, S. Piegert, R. Hoehner, I. Kelbassa, and M. Brandt, “The technology of continuous fibre-reinforced polymers: a review on extrusion additive manufacturing methods,” *The International Journal of Advanced Manufacturing Technology*, 2021. https://doi.org/10.1007/s00170-021-06837-6

[9] A. V. Azarov et al., “Development of a two-matrix composite material fabricated by 3D printing,” *Polymer Science - Series D*, vol. 10, no. 1, pp. 87–90, Jan. 2017. https://doi.org/10.1134/S1995421217010026

[10] A. Adumitroaie, F. Antonov, A. Khaziev, A. Azarov, M. Golubev, and V. V. Vasiliev, “Novel continuous fiber bi-matrix composite 3-D printing technology,” *Materials*, vol. 12, no. 18, Sep. 2019. https://doi.org/10.3390/ma12183011

[11] S. Moylan, J. Slotwinski, A. Cooke, K. Jurrens, and M. A. Donmez, “An additive manufacturing test artifact,” *J Res Natl Inst Stand Technol*, vol. 119, pp. 429–459, 2014. https://doi.org/10.6028/jres.119.017

[12] L. Spitaels, E. Rivière-Lorphèvre, A. Demarbaix, V. Thielens, and F. Ducobu, “Dimensional and geometrical performance assessment of two FDM printers using a benchmark artifact,” 2021.

[13] L. Spitaels, E. Rivière-Lorphèvre, A. Demarbaix, and F. Ducobu, “Adaptive benchmarking design for additive manufacturing processes,” *Meas Sci Technol*, vol. 33, no. 6, Jun. 2022. https://doi.org/10.1088/1361-6501/ac5877

[14] L. Rebaioli and I. Fassi, “A review on benchmark artifacts for evaluating the geometrical performance of additive manufacturing processes,” *International Journal of Advanced Manufacturing Technology*, vol. 93, no. 5–8, pp. 2571–2598, Nov. 2017. https://doi.org/10.1007/s00170-017-0570-0

[15] International Organization for Standardization 1988 ISO 286–1.

[16] M. A. de Pastre, S. C. Toguem Tagne, and N. Anwer, “Test artefacts for additive manufacturing: A design methodology review,” *CIRP Journal of Manufacturing Science and Technology*, vol. 31. Elsevier Ltd, pp. 14–24, Nov. 01, 2020. doi: 10.1016/j.cirpj.2020.09.008
# An experimental study of effect of printed thickness on the mechanical properties of LPBF produced AlSi10Mg

FAHIMI Pouya<fnref n="1" />,ª*, VYSOCHINSKIY Dmitry<fnref n="2" />,ᵇ and KHADYKO Mikhail<fnref n="1" />,ᶜ

**Keywords:** Selective Laser Melting, Size Effect, AlSi10Mg, Metal Additive Manufacturing, Tensile Testing, Powder Bed Fusion

**Abstract.** Additive manufacturing process allows fabrication of parts with a broad range of sizes with high resolution. This size variation introduces new mechanical properties within the printed component, which creates a significant challenge for the qualification of additively manufactured parts. This unresolved issue hinders the implementation of additive manufacturing in high performance engineering applications. To attain optimal performance of additive components, it is imperative to gain a comprehensive understanding of the size effect. While many studies have explored the mechanical properties and microstructure of additively manufactured AlSi10Mg, the size effect remains relatively undefined. To gain more knowledge on this matter, AlSi10Mg samples with four different thicknesses were fabricated using a selective laser melting machine and tensile tests were performed to characterize the material behavior. Stress-strain curves were derived with consideration of nominal and measured cross section and the resulting diagram showed a considerable difference for the samples with minimum thickness, which was 0.5 mm. Comparing the results between the 2 mm and 0.5 mm thick specimens demonstrated more than 50 percent decrease in tensile properties including ultimate tensile strength and elongation at fracture. Also, the study of strain rate indicated no significant strain rate sensitivity for either thickness. These findings contribute to better understanding the size effects on behavior of printed AlSi10Mg, promoting further commercial adoption of this material.

**Introduction**

Additive manufacturing (AM), also known as 3D printing, is a rapidly growing technology that allows for the creation of complex and detailed objects by building up layers of material [1-3]. It offers a wide variety of process categories to suit different needs and applications. These processes allow to produce complex geometries with unique properties that would be difficult or impossible to produce using traditional manufacturing techniques. As this technology continues to advance, it has the potential to revolutionize the manufacturing industry and create new opportunities for innovation and growth. Metal additive manufacturing is a process that involves joining metallic materials, such as powders, wires, and sheets, to produce objects from 3D models, typically layer by layer [4-7].

While various metal additive manufacturing processes share similar capabilities and challenges, the focus of the current study lies in selective laser melting (SLM) which is a type of laser powder bed fusion (LPBF). In this process, a laser beam draws onto a bed of thin layer of powder, melting the powder along the laser path to create a solid layer of the part. Subsequently, with the aid of the recoating mechanism, a new layer of powder is applied over the part, and the 3D structure is incrementally built layer by layer.

<figure><img src="image_135.png" /></figure>

<footnote n="1">¹Department of Building, Energy and Material Technology,UiT-The Arctic University of Norway, Narvik, Norway</footnote>

<footnote n="2">²Jon Lilletuns vei 9, 4879, Grimstad, Mechatronics Innovation Lab, Norway</footnote>

<footnote>ªpouya.fahimi@uit.no, ᵇdmitry.vysochinskiy@uia.no, ᶜmikhail.khadyko@uit.no</footnote>
# An experimental study of effect of printed thickness on the mechanical properties of LPBF produced AlSi10Mg

FAHIMI Pouya<fnref n="1" />,ª*, VYSOCHINSKIY Dmitry<fnref n="2" />,ᵇ and KHADYKO Mikhail<fnref n="1" />,ᶜ

**Keywords:** Selective Laser Melting, Size Effect, AlSi10Mg, Metal Additive Manufacturing, Tensile Testing, Powder Bed Fusion

**Abstract.** Additive manufacturing process allows fabrication of parts with a broad range of sizes with high resolution. This size variation introduces new mechanical properties within the printed component, which creates a significant challenge for the qualification of additively manufactured parts. This unresolved issue hinders the implementation of additive manufacturing in high performance engineering applications. To attain optimal performance of additive components, it is imperative to gain a comprehensive understanding of the size effect. While many studies have explored the mechanical properties and microstructure of additively manufactured AlSi10Mg, the size effect remains relatively undefined. To gain more knowledge on this matter, AlSi10Mg samples with four different thicknesses were fabricated using a selective laser melting machine and tensile tests were performed to characterize the material behavior. Stress-strain curves were derived with consideration of nominal and measured cross section and the resulting diagram showed a considerable difference for the samples with minimum thickness, which was 0.5 mm. Comparing the results between the 2 mm and 0.5 mm thick specimens demonstrated more than 50 percent decrease in tensile properties including ultimate tensile strength and elongation at fracture. Also, the study of strain rate indicated no significant strain rate sensitivity for either thickness. These findings contribute to better understanding the size effects on behavior of printed AlSi10Mg, promoting further commercial adoption of this material.

**Introduction**

Additive manufacturing (AM), also known as 3D printing, is a rapidly growing technology that allows for the creation of complex and detailed objects by building up layers of material [1-3]. It offers a wide variety of process categories to suit different needs and applications. These processes allow to produce complex geometries with unique properties that would be difficult or impossible to produce using traditional manufacturing techniques. As this technology continues to advance, it has the potential to revolutionize the manufacturing industry and create new opportunities for innovation and growth. Metal additive manufacturing is a process that involves joining metallic materials, such as powders, wires, and sheets, to produce objects from 3D models, typically layer by layer [4-7].

While various metal additive manufacturing processes share similar capabilities and challenges, the focus of the current study lies in selective laser melting (SLM) which is a type of laser powder bed fusion (LPBF). In this process, a laser beam draws onto a bed of thin layer of powder, melting the powder along the laser path to create a solid layer of the part. Subsequently, with the aid of the recoating mechanism, a new layer of powder is applied over the part, and the 3D structure is incrementally built layer by layer.

<figure><img src="image_136.png" /></figure>

<footnote n="1">¹Department of Building, Energy and Material Technology,UiT-The Arctic University of Norway, Narvik, Norway</footnote>

<footnote n="2">²Jon Lilletuns vei 9, 4879, Grimstad, Mechatronics Innovation Lab, Norway</footnote>

<footnote>ªpouya.fahimi@uit.no, ᵇdmitry.vysochinskiy@uia.no, ᶜmikhail.khadyko@uit.no</footnote>
Recent research on additively manufactured metallic parts indicates that mechanical properties may depend on many factors of the printing process particularly building orientation [8-12], laser power [13], scan strategies [14, 15] and feature size [16]. One reason behind this difference in material behavior is thermal gradients inducing directional solidification and as a result there might be anisotropic microstructures and crystallographic texture. Consequently, this phenomenon can result in anisotropic mechanical behavior in the manufactured component. Also, the size of the printed part can affect the properties and performance of the final product. One reason behind this alteration of behavior is the size effect on the microstructure of the printed part. As the size of the part increases, the heat generated by the laser during printing and the cooling rate can vary across the part, leading to a non-uniform microstructure. This can result in variations in material properties such as mechanical strength and hardness. Another size effect is related to the level of residual stress in the printed part. Residual stresses are generated during the printing process due to non-uniform cooling and solidification of the material.

The considerable design flexibility offered by 3D printing allows for versatile creation of AM parts. In many cases, these parts include a diverse range of feature sizes, with users usually showing particular interest in smaller features. Therefore, understanding the size effect becomes essential for making informed and effective design decisions and accordingly there is ongoing research in the field of additive manufacturing to address this. For example, Takata et al. [17] investigated the size dependence of microstructure of AlSi10Mg plate samples ranging from 0.1 to 10 mm and observed a slight effect on microstructure with variation of thickness. They also reported a slight decrease of hardness with decreasing the sample width. Dong et al. [16] tested a series of additively manufactured rod shape samples made of AlSi10Mg. Their results of the uniaxial tensile test indicate that as the build diameter decreases, both the strength and Young's modulus of the specimen decrease by 30% compared to the stable state. Another interesting study in this field is the work done by Roach et al. [18] where they investigated the size-dependent tensile properties of 316L stainless steel. They scaled down their whole specimen shape and observed that the ultimate tensile strength decreased drastically with decreasing specimen size. They also reported that the surface roughness is the reason for this change in material behavior rather than the change in the microstructure. Moreover, Barba et al. [19] carried out a similar study for size and orientation effect in additively manufactured Ti-6Al-4V. They examined tensile specimens with varying thickness from 0.25 to 3 mm and their result showed a high dependency of material properties on the specimen thickness.

In summary, a review of prior studies indicates that the process parameters in SLM play a crucial role in influencing the microstructure's heterogeneity and the macroscopic performance of fabricated structures. However, existing research has predominantly centered on factors such as the orientation dependence and there is a scarcity of studies investigating the influence of the size effect on mechanical properties of additively manufactured aluminum tensile samples. So, the primary objective of this study is to examine the impact of size on the mechanical properties of AlSi10Mg flat tensile samples fabricated with SLM. Flat tensile samples with four different thickness dimensions were manufactured and uniaxial tensile tests were carried out on as-built samples.

## Materials and Methods

Four sets of flat tensile specimens with varied thicknesses were made to investigate the mechanical responses. Detailed descriptions of the manufacturing process and experimental investigation are described as follows. AlSi10Mg powder produced in TEKNA advanced material [20] was utilized as a raw material in this study. The chemical composition of the powder is 10 %wt of Si and 0.3 %wt Mg. The specimen dimensions are depicted in Fig. 1a, all the dimensions are in millimeters. The smallest thickness is 0.5 mm which is close to the minimum thickness that is feasible to print by SLM-process and the other thicknesses are 1, 1.5 and 2 mm. It should be noted that these
Recent research on additively manufactured metallic parts indicates that mechanical properties may depend on many factors of the printing process particularly building orientation [8-12], laser power [13], scan strategies [14, 15] and feature size [16]. One reason behind this difference in material behavior is thermal gradients inducing directional solidification and as a result there might be anisotropic microstructures and crystallographic texture. Consequently, this phenomenon can result in anisotropic mechanical behavior in the manufactured component. Also, the size of the printed part can affect the properties and performance of the final product. One reason behind this alteration of behavior is the size effect on the microstructure of the printed part. As the size of the part increases, the heat generated by the laser during printing and the cooling rate can vary across the part, leading to a non-uniform microstructure. This can result in variations in material properties such as mechanical strength and hardness. Another size effect is related to the level of residual stress in the printed part. Residual stresses are generated during the printing process due to non-uniform cooling and solidification of the material.

The considerable design flexibility offered by 3D printing allows for versatile creation of AM parts. In many cases, these parts include a diverse range of feature sizes, with users usually showing particular interest in smaller features. Therefore, understanding the size effect becomes essential for making informed and effective design decisions and accordingly there is ongoing research in the field of additive manufacturing to address this. For example, Takata et al. [17] investigated the size dependence of microstructure of AlSi10Mg plate samples ranging from 0.1 to 10 mm and observed a slight effect on microstructure with variation of thickness. They also reported a slight decrease of hardness with decreasing the sample width. Dong et al. [16] tested a series of additively manufactured rod shape samples made of AlSi10Mg. Their results of the uniaxial tensile test indicate that as the build diameter decreases, both the strength and Young's modulus of the specimen decrease by 30% compared to the stable state. Another interesting study in this field is the work done by Roach et al. [18] where they investigated the size-dependent tensile properties of 316L stainless steel. They scaled down their whole specimen shape and observed that the ultimate tensile strength decreased drastically with decreasing specimen size. They also reported that the surface roughness is the reason for this change in material behavior rather than the change in the microstructure. Moreover, Barba et al. [19] carried out a similar study for size and orientation effect in additively manufactured Ti-6Al-4V. They examined tensile specimens with varying thickness from 0.25 to 3 mm and their result showed a high dependency of material properties on the specimen thickness.

In summary, a review of prior studies indicates that the process parameters in SLM play a crucial role in influencing the microstructure's heterogeneity and the macroscopic performance of fabricated structures. However, existing research has predominantly centered on factors such as the orientation dependence and there is a scarcity of studies investigating the influence of the size effect on mechanical properties of additively manufactured aluminum tensile samples. So, the primary objective of this study is to examine the impact of size on the mechanical properties of AlSi10Mg flat tensile samples fabricated with SLM. Flat tensile samples with four different thickness dimensions were manufactured and uniaxial tensile tests were carried out on as-built samples.

## Materials and Methods

Four sets of flat tensile specimens with varied thicknesses were made to investigate the mechanical responses. Detailed descriptions of the manufacturing process and experimental investigation are described as follows. AlSi10Mg powder produced in TEKNA advanced material [20] was utilized as a raw material in this study. The chemical composition of the powder is 10 %wt of Si and 0.3 %wt Mg. The specimen dimensions are depicted in Fig. 1a, all the dimensions are in millimeters. The smallest thickness is 0.5 mm which is close to the minimum thickness that is feasible to print by SLM-process and the other thicknesses are 1, 1.5 and 2 mm. It should be noted that these
dimensions are not exactly in accordance with the standards of tensile testing, however, some general considerations for preparing tensile testing samples have been taken into account based on ISO 6892-1 [21]. The specimens were manufactured using a SLM®280 [22] metal printer with an output laser power of 400W and argon gas was chosen to be the build atmosphere. A schematic of the scanning strategy is depicted in Fig. 1b. The layer thickness was set to 50 µm. Arrows in Fig. 1b displays the path of movement of the laser, and the correspondence between their color, power and scanning speed is reported in Table 1. Uniaxial tension tests were conducted using a 25 kN SI-plan tension machine equipped with hydraulic grips. The machine features a load cell, a built-in position sensor, and an attachable LVDT-based extensometer with a measurement range of 25 mm to 30 mm. Load-displacement curves were generated using the output of the tensile testing machine. Fig. 1c is a picture of the build plate (after removing the printed parts) on the machine and as it can be seen from Fig. 1d, the samples of this work are a part of bigger print and the place that the tensile specimens are cut down from is shown by a red rectangle in the picture. All the samples were printed vertically on a square shaped build plate with a size of 278 mm by 278 mm.

