Modeling of martensitic phase transformation in material science: A numerical study

Abstract

Phase transformation involves the formation of new phases or constituents through re-arrangement of atoms in a material microstructure. It often results in the production of new precipitates that may enhance/degrade the overall physical and mechanical properties of the parent material. In the present study, the non-linear martensitic phase transformation (or Allen-Cahn) equation was analyzed numerically using both Galerkin’s Finite Element Method (FEM) and Fourier Spectral Method (FSM). Material properties corresponding to zirconia ceramic was selected for the analysis. The results from both the FEM and FSM were critically analyzed and compared in terms of computational intensity, efficiency and accuracy. The dependence of the computation on grid size and time step was also studied. The results show that it is more effective to model phase transformation using FSM.