Multiphysics Modeling of Selective Laser Sintering/Melting by Rishi Kumar Ganeriwala A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Engineering - Mechanical Engineering and the Designated Emphasis in Energy Science and Technology in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Tarek I. Zohdi, Chair Professor Daniel Kammen Professor Hayden Taylor Fall 2015 Multiphysics Modeling of Selective Laser Sintering/Melting Copyright 2015 by Rishi Kumar Ganeriwala 1 Abstract Multiphysics Modeling of Selective Laser Sintering/Melting by Rishi Kumar Ganeriwala Doctor of Philosophy in Engineering - Mechanical Engineering and the Designated Emphasis in Energy Science and Technology University of California, Berkeley Professor Tarek I. Zohdi, Chair A significant percentage of total global employment is due to the manufacturing industry. However, manufacturing also accounts for nearly 20% of total energy usage in the United States according to the EIA. In fact, manufacturing accounted for 90% of industrial energy consumption and 84% of industry carbon dioxide emissions in 2002. Clearly, advances in manufacturing technology and efficiency are necessary to curb emissions and help society as a whole. Additive manufacturing (AM) refers to a relatively recent group of manufacturing technologies whereby one can 3D print parts, which has the potential to significantly reduce waste, reconfigure the supply chain, and generally disrupt the whole manufacturing industry. Selective laser sintering/melting (SLS/SLM) is one type of AM technology with the distinct advantage of being able to 3D print metals and rapidly produce net shape parts with complicated geometries. In SLS/SLM parts are built up layer-by-layer out of powder particles, which are selectively sintered/melted via a laser. However, in order to produce defect-free parts of sufficient strength, the process parameters (laser power, scan speed, layer thickness, powder size, etc.) must be carefully optimized. Obviously, these process parameters will vary depending on material, part geometry, and desired final part characteristics. Running experiments to optimize these parameters is costly, energy intensive, and extremely material specific. Thus a computational model of this process would be highly valuable. In this work a three dimensional, reduced order, coupled discrete element - finite dif- ference model is presented for simulating the deposition and subsequent laser heating of a layer of metal powder particles sitting on top of a substrate. Validation is provided and parameter studies are conducted showing the ability of this model to help determine appropriate process parameters and an optimal powder size distribution for a given mate- rial. Next, thermal stresses upon cooling are calculated using the finite difference method. Different case studies are performed and general trends can be seen. This work concludes by discussing future extensions of this model and the need for a multi-scale approach to achieve comprehensive part-level models of the SLS/SLM process. i To my parents, Manju and Suri ii Contents List of Figures v List of Tables ix 1 Introduction 1 1.1 Additive Manufacturing Techniques . 1 1.2 Applications of AM . 5 1.3 Outline of this Work . 6 2 Energy and Societal Impacts of Additive Manufacturing 9 2.1 Manufacturing Energy Use and CO2 Emissions . 9 2.2 Life Cycle Impacts of AM Technologies . 11 2.3 Societal Impacts of AM . 13 3 Selective Laser Sintering Process and Considerations 18 3.1 SLS Process Description . 19 3.2 Process Parameters . 22 3.2.1 Laser power . 22 3.2.2 Scan speed . 22 3.2.3 Spot size . 23 3.2.4 Hatch spacing . 23 3.2.5 Scan strategy . 23 3.2.6 Powder material and manufacturing . 24 3.2.7 Powder size distribution . 25 3.2.8 Layer thickness . 26 3.2.9 Surrounding gas atmosphere . 26 3.3 Material Properties of Parts Fabricated via SLS/SLM . 26 3.3.1 Density . 26 3.3.2 Microstructure . 27 3.3.3 Strength . 27 3.3.4 Hardness and surface roughness . 28 3.4 Other Considerations during SLS . 28 iii 3.5 Previous Modeling Attempts . 30 4 Powder Deposition and Laser Heating Model Description 33 4.1 Particle Dynamics . 33 4.2 Particle Thermal Effects . 37 4.2.1 Particle-to-particle heat transfer . 38 4.2.2 Laser beam modeling . 39 4.2.3 Phase change . 40 4.2.4 Thermal softening and melting of particles . 42 4.3 Finite Difference Modeling of Substrate . 43 4.4 Numerical Solution Scheme . 45 4.4.1 Time-stepping . 45 4.4.2 Binning and OpenMP Parallelization . 47 4.5 Programming Algorithm . 48 5 Powder Deposition and Laser Heating Model Validation and Results 51 5.1 Material Properties and Parameter Values . 51 5.2 Model Validation . 