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

TL;DR

This paper uses a variational model in non-linear elasticity to show that nucleating martensite within austenite is energetically favorable during a cubic-to-tetragonal phase transformation, providing explicit bounds on energy differences.

Contribution

It introduces explicit upper bounds on the free energy density for nucleation, demonstrating that nucleation is always energetically preferable in this phase transformation.

Findings

Nucleation within austenite is energetically favorable.

Derived explicit bounds on free energy differences.

Quantified energy gain from nucleation.

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.