<figure><img src="image_136.png" /></figure>

<figure><img src="image_137.png" /></figure>

<figure><img src="image_138.png" /></figure>

<figure><img src="image_139.png" /><figcaption>Fig. 1 a) Tensile sample geometry b) Schematic of scanning pattern for different thickness sizes in the gauge part of the samples c) Picture of the built plate inside of the working area of the machine d) Picture of the build plate after cutting down the samples.</figcaption></figure>

<table><caption>Table 1. Processing parameters for the SLM machine</caption><thead><tr><td>Parameter</td><td>Red border</td><td>Orange border</td><td>Green in-skin</td></tr></thead><tbody><tr><td>Laser power (W)</td><td>370</td><td>350</td><td>300</td></tr><tr><td>Laser speed (mm/s)</td><td>860</td><td>1100</td><td>600</td></tr></tbody></table>
dimensions are not exactly in accordance with the standards of tensile testing, however, some general considerations for preparing tensile testing samples have been taken into account based on ISO 6892-1 [21]. The specimens were manufactured using a SLM®280 [22] metal printer with an output laser power of 400W and argon gas was chosen to be the build atmosphere. A schematic of the scanning strategy is depicted in Fig. 1b. The layer thickness was set to 50 µm. Arrows in Fig. 1b displays the path of movement of the laser, and the correspondence between their color, power and scanning speed is reported in Table 1. Uniaxial tension tests were conducted using a 25 kN SI-plan tension machine equipped with hydraulic grips. The machine features a load cell, a built-in position sensor, and an attachable LVDT-based extensometer with a measurement range of 25 mm to 30 mm. Load-displacement curves were generated using the output of the tensile testing machine. Fig. 1c is a picture of the build plate (after removing the printed parts) on the machine and as it can be seen from Fig. 1d, the samples of this work are a part of bigger print and the place that the tensile specimens are cut down from is shown by a red rectangle in the picture. All the samples were printed vertically on a square shaped build plate with a size of 278 mm by 278 mm.

<figure><img src="image_137.png" /><figcaption>Fig. 1 a) Tensile sample geometry b) Schematic of scanning pattern for different thickness sizes in the gauge part of the samples c) Picture of the built plate inside of the working area of the machine d) Picture of the build plate after cutting down the samples.</figcaption></figure>

<table><caption>Table 1. Processing parameters for the SLM machine</caption><thead><tr><td>Parameter</td><td>Red border</td><td>Orange border</td><td>Green in-skin</td></tr></thead><tbody><tr><td>Laser power (W)</td><td>370</td><td>350</td><td>300</td></tr><tr><td>Laser speed (mm/s)</td><td>860</td><td>1100</td><td>600</td></tr></tbody></table>
## Results

A total number of 41 tensile tests on as-built samples were conducted to examine the mechanical response and statistical variations related to specimen thickness size. Quasi-static tensile tests until failure were carried out at a constant displacement rate of 0.025 mm.s⁻¹ and room temperature approximately 20°C. Variation of yield strength, ultimate tensile strength and elongation at fracture for different thickness values are represented in Fig. 2. There were no statistically significant differences in strength properties between specimens of the same thickness. The bars in Fig. 2 are showing the average value and error bars denote one standard deviation. Number of tests with usable results for 0.5, 1-, 1.5- and 2-mm samples are respectively 10, 13, 6 and 12. A general increase of elongation at fracture can be observed from the results, where the average elongation at fracture for the specimens with 2 mm thickness is more than two times of the ones with 0.5 mm thickness. In addition, a broad range of elongation to failure was observed among all sample sizes, which is a characteristic of 3D printed manufactured parts that many researchers have observed [18]. Furthermore, the average ultimate tensile strength increases with increasing the thickness and the range of the ultimate tensile strength for 1, 1.5 and 2 mm thicknesses is consistent with the ones reported in the literature [23]. However, the samples with 0.5 mm thickness show a significantly lower ultimate tensile strength. Similar results are also observed for the yield strength.

<figure><img src="image_140.png" /><figcaption>Fig. 2 Variation of average yield strength, ultimate tensile strength, and elongation at fracture for different thickness of the samples. Error bars indicate one standard deviation.</figcaption></figure>

Additionally, load-displacement diagrams for different thicknesses are displayed in Fig. 3. A general consistency of the results of each thickness can be observed from the diagrams. Although, in a few cases slippage of the extensometer on the machine has occurred and caused a deviation from the general trend and for some tests this slippage has occurred very early during the experiment and caused a huge error. The results of these tests are not reported here. Samples display a semi brittle behavior, experiencing failure after undergoing some plastic deformation but before the formation of a neck. No consistently specific location of breakage in different specimens was observed.
## Results

A total number of 41 tensile tests on as-built samples were conducted to examine the mechanical response and statistical variations related to specimen thickness size. Quasi-static tensile tests until failure were carried out at a constant displacement rate of 0.025 mm.s⁻¹ and room temperature approximately 20°C. Variation of yield strength, ultimate tensile strength and elongation at fracture for different thickness values are represented in Fig. 2. There were no statistically significant differences in strength properties between specimens of the same thickness. The bars in Fig. 2 are showing the average value and error bars denote one standard deviation. Number of tests with usable results for 0.5, 1-, 1.5- and 2-mm samples are respectively 10, 13, 6 and 12. A general increase of elongation at fracture can be observed from the results, where the average elongation at fracture for the specimens with 2 mm thickness is more than two times of the ones with 0.5 mm thickness. In addition, a broad range of elongation to failure was observed among all sample sizes, which is a characteristic of 3D printed manufactured parts that many researchers have observed [18]. Furthermore, the average ultimate tensile strength increases with increasing the thickness and the range of the ultimate tensile strength for 1, 1.5 and 2 mm thicknesses is consistent with the ones reported in the literature [23]. However, the samples with 0.5 mm thickness show a significantly lower ultimate tensile strength. Similar results are also observed for the yield strength.

<figure><img src="image_138.png" /><figcaption>Fig. 2 Variation of average yield strength, ultimate tensile strength, and elongation at fracture for different thickness of the samples. Error bars indicate one standard deviation.</figcaption></figure>

Additionally, load-displacement diagrams for different thicknesses are displayed in Fig. 3. A general consistency of the results of each thickness can be observed from the diagrams. Although, in a few cases slippage of the extensometer on the machine has occurred and caused a deviation from the general trend and for some tests this slippage has occurred very early during the experiment and caused a huge error. The results of these tests are not reported here. Samples display a semi brittle behavior, experiencing failure after undergoing some plastic deformation but before the formation of a neck. No consistently specific location of breakage in different specimens was observed.
<figure><img src="image_141.png" /><figcaption>Fig. 3 Load-Displacement diagram for all samples: a) 2 mm thickness samples b) 1.5 mm thickness samples c) 1 mm thickness samples d) 0.5 mm thickness samples.</figcaption></figure>

Fig. 4 demonstrates the engineering stress versus engineering strain curves for variation of thickness. Three different test results for each thickness have been displayed in these figures and each thickness is displayed with its own distinct color in the diagram. For Fig. 4a the nominal cross-section has been used and for Fig. 4b measured cross-section has been considered. Both cross-section measurements are referring to the initial section area before the tensile test. For considering the measured cross-section, the thickness and width of each sample has been measured three times at different random locations and then an average of the measured values was found. The difference between the average measured width and nominal width of the samples was less than one percent. So, it was assumed that the measured width for all of the samples is equal to the nominal width which is 6.25 mm and only the thickness measurement has defined the difference between the nominal and measured cross-section areas. It should be also noted that, for the samples with 0.5 mm thickness the average measured thickness was 0.58 mm which produces a huge difference in the stress between the nominal results and measured results. For the other samples the difference between the nominal and measured thickness is much less significant. Also, the considerable difference in the stress levels between the 0.5 mm samples and the other thicknesses becomes even larger when the measured cross-sections is used.
<figure><img src="image_139.png" /><figcaption>Fig. 3 Load-Displacement diagram for all samples: a) 2 mm thickness samples b) 1.5 mm thickness samples c) 1 mm thickness samples d) 0.5 mm thickness samples.</figcaption></figure>

Fig. 4 demonstrates the engineering stress versus engineering strain curves for variation of thickness. Three different test results for each thickness have been displayed in these figures and each thickness is displayed with its own distinct color in the diagram. For Fig. 4a the nominal cross-section has been used and for Fig. 4b measured cross-section has been considered. Both cross-section measurements are referring to the initial section area before the tensile test. For considering the measured cross-section, the thickness and width of each sample has been measured three times at different random locations and then an average of the measured values was found. The difference between the average measured width and nominal width of the samples was less than one percent. So, it was assumed that the measured width for all of the samples is equal to the nominal width which is 6.25 mm and only the thickness measurement has defined the difference between the nominal and measured cross-section areas. It should be also noted that, for the samples with 0.5 mm thickness the average measured thickness was 0.58 mm which produces a huge difference in the stress between the nominal results and measured results. For the other samples the difference between the nominal and measured thickness is much less significant. Also, the considerable difference in the stress levels between the 0.5 mm samples and the other thicknesses becomes even larger when the measured cross-sections is used.
<figure><img src="image_142.png" /><figcaption>Fig. 4 Stress-Strain curve for variation of the thickness a) Nominal cross section b) Measured cross section.</figcaption></figure>

To study the strain rate effect, 12 more tests have been performed for 0.5 mm and 1 mm thickness samples and the results are reported in Fig. 5 and Fig. 6. These additional tests are performed at 0.1 and 0.005 mm.s⁻¹ displacement rates with three tests for each thickness at each displacement rate. Nominal cross-section has been considered for the engineering stress-strain curves in this case. According to Fig. 5, for 1 mm thickness samples the stress is generally reduced with increased strain rate, but no such trend can be observed for the results of 0.5 mm thickness tests, where the stress is not affected by the strain rate.

<figure><img src="image_143.png" /><figcaption>Fig. 5 Strain rate variation for the samples with 1 mm thickness a) Load-Displacement diagram b) Stress-Strain curve.</figcaption></figure>
<figure><img src="image_140.png" /><figcaption>Fig. 4 Stress-Strain curve for variation of the thickness a) Nominal cross section b) Measured cross section.</figcaption></figure>

To study the strain rate effect, 12 more tests have been performed for 0.5 mm and 1 mm thickness samples and the results are reported in Fig. 5 and Fig. 6. These additional tests are performed at 0.1 and 0.005 mm.s⁻¹ displacement rates with three tests for each thickness at each displacement rate. Nominal cross-section has been considered for the engineering stress-strain curves in this case. According to Fig. 5, for 1 mm thickness samples the stress is generally reduced with increased strain rate, but no such trend can be observed for the results of 0.5 mm thickness tests, where the stress is not affected by the strain rate.

<figure><img src="image_141.png" /><figcaption>Fig. 5 Strain rate variation for the samples with 1 mm thickness a) Load-Displacement diagram b) Stress-Strain curve.</figcaption></figure>
<figure><img src="image_144.png" /><figcaption>Fig. 6 Strain rate variation for the samples with 0.5 mm thickness a) Load-Displacement diagram b) Stress-Strain curve.</figcaption></figure>

## Summary and Discussion

Uniaxial tensile tests were performed on AlSi10Mg as-built samples with 4 different thicknesses. The results show a trend of decreasing ultimate tensile strength with decreasing sample thickness. Another trend is a consistent increase in elongation at fracture with increasing thickness, where the average elongation at fracture for the specimens with 2 mm thickness are more than twice that of the specimens with 0.5 mm thickness. Moreover, samples with a thickness of 0.5 mm exhibit significantly lower strength compared to the larger thickness samples. One likely reason for the differences can be different input energy and scanning speed. As the schematic picture displayed in Fig. 1b indicates, for the 0.5 mm thickness, the cross-section of the specimen is made by only two passes of the laser beam over the powder and the laser power and speed for the border of the cross-section is different from the in-skin of the cross-section. Therefore, the material of specimens with different thicknesses has different thermal history, resulting in different material properties. Observation of the surface of samples (even without magnification) also indicates a difference in the surface roughness and morphology between 0.5 mm thickness samples and other samples. Accordingly, as the sample size decreases, there might be microstructural alterations which are attributed to variations in the ratio between border and in-skin laser strategies. Therefore, conducting a follow-up study on the properties created by different scanning strategies would be beneficial in providing further clarity on this issue.

The work done by [24] is an experimental study similar to this work with the same material and printing machine, but a different size and shape of the samples. Comparing the presented results with the results of this study shows the same trend of a general decrease in strength with decreasing size. For the 2 mm samples in the present work the average ultimate strength is about 15% lower than for the ones reported in [24].

Stress-strain curves were calculated based on two different cross-section considerations: nominal and measured. In the case of samples with a thickness of 0.5 mm, the average measured thickness was 0.58 mm, signifying a substantial difference between the nominal and measured results. Furthermore, the significant difference in the behavior of the 0.5 mm samples, in comparison to other thicknesses, becomes even more evident when measured cross-sections are utilized. According to the results with variation of strain rate, for samples with a thickness of 1 mm, the stress-strain curve generally shifts downward with an increase in strain rate. In contrast, no noticeable trend is observed in the results for 0.5 mm thickness, indicating no significant change with varying strain rates.
<figure><img src="image_142.png" /><figcaption>Fig. 6 Strain rate variation for the samples with 0.5 mm thickness a) Load-Displacement diagram b) Stress-Strain curve.</figcaption></figure>

## Summary and Discussion

Uniaxial tensile tests were performed on AlSi10Mg as-built samples with 4 different thicknesses. The results show a trend of decreasing ultimate tensile strength with decreasing sample thickness. Another trend is a consistent increase in elongation at fracture with increasing thickness, where the average elongation at fracture for the specimens with 2 mm thickness are more than twice that of the specimens with 0.5 mm thickness. Moreover, samples with a thickness of 0.5 mm exhibit significantly lower strength compared to the larger thickness samples. One likely reason for the differences can be different input energy and scanning speed. As the schematic picture displayed in Fig. 1b indicates, for the 0.5 mm thickness, the cross-section of the specimen is made by only two passes of the laser beam over the powder and the laser power and speed for the border of the cross-section is different from the in-skin of the cross-section. Therefore, the material of specimens with different thicknesses has different thermal history, resulting in different material properties. Observation of the surface of samples (even without magnification) also indicates a difference in the surface roughness and morphology between 0.5 mm thickness samples and other samples. Accordingly, as the sample size decreases, there might be microstructural alterations which are attributed to variations in the ratio between border and in-skin laser strategies. Therefore, conducting a follow-up study on the properties created by different scanning strategies would be beneficial in providing further clarity on this issue.

The work done by [24] is an experimental study similar to this work with the same material and printing machine, but a different size and shape of the samples. Comparing the presented results with the results of this study shows the same trend of a general decrease in strength with decreasing size. For the 2 mm samples in the present work the average ultimate strength is about 15% lower than for the ones reported in [24].

Stress-strain curves were calculated based on two different cross-section considerations: nominal and measured. In the case of samples with a thickness of 0.5 mm, the average measured thickness was 0.58 mm, signifying a substantial difference between the nominal and measured results. Furthermore, the significant difference in the behavior of the 0.5 mm samples, in comparison to other thicknesses, becomes even more evident when measured cross-sections are utilized. According to the results with variation of strain rate, for samples with a thickness of 1 mm, the stress-strain curve generally shifts downward with an increase in strain rate. In contrast, no noticeable trend is observed in the results for 0.5 mm thickness, indicating no significant change with varying strain rates.
The observed reduction in strength for smaller thicknesses can result in significant discrepancies between expected and actual material performance. Designers utilizing additive manufacturing components must be considerate of this and utilize corrective measures. This includes incorporating an effective feature thickness and employing an appropriate material model parameters to ensure accurate and reliable performance of components.

