Correlating Dimensionless Enthalpy, Pyrometry, and Melt Pool Geometry Within the Laser Powder Bed Fusion Energetic Regime: A Path to In-Situ Melt Pool Control Demonstrated on Tungsten. Janko Stajkovic,Manuel Kahl,Lukas Kaserer,Jakob Braun,Sophie Scheuringer,Bernhard Mayr-Schmölzer,Benedikt Distl,Gerhard Leichtfried Count 1 2 Signal Aspect Ratio Pyro. Signal Enthalpy2 1NORMALIZED PYROMETRIC SIGNAL ≈ MELT POOL DEPTH Signal Width ≈ Melt Pool Variance Signal Position ≈ Melt Pool Depth Laser SubstrateMeltpool Case 1 Case 2Pyrometer Highlights Correlating Dimensionless Enthalpy, Pyrometry, and Melt Pool Geometry Within the Laser Powder Bed Fusion Energetic Regime: A Path to In-Situ Melt Pool Control Demonstrated on Tungsten. Janko Stajkovic,Manuel Kahl,Lukas Kaserer,Jakob Braun,Sophie Scheuringer,Bernhard Mayr-Schmölzer,Benedikt Distl,Gerhard Leichtfried •Pyrometer signal normalized by the spot size squared scales linearly to dimensionless enthalpy •Pyrometric signal is mainly influenced by the depth of the keyhole •Histographic signatures of pyrometric data correlate to keyhole stability and melting mode •Enthalpy models can be used to predict the aspect ratio of a single line Correlating Dimensionless Enthalpy, Pyrometry, and Melt Pool Geometry Within the Laser Powder Bed Fusion Energetic Regime: A Path to In-Situ Melt Pool Control Demonstrated on Tungsten. Janko Stajkovica,∗, Manuel Kahla, Lukas Kaserera, Jakob Brauna, Sophie Scheuringera, Bernhard Mayr-Schmölzerb, Benedikt Distlband Gerhard Leichtfrieda aFaculty of Engineering Sciences, Department of Mechatronics, Materials Science, Universität Innsbruck, Innrain 52, Innsbruck 6020, Austria bPlansee SE, Metallwerk-Plansee-Straße 71, Reutte 6600, Austria ARTICLE INFO Keywords : LPBF Pyrometry Dimensionless enthalpy TungstenABSTRACT In the realm of laser powder bed fusion (LPBF), controlling the melt pool in situ represents a critical challenge, as numerous defects are associated with its dynamics. This research demonstrates the utility of pyrometric signals in gaining insights into the depth of vapor capillaries during LPBF processes. By establishing a correlation between a semi-empirical enthalpymodelandpyrometricdata,gatheredonapowder-freesubstrate,apathwaytowardsthe in-situcontrolofmeltpoolgeometryisunveiled.Thestudyintroducesadimensionlessenthalpy model designed for predicting the aspect ratio of melt pools in LPBF. A linear relationship between the depth of melt pools, pyrometric signals, and dimensionless enthalpy is established through correlation with this model and measurements from metallographic cross sections. Histographicanalysisofpyrometricdatarevealsuniquesignaturesthatcorrelatewithconduction and keyhole mode melting, suggesting that these distinct histogram forms are indicative of keyholestability.Thefindingsconfirmthattherelationshipsdefinedinthisstudyareapplicable across varying spot sizes and hatch distances, allowing for the inference of optimal parameters directly from pyrometric signals. This research lays the groundwork for real-time control of melt pool geometry, marking a significant advancement towards enhancing the quality and consistency of LPBF and holds potential applications to laser welding processes. 1. Introduction The geometry of a melt pool, created by a single laser scan in the Laser Powder Bed Fusion (LPBF) process [1], servesasthecornerstoneoftheentiremanufacturingmechanism,muchliketheroleofthefoundationinsupportingand shapingthestructureofabuilding.Justasthestrength,stabilityandintegrityofabuilding,dependonitsfoundation, the success and quality of LPBF-produced components rely among other process parameters on the precise control and understanding of melt pool geometry. In LPBF, a part is created by arranging a myriad of single hatch lines next toandontopofeachother[1].ContemporaryLPBFpartsareriddledwithdefects,someofwhichcanbetracedback to the specific melt pool geometries [2]. It has been observed that primary laser parameters, including laser power, speed, and spot size, when set to levels that result in low energy input, can lead to the formation of lack of fusion pores [3, 4]1. Under these conditions, the cross section of the melt pool is typically semicircular, characterized by minimal to no vaporization. The majority of ∗Corresponding author janko.stajkovic@uibk.ac.at (J. Stajkovic) ORCID(s):0000-0002-7799-4846 (J. Stajkovic) 1Note that lack of fusion pores do not exclusively form due to low energy input. Other parameters, such as the choice of an adverse hatch distance, can yield an increase in lack of fusion porosity [5] Janko Stajkovic et al.: Preprint submitted to Elsevier Page 1 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF thelaserenergyinsuchscenariosisdissipatedthroughthermalconduction,leadingtotheclassificationofthisprocess regime as conduction mode. Incontrast,whenlaserparametersareadjustedtohighenergylevels,significantvaporizationoccurs.Thisprocess generatesarecoilpressurethatdisplacesmoltenmateriallaterally,facilitatingadrillingeffectbythelaserandresulting in the formation of a vapor depression [6, 7]. The depth of the vapor depression often surpasses its width due to multiple reflections within the depression [6, 8–11], leading to a cross sectional geometry akin to keyholes. This phenomenonisknownaskeyholemodemeltingorkeyholing.Inthiscase,theenergyinputbythelaserexceedswhat canbedissipatedthroughthermalconductionalone.Instead,convectivemeltpoolflows,spurredbythevaporization, predominantlycontributetoenergydissipation.Defectscharacteristicofthisregimeincludekeyholepores[10,12–14], which are remnants of keyhole collapse [11, 13], and centerline