Computer simulation of microscopic stress distribution in complex microstructure using a phase field model

Microscopic stress distribution in a metallic material which has complex microstructure is simulated using a phase field model. The fundamental equations which take into account the coupling effects among phase transformation, temperature and stress/strain are used, while thermal effects are neglected to focus on the volumetric change due to phase transformation in this paper. A two-dimensional square region is considered, and the evolution of microscopic stress and the resultant residual stress distribution are calculated using the finite element method. As the phase transformation progresses and grains grow larger, stress is generated around the growing interface. When a grain collides with another one, specifically large stress is observed. Residual stress is finally distributed in the microstructure formed, and apparently large stresses are retained along the grain boundaries. Subsequently, dependency of the stress distribution on microstructure pattern is investigated. First, variously sized square grains are tested, and it reveals that the maximum stress tends to decrease as the grain size becomes smaller. Next, the shapes of the grains are varied. As a result, the stress distribution is remarkably affected, while the maximum stress value does not change so much. More complicated grain arrangement is finally tested with eight or nine grain models. Then, it is revealed as a common feature that large stress is generated along the grain boundaries and that the stress distribution is dependent on the grain arrangement.