Modeling framework for materials capable of solid-solid phase transformation: application to the analytical solution of the semi-infinite mode III crack problem in an idealized shape memory alloy

Wael Zaki; Ziad Moumni

doi:10.1117/12.2085291

2 April 2015 Modeling framework for materials capable of solid-solid phase transformation: application to the analytical solution of the semi-infinite mode III crack problem in an idealized shape memory alloy

Wael Zaki, Ziad Moumni

Author Affiliations +

Proceedings Volume 9431, Active and Passive Smart Structures and Integrated Systems 2015; 94312M (2015) https://doi.org/10.1117/12.2085291
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2015, San Diego, California, United States

Abstract

We propose two frameworks for the derivation of constitutive models for solids undergoing phase transformations. The first is based on the assumption that solid phases within the material are finely mixed whereas the second considers the material as a heterogeneous solution of phase fragments and uses the homogenization theory to derive equilibrium conditions for displacement fields and phase distributions. It is shown that in the case of reversible phase transformation, the energy of the material can be obtained by taking the convex envelope of the energy functions of the constituent phases. As an application, a schematic model is derived for an idealized shape memory alloy and used to obtain a novel analytical solution for the problem of semi-infinite mode III crack in this material. The derivation of the analytical solution uses the hodograph method to map Cartesian coordinates into the hodograph plane. The resulting boundary-value problem for the mode III crack considered becomes analytically tractable for the idealized shape memory alloy considered and leads to closed-form expressions for the displacement and phase volume fraction fields near the crack tip as well as for the boundaries between different phase regions.

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Wael Zaki and Ziad Moumni "Modeling framework for materials capable of solid-solid phase transformation: application to the analytical solution of the semi-infinite mode III crack problem in an idealized shape memory alloy", Proc. SPIE 9431, Active and Passive Smart Structures and Integrated Systems 2015, 94312M (2 April 2015); https://doi.org/10.1117/12.2085291

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KEYWORDS

Shape memory alloys

Solids

Solid modeling

Thermodynamics

Homogenization

Mathematical modeling

Chemical elements

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