Research Papers

A Line Heat Input Model for Additive Manufacturing

[+] Author and Article Information
Jeff Irwin

Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
17 Reber Building,
University Park, PA 16802
e-mail: jei5028@psu.edu

P. Michaleris

Associate Professor
Department of Mechanical
and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802;
Pan Computing LLC,
State College, PA 16803

Manuscript received July 1, 2015; final manuscript received April 29, 2016; published online June 23, 2016. Assoc. Editor: Z. J. Pei.

J. Manuf. Sci. Eng 138(11), 111004 (Jun 23, 2016) (9 pages) Paper No: MANU-15-1327; doi: 10.1115/1.4033662 History: Received July 01, 2015; Revised April 29, 2016

A line input (LI) model has been developed, which makes the accurate modeling of powder bed processes more computationally efficient. Goldak's ellipsoidal model has been used extensively to model heat sources in additive manufacturing (AM), including lasers and electron beams. To accurately model the motion of the heat source, the simulation time increments must be small enough such that the source moves a distance smaller than its radius over the course of each increment. When the source radius is small and its velocity is large, a strict condition is imposed on the size of time increments regardless of any stability criteria. In powder bed systems, where radii of 0.1 mm and velocities of 500 mm/s are typical, a significant computational burden can result. The line heat input model relieves this burden by averaging the heat source over its path. This model allows the simulation of an entire heat source scan in just one time increment. However, such large time increments can lead to inaccurate results. Instead, the scan is broken up into several linear segments, each of which is applied in one increment. In this work, time increments are found that yield accurate results (less than 10% displacement error) and require less than 1/10 of the central processing unit (CPU) time required by Goldak's moving source model. A dimensionless correlation is given that can be used to determine the necessary time increment size that will greatly decrease the computational time required for any powder bed simulation while maintaining accuracy.

