A semi-analytical model for rapid prediction of residual stress and deformation in laser powder bed fusion

The build-up of residual stress and the resultant deformation in laser powder bed fusion (LPBF) play vital roles in the performance of the as-built parts. Due to the complex physical phenomena across multi-scales during LPBF, the accurate prediction of residual stress and the deformation related to the temperature variation have exposed the requirement for the computationally efficient modeling of thermo-mechanical field evolution. However, an efficient solution scheme for residual stress and deformation histories is still challenging. In this paper, a three-dimensional thermo-mechanical model is developed based on the semi-analytical method. The complex physical phenomena that occur during LPBF and a moving volumetric heat source is considered in the model. The residual stress and deformation evolutions are predicted using the separation of variables and the state space method. The accuracy of the proposed model is verified by the comparison with the previous prediction in the literature. The effect of the process parameters, geometrical parameters, and laser loads on the history and distribution of residual stress and displacement within the LPBF-printed parts is also investigated. The results show that residual stress and displacement increase with higher energy densities and the elevated length-to-thickness ratio of printed parts. In addition, it is shown that the computational cost of the proposed model is highly small, which can be served as an effective path for designing and guiding the manufacturing of parts via LPBF.