Three-dimensional field model and computer modeling of martensitic transformations

A three-dimensional (3D) continuum stochastic field kinetic model of martensitic transformations which explicitly takes into account the transformation-induced elastic strain is developed. The model is able to predict the major structural characteristics of martensite during the entire transformation including nucleation, growth and eventually formation of internally twinned plates which are in thermoelastic equilibrium with the parent phase. No a priori constraints are made on the possible configurations and sequences of structural patterns formed by orientation variants of the martensite. 3D computer simulations are performed for a generic cubic → tetragonal martensitic transformation in a prototype crystal which is elastically isotropic and elastically homogeneous. The simulations predict that (i) nucleation of martensite in a perfect crystal occurs collectively to accommodate the coherency strain, e.g. the critical nuclei are formed by two internally twinned orientation variants; (ii) the ultimate structure consists of plate-like martensite and retaining parent phase. The martensitic plates consist of twin-related platelets of two orientation variants and the habits of the plates meet the invariant plane requirement. These simulation results are in good agreement with experimental observations.

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