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Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation

Christoph Meier, Ryan W. Penny, Yu Zou, Jonathan S. Gibbs, A. John Hart

arXiv:1709.09510v1physics.app-phcs.CE

TL;DR

Predicting part-scale SLM behavior is complicated by the limits of homogenized powder models and the role of melt-pool hydrodynamics. This review surveys multiscale models, numerical approaches, and powder-bed characterization. It identifies ways mesoscopic information and hydrodynamic modeling could improve macroscopic predictions.

  • Problem

    Macroscopic SLM models homogenize the powder phase, while melt-pool shape and temperature depend on radiation transfer and melt-phase heat convection that such models may not resolve.

    Source: §2.5 · p. 36

  • Method

    The review surveys SLM models across scales, numerical solution schemes, and experimental characterization of powder optical properties.

    Source: §2 · p. 7, §2.5 · p. 36, §3.1 · p. 39

  • Results

    The review identifies homogenized powder treatment and unmodeled melt-pool hydrodynamics as opportunities to improve macroscopic SLM models.

    Source: §2.5 · p. 36

  • Takeaways & Limitations

    Transferring mesoscopic information or explicitly representing melt-pool hydrodynamics could improve macroscopic predictions of temperature and melt-pool behavior.

    Source: §2.5 · p. 36

    Multiple-reflection powder-bed ray tracing applies to sintering or point-wise modulated scans when no melt pool is present, not continuous linear scanning.

    Source: §2.1.4 · pp. 15–16

Abstract

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Among the many additive manufacturing (AM) processes for metallic materials, selective laser melting (SLM) is arguably the most versatile in terms of its potential to realize complex geometries along with tailored microstructure. However, the complexity of the SLM process, and the need for predictive relation of powder and process parameters to the part properties, demands further development of computational and experimental methods. This review addresses the fundamental physical phenomena of SLM, with a special emphasis on the associated thermal behavior. Simulation and experimental methods are discussed according to three primary categories. First, macroscopic approaches aim to answer questions at the component level and consider for example the determination of residual stresses or dimensional distortion effects prevalent in SLM. Second, mesoscopic approaches focus on the detection of defects such as excessive surface roughness, residual porosity or inclusions that occur at the mesoscopic length scale of individual powder particles. Third, microscopic approaches investigate the metallurgical microstructure evolution resulting from the high temperature gradients and extreme heating and cooling rates induced by the SLM process. Consideration of physical phenomena on all of these three length scales is mandatory to establish the understanding needed to realize high part quality in many applications, and to fully exploit the potential of SLM and related metal AM processes.

1. Introduction

SLM builds metal parts layer by layer, offering geometric flexibility while its coupled thermal and physical phenomena make process outcomes difficult to predict. The section introduces how powder-bed, melt-pool, and solidification behavior shape part quality, then situates SLM among related processes and outlines the article.

1. Introduction

  • SLM forms a 3D part by selectively melting contours in successive powder layers, with part orientation relative to the build direction influencing resulting properties.After each layer is scanned, the platform lowers and a fresh powder layer is deposited.Source: §1 · p. 1

1.1. Physical phenomena within the powder bed

  • Powder-bed absorption and heat transfer depend on beam, powder, and surface conditions, while weak inter-particle conduction and limited melting times preserve non-uniform temperatures that can cause pores or inclusions.Powder particle, layer, and beam dimensions are comparable; hatch spacing is typically chosen to promote overlap and remelting between tracks.Source: §1.1 · pp. 2–3

1.2. Physical phenomena within the melt pool

  • Surface tension, capillarity, wetting, and inertia shape melt-pool dynamics, while convection—especially Marangoni flow—dominates heat transfer within the pool.Oxidation can reduce wetting and contribute to unstable, balled melt pools, rough surfaces, pores, or insufficient layer adhesion.Source: §1.2 · pp. 3–4

