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arXiv · 1507.05997

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

Anton Muehlemann
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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.

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Anton Muehlemann. 2015-07-20. Interior Nucleation of Martensite in a Cubic-to-Tetragonal Phase Transformation. https://doi.org/10.1016/j.matpr.2015.07.357

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