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Modeling of additive manufacturing processes for metals: Challenges and opportunities
Current Opinion in Solid State and Materials Science xxx (2017) xxx–xxx
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Current Opinion in Solid State and Materials Science journal homepage: www.elsevier.com/locate/cossms
Modeling of additive manufacturing processes for metals: Challenges and opportunities M.M. Francois a,⇑, A. Sun b, W.E. King c, N.J. Henson a, D. Tourret a, C.A. Bronkhorst a, N.N. Carlson a, C.K. Newman a, T. Haut a, J. Bakosi a, J.W. Gibbs a, V. Livescu a, S.A. Vander Wiel a, A.J. Clarke a, M.W. Schraad a, T. Blacker b, H. Lim b, T. Rodgers b, S. Owen b, F. Abdeljawad b, J. Madison b, A.T. Anderson c, J-L. Fattebert c, R.M. Ferencz c, N.E. Hodge c, S.A. Khairallah c, O. Walton c a
Los Alamos National Laboratory, USA Sandia National Laboratories, USA c Lawrence Livermore National Laboratory, USA b
1. Introduction With the technology being developed to manufacture metallic parts using increasingly advanced additive manufacturing processes, a new era has opened up for designing novel structural materials, from designing shapes and complex geometries to controlling the microstructure (alloy composition and morphology). The material properties used within specific structural components are also designable in order to meet specific performance requirements that are not imaginable with traditional metal forming and machining (subtractive) techniques. Modeling and simulation will play a critical role, in this new era, to enable enhancements to traditional trial and error approaches for the design and optimization of components and materials. Modeling and simulation will also advance our capability to quantify the influence of process variables on resulting component properties. It can help both from a fundamental understanding of the underlying physical processes and enable accelerated design to reduce the qualification cycle of additive manufactured parts. Current modeling and simulation tools used to simulate materials processing are being extended to model additive manufacturing. Models are needed at multiple length scales to account for the structural details of this new class of materials and to understand the basic physical processes that are active in the performance response of these materials. Models at multiple length scales will enable the development of the dominant physics basis within macro-scale models for use in component performance simulations. This includes an elasto-plastic representation to allow prediction of the propensity for damage in these components – a long term endeavor. Constitutive equations commonly used for standard casting processes do not always provide an appropriate description for additive manufacturing, as suggested by experimental measurements [1,2]. Further multiscale model and algorithm developments are needed that will incorporate knowledge
⇑ Corresponding author. E-mail address: [email protected] (M.M. Francois).
of the microstructure within the macro-scale continuum codes on both the processing (solidification) and solid mechanics sides. The microstructure of materials that results from the solidification process determines the material properties (such as its response to deformation). Fig. 1 illustrates the integration needed in modeling and simulation to allow the connection between performance and process through knowledge of the microstructure and properties of the material. The needs for and benefits of a process modeling and simulation capability have been detailed in several roadmaps for additive manufacturing [3–6]. In this article, we review the challenges and opportunities that we are facing in the modeling and simulation of additive manufacturing processes for metals and the predictive representation of their mechanical performance at the different scales. This article is divided into five sections in which we highlight the current modeling efforts taking place at the U.S. Department of Energy National Nuclear Security Administration (NNSA) Laboratories: process modeling, microstructure modeling, properties modeling, performance and topology and process optimization. All these various modeling developments at different scales and regimes are necessary in order to move toward an integrated computational approach of process-structure-properties-performance that will ultimately enable the engineering and optimization of materials to specific performance requirements.
2. Process modeling Two main technologies exist for additive manufacturing of metals: powder-bed and directed energy deposition. In powder-bed technology, a thin layer of metallic powder (20–100 lm) is deposited on a flat surface and then melted using a laser beam according to computer-programmed patterns. The process repeats itself layer by layer with varying laydown patterns and topologies per layer until the part is completed. The remaining powder is then blown and recycled. Laser powder bed fusion additive manufacturing is an inherently multiscale process: material transformations take place locally (O(10–100 lm)) over short times O(10 ms), but parts
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Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001
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Fig. 1. Illustration of the envisioned integrated process-structure-properties-performance modeling and simulation approach and associated length scales.
are O(10 cm)3 and take O(hours-days) to build. This calls for an approach using multiple coupled models. In the direct energy technology, either powder fed or wire fed, the material deposition is localized and occurs at the same time as the laser heat deposition. Typical laser powers are of the order of O(100 W), beam speeds of O(mm/s) and cooling rates can reach 102–104 K/s [7–9]. These parameters as well as the powder (or wire) composition will affect the resulting microstructure and residual stresses in the part. Determining defects and residual stresses in the part are what process modeling at the macroscale can achieve. In addition, we would eventually need to predict the various grain morphologies and crystallographic orientations as well as grain size distributions as a function of position in the part and have microstructure-aware solidification models. At the macro-scale, simulations of solidification processes are achieved using Computational Fluid Dynamics (CFD) software [10] and resulting residual stresses from solidification are typically computed using Finite-Element Analysis (FEA) software [11,12]. CFD software solves a system of non-linear partial differential equations that represents the motion of fluids, species diffusion and phase changes and ensures mass, momentum and energy conservation. Finite-element analysis software is used for thermomechanical modeling during processing solving the coupled governing equations for heat transfer and solid deformation. Please note that our approach is pursued in the context of large scale and high performance computational resources available at DOE national laboratories.
2.1. Direct energy deposition Simulation of direct energy deposition requires modeling a moving heat and mass source that represent the addition of heat (coming from the laser or electron-beam) and mass coming (from the powder or wire feed) as the part is being built. Such simulation will increase our understanding of the effect of the temperature
history, melting-solidification cycles, various scan patterns effects and final residual stress state. Truchas, a continuum thermo-mechanical modeling tool [13], originally designed for the simulation of casting processes, is being extended to simulate directed energy deposition additive manufacturing processes. Fig. 2a illustrates the simulated melt pool region during a single weld pass in a 304L stainless steel. Fig. 2b shows the modeling of mass and energy deposition in Truchas. One of the major challenges in CFD modeling of such processes is the description of surface tension and its local variations with temperature and chemical composition. These variations are at the origin of Marangoni flow within the liquid, which significantly affects the shape and depth of the melt pool. Accurate simulation of the melt pool geometry and the possible gas entrapment at the origin of voids and defects are crucial to the prediction of the final quality of the parts. Therefore, simulation tools like Truchas are expected to play a key role in refining/optimizing processing conditions, such as the laser power and its traveling speed to design and produce optimized parts.
2.2. Powder bed system Simulation at the scale of the powder has the potential to increase our understanding of the physics of the additive manufacturing process, contribute to improving the process, provide insight when extrapolating beyond current experience, and contribute to improving the design of laser powder bed fusion additive manufacturing machines. Powder scale models capture the details of laser interaction with the powder, including vaporization effects, that can be used to determine the net laser energy input for the part scale models and to investigate such phenomena as spattering and denudation. These models give temperature and time histories of the melt pool, with applications to real-time process diagnostics and microstructure development. Powder scale models can also be used to study issues of surface finish and part density.
Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001
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Fig. 2. Truchas simulation (a) Marangoni flow in weld pool during single weld bead pass in 304L SS (colors represent temperature, and velocity is represented by vectors colored by their magnitude) and (b) temperature distribution and liquid (red), solid (blue) distribution in a simulation of directed energy deposition AM process for 304L SS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The ALE3D multiphysics code [14] has been extended to model the heat transfer, the formation, evolution, and solidification of the melt pool, the solid mechanics [15], phase transformations, and material motion while resolving the powder particles in the powder layer. The powder bed is computationally represented by a randomized distribution of powder particles above a uniform substrate. The laser source is modeled with energy deposition into the upward-facing metal surface within the moving laser spot, where the laser power can vary across the beam with Gaussian, top hat, or other desired distributions. The laser-material interaction is treated via ray tracing and a physics-based absorption model. The combined thermal and hydrodynamic simulations model the appropriate distribution of the laser’s energy as it interacts with the powder particles, the substrate, and the melt pool. The liquid in the melt pool flows under the influence of surface tension and vaporization recoil [16]. The powder model tracks the various modes of heat loss, including conduction, radiation, and evaporation. Single-track [17] parameters such as width, height, and depth can be compared with experimental data for validation of the model. Since the variations in these dimensions along the track can be an indication of build quality, the powder model can be used to optimize process parameters. Multi-track and multilayer simulations at the powder scale can be used to investigate strategies to improve surface finish of top, bottom, and sidefacing surfaces and to minimize porosity of the final part. A detailed discussion of the powder scale simulation can be found in [18–20]. An example of the powder scale model is shown in Fig. 3 [20]. Based on these results, it is possible to subdivide the melt track into three differentiable regions: a depression region located at the laser spot, a tail end region of the melt track located near the end, and a transition region in between. This choice of subdivision is based on the exponential dominance of the recoil force at the depression and the dominance of Marangoni surface tension effects in the cooler transition and tail regions. 2.3. Feed stock modeling The powder feedstock is generally modeled using a discrete element method (DEM) approach [21] (e.g., LIGGGHTS [22]; LAMMPS [23], GEODYN-L [24]) to simulate the motion of powder particles as a new powder layer is spread onto the build plate. These simulations can be used to obtain an understanding of how the particlescale properties of the feedstock powder, and powder-spreading process parameters, affect uniformity and smoothness of the preheating-state powder-bed, especially the spatial distribution of particle-sizes, bed porosity and thickness – all of which are inputs to the downstream powder-scale model of the heating, melt-pool
and part-formation processes. Such meso-scale models bridge a scale range from particle-surface morphology effects (cohesion, friction, deformation, rolling resistance, which are approximated by mathematical models of inter-particle contact interactions) to bulk powder deformation and flow behavior on a millimeter scale, but simulated at the individual particle scale. Motion of individual powder particles is tracked as powder is scraped off the top of a reservoir bed by a spreader blade or roller, and spread across the entire build plate. Size segregation typically occurs during any shearing flow of a granular solid, and simulations have shown the potential for significant variation of the size distribution of powder after spreading across an AM build plate [25]. Interparticle cohesion, however, can significantly affect the rate at which fines rain-out of a layer during spreading. For typical 20 lm metal spheres, van der Waals cohesion at contacts can exceed the gravity acting on a single particle by well over an order of magnitude. This cohesion also creates contact-normal stresses that can exceed the elastic limit of typical metals, leading to small flat spots at contacts, and resulting in increased rolling resistance. As particle size decreases the relative ratio of cohesive contact forces to gravity acting on individual particles, increases significantly. This can reduce the rate of segregation of fines from larger particles, but can also lead to clumping and difficulty achieving a uniform layer of powder. 2.4. Part scale simulation during processing A major challenge is to develop a model that can produce information and knowledge at the overall scale of the desired part and build-process to inform engineering decisions. Quantities of interest at the part scale include: distortions that could halt machine operation or place the completed part outside the desired geometric envelope, residual stresses, that can create initial conditions detrimental to service-life concerns such as failure and fatigue, and local effective material properties, or at least indicators of where they might significantly deviate from the nominal properties expected from the process. There can be kilometers of laser paths and thousands of powder layers in a single build thus presenting a computational challenge. To be useful, the predictions must be able to be run in a reasonable amount of time while retaining sufficient physics fidelity so as to yield trustworthy results. An eventual goal is to have process models that are so efficient they could be included as part of an automated process optimization. The goal is to retain enough physics fidelity to have confidence in the simulation results. Diablo [26], a general purpose implicit nonlinear finite element code that is capable of effectively utilizing commodity parallel-processing platforms, is being adapted to
Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001
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Fig. 3. ALE3D simulation. Time snapshots of the melt flow showing spattering and denudation. The melt has a large backward flow (blue color; Vx < 0) due to Marangoni effect and recoil, compared to forward flow (Vx > 0; red color). The backward net flow breaks up later in time at the necking. The velocity scale is capped at ±1 m/s for better visualization. The right panel shows a magnified view at 270 ls (flow rotated by +90°) shows the velocity components (Vx, Vy, Vz) and the temperature (with contour lines) at the depression. The white letter O shows that the laser center is not at the bottom of the depression. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
model additive manufacturing. Early efforts focused on developing laser powder bed fusion modeling and algorithmic approaches in the context of 50 lm layer-resolved simulations for representative volumes comprising 1 mm3 [27]. These simulations highlight that it is misleading to think merely in terms of the temperature history of the material in the active powder layer and clearly show (Fig. 4) that the material located several or more layers below the active work surface is still undergoing significant temperature excursions, which will contribute to continued evolution of the local microstructure. The local laser powder bed fusion process involves thermallydriven material phase transformations. At the part scale, one neglects the details of the local laser-powder particle interactions shown previously. Instead, the goal is to describe part level behavior both during and after the build is complete. The simulation can
be cast as the thermo-mechanical response of a nonlinear solid continuum. In this approximation, the powder can be represented as a reduced-density, low-strength solid. The deposition of the laser energy into the powder can then be represented by a volumetric energy source term such as that derived by Gusarov et al. [28]. Melting can be represented thermally through a latent heat and mechanically as a near-total loss of strength. The ‘‘mushy zone” at the melt pool boundary is represented by having the temperature-dependent strength rise as temperature falls below the solidus temperature. The computational challenges of part scale thermo-mechanical simulations are driven by the disparate spatial scales of the laser energy source and the overall part geometry compounded by the disparate time scales of local heating versus overall heat transfer during the entire fabrication, which can be hours and is often days.
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Fig. 4. Build simulation part with Diablo (a) temperature history sampling points subsequently labeled (bottom-to-top) as ‘‘base” and ‘‘layers” 3, 6, 9 and 12. (b) Temperature history for five sampling points designated in (a) show recurring heating of the material.