1.3. Physical phenomena within the solidified phase

  • Near the laser, rapid heating and solidification produce fine grains and metastable phases, while repeated thermal cycles in prior layers also shape microstructure and material properties.Part geometry and heat-treatment-like cycles can modify microstructure through the build direction.Source: §1.3 · pp. 4–5
  • Thermal strains in constrained parts produce residual stresses; island scans and annealing can reduce them, whereas omitting supports may reduce stresses at the cost of dimensional warping.The thermal history can yield defects such as cracks or delamination, but also offers opportunities to tailor inhomogeneous and anisotropic properties through process parameters.Source: §1.3 · p. 5

1.4. Di

  • Compared with SLM, EBM uses an electron beam and near-vacuum conditions, while SLS only partially melts or sinters powder; DED and welding processes differ in scale or purpose.SLM’s smaller beam spots and powder grains permit finer geometric resolution and improved surface quality relative to EBM.Source: §1.4 · pp. 5–6

1.5. Organization of this article

  • The article reviews physical mechanisms and modeling and experimental approaches, organizing them around powder-bed transfer and macro-, meso-, and microscale investigations.Its final section addresses practical implementation and open questions for process improvement.Source: §1.5 · p. 6

2. Modeling and simulation approaches

SLM models are organized by the scale and physical detail they resolve, from whole-part behavior to powder-scale effects and microstructure. Their numerical schemes and coupling choices trade computational efficiency against stability and fidelity.

2. Modeling and simulation approaches

  • Macroscopic models simulate whole-part temperature, residual stress, and warping efficiently, while mesoscopic and microscopic models resolve powder-scale behavior and microstructure but are computationally limited.Mesoscopic insights can inform macroscopic continuum models, and microscopic results can support improved constitutive models.Source: §2 · pp. 6–7
  • Explicit time integration avoids nonlinear iterations but requires small time steps for stability, whereas implicit schemes allow larger steps but make fully resolved mesoscopic SLM problems challenging.Implicit schemes are suited to low-frequency responses; explicit schemes are preferable for high-frequency dynamics when small steps are needed regardless.Source: §2 · p. 7
  • Phase boundaries may be modeled as sharp interfaces, finite-width transitions tracked with a phase variable, or implicit isothermal contours; reviewed SLM models mostly use the latter two approaches.A too-narrow transition region can create steep material-property gradients and ill-conditioned numerical problems.Source: §2 · pp. 7–8
  • Monolithic and strongly coupled partitioned schemes solve fields together or iteratively, while weakly coupled schemes solve each field once per time step and may impose restrictive stability limits.Coupling strategy affects the time step size and therefore computational cost.Source: §2 · p. 8

2.1. Modeling of optical and thermal properties of powder phase

Powder-phase modeling spans continuum descriptions and particle-resolved simulations of radiation transfer and heat conduction. The appropriate level of detail depends on the physical question: continuum models are less costly, while particle-scale heterogeneity can matter for melting and defect formation.

2.1.1. Continuum model for powder bed radiation transfer

  • Gusarov et al. derive deposited-energy profiles using a homogenized RTE model for opaque particles, assuming particle sizes small relative to beam size and bed thickness.Their solution treats the problem as one-dimensional when the laser spot is much larger than the absorption depth.Source: §2.1.1 · p. 10
  • RTE and ray-tracing energy-deposition profiles agree for the selected mixed powders when the bed is sufficiently deep and the laser beam sufficiently large.The simple RTE averaging is unjustified for comparable phase fractions with substantially different optical properties.Source: Figure 4 · p. 10, §2.1.1 · p. 10
  • For mixed powders with comparable phase fractions and dissimilar optical properties, the Vector Radiation Transfer Equation tracks phase-specific intensities, but lacks an analytical solution.The conventional RTE is recovered when one phase is opaque or dominates in volume.Source: §2.1.1 · pp. 10–11

