THEORETICAL AND NUMERICAL ANALYSIS OF FRACTURE OF SHAPE MEMORY ALLOYS

Theoretical and numerical analysis of fracture of shape memory alloys 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, J. Mech. Phys. Sol, 2007) together with crack tip asymptotic stress equations. The transformation region is also calculated with finite elements (FE) by implementing Zaki-Moumni (ZM) model in ABAQUS through user defined material subroutine (UMAT). Transformation regions calculated analytically and computationally are compared to experimental results available in the literature (Robertson et al., Acta Mater., 2007). Second, fracture parameters like; Stress Intensity Factors (SIFs), J-integrals, energy release rates, crack tip opening displacements (CTODs) and T-stresses are evaluated. The objective 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, ABAQUS is used with both ZM model, written through UMAT and built-in SMA model based on Auricchio's model (Auricchio et. al., Comp. Meth. Appl. Mech. Eng., 1997). J-integrals are found to be contour dependent as a result of non-homogeneity around crack tip, therefore SIFs are directly calculated from strain energy release rate and compared to the SIFs calculated using asymptotic near-tip opening displacement field equation. 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 modelled using a non-local stationary method. The model is implemented in ABAQUS using ZM model by means of UMAT to determine transformation zones around the crack tip. Steady-state crack growth is first simulated without considering reverse transformation to calculate the effect of transformation on stress distribution in the wake region, and then reverse transformation is taken into account. The effect of reorientation of martensite near the crack tip as a result of non-proportional loading is also studied. The stress distribution and the phase transformation region are compared to results obtained for the case of a static crack. Finally, phase transformation region are calculated analytically around the tip of an SMA specimen under mode III loading; at first the analytical method represented by Moumni (Ziad Moumni, PhD thesis, Ecole Nationale Des Ponts Et Chaussees, 1995) in which the material model is built based on the framework of standard materials with internal constraints (Moumni et al. Int. J. Plasticity, 2008), is revisited. Using the hodograph method, the nonlinear PDE problem is transferred to a linear boundary value problem in hodograph plane and phase transformation around the tip of a crack under mode III loading is calculated analytically. The model proposed by Moumni is improved by including the thermo-mechanical coupling. As a result of the analysis, fully coupled phase transformation region and the temperature increase due to the latent heat generation is calculated numerically around the crack tip.