A simple yet consistent constitutive law and mortar-based layer coupling schemes for thermomechanical macroscale simulations of metal additive manufacturing processes

This article proposes a coupled thermomechanical finite element model tailored to the macroscale simulation of metal additive manufacturing processes such as selective laser melting. A first focus lies on the derivation of a consistent constitutive law on basis of a Voigt-type spatial homogenization procedure across the relevant phases, powder, melt and solid. The proposed constitutive law accounts for the irreversibility of phase change and consistently represents thermally induced residual stresses. In particular, the incorporation of a reference strain term, formulated in rate form, allows to consistently enforce a stress-free configuration for newly solidifying material at melt temperature. Application to elementary test cases demonstrates the validity of the proposed constitutive law and allows for a comparison with analytical and reference solutions. Moreover, these elementary solidification scenarios give detailed insights and foster understanding of basic mechanisms of residual stress generation in melting and solidification problems with localized, moving heat sources. As a second methodological aspect, dual mortar mesh tying strategies are proposed for the coupling of successively applied powder layers. This approach allows for very flexible mesh generation for complex geometries. As compared to collocation-type coupling schemes, e.g., based on hanging nodes, these mortar methods enforce the coupling conditions between non-matching meshes in an $$L^2$$ L 2 -optimal manner. The combination of the proposed constitutive law and mortar mesh tying approach is validated on realistic three-dimensional examples, representing a first step towards part-scale predictions.

[1]  Miguel Cervera,et al.  Modeling of Microstructure Evolution of Ti6Al4V for Additive Manufacturing , 2018, Metals.

[2]  T. Zohdi,et al.  Numerical simulation of Laser Fusion Additive Manufacturing processes using the SPH method , 2018, Computer Methods in Applied Mechanics and Engineering.

[3]  P. Michaleris,et al.  Residual stress and distortion modeling of electron beam direct manufacturing Ti-6Al-4V , 2015 .

[4]  Yu Zou,et al.  Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation , 2017, ArXiv.

[5]  P. Michaleris.  Modeling metal deposition in heat transfer analyses of additive manufacturing processes , 2014 .

[6]  Ulrich Rüde,et al.  Numerical investigations on hatching process strategies for powder-bed-based additive manufacturing using an electron beam , 2014, 1403.3251.

[7]  B. Previtali,et al.  Finite element modeling of residual stress and geometrical error formations in selective laser melting of metals , 2020 .

[8]  Wolfgang A. Wall,et al.  A novel physics-based and data-supported microstructure model for part-scale simulation of laser powder bed fusion of Ti-6Al-4V , 2021, Adv. Model. Simul. Eng. Sci..

[9]  Sebastian L. Fuchs,et al.  A novel smoothed particle hydrodynamics formulation for thermo-capillary phase change problems with focus on metal additive manufacturing melt pool modeling , 2020, Computer Methods in Applied Mechanics and Engineering.

[10]  S. Khairallah,et al.  Mesoscopic Simulation Model of Selective Laser Melting of Stainless Steel Powder , 2014 .

[11]  Richard M. Everson,et al.  Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting , 2013 .

[12]  J. Kruth,et al.  Residual stresses in selective laser sintering and selective laser melting , 2006 .

[13]  J. Andersson,et al.  Simulation of additive manufacturing using coupled constitutive and microstructure models , 2016 .

[14]  Ninggang Shen,et al.  NUMERICAL THERMAL ANALYSIS IN ELECTRON BEAM ADDITIVE MANUFACTURING WITH PREHEATING EFFECTS , 2012 .

[15]  Barbara I. Wohlmuth,et al.  Dual Quadratic Mortar Finite Element Methods for 3D Finite Deformation Contact , 2012, SIAM J. Sci. Comput..

[16]  T. Childs,et al.  Selective laser sintering (melting) of stainless and tool steel powders: Experiments and modelling , 2005 .

[17]  Andrey V. Gusarov,et al.  Model of Radiation and Heat Transfer in Laser-Powder Interaction Zone at Selective Laser Melting , 2009 .

[18]  W. L. Yao,et al.  Analysis of Shell Cracking in Investment Casting with Laser Stereolithography Patterns , 1999 .

[19]  Xibing Gong,et al.  Phase-Field Modeling of Microstructure Evolution in Electron Beam Additive Manufacturing , 2015 .

[20]  M. Puso,et al.  Mesh tying on curved interfaces in 3D , 2003 .

[21]  O. Walton,et al.  Simulation of Powder Layer Deposition in Additive Manufacturing Processes Using the Discrete Element Method , 2015 .

[22]  C. Emmelmann,et al.  Additive Manufacturing of Metals , 2016 .

[23]  Yuebin Guo,et al.  On the Simulation Scalability of Predicting Residual Stress and Distortion in Selective Laser Melting , 2018 .

[24]  Wolfgang A. Wall,et al.  Physics‐based modeling and predictive simulation of powder bed fusion additive manufacturing across length scales , 2021, GAMM-Mitteilungen.

