Multiscale Modeling of Powder Bed Based Additive …...Finite element (FE) Thermodynamics, mechanics...

MR46CH05-Markl ARI 11 May 2016 17:3

Multiscale Modeling of PowderBed–Based AdditiveManufacturingMatthias Markl and Carolin KornerDepartment of Materials Science, Friedrich-Alexander-Universitat Erlangen-Nurnberg,91058 Erlangen, Germany; email: [email protected]

Annu. Rev. Mater. Res. 2016. 46:93–123

First published online as a Review in Advance onApril 21, 2016

The Annual Review of Materials Research is online atmatsci.annualreviews.org

This article’s doi:10.1146/annurev-matsci-070115-032158

Copyright c© 2016 by Annual Reviews.All rights reserved

Keywords

additive manufacturing, selective electron beam melting, selective lasermelting, lattice Boltzmann method, finite element method, cellularautomaton method

Abstract

Powder bed fusion processes are additive manufacturing technologies thatare expected to induce the third industrial revolution. Components are builtup layer by layer in a powder bed by selectively melting confined areas, ac-cording to sliced 3D model data. This technique allows for manufacturingof highly complex geometries hardly machinable with conventional tech-nologies. However, the underlying physical phenomena are sparsely under-stood and difficult to observe during processing. Therefore, an intensive andexpensive trial-and-error principle is applied to produce components withthe desired dimensional accuracy, material characteristics, and mechanicalproperties. This review presents numerical modeling approaches on multiplelength scales and timescales to describe different aspects of powder bed fusionprocesses. In combination with tailored experiments, the numerical resultsenlarge the process understanding of the underlying physical mechanismsand support the development of suitable process strategies and componenttopologies.

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ANNUAL REVIEWS Further

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http://www.annualreviews.org/doi/full/10.1146/annurev-matsci-070115-032158

http://www.annualreviews.org/toc/matsci/46/1


Additivemanufacturing (AM):a process of joiningmaterials to directlybuild up objects from3D virtual prototypes,usually layer uponlayer (1)

1. INTRODUCTION

Additive manufacturing (AM) encompasses processing technologies of component fabrication byjoining materials, usually layer by layer (1). The process is also referred to as 3D printing, rapidprototyping, rapid manufacturing, or freeform fabrication. In the media, AM is often identifiedas the third industrial revolution (2). The high industrial demand is summarized in Wohlers Report2014, which states that the market for AM, consisting of all products and services worldwide, isexpected to grow from $3 billion in 2013 to more than $21 billion by 2020 (3).

Despite the media and industrial attention to AM, there are complex technologies and pro-cesses that are yet not fully controllable, reproducible, or predictable. The evolution of AM ischallenged by processability and quality issues, such as premature process terminations or faultsdue to distortion, cracks, or porosity. These issues have been addressed mainly by the choice ofprocess parameters, which have typically been found by a trial-and-error principle. Due to thetime consumption and expense of this procedure, the potential of AM technologies has hardlybeen exploited.

One step toward a controllable and reproducible process is in situ sensing and real-time control(4). The underlying correlations between process parameters and material properties are gainedby the combination of process observations and component analysis. Kruth et al. (5) review laserand powder bed–based AM technologies and try to understand the physical mechanisms and inter-actions with the material. Although these technologies can be used to process a variety of differentmaterials, the authors identify the need for further optimizations to increase the applicability.Newer technologies replace laser with electron beams, which limits the process to metal materi-als. Murr et al. (6) give a comprehensive overview of microstructures after laser or electron beammanufacturing. They extend the conventional materials science correlations between structure,properties, processing, and performance by the microstructural architecture that is adjustablewith these technologies. Approaches to gain further insight into the consolidation mechanismsapply numerical simulations in addition to process observations. For example, Al-Bermani et al.(7) compare experimental and numerical melt pool geometries to relate them with the final mi-crostructure. Korner et al. (8) further investigate numerical simulations and compare the resultswith experiments to identify the role of certain process parameters.

The physical effects occurring during AM act on multiple length scales and timescales. Lengthscales range from tenths of a meter for residual stresses acting on complete components to mi-crometers for beam and powder diameters to nanometers for the penetration depths of laserbeams. Timescales range from hours of a global heat treatment during manufacturing to min-utes for single-layer building and milliseconds for the interaction time between the beam andthe material. Many physical phenomena during processing act on small scales that are not easilyprobed by observation and measuring devices. Nevertheless, recognizing the interplay betweenthese phenomena is crucial for a deep understanding of the process behavior and the final com-ponent quality. Therefore, modeling approaches and numerical simulations on multiple lengthscales and timescales are ideal tools to gain further insights and to enable predictions by processparameter modifications suitable for further component topology optimization.

After a short introduction into the technological concepts of powder bed–based AM processes,the operant physical phenomena and manufacturing issues are described. Subsequently, the pow-der scale and continuum approaches used to numerically model the process are discussed in detail.Issues such as melt pool geometry and dynamics, porosity, surface roughness, and residual stressesare considered. Additionally, extensions of these approaches to model the microstructure evolu-tion during solidification are addressed. Finally, optimization aspects regarding the process andthe component topology are considered. On the basis of this state of the art, future research topicsare finally recommended.

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Powder bed fusion(PBF): “an AMprocess in whichthermal energyselectively fusesregions of a powderbed” (1)

2. POWDER BED FUSION PROCESSES

AM is classified by the American Society for Testing and Materials as one of the three pillarsof manufacturing engineering technologies: additive, subtractive, and forming (1). The term isdefined as “a process of joining materials to make objects from 3D model data, usually layerupon layer, as opposed to subtractive manufacturing methodologies” (1). The definition coversall methods of adding material to a 3D physical object but highlights that many state-of-the-artapplications are layer-based approaches. Powder bed fusion (PBF) is one of seven AM categoriesand includes all technologies applying thermal energy to partially fuse a powder bed (1).

2.1. Technological Concepts

Common PBF technologies are selective laser melting (SLM) (5, 9) and selective electron beammelting (SEBM) (10). A universal process chain comprises four steps: conceptualization, prepro-cessing, manufacturing, and postprocessing. During conceptualization, a virtual component modelis constructed with the help of computer-aided design, either user designed or automatic reverseengineered. The next step preprocesses the virtual model by slicing the data into several layers,depending on the layer thickness, and converting the data to a machine-conformable file format.Subsequently, the data files and process parameters are sent to the machine. The process parame-ters either are loaded from stored templates or are manually adjusted to fit the requirements of thebuild process. The PBF manufacturing step is illustrated in Figure 1 (top) for SLM and SEBM.The process starts with preheating the current powder layer up to the processing temperatureby a heater or electron beam. Some SLM processes operate at room temperature, at which nopreheating is necessary. Second, the cross sections according to the component model are meltedby a laser or electron beam. Once melting is finished, the process platform is lowered by one layerthickness. The powder particles provided by the powder tank or powder hopper are applied asa new powder layer by a roller or rake, and the process restarts with preheating. At the end ofthe build process, the component has to be removed from the start plate before the component ispostprocessed for application purposes.

Applying lasers for melting commonly requires an additional heater for preheating but allowsfor manufacturing in a shielding gas atmosphere under ambient pressure. The electron beam isused for preheating and melting, restricting the material variety to electrically conducting materialsand requiring a vacuum inside the build chamber.

2.2. Physical Phenomena

The many physical effects (visualized in Figure 1, bottom) that occur during PBF processesinfluence the process stability and the final component quality. Identifying and understanding thesephenomena and their interplay are crucial for successful manufacturing. The applied numericalmodels on the different physical effects are summarized in Table 1 and are further described insubsequent sections.

During heating, the powder bed is irradiated by a laser or electron beam, whereby the photon orelectron energy is transformed into thermal energy by absorption. Photons are generally absorbedwithin the first nanometers at the surface of the material (31). In contrast to opaque continuousmaterial, the powder bed allows for deep penetration due to multiple reflections at the particlesurface (31, 32). The absorbed thermal energy is distributed depending on the relative densityand reflectivity of the powder bed within the top powder layers. The penetration depth of theelectrons increases with increasing acceleration voltage of the electron beam gun (33). Theyare also deflected and scattered due to the interaction with the materials’ electrons and atomicnuclei.

