Phase-field modeling of elastic effects in eutectic. growth with misfit stresses
Z. Ebrahimi, J. L. Lopes Rezende, J. Kundin.
AICES-2010/07-1, -, -, (2010)
Elastic interactions, arising from a difference of lattice spacing between two coherent phases in eutectic alloys with misfit stresses, can have an influence on microstructural pattern formation of eutectic colonies during solidification process. From a thermody- namic point of view the elastic energy contributes to the free energy of the phases and modifies their mutual stability. Therefore, the elastic stresses will have an effect on sta- bility of lamellae, lamellae spacing and growth modes. In this paper, a phase-field model is employed to investigate the influence of elastic misfits in eutectic growth. The model reduces to the traditional sharp-interface model in a thin-interface limit, where the mi- croscopic interface width is small but finite. An elastic model is designed, based on linear microelasticity theory, to incorporate the elastic energy in the phase-field model. The- oretical and numerical approaches, required to model elastic effects, are formulated and the stress distributions in eutectic solidification structures are evaluated. The two dimen- sional simulations are performed for directed eutectic growth and the simulation results for different values of the misfit stresses are illustrated.