Phase field simulation of stress evolution during solidification

Stress evolution during solidification is simulated by using the phase field model. The coupling equations for phase transformation, temperature and stress/strain are derived based on thermo-dynamical theory including elastic strain energy, which is summarized as follows: phase transformation is governed by the phase field equation in which not only temperature but also stress are introduced as parameters. In the heat conduction equation, the effect of latent heat generation due to phase change and the heat generation due to mechanical work are taken into account. The volumetric change associated with temperature variation and phase transformation is expressed in the constitutive equation, while, in this paper, the stress or flow in liquid is neglected for simplicity. In order to verify the efficiency of these equations, numerical simulations are carried out by using a simple model of the finite element method. The effects of transformation expansion coefficient for two cases of dilatation and contraction are simulated, and qualitatively adequate results are presented.