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SLM SEBM SLM SEBM

Powder tank

Powderhopper

Startplate

Processplatform

Laserbeam

Electronbeam

Heater

Part

Roller Rake

Rake

Electron orlaser beamElectron orlaser beam

Absorptionor reflectionAbsorptionor reflection

Powder layerPowder layerMelt pooldynamicsMelt pooldynamics

CapillarityCapillarity

GravityGravity

WettingWetting

Heat conductionHeat conduction

Heat radiationHeat radiation

EvaporationEvaporation

Phasetransitions

Phasetransitions

MarangoniconvectionMarangoniconvection

SinteringSintering

POWDER BED FUSION PROCESS CHAIN

MELTING PHENOMENA

Electron beam

Preheating of powder layer1

2 Melting of cross section

Application of power layer4

3 Lowering of process platform

SLM SEBM SLM SEBM

Figure 1(Top) Principles of the PBF process chain for the SLM and SEBM processes. SLM is shown on the left and SEBM on the right of eachof the four subpanels. Each layer is heated up to the preheating temperature� before melting the component cross section�.Subsequently, the mobile process platform is lowered by the layer thickness�, and a new powder layer is applied before the processrestarts�. (Bottom) The dominant physical phenomena during melting are illustrated in a partially molten powder bed. Thetemperature distribution in the powder bed and on the melt pool surface is indicated by color-coding (blue indicates coolertemperatures, and red indicates warmer temperatures). The semitransparent melt pool surface enables visualization of melt pooldynamics by velocity arrows. The bottom of the melt pool is visualized in white and the beam source in semitransparent red.

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Table 1 Numerical models and their applied topics

Model Application(s)Section(s) ofthis article References

Discrete element (DE) Powder bed generation 3.1 11, 12

Monte Carlo (MC) Beam absorption and raytracing

3.2 13–15

Lattice Boltzmann (LB) Hydrodynamics,thermodynamics

3.3, 3.4, 3.6, 5 8, 16, 17

Finite volume (FV) Hydrodynamics,thermodynamics

3.3, 3.5, 3.6, 4.1,4.2, 5

18–21

Finite element (FE) Thermodynamics, mechanics 3.6, 4.1, 4.2, 5, 6 18, 22–25

Phase field (PF) Microstructure evolution 5 26

Cellular automaton (CA) Grain structure evolution 5 27–30

Thermal radiation, thermal convection, and evaporation of volatile elements cause a heat losswith biquadratic, linear, and exponential dependence on the surface temperature of the material,respectively. During SLM, heat convection between the material and the shielding gas occurs.In contrast, heat convection to the surrounding atmosphere is negligible during SEBM becauseof the vacuum in the build chamber. Due to heat conduction, the absorbed thermal energy isfurther distributed into the material, and temperature peaks at the surfaces are reduced. Thiseffect depends mainly on the thermal diffusivity of the material and the sintering grade of thepowder bed.

If preheating is applied, the base temperature of the powder bed is elevated, simplifying meltingand reducing temperature gradients during manufacturing. If the preheating temperature is higherthan the sintering temperature of the material, the single powder particles get interconnectedby small sinter necks. These presintered powder particles act as support structures during thesubsequent manufacturing and increase the thermal and electrical conductivity. The electricalconductivity is especially crucial during SEBM for discharging (34).

During processing, the material melts and forms a melt pool. Convection depends on viscosityand is driven by external forces like gravity, buoyancy, surface tension, capillarity, Marangonieffects, and evaporation pressure. Depending on the process and the material, these phenomenahave different impacts. The melt pool lifetime is commonly short, viscosities are low, and gravityplays a minor role compared with the roles of the other forces (35). Thermal expansion inducesbuoyancy and exerts thermal stresses. The high surface tension in combination with the wettingability of metals results in a smooth surface for stable melt pools. In contrast, unstable melt poolsare split up, and the surface tension causes the formation of single melt balls (36–38). Marangoniforces induce fluid motion away from the temperature peak in the center of the melt pool andincrease heat transport (5, 39). Due to high melt pool temperatures, the material evaporates, andthe resulting recoil pressures additionally drive the fluid motion. Especially in SLM processes,these pressures cause so-called keyhole formation, in which the laser beam penetrates into thematerial up to certain layer thicknesses, forming a vapor capillary (20). Selective evaporation ofvolatile elements additionally changes the local and global material composition (40).

After melting and consolidation of the material, the temperature decreases, and the materialsolidifies. Material shrinkage during solidification induces stresses in the surrounding materialthat can partially relax during successive layer processing (41). The residual stresses inside thecomponent are the main reason for distortions (9, 42).


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Depending on the temperature gradients and the processing temperature, a certain microstruc-ture evolves (6, 7, 40, 43). Due to the layer-wise manufacturing, repeated heat treatment of theheat-affected zone around the melt pool may change the microstructure by solid-state phasetransformations.

In the last step, a new powder layer is applied. Its characteristics are influenced primarily by thepowder properties and the previous layer surface. High flowability of the powder, depending onpowder properties such as surface topology, size distribution, and shape, is necessary to achievehigh relative density of the powder bed (11).

2.3. Manufacturing Issues

Many issues regarding process stability and the quality of the final components arise during PBFmanufacturing. At the beginning of each process, a set of process parameters is chosen, and thisset defines, e.g., the preheating and scanning strategy. The final component quality is often notacceptable due to defects or poor material properties. In the worst case, the process prematurelyterminates before the component is finished.

Layer bonding defects occur due to insufficient heat input. In this case, the powder particlesdo not completely melt and are not consolidated with the bulk material; as a result, gas of the sur-rounding atmosphere is entrapped in the final material. Additionally, there may evolve connectedchannels of binding faults through many layers (44). Another source for porosity is pores insidethe powder particles, which cannot escape out of the melt pool (45).

Due to shrinkage during solidification and cooling, the dimensional accuracy, especially that ofthe first layers or overhang areas that are loosely coupled to the powder, is diminished. In addition,stresses are induced during these phases as well as during volume expansion in heating and melting(41) because, e.g., distortion and cracks diminish the component quality and mechanical properties(42). Delamination describes the effect whereby the edges of the geometry bulge out due toresidual stresses after solidification and layer bonding defects. Delamination depends mainly onthe scanning strategy and the energy input (46).

Instable melt pools cause the so-called balling effect. On the one hand, single melt balls areformed due to the dominant surface tension exceeding the local wetting ability of the previouslayer (16, 38). On the other hand, Plateau-Rayleigh instability leads to melt pool fragmentationfor length-to-width ratios larger than 2.1:1 (47).

Another effect, occurring mainly with high-energy beams, is material transport (45). Themaximum temperatures and evaporation rates increase, and a disadvantageous confluence of meltpool lifetime, surface tension, and evaporation pressure finally causes the material to accumulateat certain locations up to a height greater than the layer thicknesses.

Delamination, balling, and material transport cause an uneven component surface after meltingand solidification. If the height of these perturbations reaches the layer thickness, the powderdelivery is disturbed. In the near vicinity of these defects, grooves or empty spaces without powderparticles arise. Once the height of the defects further increases, the rake or roller may collide withthe component and become damaged, which causes premature process termination.

If none of these effects occurs, PBF-processed components achieve a flat and even top surface.Nevertheless, because SLM processes often operate in the keyhole welding mode, in which thebeam drills into the material, droplets are able to leave the melt pool and splash onto the neigh-boring surface (38). In contrast to the top surface, side walls or inclined structures exhibit surfaceroughness on the scale of the powder particle size (8, 48). Therefore, SLM processes show smallerroughness values than does SEBM due to smaller powder size distributions, layer thicknesses, andbeam diameters.

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A highly investigated research area is microstructure evolution during solidification and cool-ing; such evolution affects most of the component’s mechanical properties (7, 43, 49). Due tohigh melting temperatures, selective amounts of a metal alloy can evaporate and change the localmaterial composition and the resulting microstructure (50).

3. POWDER-SCALE APPROACHES

This section focuses on mesoscopic numerical methods, which resolve the geometry of each pow-der particle. In addition to thermodynamic aspects, these models include hydrodynamic effects.All current numerical methods are based on mesh approaches, for which spatial resolutions on theorder of micrometers are necessary to resolve the particles (16–18, 51, 52). Most of these modelsare explicit, which limits the time step by the Courant-Friedrich-Lewy condition to nanosecondsto account for high melt pool velocities. Regardless of whether 2D or 3D models are applied,the demanding numerical effort limits the computational domain on single-line or single-layerapplications to the range of micro- to millimeters. In addition, the height of the previous layersin many simulation setups is shorter than the thermal length, which is proportional to the squareroot of the simulation time and the thermal diffusivity. Therefore, the bottom boundary is anactive heat sink and cools the whole domain. Nevertheless, the most important hydrodynamiceffects during melting and solidification—such as balling, porosity, and surface roughness—canbe studied with these domains. Therefore, the incompressible Navier-Stokes equation and themass conservation equation are solved in combination with the energy conservation equation.

Many hydrodynamic effects such as wetting, capillarity, and evaporation require an appropriatesurface representation for surface points, normal directions, and curvatures. Most of these quanti-ties are computed by volume-of-fluid or level set methods. In the volume-of-fluid approach, eachelement has one value representing the amount of material inside the element. With different al-gorithms, the surface representation can be approximated. Level set approaches directly store thedistance and direction of the current element center point to the surface. Although the interfacerepresentation is more exact, interface methods have difficulties with respect to mass conservation.