## References

[1] X.Y. Cheng, S.J. Li, L.E. Murr, Z.B. Zhang, Y.L. Hao, R. Yang, F. Medina and R.B. Wicker, Compression deformation behavior of Ti-6Al-4V alloy with cellular structures fabricated by electron beam melting, J Mech Behav Biomed Mater. 16 (2012) 153-62. https://doi.org/10.1016/j.jmbbm.2012.10.005

[2] O. Al-Ketan, R. Rowshan and R.K. Abu Al-Rub, Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials, Addit. Manuf. 19 (2018) 167-183. https://doi.org/10.1016/j.addma.2017.12.006

[3] C. Yan, L. Hao, A. Hussein and P. Young, Ti-6Al-4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting, J Mech Behav Biomed Mater. 51 (2015) 61-73. https://doi.org/10.1016/j.jmbbm.2015.06.024

[4] D. Herzog, V. Seyda, E. Wycisk and C. Emmelmann, Additive manufacturing of metals, Acta Mater. 117 (2016) 371-392. https://doi.org/10.1016/j.actamat.2016.07.019

[5] W.E. Frazier, Metal Additive Manufacturing: A Review, J. Mater. Eng. Perform. 23(6) (2014) 1917-1928. https://doi.org/10.1007/s11665-014-0958-z

[6] B. Blakey-Milner, P. Gradl, G. Snedden, M. Brooks, J. Pitot, E. Lopez, M. Leary, F. Berto and A. du Plessis, Metal additive manufacturing in aerospace: A review, Mater. Des. 209 (2021). https://doi.org/10.1016/j.matdes.2021.110008

[7] S. Cooke, K. Ahmadi, S. Willerth and R. Herring, Metal additive manufacturing: Technology, metallurgy and modelling, J. Manuf. Process. 57 (2020) 978-1003. https://doi.org/10.1016/j.jmapro.2020.07.025

[8] A. Tridello, J. Fiocchi, C.A. Biffi, G. Chiandussi, M. Rossetto, A. Tuissi and D.S. Paolino, Effect of microstructure, residual stresses and building orientation on the fatigue response up to 109 cycles of an SLM AlSi10Mg alloy, Int. J. Fatigue. 137 (2020). https://doi.org/10.1016/j.ijfatigue.2020.105659

[9] C.G. Wang, J.X. Zhu, G.W. Wang, Y. Qin, M.Y. Sun, J.L. Yang, X.F. Shen and S.K. Huang, Effect of building orientation and heat treatment on the anisotropic tensile properties of AlSi10Mg fabricated by selective laser melting, J. Alloys Compd. 895 (2022). https://doi.org/10.1016/j.jallcom.2021.162665

[10] G. Tarakçı, H.M. Khan, M.S. Yılmaz and G. Özer, Effect of building orientations and heat treatments on AlSi10Mg alloy fabricated by selective laser melting: Microstructure evolution, mechanical properties, fracture mechanism and corrosion behavior, Rapid Prototyp. J. 28(8) (2022) 1609-1621. https://doi.org/10.1108/RPJ-11-2021-0325

[11] D. Yue, D. Li, X. Zhang, B. Chen, R. Qin and Z. Wang, Tensile behavior of AlSi10Mg overhanging structures fabricated by laser powder bed fusion: Effects of support structures and build orientation, Mater. Sci. Eng. A. 880 (2023) 145375. https://doi.org/10.1016/j.msea.2023.145375

[12] M. Aktürk, M. Boy, M.K. Gupta, S. Waqar, G.M. Krolczyk and M.E. Korkmaz, Numerical and experimental investigations of built orientation dependent Johnson-Cook model for selective
The observed reduction in strength for smaller thicknesses can result in significant discrepancies between expected and actual material performance. Designers utilizing additive manufacturing components must be considerate of this and utilize corrective measures. This includes incorporating an effective feature thickness and employing an appropriate material model parameters to ensure accurate and reliable performance of components.

## References

[1] X.Y. Cheng, S.J. Li, L.E. Murr, Z.B. Zhang, Y.L. Hao, R. Yang, F. Medina and R.B. Wicker, Compression deformation behavior of Ti-6Al-4V alloy with cellular structures fabricated by electron beam melting, J Mech Behav Biomed Mater. 16 (2012) 153-62. https://doi.org/10.1016/j.jmbbm.2012.10.005

[2] O. Al-Ketan, R. Rowshan and R.K. Abu Al-Rub, Topology-mechanical property relationship of 3D printed strut, skeletal, and sheet based periodic metallic cellular materials, Addit. Manuf. 19 (2018) 167-183. https://doi.org/10.1016/j.addma.2017.12.006

[3] C. Yan, L. Hao, A. Hussein and P. Young, Ti-6Al-4V triply periodic minimal surface structures for bone implants fabricated via selective laser melting, J Mech Behav Biomed Mater. 51 (2015) 61-73. https://doi.org/10.1016/j.jmbbm.2015.06.024

[4] D. Herzog, V. Seyda, E. Wycisk and C. Emmelmann, Additive manufacturing of metals, Acta Mater. 117 (2016) 371-392. https://doi.org/10.1016/j.actamat.2016.07.019

[5] W.E. Frazier, Metal Additive Manufacturing: A Review, J. Mater. Eng. Perform. 23(6) (2014) 1917-1928. https://doi.org/10.1007/s11665-014-0958-z

[6] B. Blakey-Milner, P. Gradl, G. Snedden, M. Brooks, J. Pitot, E. Lopez, M. Leary, F. Berto and A. du Plessis, Metal additive manufacturing in aerospace: A review, Mater. Des. 209 (2021). https://doi.org/10.1016/j.matdes.2021.110008

[7] S. Cooke, K. Ahmadi, S. Willerth and R. Herring, Metal additive manufacturing: Technology, metallurgy and modelling, J. Manuf. Process. 57 (2020) 978-1003. https://doi.org/10.1016/j.jmapro.2020.07.025

[8] A. Tridello, J. Fiocchi, C.A. Biffi, G. Chiandussi, M. Rossetto, A. Tuissi and D.S. Paolino, Effect of microstructure, residual stresses and building orientation on the fatigue response up to 109 cycles of an SLM AlSi10Mg alloy, Int. J. Fatigue. 137 (2020). https://doi.org/10.1016/j.ijfatigue.2020.105659

[9] C.G. Wang, J.X. Zhu, G.W. Wang, Y. Qin, M.Y. Sun, J.L. Yang, X.F. Shen and S.K. Huang, Effect of building orientation and heat treatment on the anisotropic tensile properties of AlSi10Mg fabricated by selective laser melting, J. Alloys Compd. 895 (2022). https://doi.org/10.1016/j.jallcom.2021.162665

[10] G. Tarakçı, H.M. Khan, M.S. Yılmaz and G. Özer, Effect of building orientations and heat treatments on AlSi10Mg alloy fabricated by selective laser melting: Microstructure evolution, mechanical properties, fracture mechanism and corrosion behavior, Rapid Prototyp. J. 28(8) (2022) 1609-1621. https://doi.org/10.1108/RPJ-11-2021-0325

[11] D. Yue, D. Li, X. Zhang, B. Chen, R. Qin and Z. Wang, Tensile behavior of AlSi10Mg overhanging structures fabricated by laser powder bed fusion: Effects of support structures and build orientation, Mater. Sci. Eng. A. 880 (2023) 145375. https://doi.org/10.1016/j.msea.2023.145375

[12] M. Aktürk, M. Boy, M.K. Gupta, S. Waqar, G.M. Krolczyk and M.E. Korkmaz, Numerical and experimental investigations of built orientation dependent Johnson-Cook model for selective
laser melting manufactured AlSi10Mg, JMR&T. 15 (2021) 6244-6259.
https://doi.org/10.1016/j.jmrt.2021.11.062

[13] S. Greco, K. Gutzeit, H. Hotz, B. Kirsch and J.C. Aurich, Selective laser melting (SLM) of AISI 316L—impact of laser power, layer thickness, and hatch spacing on roughness, density, and microhardness at constant input energy density, Int. J. Adv. Manuf. Technol. 108(5-6) (2020) 1551-1562. https://doi.org/10.1007/s00170-020-05510-8

[14] R.M. Gouveia, F.J.G. Silva, E. Atzeni, D. Sormaz, J.L. Alves and A.B. Pereira, Effect of Scan Strategies and Use of Support Structures on Surface Quality and Hardness of L-PBF AlSi10Mg Parts, Materials (Basel). 13(10) (2020). https://doi.org/10.3390/ma13102248

[15] H. Jia, H. Sun, H. Wang, Y. Wu and H. Wang, Scanning strategy in selective laser melting (SLM): a review, Int. J. Adv. Manuf. Technol. 113(9-10) (2021) 2413-2435. https://doi.org/10.1007/s00170-021-06810-3

[16] Z. Dong, X. Zhang, W. Shi, H. Zhou, H. Lei and J. Liang, Study of Size Effect on Microstructure and Mechanical Properties of AlSi10Mg Samples Made by Selective Laser Melting, Materials (Basel). 11(12) (2018). https://doi.org/10.3390/ma11122463

[17] N. Takata, H. Kodaira, A. Suzuki and M. Kobashi, Size dependence of microstructure of AlSi10Mg alloy fabricated by selective laser melting, Mater. Charact. 143 (2018) 18-26. https://doi.org/10.1016/j.matchar.2017.11.052

[18] A.M. Roach, B.C. White, A. Garland, B.H. Jared, J.D. Carroll and B.L. Boyce, Size-dependent stochastic tensile properties in additively manufactured 316L stainless steel, Addit. Manuf. 32 (2020). https://doi.org/10.1016/j.addma.2020.101090

[19] D. Barba, C. Alabort, Y.T. Tang, M.J. Viscasillas, R.C. Reed and E. Alabort, On the size and orientation effect in additive manufactured Ti-6Al-4V, Mater. Des. 186 (2020). https://doi.org/10.1016/j.matdes.2019.108235

[20] Information on https://www.tekna.com/

[21] Information on https://www.iso.org/standard/78322.html

[22] Information on https://www.slm-solutions.com

[23] T. Maconachie, M. Leary, J. Zhang, A. Medvedev, A. Sarker, D. Ruan, G. Lu, O. Faruque and M. Brandt, Effect of build orientation on the quasi-static and dynamic response of SLM AlSi10Mg, Mater. Sci. Eng. A. 788 (2020). https://doi.org/10.1016/j.msea.2020.139445

[24] D. Vysochinskiy and N. Akhtar, On the Influence of Cross-Section Size on Measured Strength of SLM-Produced AlSi10Mg-Alloy, KEM. 926 (2022) 132-140. https://doi.org/10.4028/p-g078sc
laser melting manufactured AlSi10Mg, JMR&T. 15 (2021) 6244-6259.
https://doi.org/10.1016/j.jmrt.2021.11.062

[13] S. Greco, K. Gutzeit, H. Hotz, B. Kirsch and J.C. Aurich, Selective laser melting (SLM) of AISI 316L—impact of laser power, layer thickness, and hatch spacing on roughness, density, and microhardness at constant input energy density, Int. J. Adv. Manuf. Technol. 108(5-6) (2020) 1551-1562. https://doi.org/10.1007/s00170-020-05510-8

[14] R.M. Gouveia, F.J.G. Silva, E. Atzeni, D. Sormaz, J.L. Alves and A.B. Pereira, Effect of Scan Strategies and Use of Support Structures on Surface Quality and Hardness of L-PBF AlSi10Mg Parts, Materials (Basel). 13(10) (2020). https://doi.org/10.3390/ma13102248

[15] H. Jia, H. Sun, H. Wang, Y. Wu and H. Wang, Scanning strategy in selective laser melting (SLM): a review, Int. J. Adv. Manuf. Technol. 113(9-10) (2021) 2413-2435. https://doi.org/10.1007/s00170-021-06810-3

[16] Z. Dong, X. Zhang, W. Shi, H. Zhou, H. Lei and J. Liang, Study of Size Effect on Microstructure and Mechanical Properties of AlSi10Mg Samples Made by Selective Laser Melting, Materials (Basel). 11(12) (2018). https://doi.org/10.3390/ma11122463

[17] N. Takata, H. Kodaira, A. Suzuki and M. Kobashi, Size dependence of microstructure of AlSi10Mg alloy fabricated by selective laser melting, Mater. Charact. 143 (2018) 18-26. https://doi.org/10.1016/j.matchar.2017.11.052

[18] A.M. Roach, B.C. White, A. Garland, B.H. Jared, J.D. Carroll and B.L. Boyce, Size-dependent stochastic tensile properties in additively manufactured 316L stainless steel, Addit. Manuf. 32 (2020). https://doi.org/10.1016/j.addma.2020.101090

[19] D. Barba, C. Alabort, Y.T. Tang, M.J. Viscasillas, R.C. Reed and E. Alabort, On the size and orientation effect in additive manufactured Ti-6Al-4V, Mater. Des. 186 (2020). https://doi.org/10.1016/j.matdes.2019.108235

[20] Information on https://www.tekna.com/

[21] Information on https://www.iso.org/standard/78322.html

[22] Information on https://www.slm-solutions.com

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[24] D. Vysochinskiy and N. Akhtar, On the Influence of Cross-Section Size on Measured Strength of SLM-Produced AlSi10Mg-Alloy, KEM. 926 (2022) 132-140. https://doi.org/10.4028/p-g078sc
# Comparison between ALE and Lagrangian finite element formulations to simulate tensile loading for FDM parts

HOMRANI Mohamed Khalil<fnref n="1" />,ᵃ*, DEMARBAIX Anthonin<fnref n="2" />, RIVIERE-LORPHÈVRE Edouard<fnref n="1" />, BEUSCART Thomas<fnref n="1" />, OCHANA Imi<fnref n="1" />,<fnref n="2" />, DUCOBU François<fnref n="1" />

**Keywords:** Finite Element, Tensile Testing, Arbitrary Lagrangian Eulerian, 3D Printing

**Abstract.** Material Extrusion (MEX) and by extension Fused Deposition Modeling (FDM) is a popular Additive Manufacturing (AM) process used to fabricate complex parts. FDM as of recent is no longer solely utilized for prototyping parts but also used for producing functional components in industrial and research applications. The investigation of material properties of these FDM parts by experimental means is a time-consuming task. Therefore, the use of numerical simulation methods is highly required. Since 1993, various Finite Element Analysis (FEA) models are found in literature attempting to effectively simulate FDM parts utilizing many formulations, each with their pros and cons. The present study aims to compare Lagrangian and Arbitrary Lagrangian-Eulerian (ALE) finite element formulations in simulating tensile loading for FDM parts. The efficiency and precision of the aforementioned methods is evaluated in the numerical simulation of the tensile loading of an ASTM D638 standard geometry ABS specimen utilizing both ABAQUS/Explicit and ABAQUS/Standard. Utilizing a paper from the literature for experimental validation, this study additionally provides insight into explicit and implicit models' computational efficiency, focusing on the advantages of explicit models for this application. The effects of mesh element type and size on results are also studied for each method. Based on these results, some useful guidelines for selecting the most suitable model of tensile loaded FDM parts are presented.

**Introduction**

The progress of Additive Manufacturing (AM) within the last few decades has been remarkable, with consistent double-digit growth, AM has transformed into a market valued at over $4 billion in 2015 [1]. Projections indicate that the AM market is expected to surpass $35.6 billion by 2024 [2]. This market expansion is primarily due to advances made through research, ranging from new findings in AM materials to studies with the goal of reducing costs by easing the development cycle [3]. This reduction can also be a consequence of the easing in research costs, increasingly digital alternatives such as digital twins and Finite Element Analysis (FEA) models allow for progress to be made at significantly reduced cost and time invested [4].