cracks [15], which arise from thermal stresses during solidification. Located between these two melting modes is a parameter region that induces the minimal number of defects [12, 16].Thisregionischaracterizedbytheformationofakeyholethroughvaporizationandrecoilpressure,yet,unlikein laser-welding, its depth and width remain similar in size (consider the keyhole geometries observed by Cunningham et al. [17]). The goal is to operate within this regime to minimize defects, though achieving this necessitates comprehensive experimentation for each LPBF machine and material combination. Various models [8, 16, 18–20] havebeendevelopedtocharacterizethisregion,therebyaimingtolessentheexperimentaleffortsrequiredtoidentify optimal parameters. Moreover,incorporating rapidlychanging,local conditionsduringthe LPBFprocess intothesemodels is,atbest, an approximation. Local conditions, such as heat accumulation at hatches in corners and overhang situations, can theoretically be addressed by some of the aforementioned models through adjustments in initial temperature or heat conductivity [20, 21]. However, for complex parts, it becomes unrealistic to accurately describe local conditions at every point in the build. The local environment in which a single hatch line is produced during LPBF can have an impact on the melt pool geometry that is as significant as the primary laser parameters chosen [22, 23]. The search for parameters that result in minimal defects thus becomes a daunting task, requiring exhaustive experimentation for eachconceivablegeometry.GiventhatamajoradvantageofusingLPBFisthemanufacturingofcomplexparts(e.g., near-net shape, embedded cooling channels, gyroids, etc.), relying solely on such models in the quest for defect-free parts appears to be only part of the solution. The solution to numerous problems outlined above is conceptually simple to articulate yet challenging to implement. The objective would be to monitor the melt pool geometry and maintain it at an optimal level previously identified. It comes as no surprise that a segment of the scientific community, including the work presented here, is endeavoring to develop methods to achieve this [24]. Janko Stajkovic et al.: Preprint submitted to Elsevier Page 2 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF High-speed optical imaging stands as one of the primary tools for investigating process dynamics in LPBF [24]. Numerous studies have shown the intricate dynamics present in LPBF: Scipioni Bertoli et al. [25] have illustrated that the laser primarily interacts with molten material. Ly et al. [26] identified the key factors in spatter generation, highlighting the effect of vapor induced powder particle entrainment, during LPBF. Bidare et al. [27, 28] employed high-speed imaging alongside a schlieren imaging setup to reveal the intricate interactions between the atmosphere, plume, and metal vapor, as well as spatter generation. It is clear that the length and width of the melt pool can be measured using top-down images from high-speed cameras. The depth of the melt pool could be inferred from the angle of the vapor plume, or the front wall angle [17, 26], although this necessitates complex image analysis. To the authors best knowledge, no publication to date has explored in-situ control of the melt pool using data gathered from high-speed optical imaging. Access to the depth of a melt pool remains challenging through these means. In the studies referenced [13, 17, 29–34], x-rays were employed to in-situ capture the dynamics of melt pool formation. Cunningham et al. [17] showed that a transition region between keyhole and conduction mode can be defined. Simonds et al. [32, 33] demonstrated that the absorption of laser energy correlates with the geometry of the keyhole.HamidiNasabetal.[13]foundthatacousticemissionsignalshaveaproportionalrelationshipwiththekeyhole geometry. Khairallah etal. [35] indicated thatperiodic oscillations in thekeyhole geometry precede the generationof keyhole pores, and described the generation of keyhole pores with high fidelity. While this list is not exhaustive, the effectiveness of x-ray imaging in revealing the complexities of melt pool and keyhole formation is clear. However, such setups require specialized, laboratory-scale equipment. The adaptation of these techniques for use on industrial machines appears unfeasible, and developing a viable concept for a feedback mechanism to respond to rapid in-situ changes seems impractical. Comparedtothepreviouslydiscussedmethodsofmonitoringthemeltpool,pyrometricdatacollectionissomewhat exotic, given the limited number of publications on the subject [24]. Lane et al. [36] showed that the intensity signal from a photodiode correlates with the absorptance of a melt pool. Further, it was hypothesized that the photodiode signal might also relate to the surface morphology of the melt pool, a plausible hypothesis considering that Simonds etal.[33]foundacorrelationbetweenabsorptanceandmeltpoolgeometry.Forienetal.[12],ineffortstodetectkeyhole pores via pyrometric signals, demonstrated that histographic analysis leads to distinct signatures for conduction, transition, and keyhole mode melting. Further, a correlation between pyrometric signals and melt pool depth was shown. Empirically, Vallabh et al. [37] utilized pyrometric data to train a support vector machine that successfully predicts the depth of a melt pool to a reasonable degree. In an experiment aimed at synthesizing oxides in-situ in stainlesssteel,Hainesetal.