2.1.2. Ray tracing model for powder bed radiation transfer

  • >96% of absorbed energy lies within 400µm of the powder-bed surface in the modeled 50µm WC and 20µm Co mixture.The absorption maximum occurs slightly below the surface, where contributions from multiple reflections are prevalent.Source: Figure 6 · p. 12, §2.1.2 · p. 12
  • Particle-scale absorption varies with polarization, while beam sizes near particle diameters produce strongly fluctuating track absorption that fast melting may preserve.The melting time is often shorter than the time for thermal conduction to homogenize energy within a particle.Source: §2.1.2 · pp. 12–13, Figure 7 · p. 13
  • Powder-bed absorptivity has a smooth functional relation to flat-surface absorptivity, allowing the former to be estimated from the latter for a material.The relation was extended across materials and experimentally verified.Source: §2.1.2 · pp. 13–14, Figure 8 · p. 14

2.1.3. Continuum models for powder bed heat conduction

  • Powder-bed heat-conduction models distinguish homogenized effective conductivity from resolved particle contacts, whose coordination number can change conductivity even at fixed density.Loose metallic powders are typically governed by gas conduction in their pores; Gusarov’s random-packing model includes volume fraction, coordination number, and contact size.Source: §2.1.3 · pp. 14–15

2.1.4. Conclusion

  • Ray tracing resolves particle-scale heterogeneity but costs more and requires particle geometry; continuum models are reasonable for macroscopic questions, but only estimate radiation transfer at powder-layer scales.Resolving melt-pool impact and mesoscopic defects calls for particle-resolved modeling, whereas homogenized macroscopic models can use continuum heat-transfer approaches.Source: §2.1.4 · pp. 15–16

2.2. Macroscopic simulation models

Macroscopic SLM models homogenize powder into a continuum to simulate builds at component scale, usually focusing on heat transfer and sometimes coupling it to mechanics to estimate residual stress and warping.

2.2. Macroscopic simulation models

  • These models use spatially averaged powder properties for efficient build-scale simulation, typically omit melt-pool fluid dynamics, and may smooth phase interfaces rather than resolve them sharply.Hodge et al. explicitly track the powder-to-melt transition, but use elevated heat capacity near melting to represent latent heat during solidification.Source: §2.2 · pp. 16–18
  • The thermal model uses an energy balance with heat-source and boundary-flux terms; macroscopic models commonly discretize it with FEM and may couple mechanics in a staggered manner.Boundary losses typically include convection and radiation, while mechanical simulations can estimate residual stresses or dimensional warping.Source: §2.2 · pp. 16–17
  • Models and agree on 316L melt-pool temperatures and shapes; increasing scan speed narrows and lengthens pools, though heat-source choice may shift predictions.Both models use the same radiation-transfer model, while the heat-source submodel may considerably influence results.Source: Figure 9 · p. 18, §2.2 · p. 18
  • Overhangs and thin walls can develop larger melt pools, excessive overheating, and evaporation under unchanged scan parameters because their surrounding powder conducts heat poorly.The review notes adapting laser parameters or adding support columns as common responses.Source: §2.2 · p. 19, Figure 10 · p. 19
  • 20% relative error in maximal displacement occurred without plastic hardening, while the hardening variant overestimated it by approximately a factor of two; preheating reduced residual-stress peaks.The comparison used DIC measurements of 316L triangular prisms and simulations at platform preheating temperatures of 303K and 1000K.Source: §2.2 · pp. 19–20, Figure 11 · p. 19, Figure 12 · p. 20
  • Commercial and research models vary in scope and efficiency, including annealing-based stress relaxation, adaptive meshing, and temperature- and phase-dependent properties in EBM simulations.The cited annealing model reported errors in maximal residual stress and distortion up to 500% without annealing effects; partitioned thermo-mechanical coupling can require smaller time steps and greater overall effort than monolithic coupling.Source: §2.2 · pp. 20–22
  • Evaporative heat loss was essential for realistic temperature fields in a finite-volume model that compared simulated phase volumes with experimental data.The model included powder, melt, solid, and evaporated gas phases.Source: §2.2 · p. 23
  • A coupled thermo-hydrodynamic approach combines homogenized powder properties with explicit melt-pool flow and passes its temperature field to a structural simulation for residual-stress prediction.The model captures effects such as wider melt pools and lower peak temperatures from outward Marangoni flow, at lower resolution and numerical cost than mesoscopic models.Source: §2.2 · p. 23

