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The effective energy and laminated microstructures in martensitic phase transformations

Goldsztein, Guillermo H. (2001) The effective energy and laminated microstructures in martensitic phase transformations. Journal of the Mechanics and Physics of Solids, 49 (4). pp. 899-925. ISSN 0022-5096. https://resolver.caltech.edu/CaltechAUTHORS:20170710-131412581

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Abstract

We study the behavior of crystals that undergo martensitic transformations. On cooling, the high-temperature phase (austenite) transforms to the martensite phase changing its crystalline symmetry. The lower crystalline symmetry of the martensite gives rise to several variants of martensite. Each variant has an associated transformation strain. These variants accommodate themselves (according to the boundary conditions) forming a microstructure that minimizes the elastic energy. This minimum value of the energy is called the effective energy. We assume that all the material is in the martensite phase (i.e. the material is at low temperatures). We show that, assuming the geometrically linear approximation, the maximum of the effective energy restricted to applied strains in the convex hull of the transformation strains is attained by an applied strain that is a convex combination of only two transformation strains. We derive a recurrence relation to compute the energy corresponding to laminated microstructures of arbitrary rank, under the assumption that the variants of martensite are linearly elastic and their elastic moduli are isotropic. We use this recurrence relation to develop an algorithm that minimizes the energy over microstructures that belong to the class of rank-r laminates. We apply our methods to the case in which the transformation is cubic to monoclinic (corresponding to TiNi). We conclude with some comments on the possible implications of our calculations on the behavior of this shape-memory alloy.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/S0022-5096(00)00057-0DOIArticle
http://www.sciencedirect.com/science/article/pii/S0022509600000570PublisherArticle
Additional Information:© 2001 Elsevier Science B.V. Received 2 November 1999, Revised 13 July 2000, Accepted 14 July 2000, Available online 28 February 2001. I would like to thank Professor Oscar Bruno for introducing me to the area of martensitic transformations and for helpful discussion throughout the progress of this research. This research was supported by the NSF through Contract No. DMS-9523292.
Funders:
Funding AgencyGrant Number
NSFDMS-9523292
Subject Keywords:A. Microstructures; A. Phase transformation; B. Layered material; C. Numerical algorithms; C. Optimization
Issue or Number:4
Record Number:CaltechAUTHORS:20170710-131412581
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170710-131412581
Official Citation:Guillermo H. Goldsztein, The effective energy and laminated microstructures in martensitic phase transformations, Journal of the Mechanics and Physics of Solids, Volume 49, Issue 4, April 2001, Pages 899-925, ISSN 0022-5096, https://doi.org/10.1016/S0022-5096(00)00057-0. (http://www.sciencedirect.com/science/article/pii/S0022509600000570)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:78900
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:10 Jul 2017 21:34
Last Modified:03 Oct 2019 18:13

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