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Nucleation barriers at corners for a cubic-to-tetragonal phase transformation

Part of: Phase transformations in solids Equilibrium (steady-state) problems

Published online by Cambridge University Press:  20 July 2015

Peter Bella  and
Michael Goldman
Peter Bella
Affiliation:
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103 Leipzig, Germany, (bella@mis.mpg.de)
Michael Goldman
Affiliation:
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103 Leipzig, Germany, (bella@mis.mpg.de)
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Abstract

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We are interested in the energetic cost of a martensitic inclusion of volume V in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of Knüpfer, Kohn and Otto (Commun. Pure Appl. Math.66 (2013), 867–904), we consider a domain with a corner and obtain a better scaling law for the minimal energy (Emin ∼ min(V2/3, V7/9)). Our predictions are in good agreement with physical experiments where nucleation of martensite is usually observed near the corners of the specimen.

Keywords

shape memory alloyscubic-to-tetragonal phase transformationscaling law

MSC classification

Primary: 74N20: Dynamics of phase boundaries
Secondary: 74G65: Energy minimization
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 4 , August 2015 , pp. 715 - 724
Copyright
Copyright © Royal Society of Edinburgh 2015