Discontinuous Galerkin FEM with Hot Element Addition for the Thermal Simulation of Additive Manufacturing

Abstract:

Despite its promising advantages, the application of directed energy deposition (DED) to produce large metal parts is hindered by challenges inherent to the process. Undesired residual stresses, distortions and heterogeneous material properties mainly originate from a part’s thermal history. Fast part-scale thermal models therefore facilitate improved applicability of DED by enabling the prediction and mitigation of these unwanted effects. In this work, the efficiency of a discontinuous Galerkin-based thermal model with heat input by hot element addition, is evaluated and improved to allow such fast simulations. It is found that the model permits the use of a coarse discretization around the heat source, which significantly reduces simulation time while maintaining accurate solutions. It is also shown that the model naturally facilitates the use of local time stepping, which can considerably improve the efficiency of thermal additive manufacturing simulations.

• Periodical: Key Engineering Materials (Volume 926)
• Pages: 297-304
• DOI: https://doi.org/10.4028/p-66s30h
• Online since: July 2022
• Authors: Björn Nijhuis*, Bert Geijselaers, Jos Havinga, Ton van den Boogaard
• Keywords: Directed Energy Deposition, Discontinuous Galerkin Method, Local Time-Stepping, Thermal Analysis

References

[1] T. Gatsos, K. A. Elsayed, Y. Zhai, and D. A. Lados, Review on Computational Modeling of Process–Microstructure–Property Relationships in Metal Additive Manufacturing, JOM 72 (2020) 403-419.

DOI: 10.1007/s11837-019-03913-x

[2] S. Cooke, K. Ahmadi, S. Willerth, and R. Herring, Metal additive manufacturing: Technology, metallurgy and modelling, J. Manuf. Process. 57 (2020) 978-1003.

DOI: 10.1016/j.jmapro.2020.07.025

[3] T. DebRoy, H. L. Wei, J. S. Zuback, T. Mukherjee, et al., Additive manufacturing of metallic components - Process, structure and properties, Prog. Mater. Sci., 92 (2018) 112-224.

DOI: 10.1016/j.pmatsci.2017.10.001

[4] K. Seleš, M. Perić, and Z. Tonković, Numerical simulation of a welding process using a prescribed temperature approach, J. Constr. Steel Res., 145 (2018) 49-57.

DOI: 10.1016/j.jcsr.2018.02.012

[5] B. Nijhuis, H. J. M. Geijselaers, and A. H. van den Boogaard, Efficient thermal simulation of large-scale metal additive manufacturing using hot element addition,, Comp. Struct., 245 (2021) 106463.

DOI: 10.1016/j.compstruc.2020.106463

[6] D. Soldner and J. Mergheim, Thermal modelling of selective beam melting processes using heterogeneous time step sizes,, Comp. Math. Appl., 78 (2019) 2183-2196.

DOI: 10.1016/j.camwa.2018.04.036

[7] L. Cheng and G. J. Wagner, An optimally-coupled multi-time stepping method for transient heat conduction simulation for additive manufacturing,, Comp. Meth. Appl. Mech. Eng., 381 (2021) 113825.

DOI: 10.1016/j.cma.2021.113825

[8] J. S. Hesthaven and T. Warburton, Nodal discontinuous Galerkin methods: algorithms, analysis, and applications, Springer, New York, (2007).

[9] J. E. Flaherty, R. M. Loy, M. S. Shephard, B. K. Szymanski, et al., Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws, J. Parallel Distrib. Comp., 47 (1997) 139-152.

DOI: 10.1006/jpdc.1997.1412

[10] J. Ding, Thermo-mechanical Analysis of Wire and Arc Additive Manufacturing Process, PhD Thesis, Cranfield University, Cranfield, (2012).

[11] L. E. Lindgren, Computational Welding Mechanics: Thermomechanical and Microstructural Simulations, Woodhead Publishing Limited, Cambridge, (2007).

[12] Information on https://www.mathworks.com/help/matlab/math/sparse-matrix-operations.html.