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

Published online by Cambridge University Press:  20 July 2015

Peter Bella
Affiliation:
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103 Leipzig, Germany, ([email protected])
Michael Goldman
Affiliation:
Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22–26, 04103 Leipzig, Germany, ([email protected])

Abstract

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2015 

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