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

Abstract

This article proposes a coupled thermomechanical finite element model tailored to the partscale 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, mortar meshtying 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 -optimal manner. The combination of the proposed constitutive law and mortar meshtying approach is validated on three-dimensional examples with rather complex geometry, representing a first step towards part-scale predictions.

Physics‐based modeling and predictive simulation of powder bed fusion additive manufacturing across length scales

“…In [91], the accuracy of the proposed thermo-mechanical model and the influence of the individual model components has been critically verified by means of elementary test cases, partly with analytical solutions.…”

“…The TUM authors recently proposed a thermo-mechanical finite element model aiming at the prediction of residual stresses and thermal distortion in the partscale simulation of metal PBFAM processes [91,92]. The most important model equations as well as exemplary results are recapitulated in the following.…”

“…Processing of a solid and hollow pyramid. Discretization with nonmatching meshes via mortar mesh-tying [91] by the fact that the base plate is initially stress-free, while solidified melt tracks are subject to tensile stresses after cooling down (e.g., snapshot at bottom right of Figure 11), which partly compensate the compressive stresses arising from thermal expansion when processing the subsequent track above.…”

“…Thus, existing models are typically classified in macroscale, mesoscale and microscale approaches [73] (see Figure 1). Macroscale or partscale approaches intend to predict physical fields such as temperature, residual stresses, and thermal distortion on the scale of design parts [7,20,37,44,45,57,83,91,97,100,120,121]. Typically, the powder and melt phase are described in a spatially homogenized and simplified sense, for example, without resolving the geometry and dynamics of powder particles and fluid flow in the melt pool.…”