We are now addressing this issue through adaptive mesh refinement to localize higher resolution in the vicinity of the active material transformation. To overcome the computational challenges when simulating the fabrication of a part with dimensions of cubic centimeters, we no longer resolve individual powder layers and individual laser scan lines. Multiple layers are lumped together and a larger ‘‘effective” laser beam is employed. A detailed discussion of our part scale simulations to date can be found in [19,27]. 3. Modeling of the microstructure evolution during solidification Achieving quantitative predictions of additively manufactured microstructures, and hence of properties and performance, will require combined efforts in solidification modeling spanning several length and time scales [29]. Atomistic simulations should enable the prediction of fundamental interfacial properties, e.g. surface tension anisotropies or kinetic coefficients particularly relevant to rapid solidification regimes [30]. At this scale, further developments, such as building reliable potentials for molecular dynamics simulations of alloys, are needed to enable quantitative predictions. At the scale of the solid-liquid interface, phase-field (PF) modeling, illustrated in Fig. 5a, has established itself as the method of choice to predict detailed morphologies and dynamics of solidification microstructures [31,32]. The PF method can yield quantitative predictions and shed light on experimentally observed microstructures [29], and is scalable on massively parallel computers [33]. PF codes include Tusas [34,35] an implicit PF method using finite-element discretization for unstructured mesh and the AMPE code (Adaptive Mesh Phase Evolution) [36,37] to
(a) Al-3wt%Cu, G = 29 K/mm, V = 290 µm/s
100 µm
model solidification in alloys. It employs a quaternion field to model the local grain orientation [38] and uses CALPHAD for diffusion coefficients and free energies. Both Tusas and AMPE have been developed with Exascale computing in mind and have favorable scalability. Yet, most direct comparisons of PF simulation results to experiments so far have been limited to directional solidification experiments, i.e. close to conventional casting parameter ranges. To be applied to additive manufacturing, further developments of PF models are needed to quantitatively incorporate non-equilibrium interfacial mechanisms of rapid solidification, such as solute trapping. Ultimately, to yield useful predictions of additively manufactured parts, the fundamental understanding from these smallerscale models should be incorporated into larger scale models, such as volume-averaged continuum scale models for solidification at the scale of entire processes, for instance models based on cellular automata [39–41]. Multi-scale models, such as the dendritic needle network (DNN) model [42,43] illustrated in Fig. 5b, should play a key role in bridging the scale gap between PF and macro-scale models. Efforts are also underway for including microstructural predictions within Truchas through the knowledge of temperature gradient (G) and the growth rate (R). An alternative approach for modeling microstructure evolution during AM is based on a kinetic Monte Carlo method and implemented in the open-source code SPPARKS [44]. SPPARKS based on the Potts Kinetic Monte Carlo technique, is introduced to model microstructure evolution during additive manufacturing and autogenous welding processes. During the simulation, a user defined melt pool is scanned through the simulation domain on a specified trajectory. The material is represented as a cubic lattice of sites with ‘‘spins” that represent specific grains. When the melt pool
(b) Al-9.8wt%Si, G = 540 K/mm, V = 106 µm/s
1 mm
Fig. 5. Simulations of dendritic solidification: (a) grain growth competition and grain boundary formation in an Al-Cu alloy, using phase-field modeling; (b) dynamical selection of microstructural features, e.g. primary dendritic spacing, under a change of mold cross-section in an Al-Si alloy, using dendritic needle network modeling [40]. In both panels, the color map represents the solute (Cu or Si) concentration field, from nominal (blue) to enriched (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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cally equivalent representation of a representative volume element (RVE) of the microstructure is generated. With that microstructure representation, one can then mesh the RVE in an interface conforming way. With the meshes generated, response of the polycrystal metallic material to high pressure and high strain rate mechanical loading histories are then calculated using finiteelement analysis. Bronkhorst and colleagues [47–60] are also developing a meso-scale and statistical modeling approach to quantitatively link microstructural details to spatial loading variability to be eventually incorporated into a macro-scale model for material damage and failure. Our ultimate goal is to integrate our modeling efforts from processing to performance through microstructure modeling. Most microstructure-aware models for simulating mechanical properties of polycrystalline materials use voxelated representation of microstructures (Fig. 7a). Lim and colleagues [61] utilized a unique SCULT capability in CUBIT meshing tool to generate conformal mesh by tracking volume fraction data of individual grains on a Cartesian grid used in a mesh. This capability is illustrated in Fig. 7b [61]. Comparison of mechanical simulations show that conformal discretization across interfaces reduces artificial stress localization commonly observed in non-conformal FE discretizations.
travels through a lattice site, the spins are randomized and any existing grain assignment is lost. Rapid grain growth occurs in the heat affected zone surrounding the melt pool, and results in the formation of elongated grains oriented along the temperature gradient. The method is capable of creating both columnar and equiaxed microstructures found in materials produced with powder bed fusion and directed energy deposition methods. Fig. 6 shows microstructures of additively manufactured stainless steel 304L using Laser Engineered Net Shaping technique (LENSÒ). Abnormal grain morphology with varying microstructural features, such as grain shapes and sizes, and interfaces is reproduced by kinetic Monte Carlo grain growth simulations [45]. However to date the simulation can only predict qualitative features and much remains to be done to discover the physics of granular solidification nucleation and growth and representing that physics properly within the simulation frameworks. From the kinetic Monte Carlo simulation results, the conformal meshing technique can then be used to generate a Finite-Element mesh to be used in crystal plasticity finite element (CPFE) calculations to predict the mechanical response and texture evolution of polycrystalline aggregates. This framework provides a step toward an integrated computational materials engineering approach, where models of materials processes are bridged to ones of properties. Key to this numerical representation is the ability to accurately represent grain boundaries and other interfaces within additively manufactured materials. This is coupled with the need to develop the proper models to represent plastic deformation and damage within the interface regions of the material structure. This includes the ability to represent subgranular dislocation motion and interaction processes much more accurately than we are generally able to do today. This enables a design loop such that models of materials properties provide key inputs to ones of processes in order to engineer materials systems with optimal performance.
5. Performance modeling Physically-based macro-scale continuum model development is essential to represent true physical quantities for documenting and tracking the evolution which takes place within metallic materials. This includes non-linear elasticity which accounts for elastic compressibility of the material, proper representation of the plastic deformation of the material which is based upon the physics of dislocation and nucleation glide, dislocation interactions and the nucleation and growth of deformation twinning. The early time events drive the initiation and propagation of damage and failure events which are strongly driven by the details of initial microstructure and evolving material structure with deformation. Finite-Element Analysis software (FEA) such as ABAQUS, Diablo are the workhorse for performance modeling. They solve a set of governing equations that represent the physical mechanisms response for various loading conditions (boundary conditions). They can predict internal stress in a part, where the part will fail, etc. Since plastic processes occur on a sub-granular length scale and the microstructure dominates the damage and failure process in most metallic materials, there is a critical need for integrating microstructure information of the material into the model at the macro-scale (e.g. [62,63]) in particular for the additively manufactured material. Additively manufactured materials in their as-built state [1] have been found to have substantially different plastic
4. Microstructure representation and modeling of material properties The role of microstructural features, which span many length scales, on the properties at the macroscopic scale falls naturally within the structure-process-property paradigm and has triggered many research efforts across various disciplines to develop microstructure-informed modeling frameworks. Knowledge of the microstructure morphology and distribution is required in order to model material properties. The microstructure representation can be obtained from experimental measurement or from simulation of the microstructure evolution. The microstructure representation meshes can be generated from EBSD data and through the use of the open-source code DREAM3D [46] a statisti-
(a)
(b)
(c)
Fig. 6. Microstructures of additively manufactured SS 304L using Laser Engineered Net Shaping (LENSÒ) technique. (a) EBSD measurement (b) kinetic Monte Carlo simulations (SPPARKS) and (c) conformal finite element mesh.
Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001
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150 MPa 30
(a) Voxelated FE mesh
(b) Conformal FE mesh
Fig. 7. Contours of von Mises stress at 10 % deformation using (a) voxelated and (b) conformal finite element meshes. Artificial non-smooth and localized stress was predicted using the voxelated mesh.
flow resistance than traditionally produced wrought material. There are potentially many physical factors – each of which could be contributing to this difference in behavior. 6. Topology optimization and toward process optimization for performance AM is facilitating access to a far richer design space for structural components. AM focused only on producing the same component designs a new way will miss the real impact of this technology. The recently released PLATO tool [64] provides a fundamentally different design paradigm using newly developed topology optimization tools where the function of the component dictates the shape. Since material is placed only where needed, these designs are often very organic in shape and a far cry from traditional CAD designs. Critical to this effort is the generation of truly printable shapes, where not only is the shape guided by the physics calculation(s), but the resulting shape is smooth, connected and
Fig. 8. Example of detailed ‘‘print-ready” design created within PLATO.
directly printable from within the design environment. This ‘‘print-ready” technology is a significant step forward as it removes large amounts of tedious design time by eliminating any topology optimization post processing steps. Fig. 8 shows an example of an intricate design produced directly within PLATO. Homogenization and meshing technologies have also been developed to allow the use of meta-materials (e.g. lattices) as part of a more traditional topology optimization. Equivalent properties are calculated for a given lattice unit cell and then these properties are employed during topology optimization to produce the optimal quasi-solid shape [65]. This solid shape can then be transformed quickly and automatically into the lattice structures using conformal hexahedral meshing techniques and unit cell representations of the lattice. Fig. 9 shows such a design and the corresponding lattice structure ready for printing. Also included in the PLATO development effort are technologies for accounting for the variability in the design (uncertainty quantification techniques) and for speeding the production of families of designs (reduced order modeling) where rich design spaces and tradeoffs can be efficiently explored. Other optimization tools include for example Tosca [66] and ParetoWorks [67]. Optimization software have mostly focused development on geometric optimization based on a set of constraints. Recent work has extended topology optimization capabilities to include constraints coming from additive manufacturing [68,69]. These methods can also be used to allow the design of variable density cellular material to alleviate some of the additive manufacturability constraints [70]. There is also a need to integrate microstructure, properties and processing parameters information in such optimization software in order to have a fully-integrated design tool. In the future such software will include additional constraints for the processing parameters in order to produce optimized materials performance in addition to optimized topology (geometry of the part).
Fig. 9. Design using homogenized lattice properties and then the insertion of the desired lattice into the calculated shape, again ready for direct printing.
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7. Perspective There are tremendous opportunities in manufacturing science within the field of additive manufacturing which offer many different economic and defense application advantages. These new classes of materials are substantially different in structure from those which have historically been produced by traditional casting, mechanical working, and subtractive manufacturing processes. The structures of these materials offer a rich avenue for scientific investigation into the long-standing endeavor of understanding and quantifying the process-to-performance linkage for material response. New modeling and simulation approaches are needed for process and performance representation and the strong linkage with discovery and validation experiment are more important that ever. Acknowledgments This work was performed for the U.S. Department of Energy’s National Nuclear Security Administration by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344, Los Alamos National Laboratory under contract DE-AC52-06NA25396, and Sandia National Laboratories under contract DE-AC04-94AL85000. The LLNL work was funded by the Laboratory Directed Research and Development Program at LLNL under project tracking code 13SI-002. The LANL work is funded by the Advanced Simulation Computing program. AJC, JWG and DT gratefully acknowledge support from AJC’s Early Career Award from U.S. DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. References [1] G.T. Gray III, V. Livescu, P.A. Rigg, C.P. Trujillo, C.M. Cady, S.R. Chen, J.S. Carpenter, T.J. Lienert, S. Fensin, Structure/property (constitutive and dynamic strength/damage) characterization of additively manufactured 316L SS, EPJ Web Conf. 94 (2015) 02006. [2] A.S. Wu, D.W. Brown, M. Kumar, G.F. Gallegos, W.E. King, An experimental investigation into additive manufacturing-induced residual stresses in 316L stainless steel, Metall. Mater. Trans. A 45 (2014) 6260. [3] D.L. Bourell, M.C. Leu, D.W. Rosen, Roadmap for Additive Manufacturing Identifying the Future of Freeform Processing, Austin TX, 2009. [4] Energetics Incorporated, Measurement Science Roadmap for Metal-Based Additive Manufacturing, Columbia, Maryland, 2013. [5] R. Berger, Additive manufacturing a game changer for the manufacturing industry? Munich, 2013. [6] S. Srivatsa, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, 2014. [7] V. Manvatkar, A. De, T. DebRoy, Spatial variation of melt pool geometry, peak temperature and solidification parameters during laser assisted additive manufacturing process, Mater. Sci. Technol. 31 (2015) 924–930. [8] B. Zheng, Y. Zhou, J.E. Smugeresky, J.M. Schoenung, E.J. Lavernia, Thermal behavior and microstructural evolution during laser deposition with laserengineered net shaping: Part I. Numerical calculations, Metall. Mater. Trans. A 39 (2008) 2228–2236. [9] M.H. Farshidianfar, A. Khajepour, A.P. Gerlich, Effect of real-time cooling rate on microstructure in Laser Additive Manufacturing, J. Mater. Process. Technol. 231 (2016) 468–478. [10] Z. Fan, F. Liou, Numerical Modeling of the Additive Manufacturing (AM) Processes of Titanium Alloy. [11] R. Martukanitz, P. Michaleris, T. Palmer, T. DebRoy, Z-K Liu, R. Otis, T.W. Heo, LQ. Chen, Towards an integrated computational system for describing the additive manufacturing process for metallic materials, Addit. Manuf. 1 (2014) 52–63. [12] P. Michaleris, Modeling metal deposition in heat transfer analyses of additive manufacturing processes, Finite Elem. Anal. Des. 86 (1) (2014) 51–60. [13] https://github.com/truchas. [14] C. McCallen, ALE3D: Arbitrary Lagrange Eulerian Three-and Two Dimensional Modeling and Simulation Capability, Livermore, CA, Report No. LLNL-ABS565212, 2012.