3.1. Powder Bed Generation

During PBF manufacturing, each new layer requires the distribution of new powder particles intothe build tank, illustrated in Figure 1 (top). In the SEBM process, the powder layer is achieved bya rake that deposits particles from two powder heaps in front of two powder hoppers. AlthoughSLM machines using a rake exist, a roller is typically applied. The powder particles are providedby a separate powder tank equipped with a mobile process platform. Depending on the productionprocess, the powder particles have different shapes and size distributions. Because high flowabilityof the powder is crucial, nearly spherical powder particles are often applied. Therefore, the shapeis numerically modeled by perfect spheres. However, many computational approaches disregardthe size distribution of the particles as well as the stochastic distribution with varying relativedensity by applying regularly packed powder beds of uniform size.

Korner et al. (16) evaluate the importance of the stochastic powder bed and apply a so-calledraindrop model to generate a powder bed for 2D simulations. This model is also expandable to3D (53). Each particle is separately placed on the previous layer by computing the vertical locationto the first contact and then rolling downward until a steady state is reached. The natural relativedensity with this approach is approximately 74% and 60% in 2D and 3D, respectively. To adjustthe relative density to a reasonable percentage, between 45% and 60%, particles are removed untilthe desired packing density is reached (16). One drawback of the particle removal is unphysical


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Discrete element(DE) method:a numerical modelcapable of handlingindividual particles ofany shape in acontinuous domain;interactions are viewedas a transient problem(54)

Monte Carlo (MC)method: a stochasticapproach in whichmultiple repeated,random samplesapproximate thesolution (13)

holes in the powder bed, which may lead to pores or defects. Additionally, the method is not wellsuited for parallel execution on computer clusters, which makes it less preferable for demanding3D simulations.

With regard to the influence of the final properties of the powder bed on melting behavior, therelative density is most important (16). A simplification of the complex distribution process is toreplace the rolling and raking process with a free-fall discrete element (DE) model (11, 17). Eachparticle is able to move in a continuous space limited by boundary walls. In addition to gravityforces, normal and tangential forces act on the particles during contact with each other and modifythe particle motion. Cohesive and static frictional forces are neglected to achieve arbitrary packingdensities. The free-fall and packing process is finally interrupted once the desired relative densityis reached. This model is well suited for parallelization, is very efficient, and consumes only a fewpercent of the total computational time for PBF simulations.

Parteli (12) investigates with a DE method the behavior of complex-shaped particles duringpowder application. Each particle is treated as a single entity but is composed of multiple spheres.Additionally, the roller and rake geometry is modeled as a moving boundary condition, drivingthe particles during distribution. Studies of particle interaction forces (55) reveal the crucial roleof cohesive forces in the final relative density of the powder bed, which is intended to be includedin the DE approach for a more realistic powder distribution simulation.

3.2. Heat Source Modeling

The temperature and its gradients are the most important quantities because many mate-rial properties—such as density, surface tension, heat conductivity, heat capacity, and thermaldiffusivity—are temperature dependent. These properties induce thermodynamic, hydrodynamic,and mechanical effects, which determine the final component quality. Due to this major influence,careful modeling of the beam as a heat source is crucial.

The heat input is divided into a horizontal intensity distribution and a vertical absorptiondistribution. The horizontal intensity is naturally very similar to a bell-shaped form and is thereforecommonly modeled by a Gaussian density function (16, 22). Efficiency factors account for energylosses for the beam control and the reflection on the material surface. The laser and electron beamshow different properties regarding the length scales of their penetration depths.

During SLM, most of the laser intensity is reflected, and only a fraction is absorbed to a depth ofseveral nanometers (56), which is commonly modeled by surface heat sources. During SEBM, eachelectron of the beam is deflected, backscattered, or absorbed once the electron hits the materialsurface. Electron beams exhibit a penetration depth on the micrometer scale, depending on thekinematic energy induced by the acceleration voltage of the electron beam gun and the atomicnumber of the material. Depending on the acceleration voltage and the atomic mass, the affectedarea forms a shape ranging from a bulb to a hemisphere. A suitable numerical approach to modelthe electron penetration into the bulk material is the Monte Carlo (MC) method. Drouin et al.(13) develop simulation software intended to assist in interpretation of imaging and microanalysisof scanning electron microscopes. Mahale (57) applies the software ability of tracking an electron’spath inside the material to estimate the absorption coefficient of different materials. However, thisprocedure does not fully exploit the capabilities of the MC approach. It is possible to determinea full absorption profile inside the material depending on, e.g., the acceleration voltage or theinclination angle to the target surface. Klassen et al. (33) study different semiempirical approachesto develop a phenomenological model of absorption profiles for an electron beam for differentmetals and compare the final model with literature values. This model and two approximations,which are also suitable for laser absorption, are well suited for parallel execution (58). Validating

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Lattice Boltzmann(LB) method:involves cellularautomaton modelingof discrete particlekinetics by discretespace, time, andparticle velocities (64)

this model using the MC method opens the opportunity for further improvements and applicationsto other materials.

In PBF processes, the beam can penetrate deeper into the powder bed than into the corre-sponding bulk material. Photons of a laser beam are highly reflected, and at each reflection onlya small fraction of its energy is absorbed at the particle surface. Therefore, the photons penetrateinto the powder bed and are absorbed in deeper regions. The energy absorption is distinctivelyhigher than the absorption coefficient of the material due to the multiple reflections. This behavioris often modeled by ray-tracing MC approaches, whereby the trajectories of the single photonsare tracked. Wang & Kruth (14) examine such a model for absorption during the laser sinteringprocess of a Fe-Cu powder mixture. The authors conclude that energy absorption is crucial fornumerical simulations to correctly predict the sintering zone. A similar approach is used by Zhouet al. (15), who examine irradiation on a bimodal powder bed. The approach is validated withexperimental data and is applied to the issue of balling.

3.3. Melt Pool Dynamics

Melt pool dynamics are driven mainly by capillary and Marangoni forces, evaporation pressure,and the wetting ability of the powder particles and the previous layer. Scharowsky et al. (35)observe these dynamics with a high-speed camera and analyze melt pool lifetime, size, andoscillations. Numerical simulations examined by Scharowsky et al. (59) show good agreementwith high-speed camera measurements.

Korner et al. (16) developed the underlying 2D numerical method. It relies on a latticeBoltzmann (LB) approach (60), which is extended by free surface boundary conditions treatingthermodynamics (61), surface tension, phase transitions (62), and wetting (63). They apply thismodel to the balling phenomenon of single scan lines during SEBM of Ti-6Al-4V. Single-spotmelting examples show the influence of the wetting conditions on balling: The larger the wettingangle, the higher is the balling tendency. Additionally, relative density and stochastic compositionhave a major influence on melt pool geometry. Figure 2 shows the temporal evolution of a meltpool during single-line scanning at 600 W and 1.1 m/s. The balling formation is not related toa large melt pool or the Rayleigh instability, but the single droplets are directly formed duringmelting influenced by local powder arrangement, wetting, and capillarity.

The studies of Korner et al. (8) are based upon these results and investigate the surface qualityof SEBM-manufactured vertical walls of Ti-6Al-4V as a function of scan speed, line energy,

1 mm

d t = 3.3 msd t = 3.3 msa t = 0.0 msa t = 0.0 ms

e t = 4.4 mse t = 4.4 msb t = 1.1 msb t = 1.1 ms

f t = 9.9 msf t = 9.9 msc t = 2.2 msc t = 2.2 ms

BeamBeam

Figure 2Temporal evolution of melt pool and balling during single-line scanning in SEBM of Ti-6Al-4V at 600 W and 1.1 m/s. Melt poolfragments during melting and single droplets are formed. Reprinted with permission from Reference 16. Copyright 2011, Elsevier.


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240 mm/s 600 mm/s 1,200 mm/s 240 mm/s 600 mm/s 1,200 mm/s

120 mm/s 300 mm/s 600 mm/s 120 mm/s 300 mm/s 600 mm/s


Layer thickness: 100 µm Layer thickness: 70 µm

0.5

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0 J/

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J/m

m

240 mm/s 600 mm/s 1,200 mm/s 240 mm/s 600 mm/s 1,200 mm/s



Layer thickness: 100 µm Layer thickness: 70 µma b

1 mm1 mm

Figure 3Comparison of wall formation of Ti-6Al-4V during SEBM, as a function of scan speed, line energy, and layer thickness, between(a) simulations and (b) experiments. Wall quality increases with smaller layer thickness and higher scan speed. Wall thickness increaseswith higher line energies. Adapted from Reference 8 under a CC BY 3.0 license.

and layer thickness, whereby the line energy is the ratio of beam power and scan speed. Figure 3illustrates the qualitative agreement between the wall quality predicted by simulations (Figure 3a)and experimental results (Figure 3b). Wall quality increases with smaller layer thickness and higherscan speed. Higher line energies enlarge the total wall thickness. The numerical simulations revealthat the balling mechanism is responsible for beads and extrusion at the surface of the walls, whichare much larger than the powder particle diameter. The interaction time of the electron beamwith the material is compared with the diffusion time through one layer, and an optimal scan speedin combination with single-particle layers is recommended.

