Archive for Rational Mechanics and Analysis

, Volume 120, Issue 3, pp 201–244 | Cite as

Self-accommodation in martensite

  • Kaushik Bhattacharya


The shape-memory effect is a phenomenon wherein an apparently plastically deformed specimen recovers all strain when heated above a critical temperature. This is observed in some crystalline solids that undergo martensitic phase transformation. The martensitic transformation is a temperature-induced, diffusionless solid-to-solid phase transformation involving a change in crystalline symmetry. Shape-memory materials are able to transform from the high-temperature austenite to the low-temperature martensite phase without any apparent change in shape. This is known as self-accommodation. Necessary and sufficient conditions that the lattice parameters of a material must satisfy for the material to form a self-accommodating microstructure are derived. The main result states that if the austenite is cubic, the material is self-accommodating if and only if the transformation is volume preserving. On the other hand, if the symmetry of the austenite is not cubic, it is not possible to construct any microstructure that is self-accommodating unless the transformation strain or the Bain strain satisfies additional, rather strict, conditions. These results show good agreement with the available experimental data. The analysis here is significantly different from previous studies because it makes no a priori assumption on the microstructure.


Austenite Martensite Phase Transformation Critical Temperature Martensitic Transformation 
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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Kaushik Bhattacharya
    • 1
  1. 1.Courant Institute of Mathematical SciencesNew York

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