Interior Nucleation of Martensite in a Cubic-to-Tetragonal Phase Transformation

Abstract

Using a variational model based on non-linear elasticity we investigate whether in a cubic-to-tetragonal phase transformation it is energetically preferable to nucleate martensite within austenite. Under minimal growth assumptions on the free energy density $W$ away from the wells, we derive explicit upper bounds on $W^{qc}({\mathbb{I}})$, i.e. on the macroscopic free energy density of a region that has been macroscopically deformed by the identity map. The bounds only depend on material parameters, the temperature difference and the growth of $W$ away from the wells. By comparing $W^{qc}({\mathbb{I}})$ and $W({\mathbb{I}})$ we conclude that nucleation is always energetically preferable and are able to provide quantitative upper bounds for the gain in negative energy due to nucleation.