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MiS Preprint
35/2011

Nucleation barriers for the cubic-to-tetragonal phase transformation

Hans Knüpfer, Robert V. Kohn and Felix Otto

Abstract

We are interested in the phase transformation from austenite to martensite. This transformation is typically accompanied by the generation and growth of small inclusions of martensite. We consider a model from geometrically linear elasticity with sharp energy penalization for phase boundaries. Focusing on a cubic-to-tetragonal phase transformation, we show that the minimal energy for an inclusion of martensite scales like max$\{V^{2/3}, V^{9/11}\}$ in terms of the volume V . Moreover, our arguments illustrate the role of self-accommodation to achieve the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy.

Received:
Jun 14, 2011
Published:
Jun 15, 2011

Related publications

inJournal
2013 Repository Open Access
Hans Knüpfer, Robert V. Kohn and Felix Otto

Nucleation barriers for the cubic-to-tetragonal phase transformation

In: Communications on pure and applied mathematics, 66 (2013) 6, pp. 867-904