Analytical mechanics modeling of in-process thermal stress distribution in metal additive manufacturing

High-temperature gradient and repetitive heating and cooling are the main sources of development of thermal stress in an additively manufactured (AM) part. Thermal stress induces residual stress, part distortion, fatigue, crack initiation and growth in the additively manufactured parts. Therefore, for a part built via AM to be used in a critical application, a high degree of confidence is required in its quality. A crucial piece of such a qualification is the ability to accurately and rapidly predict the stress state within the part. In the present study, a physics-based analytical model is proposed to accurately and rapidly predict the in-process thermal stress. A moving point heat source approach is employed to predict the temperature field. As a result of high-temperature gradient, the in-process thermal stresses induced by non-uniform heating are predicted using the Green's functions of stresses due to a point body load. The predicted thermal stress is the combination of three main sources known as stresses due to body forces, normal tension, and hydrostatic stress. The model presented in this work is based upon the premises of plane strain condition in the build of isotropic and homogeneous properties with linear elasticity behaviors. Finite element analysis is used to validate the proposed analytical model of the same problem. In both the analytical model and finite element model, the material thermal properties of Ti-6A1-4V are considered temperature-dependent. The results reveal that the increase in scan speed increases the tensile stress along the scan direction, while reduces that along the build direction.