Further model extensions include the incorporation of heat radiation and evaporation (65).Comparisons of melt pool depth and width with experiments on Ti-6Al-4V with different beampowers and scan speeds show excellent agreement. Accounting for evaporation is recommendedto achieve better predictions of melt pool geometries and processing windows in cases of hightop surface temperatures due to high melt pool dynamics induced by high evaporation pressures.This is especially the case for SLM processes operating in the keyhole welding mode. However,the numerical effort in general increases by accounting for the evaporation recoil pressure due todecreased spatial resolution from 5 to 1 µm.

3.4. Porosity

Numerical models on the powder scale are able to predict the evolution and morphology of residualporosity within the bulk material. Different formation mechanisms can be identified.

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Finite volume (FV)method: a specializedfinite element methodfor, e.g., conservationlaws computing thefluxes over theboundaries of arbitraryvolumes by an integralformulation that islocally conserving (67)

Bauereiß et al. (44) study defect generation and propagation mechanisms during SEBM byapplying the LB model of Korner et al. (16). Bauereiß et al. compare cubes of Ti-6Al-4V man-ufactured at a scan speed of 0.8 m/s and different beam powers between 90 and 180 W withnumerical results. At a beam power of 90 W, high porosity with noticeable channels across manylayers is observed; Figure 4 illustrates the mechanism behind the formation. Due to the stochasticnature of the powder bed and the insufficient melt depth, the top surface of the processed layeris uneven (layers 1 and 2). Compared with thermal diffusion, hydrodynamic motion driven bysurface tension forces is much faster. Therefore, molten particles coalesce with neighboring solidmaterial, which is not necessarily the previous layer. Thus, a defect is generated in layer 4 andevolves over more than 10 layers. Due to the process parameters, the melt pool is not large enoughto span the defect and fill it with liquid material. In contrast, the molten particles are attracted bythe defect side walls, and the channel grows.

During SLM, the formation of a keyhole stabilized by vapor or plasma pressure is common.At the end of the melt pool, the keyhole collapses and is filled with liquid material. Depending onthe solidification conditions, residual pores may evolve (66). Panwisawas et al. (51) report thosepores for Ti-6Al-4V cubes manufactured at a laser power of 400 W and scan speeds between 2and 4.2 m/s. They apply a finite volume (FV) method and compare the melt pool motion withthe resulting pore geometry. Spherical and ellipsoidal pores are found for smaller scan speeds, atwhich the beam interacts with a small material domain. In contrast, higher scan speeds can causethe new layer to tear apart from the previous layer and to form elongated pores.

3.5. Surface Roughness

Surface roughness describes small-scale surface irregularities. This is a noticeable characteristic ofPBF processes because partially molten particles primarily describe the final surface topography(48). Depending on the final application, surface roughness might be beneficial for, e.g., contactbetween bones and medical implants (69). With appropriate surface modifications to generateinterconnected macro porosity, the fixation is believed to be further improved (70). Nevertheless,in most applications surface roughness is undesirable because it weakens the mechanical propertiesas a source of crack initiation (71).

Strano et al. (48) investigate the surface roughness of an SLM component with different buildorientations made of steel 316L. On the basis of measurements, they derive a mathematical modelin which surface roughness depends on the slope angle. They conclude that surface roughness issensitive to any parameter affecting the heat distribution at the surface.

Qiu et al. (72) apply an FV method (51) to study the influence of melt pool motion on the surfacestructure of SLM-manufactured cubes of Ti-6Al-4V at a laser power of 400 W and scan speedsbetween 2 and 4 m/s. They conclude that melt pool stability is the most important determinant ofsurface roughness. In addition, a poor surface finish increases the possibility of channel-like faultsin successive layers. They identify Marangoni forces and recoil pressures as the driving forces formelt pool instabilities. Higher scan speeds increase the melt pool surface, amplifying these effectsand causing melt pool splashing. The same result is observed for larger layer thicknesses, at whichporosity and surface roughness are highly increased.

Gurtler et al. (52) apply another FV method for SLM to simulate melt pool dynamics basedon a laser welding application (20). Therefore, the model takes into account both evaporation andthe resulting recoil pressures forming the keyhole. Gurtler et al. (73) further study the influence ofpowder distribution on the process stability. They evaluate different powder size distributions ofAl-12Si-Mg and validate the resulting relative densities and thermal conductivities. Subsequently,line defects, in which no particles are distributed, are introduced into the powder bed, and the


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4

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6

5

Figure 4Evolution of a channel-like fault during SEBM of Ti-6Al-4V at 90 W and 0.8 m/s over 14 layers. Illustratedare the current layer before (left) and after (center) powder application and the temperature distributionduring melting (right); violet regions denote liquid. Capillary forces pull the liquid material out of the channelto the neighboring solid particles. Reprinted with permission from Reference 44. Copyright 2014, Elsevier.

melt pool depth and volume are compared at 100 W and 0.75 m/s. In the case of size distributionswith smaller particles, the defect can be slightly repaired by smoothing the final top surface.

3.6. 3D Approaches

The computational effort for 3D simulations increases by a factor of hundred to thousand com-pared with that for 2D simulations. The expected computational times on simulation workstations

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Finite element (FE)method: an implicitmethod to solve partialdifferential equationsby basis functions on amesh of simplegeometric elements(68)

accordingly increase from hours or days to weeks or years. Therefore, these approaches requireparallel and distributed execution on computer clusters. This results in a more complex imple-mentation task on the basis of parallel software frameworks.

Ammer et al. (17) develop a 3D LB method for the simulation of SEBM on Ti-6Al-4V, includinga statistical powder bed generation algorithm and a volume heat source model (33). The porosity isdirectly measured by the known gas fraction inside the layer due to the volume-of-fluid approachfor mass advection. These measurements are used in combination with the peak temperatureto define a process window at which appropriate components are producible. Ammer et al. (74)validate the numerical results with an experimental process window (50). On the basis of this work,Markl et al. (75) investigate the process parameter optimization for higher build rates. The beamscan area and the line offset are modified to increase the scan speed of the electron beam. Figure 5illustrates modified melt pool geometries and residual porosity during hatching of a single powderlayer on bulk material when the beam crosses the simulation domain on the fifth scan line beforereturning in the next scan line. Increasing the beam scan area with constant beam power andspeed decreases the melt pool depth and causes porous results (Figure 5c). By increasing the beampower and speed, larger melt pools reach the previous layer and are still liquid at the return of theelectron beam, resulting in almost no porosity (Figure 5d ). These results reveal the opportunity toimprove scanning strategies and process parameters regarding the porosity of the final component.The approach is also successfully applied in multilayer simulations of similar hatches (11).

Markl et al. (27) further investigate with this model the quality of walls made of Ti-6Al-4Vprocessed at a fixed beam power of 150 W and different scan speeds and beam diameters. Figure 6shows the numerical results of walls consisting of 10 layers built with two different beam diametersand line energies. The top surface of the current melt pool and some unmolten particles areillustrated in the investigated boxes of the wall. Below, the isosurfaces represent porosity and layerbonding defects emerging from the wall boundaries. Reduced beam diameters or line energiesdiminish wall quality by introducing porosity either at the beginning of the wall or as layer bondingdefects at the boundaries.

Khairallah & Anderson (18) apply a Lagrangian-Eulerian approach by combining a finiteelement (FE) and FV method on melt pool simulations of SLM. Instead of a ray-tracing approachfor the heat input to their stochastic powder bed of the laser, they use a continuous absorptionmodel (76). They investigate single scan lines of steel 316L at 2 m/s and different beam powersbetween 100 and 400 W. The melt pool always separates during melting, although the length-to-width ratio significantly changes. In contrast to the opinion of Khairallah & Anderson (18),this melt pool fragmentation is correlated not with melt pool instabilities (5), but with the localstochastics of the powder bed and the melt pool geometry. King et al. (77) applies the samemodel to study overhang areas, as illustrated in Figure 7. Severe balling occurs due to high meltpool fragmentation (Figure 7a). With almost the same line energy and a smaller scan speed, acontinuous track formation is achieved after the second layer (Figure 7b). The smaller scan speedachieves an almost fully connected melt pool. However, the model misses some crucial physicaleffects such as Marangoni forces, evaporation, and radiation. The maximum temperatures arehigher than 5,000 K, which is far away from physical values. Additionally, the melt pool geometrychanges when evaporation and Marangoni forces are taken into account.