[38]alsoconcludedthatthepyrometerisprimarilysensitivetomeltpoolgeometry.Unlike Janko Stajkovic et al.: Preprint submitted to Elsevier Page 3 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF other measurement methods mentioned earlier, Renken et al. [39] proved that in-process measurement and closed- loop control using pyrometric data are feasible. Moreover, such a closed-loop control system based on these findings is currently commercially available, with a feedback time of 22µs[40]. Given the evidence outlined previously, the development of a method for controlling melt pool geometry in-situ appearsfeasibleusingpyrometricdata.Thereisaccumulatingevidencesupportingthecorrelationbetweenpyrometric signalsandmeltpoolgeometry.However,todate,nostudyhasspecificallyfocusedondescribingandexplainingthis correlation in detail. This paper addresses the gap inknowledge by combining the models from Ye et al. [8],Fabbro [16], Lankalapalli et al. [21] and Hann et al. [20] to predict the cross sectional melt pool geometry for a specified set of parameters and linkingthepredictionsandcorrespondingexperimentalmeasurementstoin-situgatheredpyrometricdata.Themodel developedhereinisdetailedanditsplausibilityestablishedthroughexperimentation.Experimentswereconductedon a powder-free tungsten substrate, where the aspect ratios were determined through metallographic cross sections and correlated with pyrometric signals analyzed via histographic methods. An interpretation of the results should provide insightintotheimportanceofthepyrometricsignalsindeterminingcrosssectionalmeltpoolgeometry.Additionally, the relationship between pyrometric signals and the geometry of the melt pool is investigated across different spot sizes to verify whether the model is consistent. As a secondary objective, this study also explores the impact of hatch distance on a powder free substrate. 2. Model ThemodelintroducedinthispaperbuildsupontheconceptofdimensionlessenthalpyinitiallyproposedbyHann et al. [20]. Modifications have been made to the original framework, with a comprehensive derivation available in AppendixA.Thefoundationofthemodelliesinthefactorless,dimensionlessenthalpy Δ𝐻𝑓,articulatedbyEq.(1a): Δ𝐻𝑓=𝑃 ℎ𝑚√ 𝛼𝑣( 𝜎 2)3, (1a) Δ𝐻=𝐺⋅Δ𝐻𝑓⋅𝜂. (1b) Inthiscontext, 𝑃,𝑣,and𝜎representthelaserpower,speed,andspotsize( 1∕𝑒2),respectively.Theterm 𝛼=𝑘∕(𝑐𝑝𝜌) definesthethermaldiffusivityofthematerial,where 𝑘isthethermalconductivity, 𝑐𝑝thespecificheat,and 𝜌thedensity ofthematerial.Theenthalpyrequiredformelting,denotedas ℎ𝑚,isgivenbyℎ𝑚=𝑐𝑝𝜌(𝑇𝑚−𝑇0),with𝑇𝑚representing the melting point and 𝑇0the initial temperature, following the remarks set by Fabbro [16]. It is important to note that Janko Stajkovic et al.: Preprint submitted to Elsevier Page 4 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF thespotsize 𝜎isconsideredasthewidthofthekeyhole[32,33].Additionally,thedepthofthekeyholeisassumedto be approximately equal to the melt pool depth. The definition of the dimensionless enthalpy Δ𝐻, as presented in Eq. (1b), commonly incorporates 𝐺, which represents a geometric factor determined by the assumed energy distribution of the laser (e.g. 𝐺=1∕𝜋[8]). Further, the absorptance factor 𝜂is usually included as shown in Eq. (1b). In this study, the geometry factor is chosen to be 𝐺=(2∕𝜋)3∕4. The reasoning for this can be found in Appendix A. Discussion on the absorptance 𝜂is provided later in the text. AsuccessfulLPBFprocess,withminimalinduceddefects,typicallyoccursneartheconduction-keyholetransition, with a stable keyhole [12, 16, 17]. Therefore, to design experiments that elucidate the LPBF process, it is essential to choose parameter sets (different combinations of primary laser parameters) that result in melt pool geometries withinthisregion.Toevaluatetheproximityofagivenparametersettothetransitionregion,theformalismpresented byLankalapallietal.[21]wasemployedtoestimatethemeltpooldepth 𝑑ofaparametersetbeforehand.Divisionby thespotsize 𝜎yieldstheaspectratioAR =𝑑∕𝜎.Further,thedimensionlessenthalpy,asdemonstratedbyFabbro[16] can be incorporated into the formalism of Lankalapalli et al. [21] to derive Eqs. (2a) and (2b): AR=𝑑 𝜎=Δ𝐻𝑓√ 𝑃𝑒 2𝑇𝑚−𝑇0 𝑇𝑣−𝑇01 𝑔(𝑃𝑒), (2a) 𝑔(𝑃𝑒)=∫2𝜋 0−𝑃𝑒𝑒−𝑃𝑒cos(𝜃) ⋅[∞∑ 𝑛=0𝜖𝑛𝐼𝑛(𝑃𝑒)cos(𝑛𝜃)( 𝑛 𝑃𝑒−𝐾𝑛+1(𝑃𝑒) 𝐾𝑛(𝑃𝑒)−cos(𝜃))] .(2b) Where𝑃𝑒=𝑣𝜎∕(2𝛼)represents the Péclet number and 𝑇𝑣denotes the boiling point. The function 𝑔(𝑃𝑒) characterizes the temperature gradient in dependence of 𝑃𝑒within a cylindrical keyhole, the walls of which are at temperature 𝑇𝑣.WithinEq.(2b), 𝐼𝑛and𝐾𝑛refertomodifiedBesselfunctionsofthefirstandsecondkind,respectively, and of the𝑛thorder. The term 𝜖𝑛is defined as1for𝑛=0and2for𝜖𝑛≥1, as described by Lankalapalli et al. [21]. In thecontextofthisstudy,keyholingisdefinedbyanaspectratio 𝑑∕𝜎≥1.Conversely,theconductionmodeissignified whentheaspectratio 𝑑∕𝜎≤1.Basedonthisdefinition,Eq.(2a)canberearrangedtocomputethetheoreticalrequired dimensionless enthalpy at the point where the transition from conduction mode to keyhole mode occurs, as shown in Eq. (3). Δ𝐻𝑓|𝑑∕𝜎=1=2√ 𝑃𝑒𝑇𝑣−𝑇0 𝑇𝑚−𝑇0𝑔(𝑃𝑒). (3) Janko Stajkovic et al.: Preprint submitted to Elsevier Page 5 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF A notable challenge arises from the interdependence between absorptance and dimensionless enthalpy, creating a chicken-and-eggdilemma.Aparticulardimensionlessenthalpyisassociatedwithaspecificgeometry,asnotedbyHann etal.