The small-scale yielding of shape memory alloys under mode III fracture

Abstract

A model for stress-induced phase transformation surrounding the crack tip during mode III fracture of shape memory alloys (SMAs) is introduced. Considering a state of small-scale yielding and J2 plasticity (loading only), the shape and size of the martensite (M), the austenite (A) and the transformation zone ( A → M ) are fully determined. For a fixed crack length, the zones of constant strain around the crack tip develop as circles. The width of the A → M transformation zone and the martensite both depend linearly on the crack length. Moreover, the crack tip is surrounded by martensite under plastic deformation. The theoretical model is then extended to examine the mode III fracture behavior of Nickel–Titanium (Nitinol), and these results are compared to FEM analysis of a edge crack torsion (ECT) test for an isotropic material. The size of stress-induced martensite zone in the FEM analysis is underestimated by about 50% from the theoretical model, due largely to the difference in the computed and theoretical stress–strain relation. However, the model and simulation show remarkable agreement on the size of the A → M transformation zone (error<5%), which dominates the region surrounding the crack tip. In addition, the model predictions accurately match the FEM analysis in determining the radii circles of constant strain in the vicinity of the crack tip, and the shape and size of the plastically deformed martensite zone. The results presented in this paper provide a first step to better understand the mechanics of fracture in shape memory alloys under mode III loading.