4. CONTINUUM APPROACHES

Numerical grid methods representing each powder particle require fine meshes. With a meanelement size of approximately one-tenth of the mean particle size, an appropriate representation ofthe interface between the material particles and the surrounding atmosphere is achieved. Regarding


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2.5 kW, 25 m/s400-µm beam



Temperature (K)

1,200

1,400

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2,000

2,200

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1 2

1 2

1 2

a

b

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Position marker 1(domain exit,

fifth scan line)

Porosity

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(1,900 K, 2,100 K,2,300 K, 2,500 K)

Powder layer

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Position marker 2(domain entrance,sixth scan line)

Isosurface ofpowder layer

1 2

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←−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−Figure 5Melt pool geometries during SEBM hatching of one powder layer on bulk material of Ti-6Al-4V with different beam parameters.(a) Melt pool geometry, beam scan path, the powder layer surface, and residual porosity. (b–d ) The simulation results are taken at twobeam positions on the fifth and sixth scan lines. Adapted from Reference 11.

the SEBM process with mean particle diameters commonly larger than 50 µm, a simulationdomain of 1 mm3 is represented by 8 million cubic elements with a side length of 5 µm. Thecorresponding computational load requires small-scale computer clusters. For SLM processes,mean powder diameters down to 10 µm are applied. At such diameters, the number of cubicelements increases to 1 billion, which is computable only by large-scale computer clusters. Whenthe sample domain volume of 1 mm3 is compared with real component dimensions, these methodsare far from representing even small geometries.

A common approach to reduce the computational effort is to treat the powder bed as a contin-uum. The main advantages are the simpler interface between the material and the atmosphere andthe decrease in the spatial and temporal resolution. The continuum approach omits the compu-tation of a surface representation, including curvature, surface tension, and wetting effects, whichare in general computationally demanding. Depending on further approximations of the PBF pro-cess, different time steps and minimum element sizes are required. Considering each single scanline requires time steps as fine as in mesoscopic simulations. In this case, surface and volumetricheating models are available. If the ratio of penetration depth to element size is much larger than 1,

400-µm beam200-µm beam

0.25

J/m

m0.

50 J/

mm

Figure 6Multilayer simulations of SEBM-manufactured walls of Ti-6Al-4V at 150 W. Bulk material (light gray) and isosurfaces of the topsurface and interior porosity within the wall are seen. Smaller beam spot and lower line energies do not improve wall quality. Adaptedfrom Reference 27.


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Layer 1200 W2 m/s

Layer 1166 W

1.6 m/s

Layer 2166 W

1.6 m/s

a

b

Figure 7Melt pool geometry and temperature distribution at overhang areas produced by SLM. The first layer in twocases (panels a and b) is not connected due to balling. In the second layer, the track is partially remelted andis finally continuous (panel b). Adapted from Reference 77 with permission from Taylor & Francis on behalfof The Institute of Materials Minerals and Mining. Copyright 2015, The Institute of Materials Minerals andMining.

a volumetric heat source is recommended (78). However, the combination of many scan lines intoscan patches or complete scan layers enables heat input in only a few time steps. The computa-tional effort can be further reduced by combining many single layers to one composite layer. Ifthis approach is applied, the minimum element size is restricted by the thickness of the compositelayer; otherwise, the minimum element size is restricted by single-layer thickness. Multilayer sim-ulations are often achieved by the so-called active element technique; i.e., the numerical domain isinitialized with all necessary elements, and only the elements corresponding to the current layersare activated. If one assumes a single-layer or composite layer thickness of 50 µm, the samplevolume of 1 mm3 is represented by 8,000 cubic elements, and the corresponding computationaleffort is attainable on a single desktop computer. These modifications enable the application oflarger domains up to the scale of whole components.

The continuum approach introduces a new powder phase into the numerical model: Thethermal conductivity and density are different from those of the bulk material (32, 79, 80). Tocompute these properties, the porosity of the powder bed is determined, which directly reveals thepowder density. The thermal conductivity is then interpolated by using various functions betweenzero and the bulk material value depending on the porosity, e.g., a linear (24) or biquadratic (81)relation. Once the material reaches the liquidus temperature, the material properties in the affectedelements are modified to those of bulk material. Some approaches also consider the consolidationof the material, whereby excessive elements are deleted from the model (81).

Beam scattering and intensity profiles in powder beds generated by ray-tracing methods orobserved by experiments are summarized in continuous models. These models neglect the lateral

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spread by assuming compensation from neighboring regions and apply an intensity profile in thevertical direction. When one applies the absorption behavior of the compact material to a powderbed, the relative density has to be taken into account. In the simplest approach, the penetrationdepth in the bulk material is multiplied by the relative density. The higher penetration due tomultiple reflections of a laser beam is often modeled by exponential functions (82). Shen & Chou(83) assume a conical volumetric geometry with a linearly decreasing intensity. Zah & Lutzmann(22) approximate the absorption profile with a polynomial function, whereby the main energy isdeposited near one-third of the penetration depth. Gusarov & Kruth (32) develop a model for theabsorption of a laser beam in a metal powder bed. Their model is based on the radiation transferequation, and comparisons to MC approaches reveal good accordance, except that in the firstmicrometers of penetration, the absorption is overestimated.

4.1. Melt Pool Geometry

Macroscopic studies on melt pool geometry require primarily the solution of the heat conservationequation, including the beam energy source term. Additionally, heat sinks of thermal radiationand convection with the surrounding atmosphere for SLM are often taken into account. However,in general a flat top surface is assumed, and only a few of the following approaches consider heatlosses due to evaporation (81), which are in most cases not negligible. Nevertheless, these modelsallow for a rough approximation of melt pool geometries by measuring the dimensions of theisothermal at the liquidus temperature and allow for a comparison with experimental observations(22, 84–86) or the development of closed-loop control systems (82). Increasing the numerical effortby coupling it with hydrodynamic movement improves the melt pool geometry predictions (87,88). These models also require a flat top surface of the melt pool, whereby the applied Marangonieffect mainly drives the fluid and changes the resulting melt pool dimensions and heat conduction.

Loh et al. (81) apply an FE method on SLM of single lines and investigate different meltpool geometries depending on parameter modifications to beam power (150 W, 300 W) and scanspeed (0.5 m/s, 1.14 m/s). The numerical model also includes evaporation because the materialis the aluminum alloy AA6061, in which a significant portion (up to 50%) of the processed layerevaporates. This effect is taken into account in combination with the thermal volume shrinkage;the material properties in the affected elements are modified to act as atmosphere elements.That is, the thermal conductivity is lowered by certain orders of magnitude. Additionally, thedensity and specific heat capacity are almost set to zero by applying the values from aluminumgas. The corresponding numerical findings of melt pool depth and width are in accordance withexperiments.

Gusarov et al. (47) study Plateau-Rayleigh capillary instability during SLM of steel 316L, whichis one cause of the balling effect. Reducing the scan speed from 2.4 to 1.2 m/s at 45 W stabilizesthe process by decreasing the melt pool length-to-circumference ratio and increasing the contactarea of the melt pool with the substrate. Experimental results are in accordance with the stabilitycriterion and are summarized in a stability map (89). The numerical simulations of single lines aresuccessfully applied to predict melt pool length and circumference and the corresponding stability.

Zah & Lutzmann (22) study single-line and single-layer simulations of steel 316L by SEBM,using an FE method. The effects of delamination and balling are the subject of this research.However, the model only comprises thermodynamics with the dynamic electron beam as a volumesource and heat radiation at the top surface. Due to the missing hydrodynamics, Zah & Lutzmannevaluate different beam powers and scanning speeds and determine the length-to-width ratio toestimate the formation of melt balls. The best configuration with the lowest ratio is subsequentlythe starting point for further experimental investigations. Contuzzi et al. (90) apply a similar model


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a

Melt pool Melt pool Melt poolMelt pool

b c

Relative densityPowder Bulk

Figure 8Melt pool geometry and relative density from powder to bulk at overhang areas for SLM of steel 316L at 167 W and 1.6 m/s, when thebeam enters (a), returns (b), and exits (c) the overhang area. The melt pool separates at the overhang area. Adapted with permissionfrom Reference 92. Copyright 2014, Springer.

to simulate three successive layers of steel 316L during SLM. Although they omit heat radiation,they achieve similar melt line depths and widths for a laser beam at 100 W and 0.45 m/s.

Soylemez et al. (84) also investigate the length-to-width ratio and combine it with melt poolarea. On this basis, Cheng & Chou (85) study the correlation of these two values for Ti-6Al-4V during SEBM with the process parameters of scan speed, beam diameter, and beam power.The underlying idea is to find suitable process parameters to establish constant conditions duringthe whole build. Almost all parameter modifications have a significant influence on the inspectedquantities. Of secondary significance for the length-to-width ratio are modifications to beam powerand the combination of beam diameter and scan speed. For melt pool area, the combination ofbeam diameter and beam power is of minor significance.