[20],whichsubsequentlyinfluencestheabsorptance[9,10,32,41].Note,thatachangeinabsorptancechangesthe enthalpy,whichinturnchangesthegeometry.Nonetheless,tocalculate Δ𝐻inadvance,knowledgeof 𝜂isnecessary. This challenge can be addressed by consulting the results of Ye et al. [8], which show that the trend of increasing absorptance with Δ𝐻𝑓remains consistent across various materials. The study by Ye et al. [8] provides a description of the absorptance 𝜂(Δ𝐻𝑓), as outlined in Eq. (4): 𝜂=𝜂max ⋅(1−𝑒−0.66𝜂minΔ𝐻𝑓∕(𝜋√ 𝑃𝑒)). (4) Where𝜂max=0.7denotestheplateauofabsorbtion[8]and 𝜂mindenotestheminimalabsorptanceofthematerialused. The culmination of the theoretical arguments presented can be seen in Eq. (5). As a measure to determine if a parameter set is close to the conduction-keyhole transition, the enthalpy threshold difference (ETD) is calculated according to Eq. (5). Parameter sets resulting in ETD <0are more likely to be in the conduction regime, whereas those with ETD ≥0fall into the keyhole regime. ETD=Δ𝐻−Δ𝐻|𝑑∕𝜎=1= 𝐺𝜂max( 1−𝑒−0.66𝜂minΔ𝐻𝑓∕(𝜋√ 𝑃𝑒)) ⋅(Δ𝐻𝑓−Δ𝐻𝑓|𝑑∕𝜎=1).(5) A fundamental premise of the model proposed by Lankalapalli et al. [21] is the insignificance of heat conduction into the part in the z-direction2, which holds true if the thermal diffusion length 𝛿=√ 𝛼𝜎∕(2𝑣)< 𝜎∕2[8]. Consequently, for this assumption to be valid, the condition 2𝛼∕𝜎 < 𝑣needs to be met3. This has to be taken into consideration when utilizing the presented model to choose parameter sets. In this study, unlike in the approaches of Fabbro [16] and Lankalapalli et al. [21], Eq. (2b) was not approximated bypolynomialorlinearfunctions.Itwasdeterminednumericallybysumming100terms,ensuringrapidconvergence of the sum function with higher-order terms contributing changes on the order of 10−6. This numerical method is applicable for Péclet numbers up to 15, which typically surpasses the range observed in LPBF processes. For example,theparametercombination{𝑣=4ms−1;𝜎=80 µm}resultsinaPécletnumberofapproximately 9,whereas {𝑣=0.6ms−1;𝜎=80 µm}leads to a Péclet number of approximately 1. It should be noted that the first example represents an excessively high speed, which is not realistic for current LPBF processes. However, it could still be 2Consider that the laser scans on the plane given by the x- and y- direction 3NotethatthethermaldiffusiondepthshownhereisanapproximationwhenusedinthecontextofGaussianbeams.Inordertoverifywhether the model can be used this approximation is sufficient. Nevertheless, a discussion on the thermal diffusion depth can be found in Appendix A Janko Stajkovic et al.: Preprint submitted to Elsevier Page 6 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF Table 1 Thermodynamic quantities of tungsten used (* near liquidus) Symbol Value Unit Reference 𝜌∗ 17200 kgm−3[42] 𝑐𝑝∗ 308 Jkg−1K−1[43] 𝜂min0.26 [41] 𝑘∗ 92 Wm−1K[44] 𝑇𝑚3695 K 𝑇𝑣5828 K 𝑇0300 K incorporated into the model, provided the condition for thermal diffusion in the z-direction is met. Additionally, the methodemployedforcomputing 𝑓(𝑃𝑒)iscomputationallyefficient,takingonlyminutestoprocess100parametersets on a standard office PC. 3. Methodology 3.1. Experimental Based on the model outlined in Section 2, calculations were performed for over 200 different parameter sets. The thermodynamicquantitiesusedforthecalculationscanbefoundinTable1.Outofthese,18combinationswereselected sothattheETDandpredictedARissituated,between −3.5to16andbetween0.5to2.2respectively.Theprimarylaser parametersvariedwithinthefollowingranges:powerbetween 400Wto900W,speedbetween 0.1ms−1to1.7ms−1, and spot sizes of 80µm,120µmand160µm. The Péclet numbers selected for this study ranged from 0.4to6. It is important to note that Eq. (2b) was individually computed for each of the 200 parameter combinations, ensuring a unique comparison of each parameter against its corresponding threshold, according to Eq. (3). Eachselectedparametersetwasappliedtothreehatchblocks,asillustratedinFig.1,withvaryinghatchdistances. These distances correspondedto overlaps of 75%,50%, and25%relative to theutilized spot size. Hatch blockshave beenassignedawidthof 1mm.Thenumberofhatchlinesusedvarieddependingonthehatchdistancetofillthewidth of a hatch block adequately. The length of each hatch block was consistently maintained at 30mm, in order to reduce the thermal effect each line has on the next one. The hatch blocks were created on an Aconity 3D Midi (Aconity3D GmbH, Germany, Herzogenrath). Allhatchblockswerecreatedonapowder-freetungstensubstrate.AsnotedbyScipioniBertolietal.[25],powder infrontofthelaserbeamtypicallymeltsbythetimethelaserreachesthelocationoftheparticle.Thisimpliesthatthe laser primarily interacts with the substrate and the molten material, similar to laser-welding processes as discussed by Ye et al. [8].4Additionally, Trapp et al. [41] found that the absorptance, linked to the melt pool geometry as 4Consequently, the thermodynamic quantities presented in Table 1 are set close to the melting point of tungsten Janko Stajkovic et al.: Preprint submitted to Elsevier Page 7 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF 30 mm Overlap50%1 mm 0.5 mm 75% 25%Hatchblock100 mm 1 22 54Hatchblock A A Section A-A Hatchblock 53 100 µm d1 ... dn dmean Figure 1: Illustration of the experimental setup: 18 parameter sets were selected based on the model described in Section 2. These parameter sets were utilized in conjunction with various hatch distances, corresponding to spot overlaps of 75%, 50%, and35%. Hatch blocks were sectioned using wire electrical discharge machining (WEDM), as indicated by the cut line A-A. The lower half was further reduced by approximately 4mmin height, through grinding. Cross sections were metallographically prepared and imaged. The depth of each individual hatch line was measured, and the mean and standard deviation of these depths were calculated for each hatch block. indicatedbySimondsetal.[32],remainsqualitativelyunchangedwithorwithoutpowderinthecontextofkeyholing. Bitharasetal.