[25]  R. M. Ferencz,et al.  Experimental comparison of residual stresses for a thermomechanical model for the simulation of selective laser melting , 2016 .

[26]  Santiago Badia,et al.  A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing , 2018, International Journal for Numerical Methods in Engineering.

[27]  Andrey V. Gusarov,et al.  Homogenization of radiation transfer in two-phase media with irregular phase boundaries , 2008 .

[28]  F. Auricchio,et al.  An immersed boundary approach for residual stress evaluation in selective laser melting processes , 2021 .

[29]  Vasily Ploshikhin,et al.  NEW METHOD FOR FAST PREDICTIONS OF RESIDUAL STRESS AND DISTORTION OF AM PARTS , 2014 .

[30]  A. Menzel,et al.  A computational phase transformation model for selective laser melting processes , 2020, Computational Mechanics.

[31]  Frank W. Liou,et al.  Probabilistic Simulation of Solidification Microstructure Evolution During Laser-based Metal Deposition , 2013 .

[32]  Sebastian D. Proell,et al.  On phase change and latent heat models in metal additive manufacturing process simulation , 2019, Advanced Modeling and Simulation in Engineering Sciences.

[33]  Wolfgang A. Wall,et al.  A dual mortar approach for 3D finite deformation contact with consistent linearization , 2010 .

[34]  Alessandro Reali,et al.  Accurate Prediction of Melt Pool Shapes in Laser Powder Bed Fusion by the Non-Linear Temperature Equation Including Phase Changes , 2019, Integrating Materials and Manufacturing Innovation.

[35]  Pan Michaleris,et al.  Thermomechanical Modeling of Additive Manufacturing Large Parts , 2014 .

[36]  Feng Lin,et al.  Meso-scale modeling of multiple-layer fabrication process in Selective Electron Beam Melting: Inter-layer/track voids formation , 2018 .

[37]  T. K. Kundra,et al.  Additive Manufacturing Technologies , 2018 .

[38]  Michele Chiumenti,et al.  Empirical methodology to determine inherent strains in additive manufacturing , 2019, Comput. Math. Appl..

[39]  Andreas Menzel,et al.  Towards the simulation of Selective Laser Melting processes via phase transformation models , 2019, Comput. Math. Appl..

[40]  J. Kruth,et al.  Modelling of radiation transfer in metallic powders at laser treatment , 2005 .

[41]  Miguel Cervera,et al.  Numerical modelling of heat transfer and experimental validation in Powder-Bed Fusion with the Virtual Domain Approximation , 2018, ArXiv.

[42]  Jerome Solberg,et al.  Implementation of a thermomechanical model for the simulation of selective laser melting , 2014 .

[43]  A multi-level model for the simulation of AM processes , 2017 .

[44]  Gabriel Bugeda Miguel Cervera,et al.  Numerical prediction of temperature and density distributions in selective laser sintering processes , 1999 .

[45]  Wolfgang A. Wall,et al.  Modeling and Characterization of Cohesion in Fine Metal Powders with a Focus on Additive Manufacturing Process Simulations , 2018, Powder Technology.

[46]  Yuebin Guo,et al.  Residual Stress in Metal Additive Manufacturing , 2018 .

[47]  Michael F. Zäh,et al.  Investigations on residual stresses and deformations in selective laser melting , 2010, Prod. Eng..

[48]  Ian A. Ashcroft,et al.  Understanding the effect of laser scan strategy on residual stress in selective laser melting through thermo-mechanical simulation , 2016 .

[49]  M. Shephard,et al.  Heat transfer model and finite element formulation for simulation of selective laser melting , 2018 .

[50]  Paul Steinmann,et al.  Macroscopic simulation and experimental measurement of melt pool characteristics in selective electron beam melting of Ti-6Al-4V , 2017 .

[51]  Matthias Markl,et al.  A coupled Cellular Automaton–Lattice Boltzmann model for grain structure simulation during additive manufacturing , 2016 .

[52]  Wolfgang A. Wall,et al.  Critical Influences of Particle Size and Adhesion on the Powder Layer Uniformity in Metal Additive Manufacturing , 2018, Journal of Materials Processing Technology.

[53]  C. Körner,et al.  Mesoscopic simulation of selective beam melting processes , 2011 .

[54]  Michel Bellet,et al.  Macroscopic thermal finite element modeling of additive metal manufacturing by selective laser melting process , 2018 .

[55]  J. Kruth,et al.  Assessing and comparing influencing factors of residual stresses in selective laser melting using a novel analysis method , 2012 .

[56]  Peter Wriggers,et al.  Metal particle fusion analysis for additive manufacturing using the stabilized optimal transportation meshfree method , 2018, Computer Methods in Applied Mechanics and Engineering.

[57]  F. Auricchio,et al.  Modeling and experimental validation of an immersed thermo-mechanical part-scale analysis for laser powder bed fusion processes , 2020 .