Ilin et al. (91) investigate manufacturing of steel 316L samples by SLM with inclined side wallsby a 2D FE method with different parameters from 100 to 300 W and 6 to 10 m/s. Numericalsimulations reveal overheating at inclined walls, which cause balling and bad dimensional accuracy.Ilin et al. develop a correction coefficient depending on the layer height of the sample, whichincreases the scan speed linearly up to the tenth layer by 10% to 25% in accordance with theinclination angle. This modification results in a continuous melt pool geometry and therefore inmore stable build conditions. Hodge et al. (92) study melt pool behavior at overhang areas for SLMof steel 316L [as do King et al. (77)], as illustrated in Figure 8. Similar overheating as with inclinedwalls occurs at the overhang area, and a separated melt pool is visible. The same strategy of reducedbeam intensity can homogenize the local build conditions and improve dimensional accuracy.

On the route to reliable and reproducible quality standards, process monitoring is a crucial fac-tor (4). Schilp et al. (82) therefore compare thermodynamic SLM simulation results with thermalmeasurements. They subject a complete model of an IN718 turbine blade to an FE approach. Thegeometry is transferred by the sliced representation into the mesh, and the scan paths are collectedto so-called load steps, whereby the complete scanning of one layer is combined in four load cycles.After application of several layers, temperature accumulations are detectable and indicate regionswhere the scan parameters should be modified.

Jamshidinia et al. (87) use an FE approach in combination with an FV method to simulateheat distribution during SEBM of Ti-6Al-4V, including the hydrodynamic movement of the

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1 2

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z = 0.0 mm (top surface)

z = –0.35 mm

x = –0.35 mm

x = 0.35 mm

Scanning direction

y

x

z

x

y

x

Temperature (K)

1,870

2,116

2,362

2,608

2,854

3,100

Temperature (K)

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1,699

3,100

a cb

Pure thermal modelThermal-fluid flow model

12

Figure 9Melt pool comparison of SEBM at 840 W and 0.1 m/s between a pure thermal model (1) and a thermal-fluid flow model (2) in top view(a,c) and cross section (b). Fluid motion in the melt pool reduces peak temperatures and causes wider and shallower melt pool geometry.Reprinted with permission from Reference 87.

melt pool. In addition to heat, mass, and momentum conservation, the model covers frictionaldissipation, buoyancy, phase transformations, radiation, and Marangoni convection. Because themodel assumes a flat top surface of the melt pool, no surface tension–induced fluid motion istaken into account. The approach of Zah & Lutzmann (22) to couple the electron beam as a heatsource is applied. Melt pool dimensions of single-line tracks with beam powers between 480 and840 W and scan speeds between 0.1 and 0.5 m/s are compared with experiments and show goodagreement. Furthermore, the differences between this model and a pure thermal model withouthydrodynamics (illustrated in Figure 9) are highlighted; deeper, narrower, and hotter melt poolsare predicted. Yuan & Gu (88) study similar topics. They apply an FV method to the physicalmechanism during SLM of a nanocomposite, whereby the laser heat input is treated as a surfacesource. They further compare the influence of modifications to laser power and speed on melt poolgeometry and lifetime with experimental results on porosity, microcracks, and melt ball formation.

Jamshidinia & Kovacevic (93) study the influence of different spacings between SEBM-manufactured thin plates made of Ti-6Al-4V from 5 to 20 mm on the surface roughness. Their FEapproach (87) modeling solely heat conduction. Heat input is applied by investigating single-layerexperiments of melting two plates at 600 W and 0.1 m/s. During melting, the distance is largeenough that no interaction occurs. In contrast, after cooling down for 5 s, the maximum temper-atures of the larger distances are significantly reduced. Multilayer experiments of five successivelayers reveal the same trend. In accordance with Strano et al. (48), Jamshidinia & Kovacevic con-clude that lower surface temperatures reduce surface roughness, which is achieved by applyingthe maximum plate spacing of 20 mm.

King et al. (66) investigate keyhole mode SLM of steel 316L by applying the numerical modeldescribed by Verhaeghe et al. (94). The simulation results agree with experimental observations ofmelt pool geometry. Additionally, King et al. introduce the relationship of normalized enthalpy,which combines the effects of beam power, scan speed, and beam size in one quantity. Theyconclude for many different parameter combinations, assuming a 50-µm layer thickness and acertain particle size distribution, that a constant threshold is suitable for distinguishing between


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conduction and keyhole mode melting. This parameter combination into a single quantity is adesired goal for understanding and predicting a certain process behavior.

4.2. Residual Stress and Distortion

The stresses remaining inside a component after fabrication are termed residual stresses (41).The underlying mechanism is termed the temperature gradient mechanism (TGM). Due to thelocal heat input, temperature gradients arise, the material strength decreases, and the materialexpands. The surrounding material suppresses the expansion, and upon reaching the yield strength,the material is plastically deformed. During cooldown, the material shrinks and induces stressesdependent on the position and solid-state phase transformations.

After the component is removed from the surrounding powder bed and the support structures,these stresses partially relax, depending on the geometry, and deform the final component. Thegeometry, the sintering degree of the surrounding powder, or the size and amount of supportsinfluence thermal cooling behavior and have a major influence on residual stresses. To investigatethese issues, it is necessary to model the whole component, including support structures, thesurrounding particle bed, and the building platform.

Mercelis & Kruth (41) derive a simplified mathematical model to investigate residual stresses.Many assumptions, e.g., room temperature manufacture and uniform stress in each layer, arenecessary. Nevertheless, this model is able to predict the described general appearance of residualstresses.

Suitable numerical methods are thermo-mechanical FE models on the macroscopic scale, atwhich the powder bed is considered as a continuum with homogenized properties. Large temper-ature gradients in combination with small beam diameters and layer thicknesses cause fine gridresolution if single melt lines are resolved (95, 96). Due to the high computational effort, approx-imations of the manufacturing process for complete components, e.g., heat input for scan patchesor complete layers and the combination of many layers into one process step, are common.

Matsumoto et al. (97) have done early work on residual stresses during SLM, applying a 2D FEmethod. They study the top view of melting a single layer of powder and analyze the residual stressdepending on the track length. On the basis of these results, they propose today’s state-of-the-artisland scan strategy, whereby the whole layer is segmented into subareas with short track lengths.

Jamshidinia et al. (21) extend their numerical FV model for heat distribution (87) and coupleit to an FE method to investigate residual stresses during SEBM of Ti-6Al-4V. Both modelsare solved simultaneously, whereby only the temperature information is exported from the FVto the FE solver. They perform single-line tracks at 0.1, 0.5, and 1.0 m/s and 840 W and evaluatethe stresses during melting and after cooldown. During melting, the lowest scan speed causes thehighest transient stresses due to the largest temperature gradient. After cooldown the maximumresidual stresses occur at the highest scan speed due to the highest cooling rate. Larger domainsizes covering whole components are not applicable due to the high computational effort, althoughfindings from this coupling can be used to approximate better load steps for complete layers.

Li et al. (98) investigate a thermo-mechanical model, which they couple with a convection-diffusion FE method (99), to study phase changes, thermal stresses, and the implication of cracksduring SLM. Melt pool geometry and the location of residual stresses are related to melt pooldynamics. In contrast, there is no dependence between the absolute residual stress values and thehydrodynamics. To decrease the computational effort, hydrodynamics is excluded from modeling.

Hussein et al. (24) study residual stresses by using SLM for cubic domains. Their simulationscomprise five scan lines applying a laser beam of 100 W at a scan speed of 0.1 to 0.3 m/s. Theirfindings are in accordance with the TGM, and compressive stresses are exerted due to thermal

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expansion during melting. After solidification and cooldown, tensile stresses emerge due to ma-terial shrinkage. These stresses slightly relax due to the heat treatment of neighboring scan lines,resulting in almost vanishing residual stresses perpendicular to the scan direction.

Dai & Shaw (100) investigate SLM-manufactured multimaterial dental restorations consist-ing of nickel and porcelain. Their model is based on an FE method, which is able to treat bothmaterials, the powder shrinkage (101), and the thermo-mechanical evolution during the man-ufacturing process (23, 102). In addition to the temperature gradient during single-componentmanufacturing, the mismatch between the thermal expansion of both materials is a second sourceof residual stresses. The expansion coefficient of nickel is at least twice as high as that of porcelain.During solidification, material shrinkage causes high tensile and compressive stresses in nickeland porcelain, respectively, at the interface between both materials. To reduce residual stressesto avoid cracks at the material interface, the preheating temperature or the layer thickness can beincreased.

