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Research Papers

Fundamental Formulation for Transformation Toughening in Anisotropic Solids

[+] Author and Article Information
Lifeng Ma

S&V Lab,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
710049, China

Alexander M. Korsunsky

Department of Engineering Science,
University of Oxford,
Oxford OX1 3PJ, UK

Robert M. McMeeking

Department of Mechanical Engineering and
Materials Department,
University of California,
Santa Barbara, CA 93106;
School of Engineering,
University of Aberdeen,
Aberdeen AB24 3UE, UK;
INM - Leibniz Institute for New Materials,
Campus D2 2,
66123 Saarbrücken, Germany

Manuscript received May 18, 2011; final manuscript received April 23, 2012; accepted manuscript posted January 22, 2013; published online July 12, 2013. Assoc. Editor: Kenneth M. Liechti.

J. Appl. Mech 80(5), 051001 (Jul 12, 2013) (9 pages) Paper No: JAM-11-1153; doi: 10.1115/1.4023476 History: Received May 18, 2011; Revised April 23, 2012; Accepted January 22, 2013

In this paper the problem of transformation toughening in anisotropic solids is addressed in the framework of Stroh formalism. The fundamental solutions for a transformed strain nucleus located in an infinite anisotropic elastic plane are derived first. Furthermore, the solution for the interaction of a crack tip with a residual strain nucleus is obtained. On the basis of these expressions, fundamental formulations are presented for the toughening arising from transformations using the Green's function method. Finally, a representative example is studied to demonstrate the relevance of the fundamental formulation.

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Figures

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Fig. 1

An infinitesimal element with transformation strain located in an infinite plane solid

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Fig. 2

A transformation strain nucleus interacting with a semi-infinite crack in an infinite body

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Fig. 3

Two subproblems forming the decomposition of the original problem in Fig. 2. (a) Transformation strain nucleus in an infinite plane without a crack. (b) Application on the semi-infinite crack surfaces of the negative of the tractions due to the transformation strain nucleus.

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Fig. 4

A circular transformation strain zone in an anisotropic solid with a semi-infinite crack

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Fig. 5

Normalized stress intensity factor contributions due to a cylindrical transformation strain zone at angle θ

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Fig. 6

A crack is enclosed by a transformed wake

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