Int J Fract (2011) 169:1–13 DOI 10.1007/s10704-010-9577-3 ORIGINAL PAPER Analytical prediction of the phase transformation onset zone at a crack tip of a shape memory alloy exhibiting asymmetry between tension and compression C. Lexcellent · M. R. Laydi · V. Taillebot Received: 2 February 2010 / Accepted: 8 November 2010 / Published online: 15 December 2010 © Springer Science+Business Media B.V. 2010 Abstract Shape Memory Alloys (SMAs) such as NiTi exhibit stress induced martensitic phase transfor- mation. The purpose of this paper is to provide a better understanding of SMA (such as NiTi) fracture behav- ior, by considering the vicinity of the crack tip where the transformation occurs. This analysis integrates the asymmetry between tension and compression in an ana- lytical prediction of the surface of phase transforma- tion around the crack tip for loading modes 1, 2, 3 and mixed 1+2. The influence of the asymmetry between tension-compression is more important in plane stress conditions than in plane strain conditions, particularly for mode 1 loading. In order to validate this model, we are currently setting up an experimental investigation to observe strain localization during crack propagation (transformation and martensitic saturation regions) on NiTi thin sheets. Keywords Fracture · Crack · Phase transformation · Shape memory alloys · Transformation surface 1 Introduction Shape Memory Alloys (SMAs) are potential materials for use in smart structures,actuators, medical devices C. Lexcellent (B) · M. R. Laydi · V. Taillebot Institute Femto-St, Applied Mechanics Department, 24, rue de l’Epitaphe, 25000 Besançon, France e-mail: christian.lexcellent@univ-fcomte.fr and aeronautical materials. This is because of the very large recoverable strains (on the order of 8% for equiatomic NiTi) associated with their superelastic or pseudoelastic behaviour. The extended use of SMA elements, which are sometimes subjected to rather complex loadings, raises the issue of the service life of systems and leads us to investigate SMA fracture and/or fatigue damage. As discussed by Daly et al. (2007), fatigue and fracture behaviours, and their pos- sible consequences on patients’ health, are of a great concern in the medical industry, where NiTi is widely used for medical devices like stents. Pseudoelasticity is associated with a martensitic ph- ase transformation (MPT), induced by an applied load, between high-symmetry austenite and low-symmetry martensite. SMAs accommodate the applied stress through MPT in which martensite variants (twinned or untwinned martensite) are created. The untwinned martensite differs in its crystallographic orientations. The mechanism of the MPT is well understood for sin- gle crystal (Miyazaki et al. 1983; Patoor et al. 2006) but not completely for polycrystal. The linear elastic fracture mechanics (LEFM) theory provides the stress field around the crack tip, depending on the loading mode (1, 2, 3 or mixed). Theoretically, the stress field around the crack tip is unbounded. How- ever, whereas other elastic-plastic materials undergo yielding at the crack tip, SMAs initiate an MPT in the vicinity of the crack tip where a phase transformation zone (from austenite through martensite states) appears locally. 123