Elasto-plastic simulation of stress evolution during grain growth using a phase field model

Coupling effects among phase transformation, temperature and stress/strain are formulated based on thermodynamics using a phase field model. The elasto-plastic constitutive relationship is applied for stress analysis considering thermal expansion, transformation dilatation, and the effect of stress on phase transformation is included in the formulation. Subsequently, equations are numerically solved using a finite element method and stress evolution due to phase transformation and residual stress distribution are simulated. The results obtained show that large stresses are generated around phase interfaces. The high-stress regions move as grains grow, and finally residual stress distribution is observed along grain boundaries. The distribution and values at the grain boundaries are revealed to depend on the timing of collision and positioning of nuclei.