Research Papers

Thermomechanical Modeling of Additive Manufacturing Large Parts

[+] Author and Article Information
Erik R. Denlinger

Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: erd5061@psu.edu

Jeff Irwin

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

Pan Michaleris

Associate Professor
Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
Pan Computing LLC,
University Park, PA 16802
e-mail: pxm32@psu.edu

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received April 14, 2014; final manuscript received September 19, 2014; published online October 24, 2014. Assoc. Editor: David L. Bourell.

J. Manuf. Sci. Eng 136(6), 061007 (Oct 24, 2014) (8 pages) Paper No: MANU-14-1173; doi: 10.1115/1.4028669 History: Received April 14, 2014; Revised September 19, 2014

A finite element modeling strategy is developed to allow for the prediction of distortion accumulation in additive manufacturing (AM) large parts (on the order of meters). A 3D thermoelastoplastic analysis is performed using a hybrid quiet inactive element activation strategy combined with adaptive coarsening. At the beginning for the simulation, before material deposition commences, elements corresponding to deposition material are removed from the analysis, then elements are introduced in the model layer by layer in a quiet state with material properties rendering them irrelevant. As the moving energy source is applied on the part, elements are switched to active by restoring the actual material properties when the energy source is applied on them. A layer by layer coarsening strategy merging elements in lower layers of the build is also implemented such that while elements are added on the top of build, elements are merged below maintaining a low number of degrees of freedom in the model for the entire simulation. The effectiveness of the modeling strategy is demonstrated and experimentally validated on a large electron beam deposited Ti–6Al–4V part consisting of 107 deposition layers. The simulation and experiment show good agreement with a maximum error of 29%.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Taminger, K. M., and Hafley, R. A., 2003, “Electron Beam Freeform Fabrication: A Rapid Metal Deposition Process,” Proceedings of the 3rd Annual Automotive Composites Conference, Troy, MI, Sept. 9–10, pp. 1–6.
Hibbitt, H. D., and Marcal, P. V., 1973, “A Numerical, Thermo-Mechanical Model for the Welding and Subsequent Loading of a Fabricated Structure,” Comput. Struct., 3(5), pp. 1145–1174. [CrossRef]
Friedman, E., 1975, “Thermomechanical Analysis of the Welding Process Using the Finite Element Method,” ASME J. Pressure Vessel Technol., 97(3), pp. 206–213. [CrossRef]
Andersson, B., 1978, “Thermal Stresses in a Submerged-Arc Welded Joint Considering Phase Transformations,” ASME J. Eng. Mater. Technol., 100(4), pp. 356–362. [CrossRef]
Argyris, J. H., Szimmat, J., and Willam, K. J., 1982, “Computational Aspects of Welding Stress Analysis,” Comput. Methods Appl. Mech. Eng., 33(1), pp. 635–665. [CrossRef]
Papazoglou, V., and Masubuchi, K., 1982, “Numerical Analysis of Thermal Stresses During Welding Including Phase Transformation Effects,” ASME J. Pressure Vessel Technol., 104(3), pp. 198–203. [CrossRef]
Free, J. A., and Porter Goff, R. F., 1989, “Predicting Residual Stresses in Multi-Pass Weldments With the Finite Element Method,” Comput. Struct., 32(2), pp. 365–378. [CrossRef]
Tekriwal, P., and Mazumder, J., 1988, “Finite Element Analysis of Three-Dimensional Transient Heat Transfer in GMA Welding,” Weld. J., 67(5), pp. 150–156.
Michaleris, P., Tortorelli, D. A., and Vidal, C. A., 1995, “Analysis and Optimization of Weakly Coupled Thermoelastoplastic Systems With Applications to Weldment Design,” Int. J. Numer. Methods Eng., 38(8), pp. 1259–1285. [CrossRef]
Lindgren, L. E., Runnemalm, H., and Näsström, M. O., 1999, “Simulation of Multipass Welding of a Thick Plate,” Int. J. Numer. Methods Eng., 44(9), pp. 1301–1316. [CrossRef]
Asadi, M., and Goldak, J. A., 2014 “An Integrated Computational Welding Mechanics With Direct-Search Optimization for Mitigation of Distortion in an Aluminum Bar Using Side Heating,” ASME J. Manuf. Sci. Eng., 136(1), p. 011007. [CrossRef]
Lindgren, L. E., 2001, “Finite Element Modeling and Simulation of Welding Part 1: Increased Complexity,” J. Therm. Stresses, 24(2), pp. 141–192. [CrossRef]
Lindgren, L. E., 2001, “Finite Element Modeling and Simulation of Welding. Part 2: Improved Material Modeling,” J. Therm. Stresses, 24(3), pp. 195–231. [CrossRef]
Lindgren, L. E., 2001, “Finite Element Modeling and Simulation of Welding. Part 3: Efficiency and Integration,” J. Therm. Stresses, 24(4), pp. 305–334. [CrossRef]