[45]observedthatthepresenceofapowderlayerdoesnotaltermeltpoolgeometry.Theseobservations providearationaleforemployinglaser-weldingmodels[20,21]alongsideapowder-freesubstratetoanalyzetheLPBF process. Due to the anticipated more dynamic environment resulting from the use of powder [17, 26], it was omitted to facilitate an understanding of the principal usability of the pyrometer in determining the melt pool geometry. The substrate surface used for the experiment was smoothed using a plane grinder, resulting in a surface roughness 𝑅𝑎of approximately 2µm. The powder-free substrate containing the hatch blocks was partitioned using wire electrical discharge machining (WEDM) on a Sodic VZ300L (Sodick Co., Ltd, Yokohama, Japan) as shown in Fig. 1. Subsequently, one half was grounddownabout 4mmwithaplanegrinderinordertomeasurethedepthofthemeltpoolattwodifferentlocations along the hatch block. ThemetallographicpreparationofthepartitionedcrosssectionsinvolvedgrindingusingSiCpaperwithsequential grit sizes of220,500,800and1000. Subsequent fine grinding was done on a Struers Largo using a 9µmDiamond- Water Suspension (Dia-Pro). Post-Grinding, the polishing process comprised two stages: a 3µmstep using Struers Janko Stajkovic et al.: Preprint submitted to Elsevier Page 8 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF Floc and a1µmstep with Struers Nap. To improve the visibility of grain boundaries and the melt pool, Murakami’s etchant [46] was applied to the samples. Metallographic imaging was conducted using an Alicona InfiniteFocus G5+ (Alicona Imaging GmbH, Raaba, Austria). Images from both cross sections were measured using ImgageJ [47] as shown in Fig. 1. With the obtained depth the measured aspect ratio could be defined as the ratio between measured depth and spot size 𝑑∕𝜎. 3.2. Pyrometric Data PyrometricdatawascollectedforeachhatchblockusingaKleiberKG740-LOpyrometer(KleiberInfraredGmbH, Unterwellenborn,Germany).Theemployedpyrometerrecordedtherawsignalin mVatapollingrateof 100kHz.The position of each measurement was determined using the data from the laser scanning system, as the two systems are interconnected.Thewavelengthoflighttowhichthispyrometerissensitivewas 1753nm.Themeasurementareawas acircularregionwithadiameterofapproximately 300µm,concentrictothelaserspot.ThesetupisdepictedinFig.2. The concentricity of the pyrometer measurement spot and the laser spot was verified through preliminary experiments. These experiments involved creating hatch patterns in six different scanning directions. The collected pyrometric data were analyzed to identify any directional bias towards higher or lower signals. The system’s optical lenses were adjusted until no directional bias was observed, and the signal was maximized, ensuring adequate concentricity between the pyrometer measurement spot and the laser spot. Although a pyrometer was used in this study, temperature calibration was unnecessary, as only the raw signal was analyzed. Theanalysisoftherawdatawasconductedusingascriptdevelopedin-house.Thedatasetcomprisedapproximately 11million lines, making the full analysis and graphical representation computationally demanding. The primary function of the custom-developed script involves creating a 2D array, where each element corresponds to a 20µm× 20µmarea. Every measured data point was allocated to one element of this array. In instances where multiple measurements corresponded to the same coordinates within the predefined array, the highest value was selected to represent the pixel in question. The choice of 20µmas the element size was a compromise to balance resolution with data volume. The generated image size was 1622px×3819px , which, even with the smallest spot size utilized in these experiments, suffices to distinctly resolve the melt pool. A schematic illustrating this algorithm can be found in Fig. 2. To mitigate signal noise, a background analysis was conducted. This involved tracking the laser scanning pathwithdeactivatedlaser,aprocessrepeatedsixtimes.Thisyieldeddataonsignalnoiseencompassingapproximately 66millionpoints.Toensuretheintegrityofthedatapresentedinthiswork,themaximumintensityvaluefromthese66 millionpointswasidentified( 875mV)andsubsequentlysubtractedfromallpointsintheactualdata,beforemapping to the array occurred. Janko Stajkovic et al.: Preprint submitted to Elsevier Page 9 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF Section A-A 300 µm Pyrometer Scanner SubstrateA A Laser є1є2 є3єmaxєmax Resolution 20 µm x1XY y1є1є єnynxn.........б MeltpoolPyro. Spot Figure 2: Pyrometric data was captured within an area given by a measurement spot diameter of 300µm, concentric to the laser spot. The laser scanner system and the pyrometer were interconnected, allowing for synchronized data acquisition. Pyrometer measurements, recorded at a polling rate of 100kHz, were associated with xy-positions obtained from the laser scanning system and presented in a tabular format. An in-house developed script aligned the tabulated data with an array, where each array element represented an area of 20µm×20 µm. AsectionoftheresultantimageisdisplayedinFig.3.Itshouldbenotedthatthisimageonlyillustratesfiveoutof the54 hatchblocks created.For adetailed analysis,the imagewas segmentedinto individualhatch blocks,facilitated bypreciseknowledgeofthespacingandpositionsofthehatchblocks.Foreachhatchblockhistogramswithabinsize of15mVwere created. Note that the bin size was chosen as the ceiling of the standart deviation of the background signal. A representative excerpt of the 54 created histograms can be seen in Fig. 6. The created histograms show a set of distinct peaks. A Gaussian Mixture Model (GMM) [48] was employed to identify the position and shape of all modesinthehistogramdata.EachhatchblockwasusedtotrainaseparateGMMmodelutilizingtheentiredataset.This resultedin54differentmodelsdescribingthe54differenthistograms.Thedeterminationofthenumberofcomponents of each histogram was informed by using the Bayesian Information Criterion (BIC) in the range 0to5components. TheselectionprocessinvolvedchoosingthenumberofcomponentsbasedontheminimumBICvaluewiththehighest gradient, alongside visual analysis by the author. The mean value and standard deviation of each Gaussian peak were extracted for each histogram. 