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Khaing, M. , Fuh, J. , and Lu, L. , 2001, “ Direct Metal Laser Sintering for Rapid Tooling: Processing and Characterisation of EOS Parts,” J. Mater. Process. Technol., 113(1), pp. 269–272. [CrossRef]
Zhang, P. , Toman, J. , Yu, Y. , Biyikli, E. , Kirca, M. , Chmielus, M. , and To, A. , 2015, “ Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation,” ASME J. Manuf. Sci. Eng., 137(2), p. 021004. [CrossRef]
Kolossov, S. , Boillat, E. , Glardon, R. , Fischer, P. , and Locher, M. , 2004, “ 3D FE Simulation for Temperature Evolution in the Selective Laser Sintering Process,” Int. J. Mach. Tools Manuf., 44(2), pp. 117–123. [CrossRef]
Yin, J. , Zhu, H. , Ke, L. , Lei, W. , Dai, C. , and Zuo, D. , 2012, “ Simulation of Temperature Distribution in Single Metallic Powder Layer for Laser Micro-Sintering,” Comput. Mater. Sci., 53(1), pp. 333–339. [CrossRef]
Paul, S. , Gupta, I. , and Singh, R. , 2015, “ Characterization and Modeling of Microscale Preplaced Powder Cladding Via Fiber Laser,” ASME J. Manuf. Sci. Eng., 137(3), p. 031019. [CrossRef]
Bugeda, G. , Cervera, M. , and Lombera, G. , 1999, “ Numerical Prediction of Temperature and Density Distributions in Selective Laser Sintering Processes,” Rapid Prototyping J., 5(1), pp. 21–26. [CrossRef]
Contuzzi, N. , Campanelli, S. , and Ludovico, A. , 2011, “ 3D Finite Element Analysis in the Selective Laser Melting Process,” Int. J. Simul. Modell. (IJSIMM), 10(3), pp. 113–121. [CrossRef]
Roberts, I. , Wang, C. , Esterlein, R. , Stanford, M. , and Mynors, D. , 2009, “ A Three-Dimensional Finite Element Analysis of the Temperature Field During Laser Melting of Metal Powders in Additive Layer Manufacturing,” Int. J. Mach. Tools Manuf., 49(12), pp. 916–923. [CrossRef]
Morgan, R. , Sutcliffe, C. , and O'neill, W. , 2004, “ Density Analysis of Direct Metal Laser Re-Melted 316l Stainless Steel Cubic Primitives,” J. Mater. Sci., 39(4), pp. 1195–1205. [CrossRef]
O'neill, W. , Sutcliffe, C. , Morgan, R. , Landsborough, A. , and Hon, K. , 1999, “ Investigation on Multi-Layer Direct Metal Laser Sintering of 316l Stainless Steel Powder Beds,” CIRP Ann. Manuf. Technol., 48(1), pp. 151–154. [CrossRef]
Zhang, L. , Reutzel, E. , and Michaleris, P. , 2004, “ Finite Element Modeling Discretization Requirements for the Laser Forming Process,” Int. J. Mech. Sci., 46(4), pp. 623–637. [CrossRef]
Fell, A. , and Willeke, G. , 2010, “ Fast Simulation Code for Heating, Phase Changes and Dopant Diffusion in Silicon Laser Processing Using the Alternating Direction Explicit (ADE) Method,” Appl. Phys. A, 98(2), pp. 435–440. [CrossRef]
Michaleris, P. , 2014, “ Modeling Metal Deposition in Heat Transfer Analyses of Additive Manufacturing Processes,” Finite Elem. Anal. Des., 86, pp. 51–60. [CrossRef]
Zienkiewicz, O. C. , and Zhu, J. Z. , 1987, “ A Simple Error Estimator and Adaptive Procedure for Practical Engineering Analysis,” Int. J. Numer. Methods Eng., 24(2), pp. 337–357. [CrossRef]
Picasso, M. , 2003, “ An Anisotropic Error Indicator Based on Zienkiewicz–Zhu Error Estimator: Application to Elliptic and Parabolic Problems,” SIAM J. Sci. Comput., 24(4), pp. 1328–1355. [CrossRef]
Berger, M. J. , and Oliger, J. , 1984, “ Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations,” J. Comput. Phys., 53(3), pp. 484–512. [CrossRef]
Berger, M. J. , and Colella, P. , 1989, “ Local Adaptive Mesh Refinement for Shock Hydrodynamics,” J. Comput. Phys., 82(1), pp. 64–84. [CrossRef]
Bell, J. , Berger, M. , Saltzman, J. , and Welcome, M. , 1994, “ Three-Dimensional Adaptive Mesh Refinement for Hyperbolic Conservation Laws,” SIAM J. Sci. Comput., 15(1), pp. 127–138. [CrossRef]
Bank, R. E. , Sherman, A. H. , and Weiser, A. , 1983, “ Some Refinement Algorithms and Data Structures for Regular Local Mesh Refinement,” Sci. Comput. Appl. Math. Comput. Phys. Sci., 1, pp. 3–17.
Shepherd, J. F. , Dewey, M. W. , Woodbury, A. C. , Benzley, S. E. , Staten, M. L. , and Owen, S. J. , 2010, “ Adaptive Mesh Coarsening for Quadrilateral and Hexahedral Meshes,” Finite Elem. Anal. Des., 46(1), pp. 17–32. [CrossRef]
Prasad, N. S. , and Narayanan, S. , 1996, “ Finite Element Analysis of Temperature Distribution During Arc Welding Using Adaptive Grid Technique,” Weld. J., 75(4), pp. 123–128.
Runnemalm, H. , and Hyun, S. , 2000, “ Three-Dimensional Welding Analysis Using an Adaptive Mesh Scheme,” Comput. Methods Appl. Mech. Eng., 189(2), pp. 515–523. [CrossRef]
Liu, X. , Lan, S. , and Ni, J. , 2015, “ Thermal Mechanical Modeling of the Plunge Stage During Friction-Stir Welding of Dissimilar Al 6061 to Trip 780 Steel,” ASME J. Manuf. Sci. Eng., 137(5), p. 051017. [CrossRef]
Choi, W. , and Chung, H. , 2015, “ Variation Simulation of Compliant Metal Plate Assemblies Considering Welding Distortion,” ASME J. Manuf. Sci. Eng., 137(3), p. 031008. [CrossRef]
Patil, N. , Pal, D. , Rafi, K. , Zeng, K. , Moreland, A. , Hicks, A. , and Beeler, D. , 2015, “ A Generalized Feed Forward Dynamic Adaptive Mesh Refinement and Derefinement Finite Element Framework for Metal Laser Sintering—Part I: Formulation and Algorithm Development,” ASME J. Manuf. Sci. Eng., 137(4), p. 041001. [CrossRef]
Garrido, I. , Lee, B. , Fladmark, G. , and Espedal, M. , 2006, “ Convergent Iterative Schemes for Time Parallelization,” Math. Comput., 75(255), pp. 1403–1428. [CrossRef]
Farhat, C. , and Chandesris, M. , 2003, “ Time-Decomposed Parallel Time-Integrators: Theory and Feasibility Studies for Fluid, Structure, and Fluid–Structure Applications,” Int. J. Numer. Methods Eng., 58(9), pp. 1397–1434. [CrossRef]
Cortial, J. , and Farhat, C. , 2009, “ A Time-Parallel Implicit Method for Accelerating the Solution of Non-Linear Structural Dynamics Problems,” Int. J. Numer. Methods Eng., 77(4), pp. 451–470. [CrossRef]
Christlieb, A. , and Ong, B. , 2011, “ Implicit Parallel Time Integrators,” J. Sci. Comput., 49(2), pp. 167–179. [CrossRef]
Wu, S. , Shi, B. , and Huang, C. , 2009, “ Parareal–Richardson Algorithm for Solving Nonlinear ODEs and PDEs,” Commun. Comput. Phys., 6(4), pp. 883–902. [CrossRef]
Wanxie, Z. , Zhuang, X. , and Zhu, J. , 1998, “ A Self-Adaptive Time Integration Algorithm for Solving Partial Differential Equations,” Appl. Math. Comput., 89(1), pp. 295–312.
Horton, G. , and Vandewalle, S. , 1995, “ A Space-Time Multigrid Method for Parabolic Partial Differential Equations,” SIAM J. Sci. Comput., 16(4), pp. 848–864. [CrossRef]
Fischer, P. , Romano, V. , Weber, H. , Karapatis, N. , Boillat, E. , and Glardon, R. , 2003, “ Sintering of Commercially Pure Titanium Powder With a Nd:Yag Laser Source,” Acta Mater., 51(6), pp. 1651–1662. [CrossRef]
Shiomi, M. , Yoshidome, A. , Abe, F. , and Osakada, K. , 1999, “ Finite Element Analysis of Melting and Solidifying Processes in Laser Rapid Prototyping of Metallic Powders,” Int. J. Mach. Tools Manuf., 39(2), pp. 237–252. [CrossRef]
Wang, X. , Laoui, T. , Bonse, J. , Kruth, J.-P. , Lauwers, B. , and Froyen, L. , 2002, “ Direct Selective Laser Sintering of Hard Metal Powders: Experimental Study and Simulation,” Int. J. Adv. Manuf. Technol., 19(5), pp. 351–357. [CrossRef]
Tolochko, N. K. , Arshinov, M. K. , Gusarov, A. V. , Titov, V. I. , Laoui, T. , and Froyen, L. , 2003, “ Mechanisms of Selective Laser Sintering and Heat Transfer in TI Powder,” Rapid Prototyping J., 9(5), pp. 314–326. [CrossRef]
Zeng, K. , Pal, D. , and Stucker, B. , 2012, “ A Review of Thermal Analysis Methods in Laser Sintering and Selective Laser Melting,” Solid Freeform Fabrication Symposium, Vol. 23, p. 796.
Ibraheem, A. K. , Derby, B. , and Withers, P. J. , 2003, “ Thermal and Residual Stress Modelling of the Selective Laser Sintering Process,” DTIC Document, Contract No. N00014-02-1-0820.
Liu, H. , 2014, “ Numerical Analysis of Thermal Stress and Deformation in Multi-Layer Laser Metal Deposition Process,” Master's thesis, Missouri University of Science and Technology, Rolla, MO.
Song, J. , Shanghvi, J. , and Michaleris, P. , 2004, “ Sensitivity Analysis and Optimization of Thermo-Elasto-Plastic Processes With Applications to Welding Side Heater Design,” Comput. Methods Appl. Mech. Eng., 193(42), pp. 4541–4566. [CrossRef]
Goldak, J. , Chakravarti, A. , and Bibby, M. , 1984, “ A New Finite Element Model for Welding Heat Sources,” Metall. Trans. B, 15(2), pp. 299–305. [CrossRef]
Denlinger, E. R. , Heigel, J. C. , and Michaleris, P. , 2014, “ Residual Stress and Distortion Modeling of Electron Beam Direct Manufacturing Ti–6AL–4V,” Proc. Inst. Mech. Eng., Part B, 229(10), pp. 1803–1813. [CrossRef]


