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

Peter Bella; Michael Goldman

doi:10.1017/S0308210515000086

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

Peter Bella, Michael Goldman

Max Planck Institute for Mathematics in the Sciences

Research output: Contribution to journal › Article › peer-review

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 (E_min ∼ min(V^2/3, V^7/9)). Our predictions are in good agreement with physical experiments where nucleation of martensite is usually observed near the corners of the specimen.

Original language	English
Pages (from-to)	715-724
Number of pages	10
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	145
Issue number	4
DOIs	https://doi.org/10.1017/S0308210515000086
Publication status	Published - 20 Jul 2015
Externally published	Yes

Keywords

cubic-to-tetragonal phase transformation
scaling law
shape memory alloys

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10.1017/S0308210515000086

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title = "Nucleation barriers at corners for a cubic-to-tetragonal phase transformation",

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 Kn{\"u}pfer, 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 = "cubic-to-tetragonal phase transformation, scaling law, shape memory alloys",

author = "Peter Bella and Michael Goldman",

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AU - Goldman, Michael

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AB - 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.

KW - cubic-to-tetragonal phase transformation

KW - scaling law

KW - shape memory alloys

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JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 4

ER -

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

Abstract

Keywords

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