2.3. Mesoscopic simulation models

Mesoscopic models resolve powder particles and melt-pool dynamics to study heat transport, wetting, adhesion, surface quality, and defects; their high spatial and temporal resolution makes simulations computationally costly. Across the reviewed studies, surface tension, recoil pressure, powder packing, and processing conditions shape melt-pool behavior and resulting tracks.

Mesoscopic simulation models

  • Explicitly resolving powder particles enables mesoscopic models to predict melt-pool dynamics, heat transport, wetting, adhesion, surface quality, and defects, but fine meshes and explicit time stepping constrain simulations to short tracks.The model used 3µm elements and required about 100,000 CPU hours for a roughly 1mm track; it omitted Marangoni effects.Source: §2.3 · pp. 23–25
  • Surface tension smooths melt-pool geometry and increases heat transfer, producing faster cooling and smaller pools; high scan velocities also produce balling.For stainless steel 316 powder at 45% packing density, modeled conductivity was only three times that of air in the pores.Source: §2.3 · p. 25
  • In, ray tracing resolves particle-scale absorption, while temperature-dependent surface tension drives rearward Marangoni flow and recoil pressure deepens the pool and increases cooling.The combined recoil-pressure and evaporative/radiative cooling case stored the least heat; also considered denudation, with proposing gas-flow-driven particle ejection as an additional contributor.Source: §2.3 · pp. 26–27
  • In, denser powder packing reduced balling, whereas faster travel and lower laser power could foster it; the study did not discuss its time integrator or step size.The model used DEM for recoating and CFD for melt flow, without evaporation-related phenomena.Source: §2.3 · p. 27
  • The differing balling trends reported in,, and may reflect lower and upper bounds of an energy-density interval for stable processing, rather than a contradiction.The reviewed discussion relates faster travel at constant power to longer, more slender pools that foster Plateau-Rayleigh instabilities.Source: §2.3 · p. 28
  • With point-wise laser modulation, found that growing, initially separate deep pools join into a continuous track; deeper peaks may provide additional anchorage to the prior layer.The review suggests modulation may also increase absorption through multiple reflections and reduce surface temperatures, evaporation loss, and recoil pressure.Source: §2.3 · p. 28
  • In, wetting angle and powder-bed packing affect melt-pool shape, while packing density had the strongest effect on melt-pool characteristics.At constant laser power, slower scanning increased stability; comparable track topologies were found at constant spatial energy density.Source: §2.3 · p. 29
  • The framework was extended in to layer-wise 2D buildup; analysis found surface-tension coalescence nearly instantaneous relative to thermal diffusion and proposed a scan-velocity recommendation.The model was also used to illustrate pore formation, extended for alternative EBM energy-dissipation models, and extended to 3D in.Source: §2.3 · p. 30

2.4. Microscopic simulation models

Microscopic models link SLM’s thermal conditions to microstructure evolution through phase-field, cellular-automaton, and stochastic approaches. The examples relate scan speed and cooling conditions to grain structure and Laves-phase formation.