Zah & Branner (42) investigate residual stresses and deformations of steel cantilevers duringSLM. They extract the exact geometry from the manufacturing machine only with a minor mod-ification of the support structures and combine 20 single layers into one composite layer withone load step. These simplifications require thorough modification of the thermal input to ensurecompatibility with experiments, in which the main focus is on equal temperature gradients. Inaddition to these approximations, they study most of the physical effects of manufacturing, such astemperature-dependent material properties, phase transformations, plasticity, radiation, and heatconduction. They conclude by comparing residual stresses and deformations with experimen-tal values, which further allow for correlation studies of both the sensitivity of different processparameters (103) and the influence of support structures on residual stresses (104). Neverthe-less, the simplifications cause numerical artifacts and errors, e.g., unrealistically large stress peaks.Therefore, smaller FEs and full-layer resolution are recommended. Additionally, a pattern-basedthermal load indicates more realistic thermal behavior, especially in filigree regions (105).

Papadakis et al. (25), applying similar model approximations, investigate a cantilever of IN718manufactured by SLM. They exploit the resulting symmetry by simulating only half of the can-tilever. Three single layers are combined, and the thermal load is applied in one step for thecomposite layer. This approximation results in higher discrepancies to the final distortion in thevertical direction than in the horizontal direction (106). Therefore, their volume heat input ap-proximation underestimates the final deformations, as illustrated in Figure 10; sample simulationswith full-layer resolution indicate higher residual stresses and deformations.

Keller et al. (107) develop a 3D FE model, which is highly simplified to allow thermo-mechanical simulations of aerospace components. The model is further reduced by replacingthe start plate with a boundary condition (108). The sliced FE meshes with a combined layerthickness of 400 µm, along with layer-based heat input, enable simulations of the complete im-peller geometry. Although the numerical results indicate realistic residual stresses and distortions,experimental validation is missing.

Due to the high computational demands of thermo-mechanical simulations, they are oftenrestricted to a few layers or combine layers to achieve whole-component simulations. Never-theless, some simulations with full-layer resolution are reported and involve small components(25). Additionally, the first attempts to investigate scan patterns per layer instead of investigatingwhole-layer heat input have been made (82, 105). However, the sequential scan patterns almost al-ways destroy the process symmetry. Therefore, the whole component instead of a half componentwith a symmetry boundary needs to be simulated, which additionally increases the computationaleffort. Nevertheless, the combination of both approaches can further improve residual stress anddeformation predictions.


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Model shapebefore support cutting

Final model shape aftersupport cutting

Final shape of real componentafter support cutting

Measureddisplacement: 0.8 mmCalculated

deformation: 0.6 mm

Deformation in thevertical direction (mm)

0.6 0.70.40.30.1 0.2 0.50.0

Figure 10Comparison of distortion of an SLM-manufactured IN718 cantilever between simulation (left) andexperiment (right). In the model, after the cantilever is cut from the support structures, the residual stressesrelax and deform the cantilever by a maximum envelope of 0.6 mm, which underestimates the experimentalresult of 0.8 mm. Maximum deformations are marked by the circles. Adapted from Reference 106 withpermission from Taylor & Francis.

Cellular automaton(CA) method:involves explicitmathematicalidealization of adiscretized physicalsystem on a grid,whereby the local cellvariables are modifiedby its neighborhood(113)

5. MICROSTRUCTURE APPROACHES

The microstructure of processed materials plays an important role in the prediction of materialthermo-mechanical properties. In continuum models, an isotropic material is often assumed.However, layer-by-layer manufacturing of PBF processes and the corresponding solidificationconditions result in a more or less anisotropic material. A broad community deals with solidificationphenomena by mainly applying phase field (PF) approaches (109, 110), often modeled by FV orFE methods, and cellular automaton (CA) models (111), of which Boettinger et al. (112) providea comprehensive overview. Only a few approaches combine these models with the solidificationconditions of PBF processes, for which subsequent material addition, melt pool dynamics, andtransient temperature gradients are challenging issues.

Gong & Chou (26) apply a PF model to study microstructure evolution during SEBM of Ti-6Al-4V. They investigate different undercooling conditions at different scan speeds of the electronbeam and conclude that faster dendrite growth occurs for higher undercooling. The microstructuresimulations mainly show multicolumnar grain growth comparable to that of experimental results.

Korner et al. (114) investigate tailoring of grain structure by modifying the process parametersduring SEBM of IN718. Therefore, they track the direction and magnitude of the temperaturegradient by numerical simulations, using their LB model (8). A columnar grain structure in thebuild direction evolves with minor gradient direction misorientations to the build direction. Mod-ifications to the line offset for hatching from 150 to 37.5 µm and to scan speed from 2.2 to 8.8 m/sat 594 W lead to higher misorientations and cause an equiaxed grain structure. Markl et al. (27)further investigate this topic by coupling the underlying LB approach with a CA method (111),as illustrated in Figure 11. The model is coupled with the LB approach by interchanging the

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LB: melt pool dynamics CA: grain growth

Beam

Beam

Orientation (degrees)403010 200

Temperature (K)3,0002,5001,500 2,0001,000

Phase information

Temperature field

Figure 11Scheme coupling the LB and CA approaches to microstructure evolution modeling during SEBM. The LBmodel (left) provides temperature information applied to grain growth, and the CA model (right) providescurrent phase information to the LB model. Adapted from Reference 27.

current temperature field and the phase state information. The underlying numerical concept isbased on growing squares on a regular grid representing a face-centered-cubic grain geometry.Each square is allowed to grow during solidification until it reaches all neighboring grid nodes. Ateach reached neighbor, a new square is initialized where the growth continues, which is termedcapturing. Figure 11 shows a multilayer hatch; the beam and melt pool of the top layer are visible.The resulting grain structure is columnar, with stray grain growth from the side surfaces. Theseresults are based on the work of Rai et al. (28), who describe in detail a numerical scheme couplingthe LB and CA approaches and investigate the influence of different melting strategies on the finalgrain structure. On the basis of this work, Rai et al. (29) observe morphological characteristics ofSEBM-manufactured IN718, such as grain penetration from side walls or grain boundary wig-gling. They conclude that the numerical simulations are in good qualitative agreement with theseobservations.

Zhang et al. (30) apply a coupled thermal FE and CA model that is based on the CA modelof Rappaz & Gandin (111) to the solidification of steel 316L. Proof-of-concept simulations showrealistic solidification and show that an extension to 3D simulations is intended. However, exper-imental validation is missing.

6. OPTIMIZATION APPROACHES

To meet the high requirements of typical application areas such as medical engineering oraerospace, the material properties and the topology of the components have to be optimized.Because the material properties are functions of the process parameters, the best set has to beidentified. The most common approach is design of experiments (DoE), in which certain samplebuilds are performed and the best parameter setup is interpolated depending on certain propertycriteria. The described numerical models are applied to exactly this optimization procedure inorder to replace most experiments with simulations. Once the model is validated by comparing itwith sample experiments, a preoptimization of the process parameters is possible before the firstcomponent is built. Apart from the process parameters, the component itself is hardly a topic ofoptimization research regarding AM, although topology optimization and material optimization


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improve overall component performance and may compensate for process defects such asdistortion.

6.1. Process Parameter Optimization

Process parameter optimization is very complex because many component properties—e.g., poros-ity, crack density, dimensional accuracy, surface roughness, strength, and stiffness—are desired anda variety of material, powder, and process parameters are adjustable. Therefore, expert knowledgeis crucial to define a suitable parameter set for DoE. Furthermore, most literature investigatesonly one to three process parameters and optimization criteria, whereas artificial intelligenceapproaches like neural networks are applied for interpolation.

Garg et al. (115) study empirical modeling of AM and apply a genetic algorithm to predictthe compressive strength of the final components. The model is trained solely with experimentalresults and can identify the significant input parameters. Munguıa et al. (116) perform build timepredictions by neural networks trained with experimental results. Boillat et al. (117) proposea neural network approach replacing experiments with numerical results of an FE method tooptimize the production of a cylinder. They train their network to predict radii with numericalsimulations. Afterward, the model is inverted to predict the necessary process parameters by thedesired properties. The inverted model is finally applied on a greedy search to find the localoptimum. This procedure has two advantages. First, there is less expert knowledge necessarybecause the initial parameters can be chosen in a wide range to train the neural network. Second,the optimization routine is automated and needs no interpretation or manual postprocessing ofthe numerical results. This procedure allows for only a few experiments, starting with the bestparameter set found by the limits of the FE model.

6.2. Topology and Material Optimization

Topology optimization approaches are covered mainly by FE methods, through which the materialdistribution in a single element is optimized. Each element is one design variable on which a solidisotropic material with penalization (SIMP) method or a bidirectional evolutionary structuraloptimization (BESO) method is applied. The SIMP approach (118) uses, for each element, avariational density, which is later realized by, e.g., cellular structures in the component. In contrast,the BESO method (119) applies void-solid elements during their optimization procedure; i.e.,elements are either completely filled or empty. Brackett et al. (120) present an overview of currentresearch areas and ideas regarding topology optimization for AM.

