Theoretical and numerical analysis of fracture of shape memory alloys

Abstract

The subject of this thesis is theoretical and numerical analysis of the fracture of SMAs. First, the size of the martensitic region surrounding the tip of an edge-crack in a SMA plate is calculated analytically using the transformation function proposed by Zaki and Moumni (Zaki and Moumni, 2007) together with crack tip asymptotic stress equations. Transformation regions calculated analytically and computationally are compared to experimental results available in the literature (Robertson et al., 2007). Second, fracture parameters such as stress intensity factors (SIFs), J-integrals, energy release rates, crack tip displacements and T-stresses are evaluated. The objective at this point is to understand the effect of phase transformation on fracture behavior of an edge-cracked Nitinol plate under Mode I loading. In the FE analysis of the edge-cracked plate under Mode I loading, the ZM model as well as the built-in model (Auricchio et al., 1997) are used. Third, steady-state crack growth in an SMA plate is analysed. To this end, Mode I steady-state crack growth in an edge-cracked Nitinol plate is modeled using a non-local stationary method to implement the ZM model in Abaqus. The effects of reorientation of martensite near the crack tip, as a result of non-proportional loading, on fracture toughness is also studied. Finally, phase transformation regions are calculated analytically around the tip of an SMA specimen under Mode III loading. The analytical derivations are carried out first using a method proposed by Moumni (Moumni, PhD Thesis, ́ Ecole Nationale des Ponts et Chausśees, 1995) which relies on mapping the equations of the boundary value problem to the so-called “hodograph” plane. The influence of coupling on the extent of the phase transformation regions and on temperature distribution within the material is then investigated numerically.