Numerical analysis on microstructure formation and stress distribution by using the phase field model

Abstract

Stress distribution and the residual stress in the solidified materials are investigated by the numerical analyses based on the phase field method. The governing equations considering the coupling effects among phase transformation, temperature and stress/strain, including elasto-plastic constitutive relation, are formulated using the phase field model, and they are numerically solved by the finite element method. As a typical case of the microstructure formation, the dendritic growth processes are studied. In spite of several assumptions employed for the material properties of liquid, the complicated stress distributions in dendrites are exhibited: Strong stresses are distributed at the bottom of the side branches. Due to the plastic behavior, residual stress distributions are obtained when the solidification and cooling are completed in the whole region. When a micro structure constructed with two dendrites is formed, high stresses are generated in the regions where the liquid is remained till the very last stage of the solidification. Subsequently, two types of the morphology of microstructures are investigated, and it reveals that the residual stress distribution and the maximum value are strongly affected by the microstructure. © 2008 The Society of Materials Science.