Within this manufacturing technology classification is Material Extrusion (MEX) [5], this category encompasses AM processes where material is selectively dispensed through a nozzle or orifice to print parts layer by layer. Fused Deposition Modeling (FDM) in particular starts with materials undergoing a liquefaction process. Subsequently, the liquefied material is precisely deposited layer by layer through a known diameter nozzle [6], aligning with the input Computer Assisted Drawing (CAD) model provided in .STL format [7]. The material gradually cools and solidifies layer by layer [8]. To allow solidification to occur, the heated bed temperature is

<figure><img src="image_145.png" /></figure>

<footnote n="1">¹Machine Design and Production Engineering Lab – Research Institute for Science and material Engineering – University of Mons, Place du Parc 20, Mons, Belgium</footnote>

<footnote n="2">²Science and Technology Research Unit – Science and Technology Department, HEPH-Condorcet University Square Hiernaux 2, 6000 Charleroi, Belgium</footnote>

<footnote>ªMohamedkhalil.homrani@umons.ac.be</footnote>
# Comparison between ALE and Lagrangian finite element formulations to simulate tensile loading for FDM parts

HOMRANI Mohamed Khalil<fnref n="1" />,ᵃ*, DEMARBAIX Anthonin<fnref n="2" />, RIVIERE-LORPHÈVRE Edouard<fnref n="1" />, BEUSCART Thomas<fnref n="1" />, OCHANA Imi<fnref n="1" />,<fnref n="2" />, DUCOBU François<fnref n="1" />

**Keywords:** Finite Element, Tensile Testing, Arbitrary Lagrangian Eulerian, 3D Printing

**Abstract.** Material Extrusion (MEX) and by extension Fused Deposition Modeling (FDM) is a popular Additive Manufacturing (AM) process used to fabricate complex parts. FDM as of recent is no longer solely utilized for prototyping parts but also used for producing functional components in industrial and research applications. The investigation of material properties of these FDM parts by experimental means is a time-consuming task. Therefore, the use of numerical simulation methods is highly required. Since 1993, various Finite Element Analysis (FEA) models are found in literature attempting to effectively simulate FDM parts utilizing many formulations, each with their pros and cons. The present study aims to compare Lagrangian and Arbitrary Lagrangian-Eulerian (ALE) finite element formulations in simulating tensile loading for FDM parts. The efficiency and precision of the aforementioned methods is evaluated in the numerical simulation of the tensile loading of an ASTM D638 standard geometry ABS specimen utilizing both ABAQUS/Explicit and ABAQUS/Standard. Utilizing a paper from the literature for experimental validation, this study additionally provides insight into explicit and implicit models' computational efficiency, focusing on the advantages of explicit models for this application. The effects of mesh element type and size on results are also studied for each method. Based on these results, some useful guidelines for selecting the most suitable model of tensile loaded FDM parts are presented.

**Introduction**

The progress of Additive Manufacturing (AM) within the last few decades has been remarkable, with consistent double-digit growth, AM has transformed into a market valued at over $4 billion in 2015 [1]. Projections indicate that the AM market is expected to surpass $35.6 billion by 2024 [2]. This market expansion is primarily due to advances made through research, ranging from new findings in AM materials to studies with the goal of reducing costs by easing the development cycle [3]. This reduction can also be a consequence of the easing in research costs, increasingly digital alternatives such as digital twins and Finite Element Analysis (FEA) models allow for progress to be made at significantly reduced cost and time invested [4].

Within this manufacturing technology classification is Material Extrusion (MEX) [5], this category encompasses AM processes where material is selectively dispensed through a nozzle or orifice to print parts layer by layer. Fused Deposition Modeling (FDM) in particular starts with materials undergoing a liquefaction process. Subsequently, the liquefied material is precisely deposited layer by layer through a known diameter nozzle [6], aligning with the input Computer Assisted Drawing (CAD) model provided in .STL format [7]. The material gradually cools and solidifies layer by layer [8]. To allow solidification to occur, the heated bed temperature is

<figure><img src="image_143.png" /></figure>

<footnote n="1">¹Machine Design and Production Engineering Lab – Research Institute for Science and material Engineering – University of Mons, Place du Parc 20, Mons, Belgium</footnote>

<footnote n="2">²Science and Technology Research Unit – Science and Technology Department, HEPH-Condorcet University Square Hiernaux 2, 6000 Charleroi, Belgium</footnote>

<footnote>ªMohamedkhalil.homrani@umons.ac.be</footnote>
maintained lower than the extrusion temperature [9]. Afterward, post-processing techniques and geometry modifications are utilized to achieve the desired final shape [10].

An often-studied mechanical property that has the most reoccurring research in AM is tensile strength. This refers to the maximum amount of tensile stress a material can withstand before failure. Understanding the factors that influence it is essential to improve the printing process and achieve the desired part properties. Studies focusing on this property mainly utilize ASTM D638 types I to IV geometry [11]. This document is a standard test method published by the American Society for Testing and Materials (ASTM) that is used to determine the tensile properties of plastic materials. The anisotropy resulting from AM parts results in a significant discrepancy between the mechanical properties along different axes, this poses a unique challenge in testing mechanical strength across the construction direction of the printed parts.

<figure><img src="image_146.png" /><figcaption>Figure 1: Typical finite element analysis steps, showing geometry creation (a), defining the mesh and material properties (b), solving (c), and results processing (d)</figcaption></figure>

FEA has become an important and useful tool for solving complex eigenvalue problems, initial value, and boundary value problems. The workflow of which shown in Fig. 1 shows its simplicity which comes from representing each finite element as simple mesh geometry [12] which can be seen in Fig. 1.b. Furthermore, several recent optimizations have increased the popularity of FEA in research with the benefit of reducing development costs. As an example, we can take the study this work utilizes for experimental validation. Garg et al. [13] focus on the deformation of FDM samples, examining important printing parameters such as layer thicknesses and raster orientations under tension. FEA is conducted to simulate the elastoplastic behavior of ABS-printed specimens, the results of which are compared to experiments.

FE models can be performed implicitly or explicitly, with distinct differences and advantages to each. Explicit FE analysis is characterized by incrementally advancing the kinematic state from the previous increment; results from these models may deviate from experimental values if the time increment remains insufficiently low. These models often present stability problems: the results are only conditionally stable but still often offer significantly faster converging times with lower computational costs. Implicit analysis, on the other hand, iterates to determine the solution to a non-linear problem. It often provides better results for elastoplastic models while requiring significantly larger computational resources.

The two primary types of models encountered in the literature utilize Lagrangian, Eulerian, and Arbitrary Lagrangian-Eulerian (ALE) formulations, all popular candidates for FEA mathematical formulations [14]. The Eulerian formulation is used for large deformation problems. These problems are defined in a way where the mesh is fixed while the material moves freely through
maintained lower than the extrusion temperature [9]. Afterward, post-processing techniques and geometry modifications are utilized to achieve the desired final shape [10].

An often-studied mechanical property that has the most reoccurring research in AM is tensile strength. This refers to the maximum amount of tensile stress a material can withstand before failure. Understanding the factors that influence it is essential to improve the printing process and achieve the desired part properties. Studies focusing on this property mainly utilize ASTM D638 types I to IV geometry [11]. This document is a standard test method published by the American Society for Testing and Materials (ASTM) that is used to determine the tensile properties of plastic materials. The anisotropy resulting from AM parts results in a significant discrepancy between the mechanical properties along different axes, this poses a unique challenge in testing mechanical strength across the construction direction of the printed parts.

<figure><img src="image_144.png" /><figcaption>Figure 1: Typical finite element analysis steps, showing geometry creation (a), defining the mesh and material properties (b), solving (c), and results processing (d)</figcaption></figure>

FEA has become an important and useful tool for solving complex eigenvalue problems, initial value, and boundary value problems. The workflow of which shown in Fig. 1 shows its simplicity which comes from representing each finite element as simple mesh geometry [12] which can be seen in Fig. 1.b. Furthermore, several recent optimizations have increased the popularity of FEA in research with the benefit of reducing development costs. As an example, we can take the study this work utilizes for experimental validation. Garg et al. [13] focus on the deformation of FDM samples, examining important printing parameters such as layer thicknesses and raster orientations under tension. FEA is conducted to simulate the elastoplastic behavior of ABS-printed specimens, the results of which are compared to experiments.

FE models can be performed implicitly or explicitly, with distinct differences and advantages to each. Explicit FE analysis is characterized by incrementally advancing the kinematic state from the previous increment; results from these models may deviate from experimental values if the time increment remains insufficiently low. These models often present stability problems: the results are only conditionally stable but still often offer significantly faster converging times with lower computational costs. Implicit analysis, on the other hand, iterates to determine the solution to a non-linear problem. It often provides better results for elastoplastic models while requiring significantly larger computational resources.

The two primary types of models encountered in the literature utilize Lagrangian, Eulerian, and Arbitrary Lagrangian-Eulerian (ALE) formulations, all popular candidates for FEA mathematical formulations [14]. The Eulerian formulation is used for large deformation problems. These problems are defined in a way where the mesh is fixed while the material moves freely through
the mesh. Despite being best suited for large deformation problems, Eulerian simulations are expensive in view of the computation time due to the advection step. Meanwhile, Lagrangian algorithms are used to assess material behavior under static, quasi-static, and dynamic loads, which induces deformations on the mesh. Each individual node in this mesh formulation is attached to the model. Advanced material simulations can still be implemented by this method. There are literature cases of Lagrangian method application in problems with large deformations, such as Thije et al. [17]. However, Lagrangian formulation is generally ill-suited for these problems since it usually terminates at an early stage of an extreme mesh distortion.

To bypass the issues plaguing the two prior mentioned methods, the ALE method is employed, which describes a broad range of analysis approaches, from purely Lagrangian analysis to purely Eulerian analysis. Typically, an ALE analysis follows an approach between these extremes. The ALE "Operator split" during each increment consists of a Lagrangian step where the mesh adheres to the material, an equilibrated "Lagrangian configuration" is computed at the next time increment, followed by an Eulerian step where a new mesh is defined. Finally, an advection step is performed where data is transferred from the old mesh to the new one.

The ALE formulation has been extensively used to model material cutting [15], with no prior applications in AM FEA studies. The goal of this study is to draw a direct comparison between the prior mentioned FE formulations in implicit and explicit simulations.

## Development of the FE model

The simulation of the entire tensile test is recreated using ABAQUS/Standard and ABAQUS/Explicit for the finite element codes. In total, eight FE models were developed. Using Both Lagrangian and ALE techniques, each in explicit and implicit. All the created models consisting of a deformable dog-bone specimen in accordance with ASTM D638. The specimen geometry and dimensions are presented in Fig. 2(c), while gripper arrangement and loads are shown respectively in fig. 2(b) and 2(a).

<figure><img src="image_147.png" /><figcaption>Figure 2: Boundary conditions applied to the model (a), experimental gripper arrangement (b), and ASTM D638 sample geometry (c)</figcaption></figure>

The same loading conditions, summarized in Fig. 3(b), were used in the Lagrangian implicit, Lagrangian explicit, ALE implicit, and ALE explicit models to allow the comparison of the results. Similar to the tensile testing performed by the experimental validation paper Garg et al. [13], one end of the specimen is held in place while the displacement is applied from the other end, as schematically represented in Fig. 2(a). The boundary conditions applied are further demonstrated in Fig. 2(b) where an encastre constraint is placed on one end of the dog bone by limiting all six
the mesh. Despite being best suited for large deformation problems, Eulerian simulations are expensive in view of the computation time due to the advection step. Meanwhile, Lagrangian algorithms are used to assess material behavior under static, quasi-static, and dynamic loads, which induces deformations on the mesh. Each individual node in this mesh formulation is attached to the model. Advanced material simulations can still be implemented by this method. There are literature cases of Lagrangian method application in problems with large deformations, such as Thije et al. [17]. However, Lagrangian formulation is generally ill-suited for these problems since it usually terminates at an early stage of an extreme mesh distortion.

To bypass the issues plaguing the two prior mentioned methods, the ALE method is employed, which describes a broad range of analysis approaches, from purely Lagrangian analysis to purely Eulerian analysis. Typically, an ALE analysis follows an approach between these extremes. The ALE "Operator split" during each increment consists of a Lagrangian step where the mesh adheres to the material, an equilibrated "Lagrangian configuration" is computed at the next time increment, followed by an Eulerian step where a new mesh is defined. Finally, an advection step is performed where data is transferred from the old mesh to the new one.

The ALE formulation has been extensively used to model material cutting [15], with no prior applications in AM FEA studies. The goal of this study is to draw a direct comparison between the prior mentioned FE formulations in implicit and explicit simulations.

## Development of the FE model

The simulation of the entire tensile test is recreated using ABAQUS/Standard and ABAQUS/Explicit for the finite element codes. In total, eight FE models were developed. Using Both Lagrangian and ALE techniques, each in explicit and implicit. All the created models consisting of a deformable dog-bone specimen in accordance with ASTM D638. The specimen geometry and dimensions are presented in Fig. 2(c), while gripper arrangement and loads are shown respectively in fig. 2(b) and 2(a).

<figure><img src="image_145.png" /><figcaption>Figure 2: Boundary conditions applied to the model (a), experimental gripper arrangement (b), and ASTM D638 sample geometry (c)</figcaption></figure>

The same loading conditions, summarized in Fig. 3(b), were used in the Lagrangian implicit, Lagrangian explicit, ALE implicit, and ALE explicit models to allow the comparison of the results. Similar to the tensile testing performed by the experimental validation paper Garg et al. [13], one end of the specimen is held in place while the displacement is applied from the other end, as schematically represented in Fig. 2(a). The boundary conditions applied are further demonstrated in Fig. 2(b) where an encastre constraint is placed on one end of the dog bone by limiting all six
degree of freedoms, U1=U2=U3=UR1=UR2=UR3=0. The displacement along axis is then applied from the other end as U1=U3=UR1=UR2=UR3=0, U2= displacement at failure= 2.4 mm (taken from experimental validation study [13]). Simulation time is fixed to one second for all models to match the experimental load time also equal to 1 second. The material properties applied in the following FE models are also shown in Fig. 3(a) and 3(c) as seen in Anton et al. [16]. Implementing these properties was done identically to the experimental validation paper Garg et al. [13]. First, by converting the engineering stress/strain curve into true stress/strain using the ABAQUS material calibration tool. The resulting true stress/strain curve is then used to create an elastic plastic isotropic material within the same ABAQUS material calibration tool. The material model is interpolated to the elastic modulus in Fig. 3(c), which is calculated from the selected yield point shown in Fig. 3(a) at 35.928 MPa (with a corresponding strain of 0.01633 mm/mm).

The Von Mises Yield Criterion is used to model the material with isotropic hardening using the calculated plastic deformation part of the true stress/strain data obtained from the previous step.

The FDM samples created in CAD software SolidWorks are imported to ABAQUS for the FE simulation under the unidirectional tensile loading, with the goal of studying their elastic-plastic deformation. The analysis is initially carried out utilizing the Lagrangian formulation in implicit and explicit schemes, and the modeling is considered as a load/displacement problem.

<figure><img src="image_148.png" /><figcaption>Figure 3: Stress/strain curve of the ABS material from Anton et al. [16] (a), loading conditions (b), and ABS material properties (c)</figcaption></figure>

As previously discussed, one of the requirements to run a FE simulation is to fragment the simulated part into mesh cells. By performing a mesh sensitivity study, it becomes possible to understand how different mesh configurations affect the model's results, this helps identify which meshes produce accurate results while minimizing redundant computational costs. The results of this analysis are shown in Fig. 4, the mesh element kept identical to the validation study [13] which is C3D4 (Continuum 3-dimensional 4-noded solid linear tetrahedron). Finer mesh size improves accuracy but demands higher computational resources, thus the model is meshed by tetrahedron elements. For consistency purposes, both implicit and explicit Lagrangian simulations are meshed with 1 mm elements while reducing the gauge element size to 0.5 mm (section shown in Fig. 2(c)).
degree of freedoms, U1=U2=U3=UR1=UR2=UR3=0. The displacement along axis is then applied from the other end as U1=U3=UR1=UR2=UR3=0, U2= displacement at failure= 2.4 mm (taken from experimental validation study [13]). Simulation time is fixed to one second for all models to match the experimental load time also equal to 1 second. The material properties applied in the following FE models are also shown in Fig. 3(a) and 3(c) as seen in Anton et al. [16]. Implementing these properties was done identically to the experimental validation paper Garg et al. [13]. First, by converting the engineering stress/strain curve into true stress/strain using the ABAQUS material calibration tool. The resulting true stress/strain curve is then used to create an elastic plastic isotropic material within the same ABAQUS material calibration tool. The material model is interpolated to the elastic modulus in Fig. 3(c), which is calculated from the selected yield point shown in Fig. 3(a) at 35.928 MPa (with a corresponding strain of 0.01633 mm/mm).

The Von Mises Yield Criterion is used to model the material with isotropic hardening using the calculated plastic deformation part of the true stress/strain data obtained from the previous step.

The FDM samples created in CAD software SolidWorks are imported to ABAQUS for the FE simulation under the unidirectional tensile loading, with the goal of studying their elastic-plastic deformation. The analysis is initially carried out utilizing the Lagrangian formulation in implicit and explicit schemes, and the modeling is considered as a load/displacement problem.

