International Journal of Fracture

, Volume 175, Issue 2, pp 151–166 | Cite as

A mode I fracture analysis of a center-cracked infinite shape memory alloy plate under plane stress

Original Paper


The problem of a center plane crack in an infinite, thin, pseudoelastic Shape Memory Alloy (SMA) plate subjected to an in-plane uniform tensile stress at infinity is analyzed. The analysis follows closely the Dugdale–Barenblatt model developed for conventional metals. It is found for low remote stress values—less than a critical value—that the SMA is not fully transformed in the vicinity of a crack tip. Closed form expressions for the size of the partial transformation zone, crack opening displacement and J-integral are given for this case. For remote stress levels above the critical value, the fully-transformed material near a crack tip is assumed to yield plastically. The sizes of the transformed (both partially and fully) and plastic regions are numerically evaluated by solving a system of integral equations and their sensitivity to the transformation characteristics (i.e., maximum transformation strain and temperature) is determined. Moreover, a relationship between the J-integral and the crack-tip opening displacement is derived. The results obtained are important in understanding the effect of stress-induced phase transformation in the fracture behavior of SMAs in the presence of static cracks, and subsequently in formulating conditions for initiation of crack propagation.


Shape memory alloys Superelasticity Transformation Fracture 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of Aeorospace Engineering, MS 3409Texas A&M UniversityCollege StationUSA

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