Analytical modeling of residual stress in direct metal deposition considering scan strategy

Existence of high tensile residual stress in the additively manufactured parts result in part failure due to crack initiation and propagation. Herein, a physics-based analytical model is proposed to predict the stress distribution much faster than experimentation and numerical methods. A moving point heat source approach is used to predict the in-process temperature field within the build part. Thermal stresses induced by steep temperature gradient is determined using the Green’s functions of stresses due to the point body load in a homogeneous semi-infinite medium. Then, both the in-plane and out of plane residual stress distributions are found from incremental plasticity and kinematic hardening behavior of the metal, in coupling with the equilibrium and compatibility conditions. Due to the steep temperature gradient in this process, material properties vary significantly. Hence, material properties are considered temperature dependent. Moreover, the specific heat is modified to include the latent heat of fusion required for the phase change. Furthermore, the multi-layer and multi-scan aspects of the direct metal deposition process are considered by incorporating the temperature history from the layers and scans. Results from the analytical residual stress model showed good agreement with X-ray diffraction measurements, which is used to determine the residual stresses in the IN718 specimens.