<figure><img src="image_146.png" /><figcaption>Figure 3: Stress/strain curve of the ABS material from Anton et al. [16] (a), loading conditions (b), and ABS material properties (c)</figcaption></figure>

As previously discussed, one of the requirements to run a FE simulation is to fragment the simulated part into mesh cells. By performing a mesh sensitivity study, it becomes possible to understand how different mesh configurations affect the model's results, this helps identify which meshes produce accurate results while minimizing redundant computational costs. The results of this analysis are shown in Fig. 4, the mesh element kept identical to the validation study [13] which is C3D4 (Continuum 3-dimensional 4-noded solid linear tetrahedron). Finer mesh size improves accuracy but demands higher computational resources, thus the model is meshed by tetrahedron elements. For consistency purposes, both implicit and explicit Lagrangian simulations are meshed with 1 mm elements while reducing the gauge element size to 0.5 mm (section shown in Fig. 2(c)).
<figure><img src="image_149.png" /><figcaption>Figure 4: Simulation mesh sensitivity study</figcaption></figure>

## Lagrangian formulation

The first step of this study consists of replicating the findings of the experimental validation study by Garg et al. [13], this was achieved by replicating the available simulation parameters. The FE simulations are conducted with ABAQUS/Standard, then with ABAQUS/Explicit for the same material model created with the same material parameters as the reference paper [13]. The output database results of the two simulations are then extracted by selecting multiple nodes in the necking region and comparing results to the validation paper. Simulated results are subsequently validated and compared with the experimental observations from Garg et al. [13].

<figure><img src="image_150.png" /><figcaption>Figure 5: Deformed mesh results comparison between implicit (a), explicit simulation (b) both showing Von Mises equivalent stress and resulting stress/strain compared with Garg et al. [13].</figcaption></figure>

Initial mesh deformation analysis shown in Fig. 5 demonstrates good agreement between the implicit, explicit, and validation paper results.

The initial results show good agreement between implicit and explicit simulation results with the experimental validation paper while the material is exhibiting elastic properties, then briefly diverges as material behavior transitions into plastic deformation before converging again for the rest of the curve. This discrepancy between the results could be due to the input properties of the models being slightly different, as the ABS material parameters were obtained utilizing Optical Character Recognition (OCR) software and not a numerical database. The difference could also be due to any of the missing study parameters in the reference [13] such as mesh parameters, deformation rate or loading parameters.

For explicit solvers, the computational cost of a single increment is expectedly low. However, it is necessary to maintain a low time increment since the solution could become unstable as error margins increase rapidly. The largest viable time increment is calculated by ABAQUS/explicit
<figure><img src="image_147.png" /><figcaption>Figure 4: Simulation mesh sensitivity study</figcaption></figure>

## Lagrangian formulation

The first step of this study consists of replicating the findings of the experimental validation study by Garg et al. [13], this was achieved by replicating the available simulation parameters. The FE simulations are conducted with ABAQUS/Standard, then with ABAQUS/Explicit for the same material model created with the same material parameters as the reference paper [13]. The output database results of the two simulations are then extracted by selecting multiple nodes in the necking region and comparing results to the validation paper. Simulated results are subsequently validated and compared with the experimental observations from Garg et al. [13].

<figure><img src="image_148.png" /><figcaption>Figure 5: Deformed mesh results comparison between implicit (a), explicit simulation (b) both showing Von Mises equivalent stress and resulting stress/strain compared with Garg et al. [13].</figcaption></figure>

Initial mesh deformation analysis shown in Fig. 5 demonstrates good agreement between the implicit, explicit, and validation paper results.

The initial results show good agreement between implicit and explicit simulation results with the experimental validation paper while the material is exhibiting elastic properties, then briefly diverges as material behavior transitions into plastic deformation before converging again for the rest of the curve. This discrepancy between the results could be due to the input properties of the models being slightly different, as the ABS material parameters were obtained utilizing Optical Character Recognition (OCR) software and not a numerical database. The difference could also be due to any of the missing study parameters in the reference [13] such as mesh parameters, deformation rate or loading parameters.

For explicit solvers, the computational cost of a single increment is expectedly low. However, it is necessary to maintain a low time increment since the solution could become unstable as error margins increase rapidly. The largest viable time increment is calculated by ABAQUS/explicit
when mass scaling is not in use, is called a stable time increment (STI). On the other hand, the computational cost of implicit increments is significantly larger, If the system proves to be nonlinear, the solution needs to be calculated multiple times per increment. Thus, the more nonlinear a problem is, the more computationally expensive it is to converge on a valid solution.

A comparison of computation time is established in Table 1, showing an efficiency discrepancy between the implicit and explicit solver for this type of problem. Even when no mass scaling is in use to reduce computation time, explicit models prove to be more computationally efficient. An Intel Core i7-12650H was used for all simulations, with the advent of GPU acceleration being only available for the implicit solver where a GeForce RTX 3070M aids in reducing computation time.

<table><caption>Table 1: Computation time comparison between the implicit and explicit solvers</caption><thead><tr><td>Solver type</td><td>Parallelization</td><td>Mesh element type</td><td>computation time</td><td>Max principal stress (MPa)</td></tr></thead><tbody><tr><td>Implicit</td><td>8-core CPU</td><td>C3D4</td><td>27 hrs 44 min 32 sec</td><td>39.19</td></tr><tr><td>Implicit</td><td>CUDA GPU</td><td>C3D4</td><td>8 hrs 27 min 38 sec</td><td>39.19</td></tr><tr><td>Implicit</td><td>8-core CPU/GPU</td><td>C3D4</td><td>6 hrs 9 min 15 sec</td><td>39.19</td></tr><tr><td>Implicit</td><td>8-core CPU/GPU</td><td>C3D8</td><td>5 hrs 32 min 34 sec</td><td>39.19</td></tr><tr><td>Explicit</td><td>8-core CPU</td><td>C3D4</td><td>7 hrs 17 min 31 sec</td><td>39.72</td></tr><tr><td>Explicit</td><td>8-core CPU</td><td>C3D8</td><td>4 hrs 5 min 7 sec</td><td>39.72</td></tr></tbody></table>

As prior mentioned, further reduction in computational costs can be achieved by utilizing mass scaling, which increases the material density while keeping resulting calculations unaffected. A study was conducted with the goal of further reducing computational time by testing various STIs, the resulting plastic deformation section (see Fig. 3(a)) of the stress strain curves obtained from each simulation are shown in Fig. 6 since results perfectly coincided during elastic deformation. Results of computation time are shown in Table 2.

<figure><img src="image_151.png" /><figcaption>Figure 6: Mass scaling sensitivity study</figcaption></figure>

When no mass scaling is in use, the STI calculated by ABAQUS/explicit hovers around $10^{-7}$s. This value explains why defining a target time increment (TTI) of a similar magnitude creates perfectly coinciding graphs, as can be seen in Fig. 6. Once the defined TTI value differs greatly from the default STI value, deviations in the resulting stress strain curve occur. A simple explanation to this increasing deviation is that as we increase the TTI, ABAQUS begins to modify the density of more and more mesh elements which now have a smaller STI, resulting in a material
when mass scaling is not in use, is called a stable time increment (STI). On the other hand, the computational cost of implicit increments is significantly larger, If the system proves to be nonlinear, the solution needs to be calculated multiple times per increment. Thus, the more nonlinear a problem is, the more computationally expensive it is to converge on a valid solution.

A comparison of computation time is established in Table 1, showing an efficiency discrepancy between the implicit and explicit solver for this type of problem. Even when no mass scaling is in use to reduce computation time, explicit models prove to be more computationally efficient. An Intel Core i7-12650H was used for all simulations, with the advent of GPU acceleration being only available for the implicit solver where a GeForce RTX 3070M aids in reducing computation time.

<table><caption>Table 1: Computation time comparison between the implicit and explicit solvers</caption><thead><tr><td>Solver type</td><td>Parallelization</td><td>Mesh element type</td><td>computation time</td><td>Max principal stress (MPa)</td></tr></thead><tbody><tr><td>Implicit</td><td>8-core CPU</td><td>C3D4</td><td>27 hrs 44 min 32 sec</td><td>39.19</td></tr><tr><td>Implicit</td><td>CUDA GPU</td><td>C3D4</td><td>8 hrs 27 min 38 sec</td><td>39.19</td></tr><tr><td>Implicit</td><td>8-core CPU/GPU</td><td>C3D4</td><td>6 hrs 9 min 15 sec</td><td>39.19</td></tr><tr><td>Implicit</td><td>8-core CPU/GPU</td><td>C3D8</td><td>5 hrs 32 min 34 sec</td><td>39.19</td></tr><tr><td>Explicit</td><td>8-core CPU</td><td>C3D4</td><td>7 hrs 17 min 31 sec</td><td>39.72</td></tr><tr><td>Explicit</td><td>8-core CPU</td><td>C3D8</td><td>4 hrs 5 min 7 sec</td><td>39.72</td></tr></tbody></table>

As prior mentioned, further reduction in computational costs can be achieved by utilizing mass scaling, which increases the material density while keeping resulting calculations unaffected. A study was conducted with the goal of further reducing computational time by testing various STIs, the resulting plastic deformation section (see Fig. 3(a)) of the stress strain curves obtained from each simulation are shown in Fig. 6 since results perfectly coincided during elastic deformation. Results of computation time are shown in Table 2.

<figure><img src="image_149.png" /><figcaption>Figure 6: Mass scaling sensitivity study</figcaption></figure>

When no mass scaling is in use, the STI calculated by ABAQUS/explicit hovers around $10^{-7}$s. This value explains why defining a target time increment (TTI) of a similar magnitude creates perfectly coinciding graphs, as can be seen in Fig. 6. Once the defined TTI value differs greatly from the default STI value, deviations in the resulting stress strain curve occur. A simple explanation to this increasing deviation is that as we increase the TTI, ABAQUS begins to modify the density of more and more mesh elements which now have a smaller STI, resulting in a material
model that contradicts the physical nature of the material. Another issue that could arise from increasing the TTI is unstable solutions, which induces spurious variations in the resulting properties of the model, an example of this is seen in the stress strain curve (4) in Fig. 6 where the stress value oscillates sporadically around the stable value of no mass scaling.

Table 2 summarizes the time of analysis at the which utilized 8 cores of the processor Intel i7-12650H for all simulations. It can be observed that the increase in target time increment results in an increase of the percent of mass increased (m%).

<table><caption>Table 2: Resulting processing time of each mass scaling simulation</caption><thead><tr><td>Target time increment (s)</td><td>CPU time</td><td>m (%)</td></tr></thead><tbody><tr><td>1e-7</td><td>7 hrs 2 min 31 sec</td><td>0.121</td></tr><tr><td>1e-6</td><td>4 hrs 33 min 16 sec</td><td>2.874</td></tr><tr><td>1e-5</td><td>0 hrs 3 min 38 sec</td><td>10.183</td></tr><tr><td>1e-4</td><td>0 hrs 0 min 31 sec</td><td>23.784</td></tr><tr><td>1e-3</td><td>0 hrs 0 min 15 sec</td><td>38.742</td></tr></tbody></table>

Due to the addition of non-physical mass that has a proven impact on the accuracy of our study, the energy balance is to be studied. The kinetic energy should not exceed 5% of internal energy [18]. Fig. 7 demonstrates two examples of performed simulations, the first highlighting the energy output of the TTI=1e-6s which passes the 5% kinetic energy/Internal energy ratio rule, while the second of TTI=1e-4s fails to meet the criteria.

<figure><img src="image_152.png" /><figcaption>Figure 7: Differences of internal energy and kinetic energy at TTI=1e-6 (a) and TTI=1e-4 (b)</figcaption></figure>

## Arbitrary Lagrangian Eulerian formulation

Similar to the previous section, two FE simulations are conducted with ABAQUS/Standard then the same is done with ABAQUS/Explicit for the same material model created with the same material parameters as the paper. The output database results are then extracted from the necking region and compared to previous results utilizing the Lagrangian formulation. The simulated results are subsequently validated and compared with the experimental observations from Garg et al. [13] as previously done.
model that contradicts the physical nature of the material. Another issue that could arise from increasing the TTI is unstable solutions, which induces spurious variations in the resulting properties of the model, an example of this is seen in the stress strain curve (4) in Fig. 6 where the stress value oscillates sporadically around the stable value of no mass scaling.

Table 2 summarizes the time of analysis at the which utilized 8 cores of the processor Intel i7-12650H for all simulations. It can be observed that the increase in target time increment results in an increase of the percent of mass increased (m%).

<table><caption>Table 2: Resulting processing time of each mass scaling simulation</caption><thead><tr><td>Target time increment (s)</td><td>CPU time</td><td>m (%)</td></tr></thead><tbody><tr><td>1e-7</td><td>7 hrs 2 min 31 sec</td><td>0.121</td></tr><tr><td>1e-6</td><td>4 hrs 33 min 16 sec</td><td>2.874</td></tr><tr><td>1e-5</td><td>0 hrs 3 min 38 sec</td><td>10.183</td></tr><tr><td>1e-4</td><td>0 hrs 0 min 31 sec</td><td>23.784</td></tr><tr><td>1e-3</td><td>0 hrs 0 min 15 sec</td><td>38.742</td></tr></tbody></table>

Due to the addition of non-physical mass that has a proven impact on the accuracy of our study, the energy balance is to be studied. The kinetic energy should not exceed 5% of internal energy [18]. Fig. 7 demonstrates two examples of performed simulations, the first highlighting the energy output of the TTI=1e-6s which passes the 5% kinetic energy/Internal energy ratio rule, while the second of TTI=1e-4s fails to meet the criteria.

<figure><img src="image_150.png" /><figcaption>Figure 7: Differences of internal energy and kinetic energy at TTI=1e-6 (a) and TTI=1e-4 (b)</figcaption></figure>

## Arbitrary Lagrangian Eulerian formulation

Similar to the previous section, two FE simulations are conducted with ABAQUS/Standard then the same is done with ABAQUS/Explicit for the same material model created with the same material parameters as the paper. The output database results are then extracted from the necking region and compared to previous results utilizing the Lagrangian formulation. The simulated results are subsequently validated and compared with the experimental observations from Garg et al. [13] as previously done.
<figure><img src="image_153.png" /><figcaption>Figure 8: Deformed mesh results comparison between Lagrangian explicit simulation (a), ALE explicit simulation (b), Lagrangian implicit simulation (c), and ALE implicit simulation (d) all showing Von Mises equivalent stress distribution and resulting stress/strain curve.</figcaption></figure>

Analysis shown in Fig. 8 demonstrates good agreement between the implicit, explicit, and validation paper results. The mesh element type utilized for results comparison Lagrangian explicit and ALE explicit was modified to C3D8 (8-node linear brick) to match the Lagrangian implicit and ALE implicit mesh type, this was done due to the ABAQUS solver limitations which only allows ALE formulations on a limited selection of element types within ABAQUS/standard. A mesh sensitivity study was performed for this element type and an appropriate mesh size was selected in accordance with it (1 mm element size with 0.5 mm elements for the gauge section).

A similar comparison of computation time is established in Table 3, showing an expected efficiency discrepancy between the Lagrangian and ALE algorithms for both implicit and explicit solutions.

<table><caption>Table 3: Computation time comparison between the implicit Lagrangian and implicit ALE then between explicit Lagrangian and explicit ALE (Explicit Lagrangian taken as reference study)</caption><thead><tr><th>Solver type</th><th>Formulation</th><th>Mass scaling</th><th>Parallelization</th><th>computation time (s)</th><th>Max principal stress (MPa)</th></tr></thead><tbody><tr><td>Implicit</td><td>Lagrangian</td><td></td><td>8-core CPU/GPU</td><td>+32.00% time</td><td>39.19</td></tr><tr><td>Implicit</td><td>ALE</td><td></td><td>8-core CPU/GPU</td><td>+228.18% time</td><td>38.41</td></tr><tr><td>Explicit</td><td>Lagrangian</td><td>None</td><td>8-core CPU</td><td>4 hrs 5 min 7 sec</td><td>39.72</td></tr><tr><td>Explicit</td><td>Lagrangian</td><td>1e-6s TTI</td><td>8-core CPU</td><td>-46.11% time</td><td>39.53</td></tr><tr><td>Explicit</td><td>ALE</td><td>None</td><td>8-core CPU</td><td>+68.23% time</td><td>38.74</td></tr><tr><td>Explicit</td><td>ALE</td><td>1e-6s TTI</td><td>8-core CPU</td><td>+7.09% time</td><td>38.68</td></tr></tbody></table>

The ALE formulation fails to provide a clear advantage in comparison with the Lagrangian models, after rigorous testing. Rather than demonstrating a positive outcome, ALE models raised concerns about computational efficiency without positive outcomes to match. Problems encountered with convergence time make the ALE formulation ineffective, thus questioning its application validity in this type of problem. The shortcomings of the ALE formulation in terms of convergence time compared to the Lagrangian method can be explained by the added advection step. The lack of a significant difference in results on the other hand can be explained by the low
<figure><img src="image_151.png" /><figcaption>Figure 8: Deformed mesh results comparison between Lagrangian explicit simulation (a), ALE explicit simulation (b), Lagrangian implicit simulation (c), and ALE implicit simulation (d) all showing Von Mises equivalent stress distribution and resulting stress/strain curve.</figcaption></figure>

Analysis shown in Fig. 8 demonstrates good agreement between the implicit, explicit, and validation paper results. The mesh element type utilized for results comparison Lagrangian explicit and ALE explicit was modified to C3D8 (8-node linear brick) to match the Lagrangian implicit and ALE implicit mesh type, this was done due to the ABAQUS solver limitations which only allows ALE formulations on a limited selection of element types within ABAQUS/standard. A mesh sensitivity study was performed for this element type and an appropriate mesh size was selected in accordance with it (1 mm element size with 0.5 mm elements for the gauge section).