Michaleris, P., 2014, “Modeling Metal Deposition in Heat Transfer Analyses of Additive Manufacturing Processes,” Finite Elem. Anal. Des., 86(0), pp. 51–60. [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]
Peyre, P., Aubry, P., Fabbro, R., Neveu, R., and Longuet, A., 2008, “Analytical and Numerical Modeling of the Direct Metal Deposition Laser Process,” J. Phys. D: Appl. Phys., 41(2), p. 025403. [CrossRef]
Qian, L., Mei, J., Liang, J., and Wu, X., 2005, “Influence of Position and Laser Power on Thermal History and Microstructure of Direct Laser Fabricated Ti–6Al–4V Samples,” Mater. Sci. Technol., 21(5), pp. 597–605. [CrossRef]
Shen, N., and Chou, K., 2012, “Thermal Modeling of Electron Beam Additive Manufacturing Process. Powder Sintering Effects,” ASME Paper No. MSEC2012-7253. [CrossRef]
Jamshidinia, M., Kong, F., and Kovacevic, R., 2013, “Numerical Modeling of Heat Distribution in the Electron Beam Melting® of Ti–6Al–4V,” ASME J. Manuf. Sci. Eng., 135(6), p. 061010. [CrossRef]
Sammons, P. M., Bristow, D. A., and Landers, R. G., 2013, “Height Dependent Laser Metal Deposition Process Modeling,” ASME J. Manuf. Sci. Eng., 135(5), p. 054501. [CrossRef]
Anca, A., Fachinotti, V. D., Escobar-Palafox, G., and Cardona, A., 2011, “Computational Modelling of Shaped Metal Deposition,” Int. J. Numer. Methods Eng., 85(1), pp. 84–106. [CrossRef]
Chiumenti, M., Cervera, M., Salmi, A., Agelet de Saracibar, C., Dialami, N., and Matsui, K., 2010, “Finite Element Modeling of Multi-Pass Welding and Shaped Metal Deposition Processes,” Comput. Methods Appl. Mech. Eng., 199(37), pp. 2343–2359. [CrossRef]
Lundbäck, A., and Lindgren, L. E., 2011, “Modeling of Metal Deposition,” Finite Elem. Anal. Des., 47(10), pp. 1169–1177. [CrossRef]
Marimuthu, S., Clark, D., Allen, J., Kamara, A., Mativenga, P., Li, L., and Scudamore, R., 2012, “Finite Element Modeling of Substrate Thermal Distortion in Direct Laser Additive Manufacture of an Aero-Engine Component,” Proc. Inst. Mech. Eng., Part C, 227(9), pp. 1987–1999. [CrossRef]
Mughal, M., Fawad, H., and Mufti, R., 2006, “Three-Dimensional Finite-Element Modelling of Deformation in Weld-Based Rapid Prototyping,” Proc. Inst. Mech. Eng., Part C, 220(6), pp. 875–885. [CrossRef]
Chin, R., Beuth, J., and Amon, C., 1995, “Control of Residual Thermal Stresses in Shape Deposition Manufacturing,” Proceedings of the Solid Freeform Fabrication Symposium, Austin, TX, Aug., pp. 221–228.
Klingbeil, N., Beuth, J., Chin, R., and Amon, C., 2002, “Residual Stress-Induced Warping in Direct Metal Solid Freeform Fabrication,” Int. J. Mech. Sci., 44(1), pp. 57–77. [CrossRef]
Michaleris, P., Feng, Z., and Campbell, G., 1997, “Evaluation of 2D and 3D FEA Models for Predicting Residual Stress and Distortion,” ASME, Conf. Pressure vessels and piping, Orlando, FL, pp. 91–102.
Zhang, L., and Michaleris, P., 2004, “Investigation of Lagrangian and Eulerian Finite Element Methods for Modeling the Laser Forming Process,” Finite Elem. Anal. Des., 40(4), pp. 383–405. [CrossRef]
Ding, J., Colegrove, P., Mehnen, J., Ganguly, S., Sequeira Almeida, P., Wang, F., and Williams, S., 2011, “Thermomechanical Analysis of Wire and Arc Additive Layer Manufacturing Process on Large Multilayer Parts,” Comput. Mater. Sci., 50(12), pp. 3315–3322. [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]
Jasak, H., and Gosman, A., 2000, “Automatic Resolution Control for the Finite-Volume Method, Part 1: Aposteriori Error Estimates,” Numer. Heat Transfer: Part B, 38(3), pp. 237–256. [CrossRef]
Zienkiewicz, O. C., and Zhu, J. Z., 1987, “A Simple Error Estimator and Adaptive Procedure for Practical Engineerng Analysis,” Int. J. Numer. Methods Eng., 24(2), pp. 337–357. [CrossRef]
Picasso, M., 2003, “An Anisotropic Error Indicator Based on ZienkiewiczZhu Error Estimator: Application to Elliptic and Parabolic Problems,” SIAM J. Sci. Comput., 24(4), pp. 1328–1355. [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]
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. [CrossRef]
Yu, G., Masubuchi, K., Maekawa, T., and Patrikalakis, N. M., 1999, “A Finite Element Model for Metal Forming by Laser Line Heating,” Proceedings of the First International Conference on Computer Applications in Shipbuilding, ICCAS, Cambridge, MA, June, Vol. 99, pp. 409–418.
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]
Boyer, R. F., and Collings, E., 1994, Materials Properties Handbook: Titanium Alloys, ASM International, Materials Park, OH.
Hughes, T. J., 2000, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover, Mineola, NY.
Lee, N. S., and Bathe, K. J., 1994, “Error Indicators and Adaptive Remeshing in Large Deformation Finite Element Analysis,” Finite Elem. Anal. Des., 16(2), pp. 99–139. [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]


