Computer simulation of microstructure Development during a Martensitic Transformation

Abstract

The microstructure that results from a martensitic transformation is largely determined by the elastic strain that develops as martensite particles grow and interact. To study the development of microstructure, it is useful to have computer simulation models that mimic the process. One such model is a finite-element model in which the transforming body is divided into elementary cells that transform when it is energetically favorable to do so. Using the linear elastic theory, the elastic energy of an arbitrary distribution of transformed cells can be calculated, and the elastic strain field can be monitored as the transformation proceeds. In the present article, a model of this type is developed and evaluated by testing its ability to generate the preferred configurations of isolated martensite particles, which can be predicted analytically from the linear elastic theory. Both two- and three-dimensional versions of the model are used. The computer model is in good agreement with analytic theory when the latter predicts single-variant martensite particles. The three-dimensional model also generates twinned martensite in reason- able agreement with the analytic predictions when the fractions of the two variants in the particle are near 0.5. It is less successful in reproducing twinned martensites when one variant is dom- inant; however, in this case, it does produce unusual morphologies, such as “butterfly mar- tensite,” that have been observed experimentally. Neither the analytic theory nor the computer simulation predicts twinned martensites in the two-dimensional transformations considered here, revealing an inherent limitation of studies that are restricted to two dimensions.