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Fig. 6

Schematic of the dimensions of the substrate (square outline) and laser scans (single-headed arrows), not to scale

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Fig. 7

Temperature-dependent material properties for Ti–6Al–4V

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Fig. 5

The mesh used to verify the heat input model, displacement boundary conditions (markers on the −x face), and heat source scans (lines on the +z face, not to scale). The hatch spacing between scans is 0.1 mm.

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Fig. 1

Illustration of the ellipsoidal heat distribution and the local heat source coordinate system with the origin at the start of the heating path. For vs > 0, the heat source moves in the local −z direction.

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Fig. 2

Temperature versus x location for two heat input models with different time increments compared to Goldak's model at the end of the third scan along the thermal line shown in Fig. 10: (a) line heat input models and (b) EE models

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Fig. 3

Power density versus global x location for two subsequent segments of a heat source scan using the EE model. The elongated length c̃ is chosen such that superposing these two segments gives a flat distribution.

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Fig. 4

Goldak's moving source (left) compared to LI (middle) and EE (right) power densities. LI and EE are scaled so that they are visible. Unscaled, their peak values are less intense than that of Goldak's model.

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Fig. 8

Temperature contours (°C) at the end of the first scan (top) and final scan (bottom)

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Fig. 9

Displacement contours (mm) magnified by a factor of 200 at the end of the first scan (top) and final scan (bottom)

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Fig. 10

Illustration of the point and lines at which the following results are shown

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Fig. 11

Longitudinal distortion (z displacement versus x location) for different heat input models at the end of the final scan along the longitudinal line shown in Fig. 10: (a) line heat input models and (b) EE models

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Fig. 15

Sectioned view of the mesh, showing how the element sizes vary in the z direction

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Fig. 12

Convergence study at node 1 for Inconel® 625 with a heat source speed of 450 mm/s (a) and CPU time reduction as a function of heat source speed for Ti–6Al–4V (b)

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Fig. 13

Temperature-dependent thermal and mechanical material properties for Inconel® 625

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Fig. 14

A correlation of the dimensionless parameters that can be used to find the necessary time increment, given material properties, and processing parameters



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