Nucleation barriers for the cubic-to-tetragonal phase transformation

Hans Knüpfer, Robert Kohn, Felix Otto

Research output: Contribution to journalArticle

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 importance of self-accommodation for achieving the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy.

Original languageEnglish (US)
Pages (from-to)867-904
Number of pages38
JournalCommunications on Pure and Applied Mathematics
Volume66
Issue number6
DOIs
StatePublished - Jun 2013

Fingerprint

Martensite
Phase Transformation
Nucleation
Phase transitions
Inclusion
Energy
Minimal Energy
Penalization
Linear Elasticity
Phase boundaries
Austenite
Elasticity
Scaling
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Nucleation barriers for the cubic-to-tetragonal phase transformation. / Knüpfer, Hans; Kohn, Robert; Otto, Felix.

In: Communications on Pure and Applied Mathematics, Vol. 66, No. 6, 06.2013, p. 867-904.

Research output: Contribution to journalArticle

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