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Contents lists available at ScienceDirect
Current Opinion in Solid State and Materials Science journal homepage: www.elsevier.com/locate/cossms
Modeling of additive manufacturing processes for metals: Challenges and opportunities M.M. Francois a,⇑, A. Sun b, W.E. King c, N.J. Henson a, D. Tourret a, C.A. Bronkhorst a, N.N. Carlson a, C.K. Newman a, T. Haut a, J. Bakosi a, J.W. Gibbs a, V. Livescu a, S.A. Vander Wiel a, A.J. Clarke a, M.W. Schraad a, T. Blacker b, H. Lim b, T. Rodgers b, S. Owen b, F. Abdeljawad b, J. Madison b, A.T. Anderson c, J-L. Fattebert c, R.M. Ferencz c, N.E. Hodge c, S.A. Khairallah c, O. Walton c a
Los Alamos National Laboratory, USA Sandia National Laboratories, USA c Lawrence Livermore National Laboratory, USA b
1. Introduction With the technology being developed to manufacture metallic parts using increasingly advanced additive manufacturing processes, a new era has opened up for designing novel structural materials, from designing shapes and complex geometries to controlling the microstructure (alloy composition and morphology). The material properties used within specific structural components are also designable in order to meet specific performance requirements that are not imaginable with traditional metal forming and machining (subtractive) techniques. Modeling and simulation will play a critical role, in this new era, to enable enhancements to traditional trial and error approaches for the design and optimization of components and materials. Modeling and simulation will also advance our capability to quantify the influence of process variables on resulting component properties. It can help both from a fundamental understanding of the underlying physical processes and enable accelerated design to reduce the qualification cycle of additive manufactured parts. Current modeling and simulation tools used to simulate materials processing are being extended to model additive manufacturing. Models are needed at multiple length scales to account for the structural details of this new class of materials and to understand the basic physical processes that are active in the performance response of these materials. Models at multiple length scales will enable the development of the dominant physics basis within macro-scale models for use in component performance simulations. This includes an elasto-plastic representation to allow prediction of the propensity for damage in these components – a long term endeavor. Constitutive equations commonly used for standard casting processes do not always provide an appropriate description for additive manufacturing, as suggested by experimental measurements [1,2]. Further multiscale model and algorithm developments are needed that will incorporate knowledge
⇑ Corresponding author. E-mail address: [email protected] (M.M. Francois).
of the microstructure within the macro-scale continuum codes on both the processing (solidification) and solid mechanics sides. The microstructure of materials that results from the solidification process determines the material properties (such as its response to deformation). Fig. 1 illustrates the integration needed in modeling and simulation to allow the connection between performance and process through knowledge of the microstructure and properties of the material. The needs for and benefits of a process modeling and simulation capability have been detailed in several roadmaps for additive manufacturing [3–6]. In this article, we review the challenges and opportunities that we are facing in the modeling and simulation of additive manufacturing processes for metals and the predictive representation of their mechanical performance at the different scales. This article is divided into five sections in which we highlight the current modeling efforts taking place at the U.S. Department of Energy National Nuclear Security Administration (NNSA) Laboratories: process modeling, microstructure modeling, properties modeling, performance and topology and process optimization. All these various modeling developments at different scales and regimes are necessary in order to move toward an integrated computational approach of process-structure-properties-performance that will ultimately enable the engineering and optimization of materials to specific performance requirements.
2. Process modeling Two main technologies exist for additive manufacturing of metals: powder-bed and directed energy deposition. In powder-bed technology, a thin layer of metallic powder (20–100 lm) is deposited on a flat surface and then melted using a laser beam according to computer-programmed patterns. The process repeats itself layer by layer with varying laydown patterns and topologies per layer until the part is completed. The remaining powder is then blown and recycled. Laser powder bed fusion additive manufacturing is an inherently multiscale process: material transformations take place locally (O(10–100 lm)) over short times O(10 ms), but parts
http://dx.doi.org/10.1016/j.cossms.2016.12.001 1359-0286/Ó 2016 Published by Elsevier Ltd.
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Fig. 1. Illustration of the envisioned integrated process-structure-properties-performance modeling and simulation approach and associated length scales.
are O(10 cm)3 and take O(hours-days) to build. This calls for an approach using multiple coupled models. In the direct energy technology, either powder fed or wire fed, the material deposition is localized and occurs at the same time as the laser heat deposition. Typical laser powers are of the order of O(100 W), beam speeds of O(mm/s) and cooling rates can reach 102–104 K/s [7–9]. These parameters as well as the powder (or wire) composition will affect the resulting microstructure and residual stresses in the part. Determining defects and residual stresses in the part are what process modeling at the macroscale can achieve. In addition, we would eventually need to predict the various grain morphologies and crystallographic orientations as well as grain size distributions as a function of position in the part and have microstructure-aware solidification models. At the macro-scale, simulations of solidification processes are achieved using Computational Fluid Dynamics (CFD) software [10] and resulting residual stresses from solidification are typically computed using Finite-Element Analysis (FEA) software [11,12]. CFD software solves a system of non-linear partial differential equations that represents the motion of fluids, species diffusion and phase changes and ensures mass, momentum and energy conservation. Finite-element analysis software is used for thermomechanical modeling during processing solving the coupled governing equations for heat transfer and solid deformation. Please note that our approach is pursued in the context of large scale and high performance computational resources available at DOE national laboratories.
2.1. Direct energy deposition Simulation of direct energy deposition requires modeling a moving heat and mass source that represent the addition of heat (coming from the laser or electron-beam) and mass coming (from the powder or wire feed) as the part is being built. Such simulation will increase our understanding of the effect of the temperature
history, melting-solidification cycles, various scan patterns effects and final residual stress state. Truchas, a continuum thermo-mechanical modeling tool [13], originally designed for the simulation of casting processes, is being extended to simulate directed energy deposition additive manufacturing processes. Fig. 2a illustrates the simulated melt pool region during a single weld pass in a 304L stainless steel. Fig. 2b shows the modeling of mass and energy deposition in Truchas. One of the major challenges in CFD modeling of such processes is the description of surface tension and its local variations with temperature and chemical composition. These variations are at the origin of Marangoni flow within the liquid, which significantly affects the shape and depth of the melt pool. Accurate simulation of the melt pool geometry and the possible gas entrapment at the origin of voids and defects are crucial to the prediction of the final quality of the parts. Therefore, simulation tools like Truchas are expected to play a key role in refining/optimizing processing conditions, such as the laser power and its traveling speed to design and produce optimized parts.
2.2. Powder bed system Simulation at the scale of the powder has the potential to increase our understanding of the physics of the additive manufacturing process, contribute to improving the process, provide insight when extrapolating beyond current experience, and contribute to improving the design of laser powder bed fusion additive manufacturing machines. Powder scale models capture the details of laser interaction with the powder, including vaporization effects, that can be used to determine the net laser energy input for the part scale models and to investigate such phenomena as spattering and denudation. These models give temperature and time histories of the melt pool, with applications to real-time process diagnostics and microstructure development. Powder scale models can also be used to study issues of surface finish and part density.