4. Results and Discussion 4.1. Model Validation No influence of the hatch distance on melt pool depth was observed, attributed to the chosen hatch line length ensuringuniformthermalconditionsforeachline.Hence,threehatchblocks,despitehavingdifferenthatchdistances but identical laser speed, spot, and power, are grouped into a single parameter set. Consequently, the 54 hatch blocks Janko Stajkovic et al.: Preprint submitted to Elsevier Page 10 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF 10mm 200 400 600 800/epsilon1[mV] Figure 3: Optical image (top) and pyrometric image (bottom): Several defects (changes in surface quality) are visible in the optical image that correspond to signal changes in the pyrometric data. Each hatch block presented was created with different primary laser parameters. Note that changes in parameters can be identified by a change in the mean signal of each hatch block (qualitatively). Note that a small amount of aliasing could not be avoided. createdinthisstudycanbecondensedinto18parametersets.Themeasureddepths(seeFig.1onhowmeasurements wereperformed),representinganaveragefromsixuniquepositionsonthesubstrateacrossmultiplehatchlines,ensured statistically significant measurements. Fig. 4 illustrates the applicability of the model described in Section 2. Taking into account the measurement uncertainty, 16 out of 18 AR were correctly predicted. A linear relationship between dimensionless enthalpy and aspect ratio was established, corroborating findings by several researchers [8, 20, 49]. Remarkably, Fig. 4 shows that parameter sets with varying spot sizes but comparable ETD were also well predicted, andyieldsimilarAR.TheillustratedrangeinFig.4ofETDbetween −3.5to16correspondstodimensionlessenthalpies Janko Stajkovic et al.: Preprint submitted to Elsevier Page 11 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF 0 5 10 15 ∆H−∆H/vextendsingle/vextendsingle d/σ=10.00.51.01.52.02.53.03.54.0d/σ Spot Size 80µm 120µm 160µm Prediction Figure 4: Agreement between model prediction and experimental results: Approximately 90%of the predictions fell within the margins of error for experimentally measured values. A linear relationship between AR and ETD could be established. Parameters with different spot sizes but comparable ETD yield similar AR between14to39in Hann et al. [20], 2to8in King et al. [49] and Forien et al. [12] and 1to15in Ye et al. [8]5. As already noticed by Ye et al. [8] the utilization of a variable 𝜂yields a single linear response, eliminating the slope changeobservedbyKingetal.[49],Hannetal.[20]andFabbro[16].Note,thatintherangepresentedhere,theslope change should be evident. 4.2. Pyrometric Data 4.2.1. Pyrometric Image Fig. 3 displays a comparison between the pyrometric data acquired and an optical image of the hatch blocks. The creation of these hatch blocks introduced defects such as sudden changes in surface quality, as evidenced by their comparison.Thedefectscorrespondtoareaswithelevatedpyrometricsignals,arelationshipthatalignswithfindings from prior research on the potential of using pyrometric signals to identify common defects in LPBF processes [50]. However,thedetailsregardingthiscorrelationremainasubjectofdiscussion[38].Notethatassomedefectscorrelate with the melt pool geometry, as described in Section 1, a correlation between some types of defects and pyrometric signals is plausible. Following the acquisition of pyrometric data, each of the 54 hatch blocks was segmented, and a histogram for each segmented hatch block was produced, employing the methodology described in Section 3. Representative histograms can be found in Fig. 6 5ForthecomparisontoHannetal.[20]andKingetal.[49]afixed 𝜂=0.4wasused.ForthecomparisontoYeetal.[8]avariable 𝜂according to Eq. (4) was used Janko Stajkovic et al.: Preprint submitted to Elsevier Page 12 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF 0 100 200 300 400 500 600 700 /epsilon1[mV]0.0000.0050.0100.0150.020FrequencyHatch Overlap 75% 50% 25% Figure 5: Influence of hatch distance on pyrometric signal: Considering the histograms of hatch blocks created under identical primary laser parameters yet with varying hatch distances, a negligible difference in the position of the main mode is observed, considering the intrinsic variability ( 15mV) of the signal and the change that occurs due to a change in primary laser parameters. 4.2.2. Histographic Data Figure5displaysthetypicalvariationinpyrometricsignalforasingleparameterset(comprisinglaserpower,speed, and spot size) produced using different hatch distances. Note that this sample is representative of the entire dataset. Thus, for the purposes of this study, the assumption that hatch distance does not significantly impact the pyrometric signalisjustified.Notethatchangesinprimarylaserparametersyieldmuchgreaterchangesthanthechangespresented in Fig. 5. This allows for the consideration of different hatch distances as a unified parameter set in further analysis. Notethatthisismainlyduetothelengthofthehatchblocksusedinthisstudy.AsillustratedbyRenkenetal.