Evaluation of crack tip singular fields in shape memory alloys

Abstract

In this thesis crack tip singular fields of an edge cracked shape memory alloy (SMA) plate under plane stress & Mode I are studied using similarities between loading paths of a pseudoelastic SMA and a strain hardening material. The HRR (Hutchinson Rise-Rosengren) formulation derived for the crack tip stress field of a strain hardening material is used for the SMAs. The transformation plateau in the stress-strain relation of a pseudoelastic SMA is formulated by Ramberg-Osgood relation which represents the stress-strain relation of a strain hardening material. Crack tip fields of a NiTi compact tension (CT) fracture specimen are evaluated using asymptotic equations of HRR, and they are compared to the results obtained from asymptotic equations of Williams. It is found that the HRR formulation represents better the crack tip conditions in the case of SMAs. In addition, transformation region around the crack tip is evaluated using a phenomenological transformation function of an SMA model together with asymptotic stress equations. The transformation function provided reasonable results for the transformation region size; with the size of the full martensitic region which is better evaluated when HRR method is used. The HRR method is also tested with a CT specimen modeled in ABAQUS using a UMAT that includes thermomechanical coupling. Crack tip fields and transformation region size are compared to the results obtained computationally. It is observed that the crack tip fields in the transformation region of pseudoelastic SMAs can be evaluated reasonably using HRR method. In addition, energy dissipation and the contour dependence of J-integral are studied and the distribution of energy is discussed to complement the study.