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Fig. 2. Truchas simulation (a) Marangoni flow in weld pool during single weld bead pass in 304L SS (colors represent temperature, and velocity is represented by vectors colored by their magnitude) and (b) temperature distribution and liquid (red), solid (blue) distribution in a simulation of directed energy deposition AM process for 304L SS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The ALE3D multiphysics code [14] has been extended to model the heat transfer, the formation, evolution, and solidification of the melt pool, the solid mechanics [15], phase transformations, and material motion while resolving the powder particles in the powder layer. The powder bed is computationally represented by a randomized distribution of powder particles above a uniform substrate. The laser source is modeled with energy deposition into the upward-facing metal surface within the moving laser spot, where the laser power can vary across the beam with Gaussian, top hat, or other desired distributions. The laser-material interaction is treated via ray tracing and a physics-based absorption model. The combined thermal and hydrodynamic simulations model the appropriate distribution of the laser’s energy as it interacts with the powder particles, the substrate, and the melt pool. The liquid in the melt pool flows under the influence of surface tension and vaporization recoil [16]. The powder model tracks the various modes of heat loss, including conduction, radiation, and evaporation. Single-track [17] parameters such as width, height, and depth can be compared with experimental data for validation of the model. Since the variations in these dimensions along the track can be an indication of build quality, the powder model can be used to optimize process parameters. Multi-track and multilayer simulations at the powder scale can be used to investigate strategies to improve surface finish of top, bottom, and sidefacing surfaces and to minimize porosity of the final part. A detailed discussion of the powder scale simulation can be found in [18–20]. An example of the powder scale model is shown in Fig. 3 [20]. Based on these results, it is possible to subdivide the melt track into three differentiable regions: a depression region located at the laser spot, a tail end region of the melt track located near the end, and a transition region in between. This choice of subdivision is based on the exponential dominance of the recoil force at the depression and the dominance of Marangoni surface tension effects in the cooler transition and tail regions. 2.3. Feed stock modeling The powder feedstock is generally modeled using a discrete element method (DEM) approach [21] (e.g., LIGGGHTS [22]; LAMMPS [23], GEODYN-L [24]) to simulate the motion of powder particles as a new powder layer is spread onto the build plate. These simulations can be used to obtain an understanding of how the particlescale properties of the feedstock powder, and powder-spreading process parameters, affect uniformity and smoothness of the preheating-state powder-bed, especially the spatial distribution of particle-sizes, bed porosity and thickness – all of which are inputs to the downstream powder-scale model of the heating, melt-pool
and part-formation processes. Such meso-scale models bridge a scale range from particle-surface morphology effects (cohesion, friction, deformation, rolling resistance, which are approximated by mathematical models of inter-particle contact interactions) to bulk powder deformation and flow behavior on a millimeter scale, but simulated at the individual particle scale. Motion of individual powder particles is tracked as powder is scraped off the top of a reservoir bed by a spreader blade or roller, and spread across the entire build plate. Size segregation typically occurs during any shearing flow of a granular solid, and simulations have shown the potential for significant variation of the size distribution of powder after spreading across an AM build plate [25]. Interparticle cohesion, however, can significantly affect the rate at which fines rain-out of a layer during spreading. For typical 20 lm metal spheres, van der Waals cohesion at contacts can exceed the gravity acting on a single particle by well over an order of magnitude. This cohesion also creates contact-normal stresses that can exceed the elastic limit of typical metals, leading to small flat spots at contacts, and resulting in increased rolling resistance. As particle size decreases the relative ratio of cohesive contact forces to gravity acting on individual particles, increases significantly. This can reduce the rate of segregation of fines from larger particles, but can also lead to clumping and difficulty achieving a uniform layer of powder. 2.4. Part scale simulation during processing A major challenge is to develop a model that can produce information and knowledge at the overall scale of the desired part and build-process to inform engineering decisions. Quantities of interest at the part scale include: distortions that could halt machine operation or place the completed part outside the desired geometric envelope, residual stresses, that can create initial conditions detrimental to service-life concerns such as failure and fatigue, and local effective material properties, or at least indicators of where they might significantly deviate from the nominal properties expected from the process. There can be kilometers of laser paths and thousands of powder layers in a single build thus presenting a computational challenge. To be useful, the predictions must be able to be run in a reasonable amount of time while retaining sufficient physics fidelity so as to yield trustworthy results. An eventual goal is to have process models that are so efficient they could be included as part of an automated process optimization. The goal is to retain enough physics fidelity to have confidence in the simulation results. Diablo [26], a general purpose implicit nonlinear finite element code that is capable of effectively utilizing commodity parallel-processing platforms, is being adapted to
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Fig. 3. ALE3D simulation. Time snapshots of the melt flow showing spattering and denudation. The melt has a large backward flow (blue color; Vx < 0) due to Marangoni effect and recoil, compared to forward flow (Vx > 0; red color). The backward net flow breaks up later in time at the necking. The velocity scale is capped at ±1 m/s for better visualization. The right panel shows a magnified view at 270 ls (flow rotated by +90°) shows the velocity components (Vx, Vy, Vz) and the temperature (with contour lines) at the depression. The white letter O shows that the laser center is not at the bottom of the depression. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
model additive manufacturing. Early efforts focused on developing laser powder bed fusion modeling and algorithmic approaches in the context of 50 lm layer-resolved simulations for representative volumes comprising 1 mm3 [27]. These simulations highlight that it is misleading to think merely in terms of the temperature history of the material in the active powder layer and clearly show (Fig. 4) that the material located several or more layers below the active work surface is still undergoing significant temperature excursions, which will contribute to continued evolution of the local microstructure. The local laser powder bed fusion process involves thermallydriven material phase transformations. At the part scale, one neglects the details of the local laser-powder particle interactions shown previously. Instead, the goal is to describe part level behavior both during and after the build is complete. The simulation can
be cast as the thermo-mechanical response of a nonlinear solid continuum. In this approximation, the powder can be represented as a reduced-density, low-strength solid. The deposition of the laser energy into the powder can then be represented by a volumetric energy source term such as that derived by Gusarov et al. [28]. Melting can be represented thermally through a latent heat and mechanically as a near-total loss of strength. The ‘‘mushy zone” at the melt pool boundary is represented by having the temperature-dependent strength rise as temperature falls below the solidus temperature. The computational challenges of part scale thermo-mechanical simulations are driven by the disparate spatial scales of the laser energy source and the overall part geometry compounded by the disparate time scales of local heating versus overall heat transfer during the entire fabrication, which can be hours and is often days.
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Fig. 4. Build simulation part with Diablo (a) temperature history sampling points subsequently labeled (bottom-to-top) as ‘‘base” and ‘‘layers” 3, 6, 9 and 12. (b) Temperature history for five sampling points designated in (a) show recurring heating of the material.