51 5.3 Numerical Examples . 54 6 Residual Stress Modeling 60 6.1 Background . 60 6.2 Modeling Framework . 62 6.2.1 Mechanical effects - balance of linear momentum . 62 6.2.2 Thermal effects - balance of energy . 65 6.2.3 Numerical solution scheme . 66 6.3 Numerical Examples . 67 6.3.1 Cooling of a solid block . 67 6.3.2 Cooling of a porous block . 75 6.3.3 Cooling of a single laser scan . 81 7 Conclusions and Future Extensions 90 7.1 Summary of this Work . 90 7.2 Model Limitations and Future Extensions . 93 Bibliography 97 A Economics and Projected Growth of Additive Manufacturing 110 B Numerical Derivatives 114 B.1 Spatial Derivatives using Finite Differences . 114 B.2 Time Marching Schemes . 117 B.2.1 Euler Methods . 117 iv B.2.2 Runge-Kutta Schemes . 118 B.2.3 Other Schemes . 120 C Basic Parallelization Techniques 121 C.1 Binning Algorithm . 121 C.2 OpenMP . 122 v List of Figures 1.1 List of common industrial AM processes, adapted from [66] . 3 1.2 Devices produced using AM techniques. SLS produced fuel nozzle for GE LEAP jet engines (left) [5] and acetabular cup for a hip implant (right) [3] 7 2.1 Global energy related CO2 emissions by scenario. 450 scenario is considered necessary to limit global temperature rise to 2 ◦C [50] . 10 2.2 US greenhouse gas emissions by sector [133] . 10 2.3 LCAs showing largest impact sources for the SLS of PA2200 nylon (left) and SLM of stainless steel (right) [57] . 13 2.4 IEA projections of energy related CO2 emissions per manufacturing sector by 2050 (left) and employment per manufacturing sector by 2050 (right). Two business as usual (BAU) scenarios and the efficient G2 scenario are depicted [102] . 16 3.1 Different stages depicting the solid state sintering of metal powders [69] . 19 3.2 Schematic of a typical SLS/ SLM set-up . 20 3.3 EOS P 800 SLS machine [1] . 20 3.4 Different scanning strategies used during SLS. Typical parallel zig-zag pat- tern (left) and island scanning strategy (right). Dashed lines refer to laser path. 24 3.5 Bimodal packing distribution . 25 3.6 Microstructure of SLM-processed Inconel 718 [51] . 27 3.7 Comparison against standard bulk material properties of yield strength, tensile strength, and breaking at elongation for stainless steel parts pro- duced via SLM. Bar color indicates direction tested [65] . 28 3.8 SEM images depicting balling behavior of a single laser scan at different scan speeds [74] . 29 3.9 Warping of parts due to uneven thermal expansion/contraction [89] . 30 4.1 Discrete element representation of pre-sintered powder particles (SEM im- age from [151]) . 34 4.2 Particle-to-particle overlap . 35 4.3 Heat transfer to an individual particle . 38 vi 4.4 Contact area of two intersecting particles . 39 4.5 Gaussian laser beam depiction . 40 4.6 Laser beam illustration as a series of light rays (length of each ray corre- sponds to intensity). Note that this approach is not used in the current work. 41 4.7 Illustration of how heat capacity is updated (left) and ensuing phase change diagram (right) . 42 4.8 Finite difference stencil and coordinate system used for an arbitrary mate- rial property A. Indices i, j, and k are used to represent the x, y, and z coordinates, respectively. 44 4.9 Depiction of boundary conditions used for the finite difference mesh: all B.C.s (left), Neumann B.C. for top face (right) . 45 4.10 Simulation flow chart . 47 4.11 Illustration of binning algorithm. Only particles in the shaded boxes will be checked for contact with the red particle in the center box. 48 5.1 Comparison of experimental melt pool size by Khairallah and Anderson (left) [58] and simulation melt pool size depicted in red (right). Note that the figure on the left is Figure 5(a) from [58]. The experimental melt height, width, and depth are 26 µm, 75 µm, and 30 µm, respectively. The simulation melt pool dimensions are 30 µm, 85 µm, and 20 µm. 54 5.2 Screenshots depicting the deposition of a layer of 316L SS particles (600 particles total) . 55 5.3 Screenshots showing the temperature evolution of a layer of 316L SS par- ticles and the underlying 316L SS substrate as a laser is passed over (tem- perature in Kelvin). Top view on upper row. Cross-sectional view from the side on bottom row. 56 5.4 Screenshots depicting the melt pool (red) of a layer of 316L SS particles and the undelying 316L SS substrate as a laser is passed over. Top view on upper row. Cross-sectional view from the side on bottom row. 56 5.5 Melt pool size as laser power is varied from 40 - 400 W , scan speed is constant at 2.0 m/s .............................. 57 5.6 Melt pool size as scan speed is varied from 0.4 to 4.0 m/s, laser power is constant at 200 W ..............................