Grahic Jump Location
Fig. 1

The mesh coarsening algorithm merges two layers of elements and deletes an entire plane of nodes. This is combined with a hybrid quiet inactive element activation method.

Grahic Jump Location
Fig. 2

Mesh 1 has a uniform density in the z direction. Element edges, which are subsequently eliminated by coarsening, are highlighted. (a) Mesh 1, (b) mesh 2, (c) mesh 3, and (d) mesh 4.

Grahic Jump Location
Fig. 3

Displacement magnitude results (mm) at the end of simulation for the uniformly fine baseline case of the small model

Grahic Jump Location
Fig. 4

Displacement magnitude results (mm) at the end of simulation for the coarse case of the small model

Grahic Jump Location
Fig. 5

Displacement magnitude at two different nodes versus time for both cases of the small model. The locations of these nodes are shown in Fig. 3. (a) Node 1 at free end of substrate and (b) node 2 between fifth and sixth layers

Grahic Jump Location
Fig. 6

Displacement versus y location at end of simulation along line AA for both cases of the small model

Grahic Jump Location
Fig. 7

Large workpiece, deposited on 3810 mm long substrate, for model validation. (Figure provided by Sciaky, Inc.)

Grahic Jump Location
Fig. 8

Illustration of the mesh used for layers 1–9. (a) Top view of mesh with mechanical constraints and (b) magnified isometric view of the mesh.

Grahic Jump Location
Fig. 9

Mechanical results (mm) after nine layers of deposition (a) while clamped in the fixture (b) after release of the clamps. Significant distortion can be seen after the release of the clamps (2× magnification).

Grahic Jump Location
Fig. 10

Displacement magnitude (mm) results after the model has been rotated to the same orientation as the scan results (2× magnification)

Grahic Jump Location
Fig. 11

Top view of the coordinate system used for the simulated and experimental results (Figure provided by Neomek, Inc.)

Grahic Jump Location
Fig. 12

Experimental and simulated distortion results in the x–z plane at y = 457 mm



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In