We are now addressing this issue through adaptive mesh refinement to localize higher resolution in the vicinity of the active material transformation. To overcome the computational challenges when simulating the fabrication of a part with dimensions of cubic centimeters, we no longer resolve individual powder layers and individual laser scan lines. Multiple layers are lumped together and a larger ‘‘effective” laser beam is employed. A detailed discussion of our part scale simulations to date can be found in [19,27]. 3. Modeling of the microstructure evolution during solidification Achieving quantitative predictions of additively manufactured microstructures, and hence of properties and performance, will require combined efforts in solidification modeling spanning several length and time scales [29]. Atomistic simulations should enable the prediction of fundamental interfacial properties, e.g. surface tension anisotropies or kinetic coefficients particularly relevant to rapid solidification regimes [30]. At this scale, further developments, such as building reliable potentials for molecular dynamics simulations of alloys, are needed to enable quantitative predictions. At the scale of the solid-liquid interface, phase-field (PF) modeling, illustrated in Fig. 5a, has established itself as the method of choice to predict detailed morphologies and dynamics of solidification microstructures [31,32]. The PF method can yield quantitative predictions and shed light on experimentally observed microstructures [29], and is scalable on massively parallel computers [33]. PF codes include Tusas [34,35] an implicit PF method using finite-element discretization for unstructured mesh and the AMPE code (Adaptive Mesh Phase Evolution) [36,37] to
(a) Al-3wt%Cu, G = 29 K/mm, V = 290 µm/s
100 µm
model solidification in alloys. It employs a quaternion field to model the local grain orientation [38] and uses CALPHAD for diffusion coefficients and free energies. Both Tusas and AMPE have been developed with Exascale computing in mind and have favorable scalability. Yet, most direct comparisons of PF simulation results to experiments so far have been limited to directional solidification experiments, i.e. close to conventional casting parameter ranges. To be applied to additive manufacturing, further developments of PF models are needed to quantitatively incorporate non-equilibrium interfacial mechanisms of rapid solidification, such as solute trapping. Ultimately, to yield useful predictions of additively manufactured parts, the fundamental understanding from these smallerscale models should be incorporated into larger scale models, such as volume-averaged continuum scale models for solidification at the scale of entire processes, for instance models based on cellular automata [39–41]. Multi-scale models, such as the dendritic needle network (DNN) model [42,43] illustrated in Fig. 5b, should play a key role in bridging the scale gap between PF and macro-scale models. Efforts are also underway for including microstructural predictions within Truchas through the knowledge of temperature gradient (G) and the growth rate (R). An alternative approach for modeling microstructure evolution during AM is based on a kinetic Monte Carlo method and implemented in the open-source code SPPARKS [44]. SPPARKS based on the Potts Kinetic Monte Carlo technique, is introduced to model microstructure evolution during additive manufacturing and autogenous welding processes. During the simulation, a user defined melt pool is scanned through the simulation domain on a specified trajectory. The material is represented as a cubic lattice of sites with ‘‘spins” that represent specific grains. When the melt pool
(b) Al-9.8wt%Si, G = 540 K/mm, V = 106 µm/s
1 mm
Fig. 5. Simulations of dendritic solidification: (a) grain growth competition and grain boundary formation in an Al-Cu alloy, using phase-field modeling; (b) dynamical selection of microstructural features, e.g. primary dendritic spacing, under a change of mold cross-section in an Al-Si alloy, using dendritic needle network modeling [40]. In both panels, the color map represents the solute (Cu or Si) concentration field, from nominal (blue) to enriched (red). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001
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cally equivalent representation of a representative volume element (RVE) of the microstructure is generated. With that microstructure representation, one can then mesh the RVE in an interface conforming way. With the meshes generated, response of the polycrystal metallic material to high pressure and high strain rate mechanical loading histories are then calculated using finiteelement analysis. Bronkhorst and colleagues [47–60] are also developing a meso-scale and statistical modeling approach to quantitatively link microstructural details to spatial loading variability to be eventually incorporated into a macro-scale model for material damage and failure. Our ultimate goal is to integrate our modeling efforts from processing to performance through microstructure modeling. Most microstructure-aware models for simulating mechanical properties of polycrystalline materials use voxelated representation of microstructures (Fig. 7a). Lim and colleagues [61] utilized a unique SCULT capability in CUBIT meshing tool to generate conformal mesh by tracking volume fraction data of individual grains on a Cartesian grid used in a mesh. This capability is illustrated in Fig. 7b [61]. Comparison of mechanical simulations show that conformal discretization across interfaces reduces artificial stress localization commonly observed in non-conformal FE discretizations.
travels through a lattice site, the spins are randomized and any existing grain assignment is lost. Rapid grain growth occurs in the heat affected zone surrounding the melt pool, and results in the formation of elongated grains oriented along the temperature gradient. The method is capable of creating both columnar and equiaxed microstructures found in materials produced with powder bed fusion and directed energy deposition methods. Fig. 6 shows microstructures of additively manufactured stainless steel 304L using Laser Engineered Net Shaping technique (LENSÒ). Abnormal grain morphology with varying microstructural features, such as grain shapes and sizes, and interfaces is reproduced by kinetic Monte Carlo grain growth simulations [45]. However to date the simulation can only predict qualitative features and much remains to be done to discover the physics of granular solidification nucleation and growth and representing that physics properly within the simulation frameworks. From the kinetic Monte Carlo simulation results, the conformal meshing technique can then be used to generate a Finite-Element mesh to be used in crystal plasticity finite element (CPFE) calculations to predict the mechanical response and texture evolution of polycrystalline aggregates. This framework provides a step toward an integrated computational materials engineering approach, where models of materials processes are bridged to ones of properties. Key to this numerical representation is the ability to accurately represent grain boundaries and other interfaces within additively manufactured materials. This is coupled with the need to develop the proper models to represent plastic deformation and damage within the interface regions of the material structure. This includes the ability to represent subgranular dislocation motion and interaction processes much more accurately than we are generally able to do today. This enables a design loop such that models of materials properties provide key inputs to ones of processes in order to engineer materials systems with optimal performance.
5. Performance modeling Physically-based macro-scale continuum model development is essential to represent true physical quantities for documenting and tracking the evolution which takes place within metallic materials. This includes non-linear elasticity which accounts for elastic compressibility of the material, proper representation of the plastic deformation of the material which is based upon the physics of dislocation and nucleation glide, dislocation interactions and the nucleation and growth of deformation twinning. The early time events drive the initiation and propagation of damage and failure events which are strongly driven by the details of initial microstructure and evolving material structure with deformation. Finite-Element Analysis software (FEA) such as ABAQUS, Diablo are the workhorse for performance modeling. They solve a set of governing equations that represent the physical mechanisms response for various loading conditions (boundary conditions). They can predict internal stress in a part, where the part will fail, etc. Since plastic processes occur on a sub-granular length scale and the microstructure dominates the damage and failure process in most metallic materials, there is a critical need for integrating microstructure information of the material into the model at the macro-scale (e.g. [62,63]) in particular for the additively manufactured material. Additively manufactured materials in their as-built state [1] have been found to have substantially different plastic
4. Microstructure representation and modeling of material properties The role of microstructural features, which span many length scales, on the properties at the macroscopic scale falls naturally within the structure-process-property paradigm and has triggered many research efforts across various disciplines to develop microstructure-informed modeling frameworks. Knowledge of the microstructure morphology and distribution is required in order to model material properties. The microstructure representation can be obtained from experimental measurement or from simulation of the microstructure evolution. The microstructure representation meshes can be generated from EBSD data and through the use of the open-source code DREAM3D [46] a statisti-
(a)
(b)
(c)
Fig. 6. Microstructures of additively manufactured SS 304L using Laser Engineered Net Shaping (LENSÒ) technique. (a) EBSD measurement (b) kinetic Monte Carlo simulations (SPPARKS) and (c) conformal finite element mesh.
Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001
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150 MPa 30
(a) Voxelated FE mesh
(b) Conformal FE mesh
Fig. 7. Contours of von Mises stress at 10 % deformation using (a) voxelated and (b) conformal finite element meshes. Artificial non-smooth and localized stress was predicted using the voxelated mesh.
flow resistance than traditionally produced wrought material. There are potentially many physical factors – each of which could be contributing to this difference in behavior. 6. Topology optimization and toward process optimization for performance AM is facilitating access to a far richer design space for structural components. AM focused only on producing the same component designs a new way will miss the real impact of this technology. The recently released PLATO tool [64] provides a fundamentally different design paradigm using newly developed topology optimization tools where the function of the component dictates the shape. Since material is placed only where needed, these designs are often very organic in shape and a far cry from traditional CAD designs. Critical to this effort is the generation of truly printable shapes, where not only is the shape guided by the physics calculation(s), but the resulting shape is smooth, connected and
Fig. 8. Example of detailed ‘‘print-ready” design created within PLATO.
directly printable from within the design environment. This ‘‘print-ready” technology is a significant step forward as it removes large amounts of tedious design time by eliminating any topology optimization post processing steps. Fig. 8 shows an example of an intricate design produced directly within PLATO. Homogenization and meshing technologies have also been developed to allow the use of meta-materials (e.g. lattices) as part of a more traditional topology optimization. Equivalent properties are calculated for a given lattice unit cell and then these properties are employed during topology optimization to produce the optimal quasi-solid shape [65]. This solid shape can then be transformed quickly and automatically into the lattice structures using conformal hexahedral meshing techniques and unit cell representations of the lattice. Fig. 9 shows such a design and the corresponding lattice structure ready for printing. Also included in the PLATO development effort are technologies for accounting for the variability in the design (uncertainty quantification techniques) and for speeding the production of families of designs (reduced order modeling) where rich design spaces and tradeoffs can be efficiently explored. Other optimization tools include for example Tosca [66] and ParetoWorks [67]. Optimization software have mostly focused development on geometric optimization based on a set of constraints. Recent work has extended topology optimization capabilities to include constraints coming from additive manufacturing [68,69]. These methods can also be used to allow the design of variable density cellular material to alleviate some of the additive manufacturability constraints [70]. There is also a need to integrate microstructure, properties and processing parameters information in such optimization software in order to have a fully-integrated design tool. In the future such software will include additional constraints for the processing parameters in order to produce optimized materials performance in addition to optimized topology (geometry of the part).
Fig. 9. Design using homogenized lattice properties and then the insertion of the desired lattice into the calculated shape, again ready for direct printing.
Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001
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7. Perspective There are tremendous opportunities in manufacturing science within the field of additive manufacturing which offer many different economic and defense application advantages. These new classes of materials are substantially different in structure from those which have historically been produced by traditional casting, mechanical working, and subtractive manufacturing processes. The structures of these materials offer a rich avenue for scientific investigation into the long-standing endeavor of understanding and quantifying the process-to-performance linkage for material response. New modeling and simulation approaches are needed for process and performance representation and the strong linkage with discovery and validation experiment are more important that ever. Acknowledgments This work was performed for the U.S. Department of Energy’s National Nuclear Security Administration by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344, Los Alamos National Laboratory under contract DE-AC52-06NA25396, and Sandia National Laboratories under contract DE-AC04-94AL85000. The LLNL work was funded by the Laboratory Directed Research and Development Program at LLNL under project tracking code 13SI-002. The LANL work is funded by the Advanced Simulation Computing program. AJC, JWG and DT gratefully acknowledge support from AJC’s Early Career Award from U.S. DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. References [1] G.T. Gray III, V. Livescu, P.A. Rigg, C.P. Trujillo, C.M. Cady, S.R. Chen, J.S. Carpenter, T.J. Lienert, S. Fensin, Structure/property (constitutive and dynamic strength/damage) characterization of additively manufactured 316L SS, EPJ Web Conf. 94 (2015) 02006. [2] A.S. Wu, D.W. Brown, M. Kumar, G.F. Gallegos, W.E. King, An experimental investigation into additive manufacturing-induced residual stresses in 316L stainless steel, Metall. Mater. Trans. A 45 (2014) 6260. [3] D.L. Bourell, M.C. Leu, D.W. Rosen, Roadmap for Additive Manufacturing Identifying the Future of Freeform Processing, Austin TX, 2009. [4] Energetics Incorporated, Measurement Science Roadmap for Metal-Based Additive Manufacturing, Columbia, Maryland, 2013. [5] R. Berger, Additive manufacturing a game changer for the manufacturing industry? Munich, 2013. [6] S. Srivatsa, Air Force Research Laboratory, Wright-Patterson Air Force Base, OH 45433, 2014. [7] V. Manvatkar, A. De, T. DebRoy, Spatial variation of melt pool geometry, peak temperature and solidification parameters during laser assisted additive manufacturing process, Mater. Sci. Technol. 31 (2015) 924–930. [8] B. Zheng, Y. Zhou, J.E. Smugeresky, J.M. Schoenung, E.J. Lavernia, Thermal behavior and microstructural evolution during laser deposition with laserengineered net shaping: Part I. Numerical calculations, Metall. Mater. Trans. A 39 (2008) 2228–2236. [9] M.H. Farshidianfar, A. Khajepour, A.P. Gerlich, Effect of real-time cooling rate on microstructure in Laser Additive Manufacturing, J. Mater. Process. Technol. 231 (2016) 468–478. [10] Z. Fan, F. Liou, Numerical Modeling of the Additive Manufacturing (AM) Processes of Titanium Alloy. [11] R. Martukanitz, P. Michaleris, T. Palmer, T. DebRoy, Z-K Liu, R. Otis, T.W. Heo, LQ. Chen, Towards an integrated computational system for describing the additive manufacturing process for metallic materials, Addit. Manuf. 1 (2014) 52–63. [12] P. Michaleris, Modeling metal deposition in heat transfer analyses of additive manufacturing processes, Finite Elem. Anal. Des. 86 (1) (2014) 51–60. [13] https://github.com/truchas. [14] C. McCallen, ALE3D: Arbitrary Lagrange Eulerian Three-and Two Dimensional Modeling and Simulation Capability, Livermore, CA, Report No. LLNL-ABS565212, 2012.
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Please cite this article in press as: M.M. Francois et al., Modeling of additive manufacturing processes for metals: Challenges and opportunities, Curr. Opin. Solid State Mater. Sci. (2017), http://dx.doi.org/10.1016/j.cossms.2016.12.001