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

Sebastian D Proell,Wolfgang A Wall,Christoph Meier

doi:10.1186/s40323-021-00209-1

Sebastian D Proell, Wolfgang A Wall + Show 1 more

Open Access

https://doi.org/10.1186/s40323-021-00209-1

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Abstract

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-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.

Highlights

Metal additive manufacturing (AM) opens new opportunities in manufacturing technology [1,2]
This article proposes a coupled thermomechanical finite element model tailored to the macroscale simulation of metal additive manufacturing processes such as selective laser melting
The proposed constitutive law accounts for the irreversibility of phase change and consistently represents thermally induced residual stresses

Summary

Introduction

Metal additive manufacturing (AM) opens new opportunities in manufacturing technology [1,2]. Attention is drawn to the stress evolution in the Dirichlet case which is equal to the results from the previous section until the first peak in the temperature profile is reached This time, the stress does not reach a near-zero value for the initially solid case because the melting stops at T1 < Tl, i.e., there remains a phase fraction of solid material at T1, which exhibits thermal stresses due to the increased temperature level as compared to the stress-free configuration at T0. While no stresses occur in the powder material of layer 7 in front of the laser, the thermally induced volume expansion during heating leads to negative (compressive; red color) stresses in the solid material of the previously processed track 6, mostly pronounced in the direct vicinity of the Tl-isoline As desired, these stresses rapidly drop to zero in the narrow temperature interval T ∈ [Ts; Tl] such that no visible stresses remain in the melt pool domain. This example could be scaled up to more realistic part dimensions when using a layer-agglomeration approach [27] or effective heat track- or layerwise heat sources [37]

Conclusion

Example scenario 1

Example scenario 2

Findings

Stress after partial melt and solidification