A similar comparison of computation time is established in Table 3, showing an expected efficiency discrepancy between the Lagrangian and ALE algorithms for both implicit and explicit solutions.

<table><caption>Table 3: Computation time comparison between the implicit Lagrangian and implicit ALE then between explicit Lagrangian and explicit ALE (Explicit Lagrangian taken as reference study)</caption><thead><tr><th>Solver type</th><th>Formulation</th><th>Mass scaling</th><th>Parallelization</th><th>computation time (s)</th><th>Max principal stress (MPa)</th></tr></thead><tbody><tr><td>Implicit</td><td>Lagrangian</td><td></td><td>8-core CPU/GPU</td><td>+32.00% time</td><td>39.19</td></tr><tr><td>Implicit</td><td>ALE</td><td></td><td>8-core CPU/GPU</td><td>+228.18% time</td><td>38.41</td></tr><tr><td>Explicit</td><td>Lagrangian</td><td>None</td><td>8-core CPU</td><td>4 hrs 5 min 7 sec</td><td>39.72</td></tr><tr><td>Explicit</td><td>Lagrangian</td><td>1e-6s TTI</td><td>8-core CPU</td><td>-46.11% time</td><td>39.53</td></tr><tr><td>Explicit</td><td>ALE</td><td>None</td><td>8-core CPU</td><td>+68.23% time</td><td>38.74</td></tr><tr><td>Explicit</td><td>ALE</td><td>1e-6s TTI</td><td>8-core CPU</td><td>+7.09% time</td><td>38.68</td></tr></tbody></table>

The ALE formulation fails to provide a clear advantage in comparison with the Lagrangian models, after rigorous testing. Rather than demonstrating a positive outcome, ALE models raised concerns about computational efficiency without positive outcomes to match. Problems encountered with convergence time make the ALE formulation ineffective, thus questioning its application validity in this type of problem. The shortcomings of the ALE formulation in terms of convergence time compared to the Lagrangian method can be explained by the added advection step. The lack of a significant difference in results on the other hand can be explained by the low
deformation that the mesh exhibits, which makes utilizing the ALE formulation that is most
effective with high deformation problems counterproductive.

Conclusions

Within this study, a series of comparisons were performed between the results and performance of implicit and explicit solvers utilized for analyzing AM ASTM D638 samples under uniaxial tensile loading. Such comparison should be of high interest to researchers modeling FE studies of AM parts, as it provides a guideline to selecting an optimal solver while verifying correct results using these different solving algorithms. Initial results highlight that stress-strain results from both solvers are near identical. This proves that either of the solvers can be effectively utilized, depending on simulation parameters. The explicit solver performed faster than the implicit solver on the same hardware, but the implicit solver presents the option to utilize GPU acceleration, which significantly lessens the gap in computation time. When mass scaling and load-rate-increase assumptions were used, the gap in computational efficiency widens anew, with the explicit model performing significantly faster than implicit.

A standard energy balance study was performed to assess the validity of the simulations when utilizing mass scaling to reduce computation costs. Based on the series of explicit dynamic studies at various mass scaling values, the results of the energy balance study shows that target time increments TTI=1e-6s is an appropriate value to significantly reduce analysis time.

Finally, a series of simulations based on the ALE formulation were proposed to numerically simulate the deformation of the specimens. ALE and classical Lagrangian simulations had to be successfully carried out with a new mesh element type C3D8 due to ABAQUS/standard limitations that allows ALE formulations on a limited selection of element types. Although the considered ALE model does not present any result improvement with neither the implicit nor explicit solvers and cannot achieve a comparable CPU time savings to the Lagrangian one, this is due to the ALE formulation's usefulness in high deformation studies, which this particular problem of tensile loading does not generally possess.

Perspectives

While the ALE formulation does not present any clear advantages when it comes to FE simulations of tensile testing AM specimen during plastic deformation. Further investigation needs to be conducted on the benefits of carrying it on models continuing until material fracture, as the specimen often exhibit extreme deformations right before when fracture occurs. Utilizing the ALE formulation could help provide more accurate fracture behavior predictions for AM parts under uniaxial tensile loading.

Acknowledgements

The authors would like to thank Région Wallonne for supporting this research as part of the SKYWIN ICOM2C3D research project under grant 8820.

References

[1] Terry T Wohlers and Tim Caffrey. Wohlers report 2015: 3d printing and additive manufacturing state of the industry annual worldwide progress report. 2015.

[2] Babak Kianian. Wohlers report 2019: 3d printing and additive manufacturing state of the industry, annual worldwide progress report. 2019.

[3] Bhrigu Ahuja, Michael Karg, and Michael Schmidt. Additive manufacturing in production: challenges and opportunities. Laser 3d manufacturing II, 9353: 11–20. https://doi.org/10.1117/12.2082521
deformation that the mesh exhibits, which makes utilizing the ALE formulation that is most
effective with high deformation problems counterproductive.

Conclusions

Within this study, a series of comparisons were performed between the results and performance of implicit and explicit solvers utilized for analyzing AM ASTM D638 samples under uniaxial tensile loading. Such comparison should be of high interest to researchers modeling FE studies of AM parts, as it provides a guideline to selecting an optimal solver while verifying correct results using these different solving algorithms. Initial results highlight that stress-strain results from both solvers are near identical. This proves that either of the solvers can be effectively utilized, depending on simulation parameters. The explicit solver performed faster than the implicit solver on the same hardware, but the implicit solver presents the option to utilize GPU acceleration, which significantly lessens the gap in computation time. When mass scaling and load-rate-increase assumptions were used, the gap in computational efficiency widens anew, with the explicit model performing significantly faster than implicit.

A standard energy balance study was performed to assess the validity of the simulations when utilizing mass scaling to reduce computation costs. Based on the series of explicit dynamic studies at various mass scaling values, the results of the energy balance study shows that target time increments TTI=1e-6s is an appropriate value to significantly reduce analysis time.

Finally, a series of simulations based on the ALE formulation were proposed to numerically simulate the deformation of the specimens. ALE and classical Lagrangian simulations had to be successfully carried out with a new mesh element type C3D8 due to ABAQUS/standard limitations that allows ALE formulations on a limited selection of element types. Although the considered ALE model does not present any result improvement with neither the implicit nor explicit solvers and cannot achieve a comparable CPU time savings to the Lagrangian one, this is due to the ALE formulation's usefulness in high deformation studies, which this particular problem of tensile loading does not generally possess.

Perspectives

While the ALE formulation does not present any clear advantages when it comes to FE simulations of tensile testing AM specimen during plastic deformation. Further investigation needs to be conducted on the benefits of carrying it on models continuing until material fracture, as the specimen often exhibit extreme deformations right before when fracture occurs. Utilizing the ALE formulation could help provide more accurate fracture behavior predictions for AM parts under uniaxial tensile loading.

Acknowledgements

The authors would like to thank Région Wallonne for supporting this research as part of the SKYWIN ICOM2C3D research project under grant 8820.

References

[1] Terry T Wohlers and Tim Caffrey. Wohlers report 2015: 3d printing and additive manufacturing state of the industry annual worldwide progress report. 2015.

[2] Babak Kianian. Wohlers report 2019: 3d printing and additive manufacturing state of the industry, annual worldwide progress report. 2019.

[3] Bhrigu Ahuja, Michael Karg, and Michael Schmidt. Additive manufacturing in production: challenges and opportunities. Laser 3d manufacturing II, 9353: 11–20. https://doi.org/10.1117/12.2082521
[4] Ben Terrell. Faster FEA improves productivity and saves tens of thousands of dollars. Read on https://resources.sw.siemens.com/en-US/case-study-aquila-engineering the 6th of December 2023.

[5] Vidya Kishore and Ahmed Arabi Hassen. Polymer and composites additive manufacturing: material extrusion processes. In Additive Manufacturing, pages 183–216. 2021. https://doi.org/10.1016/B978-0-12-818411-0-00021-5

[6] Chua Chee Kai. Three-dimensional rapid prototyping technologies and key development areas. Computing & Control Engineering Journal, 5(4):200–206, 1994. https://doi.org/10.1049/cce:19940407

[7] Nicholas A Conzelmann, Lovro Gorjan, Fateme Sarraf, Lily D Poulikakos, Manfred N Partl, Christoph R Müller, and Frank J Clemens. Manufacturing complex Al2O3 ceramic structures using consumer-grade fused deposition modelling printers. Rapid Prototyping Journal, 26(6):1035–1048. https://doi.org/10.1108/RPJ-05-2019-0133

[8] Kai CC. Three-dimensional rapid prototyping technologies and key development areas. Computing & Control Engineering Journal. 1994 Aug 1;5(4):200-6.

[9] MS Khan and JP Dash. Enhancing surface finish of fused deposition modelling parts. 3D printing and additive manufacturing technologies, pages 45–57, 2019. https://doi.org/10.1007/978-981-13-0305-0 5

[10] Ian Gibson. Additive manufacturing technologies 3d printing, rapid prototyping, and direct digital manufacturing. 2015. https://doi.org/10.1007/978-1-4939-2113-3 21

[11] ASTM D638-14, “Standard Test Method for Tensile Properties of Plastics”, American Society for Testing and Materials. https://doi.org/10.1520/D0638-14

[12] Xiaoqing Wang and Kevin Chou. Microstructure simulations of inconel 718 during selective laser melting using a phase field model. The International Journal of Advanced Manufacturing Technology, 100:2147–2162, 2019. https://doi.org/10.1007/s00170-018-2814-z

[13] Ashu Garg and Anirban Bhattacharya. An insight to the failure of fdm parts under tensile loading: finite element analysis and experimental study. International Journal of Mechanical Sciences, 120:225–236, 2017. https://doi.org/10.1016/j.ijmecsci.2016.11.032.

[14] Olivier Pantalé, J-L Bacaria, Olivier Dalverny, Roger Rakotomalala, and Serge Caperaa. 2d and 3d numerical models of metal cutting with damage effects. Computer methods in applied mechanics and engineering, 193(39-41):4383–4399, 2004. https://doi.org/10.1016/j.cma.2003.12.062

[15] Pedro Jose Arrazola, Tugrul Ozel, Domenico Umbrello, M Davies, and Ibrahim S Jawahir. Recent advances in modelling of metal machining processes. Cirp Annals, 62(2):695–718, 2013. https://doi.org/10.1016/j.cirp.2013.05.006

[16] Schmailzl Anton, Amann Thomas, Glockner Markus, and Fadanelli Martin. Finite element analysis of thermoplastic probes under tensile load using Is- dyna compared to ansys wb 14 in correlation to experimental investigations. In Proceedings of the ANSYS conference & 30th CADFEM users' meeting, 2012.

[17] RHW Ten Thije, and Remko Akkerman. Large deformation simulation of anisotropic material using an updated Lagrangian finite element method. Computer methods in applied mechanics and engineering, 196(33-34):3141–3150,2007. https://doi.org/10.1016/j.cma.2007.02.010

[18] Min W, He Y, Sun ZC, Guo LG, Ou XZ. Dynamic explicit FE modeling of hot ring rolling process. Transactions of Nonferrous Metals Society of China. 2006 Dec 1;16(6):1274-80.
[4] Ben Terrell. Faster FEA improves productivity and saves tens of thousands of dollars. Read on https://resources.sw.siemens.com/en-US/case-study-aquila-engineering the 6th of December 2023.

[5] Vidya Kishore and Ahmed Arabi Hassen. Polymer and composites additive manufacturing: material extrusion processes. In Additive Manufacturing, pages 183–216. 2021. https://doi.org/10.1016/B978-0-12-818411-0-00021-5

[6] Chua Chee Kai. Three-dimensional rapid prototyping technologies and key development areas. Computing & Control Engineering Journal, 5(4):200–206, 1994. https://doi.org/10.1049/cce:19940407

[7] Nicholas A Conzelmann, Lovro Gorjan, Fateme Sarraf, Lily D Poulikakos, Manfred N Partl, Christoph R Müller, and Frank J Clemens. Manufacturing complex Al2O3 ceramic structures using consumer-grade fused deposition modelling printers. Rapid Prototyping Journal, 26(6):1035–1048. https://doi.org/10.1108/RPJ-05-2019-0133

[8] Kai CC. Three-dimensional rapid prototyping technologies and key development areas. Computing & Control Engineering Journal. 1994 Aug 1;5(4):200-6.

[9] MS Khan and JP Dash. Enhancing surface finish of fused deposition modelling parts. 3D printing and additive manufacturing technologies, pages 45–57, 2019. https://doi.org/10.1007/978-981-13-0305-0 5

[10] Ian Gibson. Additive manufacturing technologies 3d printing, rapid prototyping, and direct digital manufacturing. 2015. https://doi.org/10.1007/978-1-4939-2113-3 21

[11] ASTM D638-14, “Standard Test Method for Tensile Properties of Plastics”, American Society for Testing and Materials. https://doi.org/10.1520/D0638-14

[12] Xiaoqing Wang and Kevin Chou. Microstructure simulations of inconel 718 during selective laser melting using a phase field model. The International Journal of Advanced Manufacturing Technology, 100:2147–2162, 2019. https://doi.org/10.1007/s00170-018-2814-z

[13] Ashu Garg and Anirban Bhattacharya. An insight to the failure of fdm parts under tensile loading: finite element analysis and experimental study. International Journal of Mechanical Sciences, 120:225–236, 2017. https://doi.org/10.1016/j.ijmecsci.2016.11.032.

[14] Olivier Pantalé, J-L Bacaria, Olivier Dalverny, Roger Rakotomalala, and Serge Caperaa. 2d and 3d numerical models of metal cutting with damage effects. Computer methods in applied mechanics and engineering, 193(39-41):4383–4399, 2004. https://doi.org/10.1016/j.cma.2003.12.062

[15] Pedro Jose Arrazola, Tugrul Ozel, Domenico Umbrello, M Davies, and Ibrahim S Jawahir. Recent advances in modelling of metal machining processes. Cirp Annals, 62(2):695–718, 2013. https://doi.org/10.1016/j.cirp.2013.05.006

[16] Schmailzl Anton, Amann Thomas, Glockner Markus, and Fadanelli Martin. Finite element analysis of thermoplastic probes under tensile load using Is- dyna compared to ansys wb 14 in correlation to experimental investigations. In Proceedings of the ANSYS conference & 30th CADFEM users' meeting, 2012.

