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

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?CBarenblatt 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.