2.4. Microscopic simulation models

  • Phase-field models use phase, composition, temperature, and grain-orientation fields to represent solidification and microstructure evolution.The phase field distinguishes liquid, solid, and interface regions; temperature is an input that may come from a macroscopic model.Source: §2.4 · pp. 31–32
  • Two 3D phase-field examples demonstrate grain growth and non-equilibrium phase evolution, but their computations require substantial resources.One simulation reduced about 6,000 grains to about 200; another simulated 2 seconds of physical time in 14 hours on 64 processors and captured coring under high cooling rates.Source: §2.4 · pp. 32–33, Figure 21 · p. 32, Figure 22 · p. 33
  • A 2D EBM phase-field model for Ti-6Al-4V simplifies the alloy as binary, omits grain orientation, and predicts columnar growth along the build direction.Its temperature field comes from a finite-element energy-equation solution, and nucleation density increases with undercooling.Source: §2.4 · p. 33, Figure 23 · p. 34
  • Higher scan velocities induce higher cooling rates, greater nucleation density, and finer grains that remain oriented in the build direction.The trend agrees with experiments considered in.Source: §2.4 · p. 33, Figure 24 · p. 34
  • A cellular-automaton model weakly couples mesoscopic temperature and phase fields to predict Inconel 718 columnar and epitaxial grain growth, but omits solid-state grain coarsening.Mesoscopic powder resolution also lets the model account for stray-grain formation from partially molten particles at domain boundaries.Source: §2.4 · pp. 33–34, Figure 25 · p. 34
  • Low cooling rates and high G/v yield coarse columnar dendrite arm spacing and continuously distributed coarse Laves particles in Inconel 718.The simulations suggest increasing cooling rates and decreasing temperature gradients to obtain smaller equiaxed dendrite arm spacings and discrete Laves particles.Source: §2.4 · p. 35, Figure 26 · p. 35
  • A stochastic model of Inconel 718 simulates dendrite nucleation and growth, niobium segregation, and Laves-particle formation using a finite-element thermal solution.Source: §2.4 · p. 35, Figure 26 · p. 35

2.5. Summary of existing macro-, meso- and microscale models and potential for future developments

The review identifies computational efficiency and model accuracy as priorities for SLM simulation. It outlines potential cross-scale improvements while noting important limits in mesoscopic and microscopic modeling.

Future developments

  • Improving computational efficiency and model accuracy, alongside coupling models across scales, are identified as development priorities.Suggested efficiency measures include adaptive space and time discretization, implicit integration, parallel code, and improved material-deposition strategies.Source: §2.5 · p. 35, Figure 27 · p. 36

Macroscopic models

  • Macroscopic residual-stress predictions remain limited by simple material laws, even when temperature solutions are exact.Microscale-informed constitutive models could incorporate material inhomogeneity, anisotropy, and temperature-history dependence.Source: §2.5 · p. 36

Mesoscopic models

  • Mesoscopic models resolve powder-scale radiation, heat, and melt-pool transport, but high computational cost restricts observable tracks to a few millimeters and times to several hundred microseconds.Potential improvements include explicit ambient-gas-flow and powder-particle dynamics modeling, as well as improved boundary conditions informed by macroscopic models.Source: §2.5 · pp. 36–37

Microscopic models

  • Microscopic models remain less developed, with existing approaches often limited to simplified 2D representations and at most two chemical species.The review identifies explicit alloying-element segregation, solid-state transformations, and grain growth as possible additions.Source: §2.5 · p. 37

3. Experimental studies of thermophysical mechanisms in SLM

Experimental studies characterize thermophysical behavior in SLM across length scales, complementing models by examining powder heat transfer, residual stress and warping, melt-track quality, and defects. They relate process and thermal conditions to melt-track defects, porosity, and microstructure evolution.

3.1. Optical and thermal characterization of powders

  • For metals, absorption coefficients generally were 0.6–0.7 at 1.06µm, versus 0.25–0.45 at 10.6µm.At 1.064µm, finer powder particles yielded stronger absorption.Source: §3.1 · pp. 38–39
  • Powder-bed conductivities are two to three orders of magnitude below fused material or build-platform values; fine-particle heat transport is primarily through gas, while larger particles conduct directly.Bulk conductivities for stainless steel, iron, and copper are 15, 74, and 395 W/m K, respectively.Source: §3.1 · p. 39