[39],the pyrometric signal can change depending on local environmental circumstances. ReviewingFig.6,thehistogramsofhatchblockswithdifferentETDarepresented.Asignificantportion, 74%ofthe histograms,exhibitamonomodaldistribution,whereas 26%displayamultimodaldistributionofsignals.Multimodal distributionspredominantlyoccurinparametersetswhereETD ≤0.Additionally,parametersetswhereETD ≫0are likely to show broader distributions, with their mean mode shifted towards higher signal values. These observations regarding histogram morphology align with the findings of Forien et al. [12].6 4.2.3. Principal Mode Data Collapse The mean signal of the principal mode from histograms was selected to represent the pyrometric signal, with the standard deviation of the Gaussian fit being used as measurement uncertainty. Presenting the data in this manner and 6GiventhatForienetal.[12]conductedtheirresearchusingadifferentmaterialandafixedabsorptance,discrepanciesintheirfindingscompared tothecurrentstudyareanticipated.However,theextentofpeakbroadeningobservedinthehigh-enthalpyregimeofthisstudywasnotreportedby Forien et al. [12], despite the comparable enthalpy ranges. The origin of this discrepancy remains uncertain, underscoring the need for additional research to elucidate these differences. Janko Stajkovic et al.: Preprint submitted to Elsevier Page 13 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF 0 200 400 600 800 1000 1200 1400 /epsilon1[mV]0.000.010.020.030.04Frequency∆H−∆H/vextendsingle/vextendsingle d/σ=1 ≈0 <0 /greatermuch0 Figure 6: Histograms of hatch blocks with different ETD: Analysis shows that most histogram distributions can be approximated by a single Gaussian peak. Parameters with ETD ≤0show a multimodal distribution. The higher ETD, the higher the spread of the signal. 0 5 10 15 ∆H−∆H/vextendsingle/vextendsingle d/σ=10500100015002000/epsilon1[mV] Spot Size 80µm 120µm 160µm Figure 7: Pyrometric signal vs. ETD for different laser spot sizes. A separate linear relationship for each spot size can be found between signal intensity and ETD, which is plausible considering the results of Forien et al. [12] plotting it against ETD, as shown in Fig. 7, reveals that distinct linear relationships between the pyrometric signal 𝜖 exist for each of the investigated spot sizes. Note that a linear trend was also observed by Forien et al. [12] for one specificspotsize.Theconsistencyofthepyrometersignalacrossdifferentspotsizessuggestsitmaycontaininformation aboutthemeltpoolgeometry,raisingthequestionofwhetherthisrelationshipcanbesubstantiatedonaphysicalbasis. The pyrometer measures the intensity of radiation at a specific wavelength. As depicted in Fig. 7, an increase in ETDcorrelateswithariseinsignalintensity.Concurrently,themodelverifiedindicatesthatanincreaseinETDresults inahigherAR.Thewidthofthekeyhole,approximatelyconstantanddeterminedbythechosenspotsize[32],suggests Janko Stajkovic et al.: Preprint submitted to Elsevier Page 14 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF Section A-A SubstrateMeltpoolє KeyholeєMeltpoolб бA ArpAk Amб2rp Figure 8: Approximation of the geometries involved: The keyhole can be approximated by a cone with diameter 𝜎. The measurment spot of the pyrometer is given by the radius 𝑟𝑝. For small aspect ratios the emissive surfaces of the melt pool𝐴𝑚and the keyhole 𝐴𝑘are in a comparable range. Considering the temperature difference it is argued that the main contribution to the pyrometer signal is given by the emissive suface of the keyhole 𝐴𝑘. that an increase in AR primarily stems from a deeper keyhole. Considering the impact on the light-emitting surface detected by the pyrometer, a deeper keyhole enlarges its surface area, thereby creating more radiative surface, which leads to an enhanced signal. Tounderstandtheeffectofachangingradiativesurface,approximatingthegeometriesofthemeltpoolandkeyhole, asillustratedinFig.8,provesuseful.Thekeyholeisroughlyconical,withitsbasediameterdeterminedbythelaserspot size [21, 32]. The depth for a given parameter set can be estimated using the model outlined in Section 2 and verified inFig.4.Thus,theradiativesurfaceofthekeyholecanbeexpressedas 𝐴𝑘=𝜋𝜎∕2 ⋅√ 𝑑2+(𝜎∕2)2.Additionally,the radiativesurfaceofthemeltpoolcanbeapproximatedby 𝐴𝑚=𝜎𝑟𝑝−𝜋(𝜎∕2)2,where𝑟𝑝representstheradiusofthe pyrometer measurement spot, as depicted in Fig. 8. In order to compare the radiative contributions of melt pool and keyhole, the temperatures involved need to be approximated. The walls of the keyhole are maintained at the vaporization temperature of tungsten, which is 𝑇𝑣= 5828K.Thethermalgradient(TG)isapproximately 30Kµm−1[51,52].Giventhediameterofthepyrometerspot,the temperatureattheedgeofthepyrometermeasurementspotcanbedeterminedbycalculating 𝑇𝑒=𝑇𝑣−TG ⋅(𝑟𝑝−𝜎∕2). Forthesakeofargumentthetemperatureoftheradiativesurfacefromthemeltpool 𝐴𝑚issetequalto 𝑇𝑚=(𝑇𝑒+𝑇𝑣)∕2, which represents the average temperature between the edge and the vaporization temperature. Based on Planck’s radiation law for ideal black bodies, the band radiance for the wavelength utilized by the pyrometer used in this study can be determined by performing an integration over 𝜆within the limits 𝜆1= 1748nm and𝜆2=1758nm7, as shown in Eq. (6a). 