Khanoki & Pasini (121) apply a SIMP model for multiobjective optimization of orthopedic hipimplants. The resulting functionally graded cellular material reduces bone resorption by 76% andinterface stress by 50% relative to a fully dense implant.

Greifenstein & Stingl (122) develop a SIMP optimization algorithm for simultaneous materialoptimization and topology optimization, which allow for an efficient solution to usually com-plex problems. Mitschke et al. (123) apply similar approaches to the problem of finding auxeticframeworks in periodic tessellations. These approaches are further improved by a mathematicaloptimization process regarding the Poisson ratio (124). The nonintuitive geometry modificationsrealized by this optimization technique are not expected to be found by a designer and reveal thestrength of automated topology optimization.

Despite process strategy improvements, high-temperature gradients during PBF manufactur-ing always cause residual stresses and deformations. Therefore, the first steps are to invert the finaldistortion and build a modified geometry (25). This approach can be nicely coupled with topology

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optimization methods (123, 125). At the moment, the optimized geometries are directly appliedto mechanical FE models, testing different material characteristics. In the future, an intermediatestep will be to generate the model in a macroscopic thermo-mechanical approach to arrive atdeformed geometry, including residual stresses and other properties. This route of optimizationthen comprises the topology and applied process strategies and achieves net-shape manufacturing.

Doubrovski et al. (126) extend the process optimization goal by presenting an overview ofcurrent design optimization approaches, including all aspects related to the manufacturing process.They claim that knowledge of materials, computational optimization, computer-aided design, andsimulations is separated, although a full design optimization needs a holistic approach.

7. CONCLUSIONS ON MULTISCALE MODELING

Nearly all aspects of manufacturing issues during PBF processes are addressed by the describednumerical methods. The powder-scale approaches of the FV and LB methods are suitable fordescribing melt pool dynamics during melting and solidification in a realistic manner. For high-energy inputs resulting in keyhole welding with high evaporation, the resulting recoil pressures areof major importance and are not negligible. To also achieve realistic melt pool temperatures, heatradiation and evaporation must be taken into account. Manufacturing issues such as balling, layerbonding defects, and porosity as sources for delamination, channel faults, and surface roughnessare addressed.

The high computational demand of powder-scale approaches is reduced by continuum ap-proaches of the powder bed, which enables coarsening of the spatial and temporal resolution tomodel complete components. Almost all thermo-mechanical models are based on the FE methodand simplify the manufacturing process by applying the beam energy input in few load steps. In-vestigated residual stresses and distortion for many different geometries reveal general accordancewith experiments. Nevertheless, the simplifications cannot address the full process complexity,and the final results deviate from measurements.

Only a few approaches consider microstructure evolution during PBF, although the CA methodis well coupled with regularly meshed models. Proof-of-concept simulations reveal the most im-portant aspects of nucleation and grain growth. This coupling allows for predictions of the resultinggrain structure, depending on the applied process parameters.

Process optimization regarding many parameters or the topology and material of the compo-nent is also addressed. This is a very important topic because functionally graded materials andthe geometric freedom of manufacturing enable one to account for, e.g., later distortions.

The current state of the art in PBF manufacturing operates on a predefined fixed set of processparameters. Some machines are able to modify these parameters during the build, depending onthe local geometry. However, there is no closed-loop control mechanism by which in situ mea-surements are applied to modify the current process parameters. Hu & Kovacevic (127) describesuch a closed-loop system for a direct laser metal powder deposition AM technology, wherebypowder delivery during melting is adjusted, depending on measurements of melt pool geometry.Similar approaches are conceivable for PBF processes in which fixed functions to control the scanspeed are replaceable by closed-loop controllers. The necessary control functions can be gained bynumerical simulations and can be optimized regarding any component property such as residualstress or distortion.

The combination of PBF process and microstructure simulation has hardly been addressed. Thefirst approaches comprise competitive grain growth depending on temperature information. Dueto the melting conditions, a complex microstructure evolution appears, and nucleation and straygrain formation during solidification need to be taken into account. Depending on the processed


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material, in situ heat treatment during manufacturing of the preceding layers may influence thefinal microstructure. Therefore, the inclusion of solid-state phase transformations in numericalmodels is a further research topic.

To achieve high-quality components, material properties, process strategies, and topologyoptimization are addressed. However, all numerical approaches study the correlation of at mosttwo of these topics. A holistic investigation into the influence of different process strategies onmaterial properties in a material and topology optimization routine is recommended.

SUMMARY POINTS

1. Powder-scale approaches to hydro- and thermodynamics, including the most importantphysical effects, reveal melt pool dynamics and material consolidation mechanisms thatare difficult to gain by process observation.

2. Thermo-mechanical continuum approaches based on process assumptions allow for pre-dictions of residual stresses and distortion for whole components.

3. Proof-of-concept simulations of coupled microstructure evolution approaches reveal theopportunity to tailor the final microstructure by using appropriate process parameters.

FUTURE ISSUES

1. Closed-loop control mechanisms for constant and reproducible build properties andoptimized components should be developed.

2. Microstructure evolution, including nucleation, in situ heat treatment, and solid-statephase transformations, needs to be investigated.

3. Correlations between material properties, process strategies, and process optimizationshould be researched.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS

The authors would like to acknowledge funding from the German Research Foundation (DFG)within Collaborative Research Center 814, project B4, and Collaborative Research Center TR103,project B2; from the Cluster of Excellence Engineering of Advanced Materials at Friedrich-Alexander-Universitat Erlangen-Nurnberg; and from EU Clean Sky Joint grant 326020.

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MR46-FrontMatter ARI 4 June 2016 9:17

Annual Review ofMaterials Research

Volume 46, 2016Contents

Materials Issues in Additive Manufacturing (Richard LeSar & Don Lipkin,Editors)

Perspectives on Additive ManufacturingDavid L. Bourell � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Ceramic Stereolithography: Additive Manufacturing for Ceramics byPhotopolymerizationJohn W. Halloran � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �19

Additive Manufacturing of Hybrid CircuitsPylin Sarobol, Adam Cook, Paul G. Clem, David Keicher, Deidre Hirschfeld,

Aaron C. Hall, and Nelson S. Bell � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �41

Microstructural Control of Additively Manufactured Metallic MaterialsP.C. Collins, D.A. Brice, P. Samimi, I. Ghamarian, and H.L. Fraser � � � � � � � � � � � � � � � � � � � �63

Multiscale Modeling of Powder Bed–Based Additive ManufacturingMatthias Markl and Carolin Korner � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �93

Epitaxy and Microstructure Evolution in Metal AdditiveManufacturingAmrita Basak and Suman Das � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 125

Metal Additive Manufacturing: A Review of Mechanical PropertiesJohn J. Lewandowski and Mohsen Seifi � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 151

Architected Cellular MaterialsTobias A. Schaedler and William B. Carter � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 187

Topology Optimization for Architected Materials DesignMikhail Osanov and James K. Guest � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 211

Current Interest

The Chemistry and Applications of π-GelsSamrat Ghosh, Vakayil K. Praveen, and Ayyappanpillai Ajayaghosh � � � � � � � � � � � � � � � � � � � � 235

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MR46-FrontMatter ARI 4 June 2016 9:17

Dealloying and Dealloyed MaterialsIan McCue, Ellen Benn, Bernard Gaskey, and Jonah Erlebacher � � � � � � � � � � � � � � � � � � � � � � � � 263

Material Evaluation by Infrared ThermographyStephen D. Holland and Ricky S. Reusser � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 287

Physics of Ultrathin Films and Heterostructures of Rare-EarthNickelatesS. Middey, J. Chakhalian, P. Mahadevan, J.W. Freeland, A.J. Millis,

and D.D. Sarma � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 305

Polymer-Derived Ceramic FibersHiroshi Ichikawa � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 335

Raman Studies of Carbon NanostructuresAdo Jorio and Antonio G. Souza Filho � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 357

Recent Advances in Superhard MaterialsZhisheng Zhao, Bo Xu, and Yongjun Tian � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 383

Synthetic Micro/Nanomotors and Pumps: Fabrication andApplicationsFlory Wong, Krishna Kanti Dey, and Ayusman Sen � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 407

Thermal Boundary Conductance: A Materials Science PerspectiveChristian Monachon, Ludger Weber, and Chris Dames � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 433

Ultraincompressible, Superhard MaterialsMichael T. Yeung, Reza Mohammadi, and Richard B. Kaner � � � � � � � � � � � � � � � � � � � � � � � � � � � 465

Index

Cumulative Index of Contributing Authors, Volumes 42–46 � � � � � � � � � � � � � � � � � � � � � � � � � � � 487

Errata

An online log of corrections to Annual Review of Materials Research articles may befound at http://www.annualreviews.org/errata/matsci

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Multiscale Modeling of Powder Bed Based Additive …...Finite element (FE) Thermodynamics, mechanics...

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