3.2. Measurement of residual stresses and dimensional warping

  • Island size affected Inconel 718 density and elongation: 5mm and 7mm specimens reached 99.1% theoretical density, and elongation rose from 16.85% to 25.25% with increasing island size [106].The 2mm specimen had the lowest residual stress, attributed to crack-related relaxation; 3mm specimens had higher stresses than 5mm and 7mm specimens, consistent with greater thermal gradients.Source: §3.2 · p. 40
  • Residual stresses increased with component height, were larger perpendicular than parallel to scan direction, and fell nearly 10% with 200°C baseplate preheating; removal relaxed about 50%.Small-island scanning lowered maximum stress. Higher preheating also reduced cracking, but excessive heat or duration could sinter loose powder.Source: §3.2 · pp. 40–41

3.3. Characterization of melt track quality and defect detection

  • Initial contours and overhangs can overheat because heat has fewer conduction paths, promoting balling and poor surface finish; support-column density alters overhang temperatures, porosity, and finish.At acute U-turns, reheating and reduced heat-flow area produced blob-like formations.Source: §3.3 · p. 42
  • For cubic specimens at a 4 mm layer height, imperfection level was inversely proportional to diffusivity (correlation coefficient 0.7); data-fusion techniques predicted porosity locations verified by CT cross-sectional images.The diffusivity method showed sensitivity to delamination and porosity over a range from nearly fully dense material to a void fraction of 40%. Imaging-sensor spatial and temporal resolution was identified as the greatest challenge.Source: §3.3 · pp. 42–43
  • Across processes and alloys, Thomas et al. identified 2 < E*_0 < 8 as an effective energy range, but energy-based process maps cannot precisely assess individual-track stability or surface quality [146].Excess energy can cause overheating, cracking, and swelling; insufficient energy can cause incomplete melting and porosity. High-quality EBM Ti-6Al-4V occupied the highest-energy region of that study’s trade space.Source: §3.3 · pp. 44, 46
  • For Ti-6Al-4V, the mapped fully dense processing window contrasts with underheating and overheating porosity regimes, while severe overheating caused distortion that impeded recoater operation.The authors also identified an overheating regime and reported a similar mapping approach for 316L stainless steel.Source: §3.3 · p. 46
  • Excessive energy density can cause gas pores as recoil pressure deepens a keyhole and its incomplete collapse leaves spherical voids.SLM typically produces deeper keyholes than EBM, whereas EBM yields larger melt pools; residual porosity below 0.5% is commonly desired.Source: Figure 38 · p. 47, §3.3 · p. 48
  • µSXCT of 12 Ti-6Al-4V samples found lack-of-fusion defects effectively eliminated when layer thickness t was less than melt-pool penetration overlap depth d [31].Samples varied in laser power, scan speed, and hatch spacing; Figure 39 shows the transition from keyhole pores through dense parts to lack-of-fusion porosity.Source: Figure 39 · p. 47, §3.3 · p. 48

3.4. Microstructure evolution during the SLM process

  • In Ti-6Al-4V, rapid cooling produces acicular martensite, while epitaxial elongated grains align with heat flow along the highest thermal gradient.Because scan strategy controls the thermal field, it can also influence grain orientation.Source: Figure 40 · p. 48, §3.4 · p. 49
  • Higher energy density increases Ti-6Al-4V precipitates, while thermal cycling can decompose alpha prime martensite into alpha and beta phases with a bottom-to-top gradient,.Xu et al. observed ultra-fine lamellar alpha and beta phases from the sample bottom to top, potentially accompanying decreasing material strength in that direction.Source: §3.4 · p. 49
  • In Inconel 718, higher EBM beam current changed columnar grains to equiaxed grains, and tailored scanning wrote misoriented letters within [001] columnar bulk.The higher current raised sample temperature and lowered thermal gradients; the scanning strategy varied thermal gradients, cooling rates, and solidification-front velocities.Source: §3.4 · pp. 49–50, Figure 41 · p. 49
  • SLM-processed 304L and 316L commonly show austenitic elongated, textured grains and avoid chromium-carbide precipitation; 316L coarsens farther from the platform as cooling rates fall.Source: §3.4 · p. 50

4. Future directions and practical implementation

Future progress depends on integrated, efficient models that connect SLM process inputs to part characteristics across length scales. Experiments, in-situ measurements, and improved process and quality-control practices are also needed to address physical limits and practical trade-offs.

