An Eshelbian Homogenization Solution for the Coupled Mechanical-Diffusion Problem

When alloying elements diffuse into a metallic matrix, the matrix phase usually transforms into an inclusion phase. The phase transformation may lead to changes of diffusion coefficient tensor and elastic tensor, and formations of disturbance fields. In this paper, a stress-diffusion coupling model is proposed on the basis of Eshelby’s homogenization approach. An analytical solution to the effective diffusion coefficient tensor is developed assuming it solely depends on the inclusion volume fraction. Then, the linear relationship between lattice misfit strain and macro expansion strain is obtained based upon the framework of micromechanics. Finally, the mechanical-diffusional coupling problem is solved through considering the composites homogenization, mechanical equilibriums and the interaction between chemical potential and stress state.