Can the theory of critical distances predict the failure of shape memory alloys? Saeid Kasiri a *, Daniel J Kelly b and David Taylor c a Department of Mechanical Engineering, Green College, University of Dublin, Ireland; b Department of Mechanical Engineering, Trinity College, University of Dublin, Ireland; c Trinity Centre for Bioengineering, University of Dublin, Ireland (Received 7 December 2009; final version received 30 March 2010) Components made from shape memory alloys (SMAs) such as nitinol often fail from stress concentrations and defects such as notches and cracks. It is shown here for the first time that these failures can be predicted using the theory of critical distances (TCDs), a method which has previously been used to study fracture and fatigue in other materials. The TCD uses the stress at a certain distance ahead of the notch to predict the failure of the material due to the stress concentration. The critical distance is believed to be a material property which is related to the microstructure of the material. The TCD is simply applied to a linear model of the material without the need to model the complication of its non-linear behaviour. The non-linear behaviour of the material at fracture is represented in the critical stress. The effect of notches and short cracks on the fracture of SMA NiTi was studied by analysing experimental data from the literature. Using a finite element model with elastic material behaviour, it is shown that the TCD can predict the effect of crack length and notch geometry on the critical stress and stress intensity for fracture, with prediction errors of less than 5%. The value of the critical distance obtained for this material was L ¼ 90 mm; this may be related to its grain size. The effects of short cracks on stress intensity were studied. It was shown that the same value of the critical distance (L ¼ 90 mm) could estimate the experimental data for both notches and short cracks. Keywords: shape memory alloy; fracture; theory of critical distances; finite element model; short cracks; R-curve 1. Introduction Shape memory alloys (SMAs) have the ability to return to a memorised shape when heated. Nitinol is a biocompa- tible alloy of nickel and titanium which has been widely used in biomedical engineering due to its shape memory effect and pseudo-elasticity. Self-expanding (SX) stents are an example of its application in biomedical engineering. SX stents are crimped at a low temperature and covered with a retractable sheath. The stent is transferred to the site of the implantation using a catheter. At body temperature the stent returns to its pre-crimped shape once the constraining sheath is removed. The flexibility and elastic deformation of the SX stents has made them attractive to use, but their fracture has still remained a problem. In vivo failure of stents causes injury to the artery and restenosis (Scheinert et al. 2005). This is particularly the case in peripheral arteries, where the implanted stents are subjected to a challenging mechanical environment due to flexion of the hip and knee (Hoffmann et al. 1997). Reported cases of stent fracture illustrate that stents should be designed against overload and fatigue fracture (Kang et al. 2007; Surdell et al. 2007). Depending on the loading conditions the SMAs NiTi experience up to four different types of deformation during loading. At low stress, the material is in the form of austenite and has a linear stress/strain response (austenite zone). With increasing load, part of the material transforms to martensite (transformation zone). There are many different variants of martensite. This transient part goes up to about 5.5% strain and involves a twinning mechanism. As the load increases, the volume fraction of martensite increases until it reaches 100% and the martensite zone starts. Behaviour in this zone is linear elastic with lower stiffness compared with the austenite zone. The last step before failure is a small amount of plastic deformation (slip). Depending on the composition and testing temperature, the SMA might not undergo the martensite transformation in which case fracture occurs in the austenite zone. In this study, we considered failure of specimens containing cracks or notches; in all cases the high local stresses gave rise to zones of martensite near these features. Fatigue experiments on the struts of the stents show that the crack initiates from surface flaws or notches which increase the local stresses (Frotscher et al. 2008). The behaviour of NiTi in the presence of a notch or crack has been studied previously under conditions of cyclic loading (Robertson and Ritchie 2007; Frotscher et al. 2008; Pelton et al. 2008; Wang et al. 2008) and monotonic loading (Yi and Gao 2000; Yi et al. 2001; Chen et al. 2005; Daly et al. 2007; Gollerthan et al. 2009; ISSN 1025-5842 print/ISSN 1476-8259 online q 2011 Taylor & Francis DOI: 10.1080/10255842.2010.482527 http://www.informaworld.com *Corresponding author. Email: kasirigs@tcd.ie Computer Methods in Biomechanics and Biomedical Engineering Vol. 14, No. 6, June 2011, 491–496