[17] RHW Ten Thije, and Remko Akkerman. Large deformation simulation of anisotropic material using an updated Lagrangian finite element method. Computer methods in applied mechanics and engineering, 196(33-34):3141–3150,2007. https://doi.org/10.1016/j.cma.2007.02.010

[18] Min W, He Y, Sun ZC, Guo LG, Ou XZ. Dynamic explicit FE modeling of hot ring rolling process. Transactions of Nonferrous Metals Society of China. 2006 Dec 1;16(6):1274-80.
# Processability of aluminum-matrix composite (AMC) by ultrasonic powder atomization

JEDYNAK Angelika¹,ª*, HÄRTEL Sebastian¹,ᵇ, PIPPIG Robert²,ᶜ and CHOMA Tomasz³,ᵈ

¹Chair of Hybrid Manufacturing, Brandenburg University of Technology Cottbus - Senftenberg, Konrad - Wachsmann - Allee 17, D-03046 Cottbus, Germany

²CMMC GmbH, Emilienstrasse 45, D-09131 Chemnitz, Germany

³AMAZEMET | Warsaw University of Technology, 27 Jana Pawla II, PL-00-867 Warsaw, Poland

ªangelika.jedynak@b-tu.de, ᵇsebastian.haertel@b-tu.de,

ᶜrobert.pippig@cmmc-engineering.com, ᵈtomasz.choma@amazemet.com

**Keywords:** Additive Manufacturing, Aluminum-Matrix Composite Powder, Ultrasonic Atomization

**Abstract.** This research presents a comprehensive study on the production of aluminum-matrix composite (AMC) powders using ultrasonic atomization for additive manufacturing (AM). The impact of different heat sources—plasma, arc, and induction melting—was evaluated on the processability and resultant properties of the AMC powders, including morphology, size, and composite structure. Additionally, induction melting was considered in terms of process parameters such as pressure difference, nozzle size, and frequency. The analysis of AMC powder processability revealed that the efficiency of the ultrasonic process depended on the selected heat source. The highest efficiency, nearly 50%, was attained with the induction system. All produced AMC powders exhibited high sphericity, with average sizes ranging from 88.2 to 120 µm. However, the desired composite structure was not achieved under tested conditions due to the decrease in SiC particle content from 20% in the feed material to approximately 3.5% in the final AMC powder. Based on these results, the research highlights the potential and limitations of ultrasonic atomization in AMC powder production, emphasizing the need for further optimization to improve powder quality and process efficiency for broader industrial application in AM.

**Introduction**

In recent years, the processing of aluminum-matrix composites (AMCs) using additive manufacturing (AM) technology has attracted attention. This is due to its capability to produce highly complex AMC components without the need for tooling and the time-consuming machining required by conventional processes such as casting. However, the available technologies for producing feedstock materials from AMCs for AM still do not ensure their appropriate properties, thus limiting the adaptation of AM for this group of materials on an industrial scale [1,2]. For AMC powders utilized as feedstock materials, achieving a composite structure with a uniform distribution and the desired content of reinforcing particles in the alloy matrix is a critical property for obtaining high mechanical parameters in the final AM components [3,4]. The most common production methods of AMC powders such as gas atomization show that process difficulties in providing the composite structure described above arise already during the melting of the initial material before atomization. For example, these difficulties include the dissolution of reinforcing particles or insufficient homogenization [5]. Overcoming these challenges necessitates the development of alternative technologies to produce AMC powders.

Ultrasonic powder atomization has emerged as a cutting-edge technique for generating a variety of metal powders with exceptional spherical properties on a laboratory scale. This method

<figure><img src="image_154.png" /></figure>
# Processability of aluminum-matrix composite (AMC) by ultrasonic powder atomization

JEDYNAK Angelika<fnref n="1" />,ª*, HÄRTEL Sebastian<fnref n="1" />,ᵇ, PIPPIG Robert<fnref n="2" />,ᶜ and CHOMA Tomasz<fnref n="3" />,ᵈ

**Keywords:** Additive Manufacturing, Aluminum-Matrix Composite Powder, Ultrasonic Atomization

**Abstract.** This research presents a comprehensive study on the production of aluminum-matrix composite (AMC) powders using ultrasonic atomization for additive manufacturing (AM). The impact of different heat sources—plasma, arc, and induction melting—was evaluated on the processability and resultant properties of the AMC powders, including morphology, size, and composite structure. Additionally, induction melting was considered in terms of process parameters such as pressure difference, nozzle size, and frequency. The analysis of AMC powder processability revealed that the efficiency of the ultrasonic process depended on the selected heat source. The highest efficiency, nearly 50%, was attained with the induction system. All produced AMC powders exhibited high sphericity, with average sizes ranging from 88.2 to 120 µm. However, the desired composite structure was not achieved under tested conditions due to the decrease in SiC particle content from 20% in the feed material to approximately 3.5% in the final AMC powder. Based on these results, the research highlights the potential and limitations of ultrasonic atomization in AMC powder production, emphasizing the need for further optimization to improve powder quality and process efficiency for broader industrial application in AM.

**Introduction**

In recent years, the processing of aluminum-matrix composites (AMCs) using additive manufacturing (AM) technology has attracted attention. This is due to its capability to produce highly complex AMC components without the need for tooling and the time-consuming machining required by conventional processes such as casting. However, the available technologies for producing feedstock materials from AMCs for AM still do not ensure their appropriate properties, thus limiting the adaptation of AM for this group of materials on an industrial scale [1,2]. For AMC powders utilized as feedstock materials, achieving a composite structure with a uniform distribution and the desired content of reinforcing particles in the alloy matrix is a critical property for obtaining high mechanical parameters in the final AM components [3,4]. The most common production methods of AMC powders such as gas atomization show that process difficulties in providing the composite structure described above arise already during the melting of the initial material before atomization. For example, these difficulties include the dissolution of reinforcing particles or insufficient homogenization [5]. Overcoming these challenges necessitates the development of alternative technologies to produce AMC powders.

Ultrasonic powder atomization has emerged as a cutting-edge technique for generating a variety of metal powders with exceptional spherical properties on a laboratory scale. This method

<figure><img src="image_152.png" /></figure>

<footnote n="1">¹Chair of Hybrid Manufacturing, Brandenburg University of Technology Cottbus - Senftenberg, Konrad - Wachsmann - Allee 17, D-03046 Cottbus, Germany</footnote>

<footnote n="2">²CMMC GmbH, Emilienstrasse 45, D-09131 Chemnitz, Germany</footnote>

<footnote n="3">³AMAZEMET | Warsaw University of Technology, 27 Jana Pawla II, PL-00-867 Warsaw, Poland</footnote>

<footnote>ªangelika.jedynak@b-tu.de, ᵇsebastian.haertel@b-tu.de,</footnote>

<footnote>ᶜrobert.pippig@cmmc-engineering.com, ᵈtomasz.choma@amazemet.com</footnote>
harnesses ultrasonic vibrations to disintegrate molten metal, resulting in the formation of fine droplets of metal or metal alloy. These droplets then solidify into finely textured and spherical powder particles. The current configurations of ultrasonic atomizers facilitate the direct melting of the source material through plasma, arc, or induction melting in a crucible [6]. The utilization of heat sources with varying characteristics enables the processing of a wide array of materials. For instance, induction melting aids in mitigating the loss of low-melting elements like magnesium or aluminum. Previous research by the author [7] showcased the applicability of ultrasonic atomization in the production of AMC powder. However, the primary challenge encountered during the atomization process was the partial dissolution of SiC in the aluminum matrix of the AMC powder, due to the high temperatures generated during arc melting. Therefore, the aim of this study is to employ alternative heat sources - plasma and induction melting - to produce AMC powder with desired properties. Additionally, variations in process parameters for induction melting will be investigated.

## Materials and methods

In this study, AMC material made from AlSi9Mg aluminum alloy reinforced with 20 vol% SiC particles was investigated, with an average size of SiC particles at 29.2 µm. This material was fabricated through direct vacuum casting, following the procedure developed by CMMC GmbH [8]. The initial microstructure of AMC material is depicted in Fig. 1. The chemical composition of the AlSi9Mg aluminum alloy matrix is provided in Table 1.

<figure><img src="image_155.png" /><figcaption>Fig. 1: Initial microstructure of AMC material.</figcaption></figure>

<table><caption>Table 1: Chemical composition of AlSi9Mg alloy in [wt.%) according to the EN AC-43300.</caption><thead><tr><th>Si</th><th>Mg</th><th>Fe</th><th>Cu</th><th>Mn</th><th>Zn</th><th>Ti</th><th>Pb</th><th>Al</th><th>Others</th></tr></thead><tbody><tr><td>9.0 - 10.0</td><td>0.25 - 0.45</td><td>&lt;0.19</td><td>&lt;0.05</td><td>&lt;0.1</td><td>&lt;0.07</td><td>&lt;0.15</td><td>&lt;0.03</td><td>Balance</td><td>0.1</td></tr></tbody></table>

<table><caption>Table 2: Ultrasonic atomization process parameters for production of AMC powders.</caption><thead><tr><th>ATZ no.</th><th>Heat source</th><th>Frequency, [kHz]</th><th>Pressure difference, [mbar]</th><th>Nozzle size, [mm]</th></tr></thead><tbody><tr><td>1111</td><td>Arc</td><td>35</td><td>---</td><td>---</td></tr><tr><td>1213</td><td>Plasma</td><td>40</td><td>---</td><td>---</td></tr><tr><td>1203</td><td>Induction*</td><td>40</td><td>500</td><td>1.2</td></tr><tr><td>1197</td><td>Induction*</td><td>60</td><td>500</td><td>1.0</td></tr><tr><td>1192</td><td>Induction*</td><td>60</td><td>300</td><td>1.0</td></tr><tr><td>1195</td><td>Induction*</td><td>60</td><td>300</td><td>1.5</td></tr></tbody></table>

Ultrasonic atomization processes were carried out using two separate systems. Ultrasonic atomization through induction and plasma melting was conducted at AMAZMENT on the

<footnote>* melting in a graphite crucible at a temperature of 1100°C</footnote>
harnesses ultrasonic vibrations to disintegrate molten metal, resulting in the formation of fine droplets of metal or metal alloy. These droplets then solidify into finely textured and spherical powder particles. The current configurations of ultrasonic atomizers facilitate the direct melting of the source material through plasma, arc, or induction melting in a crucible [6]. The utilization of heat sources with varying characteristics enables the processing of a wide array of materials. For instance, induction melting aids in mitigating the loss of low-melting elements like magnesium or aluminum. Previous research by the author [7] showcased the applicability of ultrasonic atomization in the production of AMC powder. However, the primary challenge encountered during the atomization process was the partial dissolution of SiC in the aluminum matrix of the AMC powder, due to the high temperatures generated during arc melting. Therefore, the aim of this study is to employ alternative heat sources - plasma and induction melting - to produce AMC powder with desired properties. Additionally, variations in process parameters for induction melting will be investigated.

## Materials and methods

In this study, AMC material made from AlSi9Mg aluminum alloy reinforced with 20 vol% SiC particles was investigated, with an average size of SiC particles at 29.2 µm. This material was fabricated through direct vacuum casting, following the procedure developed by CMMC GmbH [8]. The initial microstructure of AMC material is depicted in Fig. 1. The chemical composition of the AlSi9Mg aluminum alloy matrix is provided in Table 1.

<figure><img src="image_153.png" /><figcaption>Fig. 1: Initial microstructure of AMC material.</figcaption></figure>

<table><caption>Table 1: Chemical composition of AlSi9Mg alloy in [wt.%) according to the EN AC-43300.</caption><thead><tr><th>Si</th><th>Mg</th><th>Fe</th><th>Cu</th><th>Mn</th><th>Zn</th><th>Ti</th><th>Pb</th><th>Al</th><th>Others</th></tr></thead><tbody><tr><td>9.0 - 10.0</td><td>0.25 - 0.45</td><td>&lt;0.19</td><td>&lt;0.05</td><td>&lt;0.1</td><td>&lt;0.07</td><td>&lt;0.15</td><td>&lt;0.03</td><td>Balance</td><td>0.1</td></tr></tbody></table>

<table><caption>Table 2: Ultrasonic atomization process parameters for production of AMC powders.</caption><thead><tr><th>ATZ no.</th><th>Heat source</th><th>Frequency, [kHz]</th><th>Pressure difference, [mbar]</th><th>Nozzle size, [mm]</th></tr></thead><tbody><tr><td>1111</td><td>Arc</td><td>35</td><td>---</td><td>---</td></tr><tr><td>1213</td><td>Plasma</td><td>40</td><td>---</td><td>---</td></tr><tr><td>1203</td><td>Induction*</td><td>40</td><td>500</td><td>1.2</td></tr><tr><td>1197</td><td>Induction*</td><td>60</td><td>500</td><td>1.0</td></tr><tr><td>1192</td><td>Induction*</td><td>60</td><td>300</td><td>1.0</td></tr><tr><td>1195</td><td>Induction*</td><td>60</td><td>300</td><td>1.5</td></tr></tbody></table>

Ultrasonic atomization processes were carried out using two separate systems. Ultrasonic atomization through induction and plasma melting was conducted at AMAZMENT on the

<footnote>* melting in a graphite crucible at a temperature of 1100°C</footnote>
rePowder system. Ultrasonic atomization using arc melting occurred at 3DLab on the ATOLab+ machine. The process parameters for both systems are detailed in Table 2. Each atomization process was conducted in an atmosphere of pure argon, with an O2 content consistently maintained below 100 ppm. Following the atomization, the powders were sieved with a mesh size under 0.2 mm.

The possibility of processing AMC powder through ultrasonic atomization was determined using the process efficiency values. Process efficiency arises from the correlation between the feedstock material and the quantity of produced powder, according to the equation (1). Based on the documentation prepared during the processes, main process effects were analyzed that could have an impact on the efficiency value.

$$process efficiency [\%] = \frac{\text{quantitiy of produced powder [g]}}{\text{quantitiy of feed material [g]}} * 100 \quad (1)$$

The powder analysis involved scrutinizing the morphology, dimensions, and composite configuration of the atomized AMC powders. Each powder batch was analyzed with approximately one hundred powder particles. To assess powder morphology and particle size, the powder particles were dispersed onto graphite tape and imaged using a scanning electron microscope (SEM) fitted with a Secondary Electron (SE) detector. The SEM SE images were analyzed to determine particle size and morphology using the Xparticle software from Thermo Scientific. Powder morphology was assessed based on the aspect ratio, where an aspect ratio of 1 signifies ideal powder sphericity. The analysis of the composite structure of the powder involved determining the content of SiC particles in the powder particles. This was achieved by embedding the powder particles and grinding them using silicon carbide papers with grit sizes from 600 to 2500. Subsequently, they underwent oxide-polishing (0.05 µm silica solution, Struers OP-S Suspension) using a vibratory polishing machine. The prepared powder samples were imaged with a scanning electron microscope (SEM) equipped with a Back-Scattered Electron (BSE) detector. The content of SiC particles in the powder particles was manually determined using ATLAS Software, employing a method based on color contrast differences.

### Processability of AMC powders.

The efficiency of the ultrasonic atomization process depended on the type of heat source used to melt the initial material (see Fig. 2a). Utilizing induction and plasma enabled the achievement of a relatively high process efficiency exceeding 40%. However, when using an arc as the heat source, the process efficiency was possible only at a level of 15%. In the case of plasma and arc heat sources, based on a similar procedure for melting the feed material, a decrease in process efficiency occurred at the same stage of the process. Instabilities appeared during the melting stage, leading to the detachment of irregular large fragments of material, as illustrated by the example of plasma melting (see Fig. 3). Consequently, this disruption led to interference in surface coverage with molten material on the sonotrode, ultimately resulting in the formation of scrap. Although the material exhibited similar behavior during melting with both heat sources, the efficiency of the process was notably lower when using the arc, at a level of 15%, compared to plasma, which achieved 41%.
rePowder system. Ultrasonic atomization using arc melting occurred at 3D Lab on the ATOLab+ machine. The process parameters for both systems are detailed in Table 2. Each atomization process was conducted in an atmosphere of pure argon, with an O2 content consistently maintained below 100 ppm. Following the atomization, the powders were sieved with a mesh size under 0.2 mm.

The possibility of processing AMC powder through ultrasonic atomization was determined using the process efficiency values. Process efficiency arises from the correlation between the feedstock material and the quantity of produced powder, according to the equation (1). Based on the documentation prepared during the processes, main process effects were analyzed that could have an impact on the efficiency value.

$$process efficiency [\%] = \frac{\text{quantitiy of produced powder [g]}}{\text{quantitiy of feed material [g]}} * 100 \quad (1)$$

The powder analysis involved scrutinizing the morphology, dimensions, and composite configuration of the atomized AMC powders. Each powder batch was analyzed with approximately one hundred powder particles. To assess powder morphology and particle size, the powder particles were dispersed onto graphite tape and imaged using a scanning electron microscope (SEM) fitted with a Secondary Electron (SE) detector. The SEM SE images were analyzed to determine particle size and morphology using the Xparticle software from Thermo Scientific. Powder morphology was assessed based on the aspect ratio, where an aspect ratio of 1 signifies ideal powder sphericity. The analysis of the composite structure of the powder involved determining the content of SiC particles in the powder particles. This was achieved by embedding the powder particles and grinding them using silicon carbide papers with grit sizes from 600 to 2500. Subsequently, they underwent oxide-polishing (0.05 µm silica solution, Struers OP-S Suspension) using a vibratory polishing machine. The prepared powder samples were imaged with a scanning electron microscope (SEM) equipped with a Back-Scattered Electron (BSE) detector. The content of SiC particles in the powder particles was manually determined using ATLAS Software, employing a method based on color contrast differences.