𝐵(𝑇)=∫𝜆2 𝜆12ℎ𝑐2 𝜆51 𝑒ℎ𝑐 𝜆𝑘𝐵𝑇−1𝑑𝜆. (6a) 7It should be noted that the specific wavelength band to which the pyrometer responds was not specified. For the purposes of this analysis, an assumption was made to consider a wavelength band of 10nm, symmetrically centered around the nominal sensitivity wavelength of 1753nm. It is crucial to emphasize that variations in the width of the assumed wavelength band do not significantly impact the conclusions derived from this analysis. Janko Stajkovic et al.: Preprint submitted to Elsevier Page 15 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF Here,𝜆representsthewavelengthoftheobservedradiation, ℎisthePlanckconstant, 𝑐denotesthespeedoflight, 𝑘𝐵is the boltzmann constant, and 𝑇refers to the temperature at which the distribution is calculated. By multiplying the previously calculated emitting surface areas of the melt pool and the keyhole with their respective band radiances, denoted as 𝐵(𝑇𝑣)⋅𝐴𝑘and𝐵(𝑇𝑒)⋅𝐴𝑚respectively, it becomes possible to compare the estimated contributions to the pyrometric signal. For spot sizes within the range of 80µm,120µmand160µm, AR from0.7to2,andapyrometermeasurementspotsizeof 300µm,itisestimatedthatthecontributionofthekeyholeto the total emitted power ranges from 82%to93%. The observation that the keyhole contributes significantly to the total emitted power is not surprising, especially when considering that even small keyholes created by a spot size of 80µmand an aspect ratio of 0.7possess approximately the same surface area as the melt pool, without accounting for the differences in radiation intensity duetothetemperatureoftheemittingsurface.8Itisimportanttonotethattheareaoftheradiativesurfaceofthemelt pool𝐴𝑚primarilyscaleswiththespotsize,whereastheradiativesurfaceofthekeyhole 𝐴𝑘alsoscaleswiththedepth. According to Simonds et al. [32], depth oscillations by a factor of 2 occur at a frequency of 10kHz, significantly affecting𝐴𝑘and consequently leading to an even higher contribution of 𝐴𝑘compared to 𝐴𝑚in the total received pyrometric signal. Furthermore, this analysis does not consider the idea proposed by Lane et al. [36], which suggests thatthekeyhole,duetoitsgeometricnature,emitsradiationinamoredirectedmanner,asopposedtothemorediffuse emissionfromshallowmeltpools.Ifapplicable,itwouldfurtherexaggeratethecontributionofthekeyholetothetotal signalmeasuredbysuchasetup,stillwithouttakingintoacountthedifferenceinbandradianceduetothetemperature (see Fig. 10). These arguments lead to the conclusion that the keyhole area is the primary contributor to the total measured pyrometric intensity. InFig.7,itisdemonstratedthatthereceivedpyrometricsignalexhibitslinearrelationshipsfordifferentspotsizes. Itwasalreadyarguedthattheprimarycomponentofthepyrometricsignalisthekeyholesurfacearea 𝐴𝑘.Toelucidate thescalingbehaviourobservedinFig.7fordifferentspotsizes,considerwhatwouldhappentothepyrometricsignal, for parameter sets that have the same AR but different spot sizes. The surface area of the keyhole, which is proportional to the recieved pyrometric signal, can be expressed in terms of the aspect ratio 𝜖∝𝐴𝑘=𝜋(𝜎∕2)2⋅√ 4(𝑑∕𝜎)2+1. When considering two different signals originating from keyholes with identical aspect ratios but different spot sizes, characterized by 𝜖1,𝑑1,𝜎1and𝜖2,𝑑2,𝜎2, where 𝑑1∕𝜎1=𝑑2∕𝜎2, it follows that 𝜖1∕𝜎2 1=𝜖2∕𝜎2 2. This implies that the received pyrometric signal scales with 𝜎2. By applying a normalization of 𝜎2to the data presented in Fig. 7, Fig. 9 is obtained. It is observed that the linear scaling previouslynotedfordifferentspotsizesinFig.7convergesontoasingleline,definingthescalingrelationshipbetween ETD and the received, normalized pyrometric signal 𝜖∕𝜎2. 8Even when a pyrometer with a larger measurement spot is utilized, accounting for the temperature difference renders the contribution of the melt pool as negligible compared to the keyhole. Janko Stajkovic et al.: Preprint submitted to Elsevier Page 16 of 26 Enthalpy, Pyrometry and Melt Pool Geometry in LPBF 0 5 10 15 ∆H−∆H/vextendsingle/vextendsingle d/σ=10.000.020.040.060.080.100.12/epsilon1/σ2[mV/µm2] Spot Size 80µm 120µm 160µm Figure 9: Normalized pyrometric signal vs. ETD. By normalizing pyrometric data to the spot size used, a single linear scaling between ETD and the recieved pyrometer signal can be obtained, implying a relationship between keyhole geometry and pyrometeric signal. To conclude this line of reasoning, recall the model described in Section 2 and verified by Fig. 4, where it was demonstrated that ETD scales linearly with the aspect ratio AR of the keyhole. It has been shown that parameter sets withdifferentspotsizesandsimilarETDyieldcomparableAR.Additionally,inFig.9,alinearscalingbetweenETD andthenormalizedpyrometricsignal 𝜖∕𝜎2wasestablished.Therefore,bytheargumentoftransitivity,alinearscaling between the normalized pyrometric signal 𝜖∕𝜎2and AR must exist. As demonstrated by Simonds et al. [32], changes in the keyhole width for a given spot size are negligible compared to changes in depth, positioning the depth of the keyhole as the principal variable determining the intensity of the pyrometric signal in this scenario.9 Theresultsdiscussedarespecifictotungsten,promptingcuriosityaboutthepossibilityofsimilarscalingbetween keyholegeometryandpyrometricsignalfordifferentmaterials.Byapplyingthesameapproximationswithadjustments for the temperatures involved, insights into different materials can be obtained. The keyhole walls are always at approximately their respective temperature of vaporization, 𝑇𝑣. In Fig. 10, the effect of a change in keyhole depth ontheradiationintensitychangeisillustratedasafunctionoftemperature.Forinstance,fortungsten,thedifferencein the received signal for a keyhole depth change from 40µmto160µmis approximately 0.32mWsr−1. For aluminum, thisdifferenceshiftsto 0.06mWsr−1.Therefore,theabilitytoresolvedifferencesindepthmaydependonthematerial and the pyrometer used. The higher the vaporization temperature, 𝑇𝑣, of the metal observed via pyrometry, the better the resolvability of different depths. 9Ascanbeinferredfrom