A model for diffusive and displacive phase transitions: evolution and interplay between the phases

A diffuse interface phase field model is proposed for the unified analysis of diffusive and displacive phase transitions under non-isothermal conditions. Two order parameters are used for the description of the phenomena: one is related to the solute mass fraction and the other to the strain. The model governing equations come from the balance of linear momentum, the solute mass balance (which will lead to the Cahn-Hilliard equation) and the balance of internal energy. The model presents a very complex computational context, it is non-linear, it involves gradient terms and it is time-dependent. Some numerical tests show that the model is able to capture both the displacive and the diffusive mechanisms as well as the interplay between the two, which results - for the chosen parameters setting - in the displacive transition occurring even if the critical temperature is not reached.