### Processability of AMC powders.

The efficiency of the ultrasonic atomization process depended on the type of heat source used to melt the initial material (see Fig. 2a). Utilizing induction and plasma enabled the achievement of a relatively high process efficiency exceeding 40%. However, when using an arc as the heat source, the process efficiency was possible only at a level of 15%. In the case of plasma and arc heat sources, based on a similar procedure for melting the feed material, a decrease in process efficiency occurred at the same stage of the process. Instabilities appeared during the melting stage, leading to the detachment of irregular large fragments of material, as illustrated by the example of plasma melting (see Fig. 3). Consequently, this disruption led to interference in surface coverage with molten material on the sonotrode, ultimately resulting in the formation of scrap. Although the material exhibited similar behavior during melting with both heat sources, the efficiency of the process was notably lower when using the arc, at a level of 15%, compared to plasma, which achieved 41%.
<figure><img src="image_156.png" /><figcaption>Fig. 2: A graphical representation of how the efficiency of particle production is affected by the process parameters. The efficiency of the ultrasonic atomization process is dependent on (a) the heat source, and when utilizing induction, in dependant on (b) pressure difference, (c) nozzle size, and (d) frequency.</figcaption></figure>

These differences arise from fundamental variances in the melting processes of the material using arc and plasma. In arc melting, the flow of electrical current is destabilized by the introduction of the feedstock material from AMC containing poorly conductive SiC particles. The similar instabilities of the arc plasma were detailed described by the same type of ceramic powder [9]. Conversely, plasma melting of the feed material occurs without direct contact. As a result, the SiC particle content in the feed material is not directly linked to the plasma, making this process more stable compared to arc melting.

<figure><img src="image_157.png" /><figcaption>Fig. 3: (a) Scrap formation during the atomization process using plasma melting, and (b) the sorted procedure of scraps from the AMC powder.</figcaption></figure>

The atomization process demonstrates its highest efficiency when employing induction, surpassing that of plasma and arc melting methods (see Fig. 2a). This method, employing a distinct procedural approach compared to other heat sources in this study, faces unique challenges in achieving a one-to-one ratio of AMC powder to feed material. Primarily, it was crucial to pour the material quickly to prevent alloy segregation and achieve a composite structure. Therefore, to influence the flow rate of AMC material, two parameters were varied: the pressure difference and the size. This assumption was based on the idea that an increase in material flow rate could be achieved by increasing either of these two parameters. However, the results show that utilizing a higher-pressure difference of 500 mbar compared to 300 mbar to a decrease in process efficiency from 38% to only 26% (see Fig. 2b). A similar effect was observed when increasing the nozzle size. The process efficiency dropped by half from 38% to 19% when the nozzle size was increased from 1.0 mm to 1.5 mm (see Fig. 2c).
<figure><img src="image_154.png" /><figcaption>Fig. 2: A graphical representation of how the efficiency of particle production is affected by the process parameters. The efficiency of the ultrasonic atomization process is dependent on (a) the heat source, and when utilizing induction, in dependant on (b) pressure difference, (c) nozzle size, and (d) frequency.</figcaption></figure>

These differences arise from fundamental variances in the melting processes of the material using arc and plasma. In arc melting, the flow of electrical current is destabilized by the introduction of the feedstock material from AMC containing poorly conductive SiC particles. The similar instabilities of the arc plasma were detailed described by the same type of ceramic powder [9]. Conversely, plasma melting of the feed material occurs without direct contact. As a result, the SiC particle content in the feed material is not directly linked to the plasma, making this process more stable compared to arc melting.

<figure><img src="image_155.png" /><figcaption>Fig. 3: (a) Scrap formation during the atomization process using plasma melting, and (b) the sorted procedure of scraps from the AMC powder.</figcaption></figure>

The atomization process demonstrates its highest efficiency when employing induction, surpassing that of plasma and arc melting methods (see Fig. 2a). This method, employing a distinct procedural approach compared to other heat sources in this study, faces unique challenges in achieving a one-to-one ratio of AMC powder to feed material. Primarily, it was crucial to pour the material quickly to prevent alloy segregation and achieve a composite structure. Therefore, to influence the flow rate of AMC material, two parameters were varied: the pressure difference and the size. This assumption was based on the idea that an increase in material flow rate could be achieved by increasing either of these two parameters. However, the results show that utilizing a higher-pressure difference of 500 mbar compared to 300 mbar to a decrease in process efficiency from 38% to only 26% (see Fig. 2b). A similar effect was observed when increasing the nozzle size. The process efficiency dropped by half from 38% to 19% when the nozzle size was increased from 1.0 mm to 1.5 mm (see Fig. 2c).
<figure><img src="image_158.png" /><figcaption>Fig. 4: (a) High-volume material flow during atomization, (b) Unprocessed material in crucible after process, (c) Visible segregation of SiC from AlSiMg in the unprocessed material.</figcaption></figure>

The decrease in efficiency in the case of pressure difference and nozzle size for induction melting was likely caused by two different effects. The first effect was the excessive volume of poured material for the ultrasonic system to handle. As a result, most of the molten AMC material fell from the ultrasonic system as large drops, failing to undergo atomization, as can be seen in Fig. 4a. The second effect was clogging or a reduction in flow rate from the spout to the drips. In Fig. 4b, an example of unprocessed material remaining in the crucible after the process is depicted, resulting from nozzle clogging. This procedural complication significantly extended the process time and caused further segregation of SiC from AlSiMg, as can be observed in the Fig. 4c depicting the solidified unprocessed material with visible SiC segregation from AlSiMg. The process observations indicate that, in the case of composites, the size of reinforcement is crucial for the size of the spout. However, it is advisable to use the smallest size of nozzle that allows for optimal pouring of the material. Furthermore, the results show that the efficiency of ultrasonic atomization process using induction melting is closely dependent on the frequency of the vibration plate (see Fig. 2d). Utilizing a 40 kHz transducer resulted in nearly double the efficiency compared to a 60 kHz transducer. The lower frequency facilitated the application of higher ultrasonic parameters, aiding in releasing droplets from the melt for subsequent solidification into powder particles.

## Properties of AMC Powders.

The analysis of the produced AMC powders revealed specific correlations between powder properties and process conditions. Significant differences were noted in terms of morphology and particle size. Considering this, the morphology of AMC powders varied depending on the heat source used to melt the initial material (see Fig. 5a).

<figure><img src="image_159.png" /><figcaption>Fig. 5: A graphical representation of how the aspect ratio of particles is affected by the process parameters. The average aspect ratio of the AMC powder is dependent on (a) the heat source, and when utilizing induction, in dependant on (b) pressure difference, (c) nozzle size, and (d) frequency.</figcaption></figure>
<figure><img src="image_156.png" /><figcaption>Fig. 4: (a) High-volume material flow during atomization, (b) Unprocessed material in crucible after process, (c) Visible segregation of SiC from AlSiMg in the unprocessed material.</figcaption></figure>

The decrease in efficiency in the case of pressure difference and nozzle size for induction melting was likely caused by two different effects. The first effect was the excessive volume of poured material for the ultrasonic system to handle. As a result, most of the molten AMC material fell from the ultrasonic system as large drops, failing to undergo atomization, as can be seen in Fig. 4a. The second effect was clogging or a reduction in flow rate from the spout to the drips. In Fig. 4b, an example of unprocessed material remaining in the crucible after the process is depicted, resulting from nozzle clogging. This procedural complication significantly extended the process time and caused further segregation of SiC from AlSiMg, as can be observed in the Fig. 4c depicting the solidified unprocessed material with visible SiC segregation from AlSiMg. The process observations indicate that, in the case of composites, the size of reinforcement is crucial for the size of the spout. However, it is advisable to use the smallest size of nozzle that allows for optimal pouring of the material. Furthermore, the results show that the efficiency of ultrasonic atomization process using induction melting is closely dependent on the frequency of the vibration plate (see Fig. 2d). Utilizing a 40 kHz transducer resulted in nearly double the efficiency compared to a 60 kHz transducer. The lower frequency facilitated the application of higher ultrasonic parameters, aiding in releasing droplets from the melt for subsequent solidification into powder particles.

## Properties of AMC Powders.

The analysis of the produced AMC powders revealed specific correlations between powder properties and process conditions. Significant differences were noted in terms of morphology and particle size. Considering this, the morphology of AMC powders varied depending on the heat source used to melt the initial material (see Fig. 5a).

<figure><img src="image_157.png" /><figcaption>Fig. 5: A graphical representation of how the aspect ratio of particles is affected by the process parameters. The average aspect ratio of the AMC powder is dependent on (a) the heat source, and when utilizing induction, in dependant on (b) pressure difference, (c) nozzle size, and (d) frequency.</figcaption></figure>
AMC powder produced by plasma and arc melting attained the highest aspect ratio of nearly 1.0, signifying nearly ideal sphericity. The aspect ratio of AMC powder produced by induction melting was significantly below 0.9, revealing a deviating powder sphericity. The cause of the specific aspect ratio can be understood by analyzing SEM images presenting AMC powder atomized using various heat sources. The AMC powder produced by arc melting exhibited an almost ideal spherical form (see Fig. 6b). In the case of AMC powders produced by plasma and induction melting (see Fig. 6a,c), some powder particles displayed an elongated shape, fractures, agglomeration, or satellites. However, the content of powder particles with morphological deviations was significantly higher in the case of AMC powder produced by induction compared to plasma melting.

When employing induction melting with various process parameters, a notable distinction in powder morphology was evident solely in relation to the pressure difference (see Fig. 5b-d). At a lower pressure difference of 300 mbar, the aspect ratio reached 0.93, whereas at a higher pressure difference of 500 mbar, it decreased to 0.84. The direct impact of frequency or nozzle size on powder size could not be precisely determined, as adjustments to these parameters resulted in minimal changes in aspect ratio. Both frequencies of 40 and 60 kHz yielded an aspect ratio of approximately 0.84. Similarly, for nozzle size, an aspect ratio of 0.91 was observed for both 1.0 mm and 1.5 mm sizes.

<figure><img src="image_160.png" /><figcaption>Fig. 6: SEM images of AMC powder atomized using (a) Plasma, (b) Arc and (c) Induction melting.</figcaption></figure>

The powder size varied also depending on the heat source used to melt the initial material (see Fig. 7). AMC powder produced by induction melting achieved the highest average powder size of 170 µm. In contrast, the average size of AMC powder produced by arc and plasma melting was significantly smaller, reaching approximately 90 µm. In the case of various process parameters using induction melting, a significant difference in powder size was only observed for the frequency. At a low frequency of 40 kHz, the powder size reached a value of 170 µm. In comparison, the powder size at the high frequency of 60 kHz was only 120 µm. The direct influence of pressure difference or nozzle size on the powder size could not be precisely determined, as changing these parameters resulted in minimal alterations in powder size. For both pressure differences of 300 and 500 mbar, the powder size was approximately 110 µm. The same effect was observed for nozzle size, where the powder size of 100 µm was defined for both nozzle sizes of 1.0 and 1.5 mm.

The SiC particle content in the AMC powder was found to be very low after all atomization processes. In the case of arc and induction melting, the SiC content was only 3.5%, while with plasma, it was approximately 2% (see Fig. 8). Additionally, the variation of parameters for induction melting did not significantly ensure the desired content of SiC particles in the powder matrix (see Fig. 8b-c).
AMC powder produced by plasma and arc melting attained the highest aspect ratio of nearly 1.0, signifying nearly ideal sphericity. The aspect ratio of AMC powder produced by induction melting was significantly below 0.9, revealing a deviating powder sphericity. The cause of the specific aspect ratio can be understood by analyzing SEM images presenting AMC powder atomized using various heat sources. The AMC powder produced by arc melting exhibited an almost ideal spherical form (see Fig. 6b). In the case of AMC powders produced by plasma and induction melting (see Fig. 6a,c), some powder particles displayed an elongated shape, fractures, agglomeration, or satellites. However, the content of powder particles with morphological deviations was significantly higher in the case of AMC powder produced by induction compared to plasma melting.

When employing induction melting with various process parameters, a notable distinction in powder morphology was evident solely in relation to the pressure difference (see Fig. 5b-d). At a lower pressure difference of 300 mbar, the aspect ratio reached 0.93, whereas at a higher pressure difference of 500 mbar, it decreased to 0.84. The direct impact of frequency or nozzle size on powder size could not be precisely determined, as adjustments to these parameters resulted in minimal changes in aspect ratio. Both frequencies of 40 and 60 kHz yielded an aspect ratio of approximately 0.84. Similarly, for nozzle size, an aspect ratio of 0.91 was observed for both 1.0 mm and 1.5 mm sizes.

<figure><img src="image_158.png" /><figcaption>Fig. 6: SEM images of AMC powder atomized using (a) Plasma, (b) Arc and (c) Induction melting.</figcaption></figure>

The powder size varied also depending on the heat source used to melt the initial material (see Fig. 7). AMC powder produced by induction melting achieved the highest average powder size of 170 µm. In contrast, the average size of AMC powder produced by arc and plasma melting was significantly smaller, reaching approximately 90 µm. In the case of various process parameters using induction melting, a significant difference in powder size was only observed for the frequency. At a low frequency of 40 kHz, the powder size reached a value of 170 µm. In comparison, the powder size at the high frequency of 60 kHz was only 120 µm. The direct influence of pressure difference or nozzle size on the powder size could not be precisely determined, as changing these parameters resulted in minimal alterations in powder size. For both pressure differences of 300 and 500 mbar, the powder size was approximately 110 µm. The same effect was observed for nozzle size, where the powder size of 100 µm was defined for both nozzle sizes of 1.0 and 1.5 mm.

The SiC particle content in the AMC powder was found to be very low after all atomization processes. In the case of arc and induction melting, the SiC content was only 3.5%, while with plasma, it was approximately 2% (see Fig. 8). Additionally, the variation of parameters for induction melting did not significantly ensure the desired content of SiC particles in the powder matrix (see Fig. 8b-c).
<figure><img src="image_161.png" /><figcaption>Fig. 7: A graphical representation of how the particle size is affected by the process parameters. The content of SiC particles in AMC powder is dependent on (a) the heat source, and when utilizing induction, is dependent on the (b) pressure difference, (c) nozzle size, and (d) frequency.</figcaption></figure>

The main reason for the deviating composite structure achieved by arc and plasma melting is the dissolution of SiC particles due to the high temperature of both heat sources during the melting of the feed material [10]. In the case of induction melting, the low content of SiC particles in the AMC powder after the induction melting process may result from the melting temperature, as SiC can react with molten Al alloy at temperatures ranging from 667°C to 1347°C [10]. However, it is presumed that the more likely reason for the low SiC content in the AMC powder is process-related effects, such as (1) insufficient material flow leading to segregation or (2) excessively fast material flow resulting in unprocessed material due to nozzle clogging.

<figure><img src="image_162.png" /><figcaption>Fig. 8: A graphical representation of how the content of SiC in powder matrix is affected by the process parameters. The average size of the AMC powder is dependent on (a) the heat source, and when utilizing induction, is dependent on (b) pressure difference, (c) nozzle size, and (d) frequency.</figcaption></figure>

## Summary

In the present work, AMC powder, comprising AlSi9Mg reinforced with SiC particles, was produced employing ultrasonic atomization technology under varied process conditions. The following conclusions can be drawn:

* The efficiency of the ultrasonic process for producing AMC powder depended on the selected heat source. The highest process efficiency (almost 50%) was achieved with the induction system. Further improvement of the efficiency for this heat source required overcoming determined process challenges.

* The morphology of ultrasonically atomized powders was similar for all utilized heat sources, with an aspect ratio above 0.93, indicating high powder sphericity. In the case of induction melting, a correlation between pressure difference and aspect ratio was determined.