Modeling and simulation of the anisotropic thermal expansion of Ti-6Al-4V processed by PBF-LB/M

Additive manufacturing (AM), particularly Laser Powder Bed Fusion of Metals (PBF-LB/M), enables the production of geometrically complex Ti-6Al-4V components with high precision and design flexibility for a wide range of applications in the aerospace, chemical and process engineering, energy, and biomedical sectors. However, rapid solidification in PBF-LB/M produces a non-equilibrium martensitic α′ microstructure with pronounced texture, leading to anisotropic mechanical and thermal behaviour. In particular, the apparent thermal expansion of PBF-LB/M Ti-6Al-4V has been found to be anisotropic due to strains induced during the 𝛼′→𝛽 phase transformation (850–1000 °C). These transformation strains lead to pronounced apparent expansion along the build-direction and reduced in-plane apparent expansion. In PBF-LB/M manufactured components, this anisotropy can lead to unexpected residual stresses during the AM process or mechanical integrity issues during post-manufacturing heat-treatments or operation. This study focusses on the modelling of the anisotropic apparent expansion of Ti-6Al-4V and its implementation for Finite Element Analysis (FEA) to enable simulative investigations of the residual stress and distortion evolution in AM components. A new model is introduced that separates isotropic thermal and transversally isotropic transformation strains. The model accounts for the path and temperature dependent transformation characteristics with varying transformation strains developing during heating (𝛼′→𝛽) and cooling (𝛽→𝛼+𝛽). To make this model available to FEA, it was implemented in the FE software Abaqus via an UEXPAN subroutine. The effectiveness of the apparent expansion model and its implementation is demonstrated by comparing simulated and experimentally measured dilatometer curves. In addition, the impact of this anisotropic expansion on the residual stress development is investigated using thermo-mechanical process simulations of 1) a single laser welding track, and 2) the distortion of a cantilever following support structure removal. The model successfully predicted the apparent expansion in a cylinder printed at a 45° angle. Furthermore, significant differences in vertical stress components and induced plastic strain in a single weld track were found. These are attributed to the additional constraints imposed by the transversally isotropic expansion underpinning the relevance of accounting for the transformation strain. Predictions of distortions in a cantilever following support removal were, however, significantly better when considering isotropic thermal strain only. This could potentially be explained by differences of the PBF-LB/M microstructure in the presence of a support structure. Understanding these mechanisms is crucial for optimizing the mechanical integrity and dimensional stability of PBF-LB/M-fabricated Ti-6Al-4V components in engineering applications subjected to post-processing heat-treatments or high-temperature applications.