4. Future directions and practical implementation

  • Integrated models should exchange information across macroscopic, mesoscopic, and microscopic scales to predict part characteristics, then support inverse optimization of local process parameters.The targets include residual porosity, residual stresses, and microstructure; computational efficiency and robustness are key requirements.Source: §4 · p. 50
  • In-situ measurements can inform model abstraction and fault identification, while comparisons with simulated field evolutions can guide process-input adjustments.The passage identifies temperature fields as an example of relevant measured and simulated physical fields.Source: §4 · p. 50
  • Accessible heating and cooling rates constrain microstructure and stress control, while powder shape, size, purity, and moisture affect processability and defect risks.Water-atomized powder is lower-cost but typically has poorer flow and packing; gas-atomized powder is more costly and produces more spherical, purer particles.Source: §4 · pp. 50–51
  • Quality control and certification are pressing needs because SLM quality is sensitive to parameter variation, defective parts are more frequent, and its failure mechanisms require sophisticated metrology.X-ray tomography is given as an example; in-situ temperature measurements might help locate defects.Source: §4 · p. 51
  • Higher throughput favors faster scans, larger spots, and higher power densities, but excessive scan speed or energy input can destabilize melt pools or degrade surface quality.Potential research directions include new scanning strategies, laser configurations, and beam-shaping approaches to seek stable, higher-throughput regimes.Source: §4 · p. 51

Nomenclature

The nomenclature lists abbreviations for additive-manufacturing processes, design tools, modeling methods, and measurement or material terms.

Nomenclature

  • AM, SLM, SLS, and EBM denote additive manufacturing and three manufacturing processes; FDM denotes finite difference method, and CAD denotes computer aided design.The nomenclature also includes EBW and LBW for welding processes.Source: Abbreviations · p. 52
  • DEM, FEM, FVM, PFM, VOF, and XFEM name modeling methods, while CA and FSI denote cellular automation and fluid structure interaction.The list also includes RTE, DIC, HAZ, LWIR, NIR, and VHN.Source: Abbreviations · p. 52

SLM process

The SLM process nomenclature defines symbols for powder-bed geometry, laser settings, and absorbed energy.

SLM process

  • The process symbols include powder-bed thickness and dimensions, particle radius, laser power and velocity, hatch spacing, and laser-beam radius.The list also defines a dimensionless-quantity marker and A as the fraction of effectively absorbed laser energy.Source: SLM process · p. 52

Mechanical problem

The mechanical-problem nomenclature defines symbols for stress, forces, displacement, strain, and melt-pool interface and pressure quantities.

Mechanical problem

  • The listed mechanical symbols include the Cauchy stress tensor, volume-force vector, displacement vector, solid strain tensor, and rate-of-deformation tensor.Additional terms cover surface tension, wetting angle, interface curvature, melt-pool and ambient-gas pressure, and evaporation-related quantities.Source: Mechanical problem · p. 52

Thermal problem

The section defines the symbols used for temperatures, radiation, heat transfer, and material and model properties in the thermal problem.

Thermal problem

  • Temperatures include process, ambient, initial, melting, boiling, liquidus, and solidus temperatures.These are denoted T, Tref, T0, Tm, Tb, Tl, and Ts, respectively.Source: Thermal problem · p. 53
  • Radiation notation covers intensity, scattering, absorption, extinction, albedo, phase function, and polarized absorptivity.The glossary also defines incidence angle, wave direction and wavelength, electric-field direction, and surface normal.Source: Thermal problem · p. 53
  • Heat-transfer terms distinguish general, radiation, emissive, evaporation, conductive, and convective heat-flux densities.The glossary also defines incident energy density, conductivity, effective conductivity, diffusivity, density, specific heat, time, velocity, and convection coefficient.Source: Thermal problem · p. 53
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