1408.6371v2.pdf (2.04 MB)
Quasiconvexity at the boundary and the nucleation of austenite
journal contribution
posted on 2023-06-09, 04:54 authored by J M Ball, Konstantinos KoumatosKonstantinos KoumatosMotivated by experimental observations of H. Seiner et al., we study the nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy stabilized as a single variant of martensite. In the experiments the nucleation process was induced by localized heating and it was observed that, regardless of where the localized heating was applied, the nucleation points were always located at one of the corners of the sample - a rectangular parallelepiped in the austenite. Using a simplified nonlinear elasticity model, we propose an explanation for the location of the nucleation points by showing that the martensite is a local minimizer of the energy with respect to localized variations in the interior, on faces and edges of the sample, but not at some corners, where a localized microstructure, involving austenite and a simple laminate of martensite, can lower the energy. The result for the interior, faces and edges is established by showing that the free-energy function satisfies a set of quasiconvexity conditions at the stabilized variant in the interior, faces and edges, respectively, provided the specimen is suitably cut.
History
Publication status
- Published
File Version
- Accepted version
Journal
Archive for Rational Mechanics and AnalysisISSN
0003-9527Publisher
Springer VerlagExternal DOI
Issue
1Volume
219Page range
89-157Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Analysis and Partial Differential Equations Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2017-01-24First Open Access (FOA) Date
2017-01-24First Compliant Deposit (FCD) Date
2017-01-24Usage metrics
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