Effect of Phase Transformation on the Fracture Behavior of Shape Memory Alloys

Over the last few decades, Shape Memory Alloys (SMAs) have been increasingly explored in order to take advantage of their unique properties (i.e., pseudoelasticity and shape memory effect), in various actuation, sensing and absorption applications. In order to achieve an effective design of SMA-based devices a thorough investigation of their behavior in the presence of cracks is needed. In particular, it is important to understand the effect of phase transformation on their fracture response. The aim of the present work is to study the effect of stress-induced as well as thermo-mechanically-induced phase transformation on several characteristics of the fracture response of SMAs. The SMA thermomechanical response is modeled through an existing constitutive phenomenological model, developed within the framework of continuum thermodynamics, which has been implemented in a finite element frame-work. The effect of stress-induced phase transformation on the mechanical fields in the vicinity of a stationary crack and on the toughness enhancement associated with crack advance in an SMA subjected to in-plane mode I loading conditions is examined. The small scale transformation assumption is employed in the analysis according to which the size of the region occupied by the transformed material forming close to the crack tip is small compared to any characteristic length of the problem (i.e. the size of the transformation zone is thirty times smaller than the size of the cracked ligament). Given this assumption, displacement boundary conditions, corresponding to the Irwin’s solution for linear elastic fracture mechanics, are applied on a circular region in the austenitic phase that encloses the stress-induced phase transformation zone. The quasi-static stable crack growth is studied by assuming that the crackpropagates at a certain critical level of the crack-tip energy release rate. The Virtual Crack Closure Technique (VCCT) is employed to calculate the energy release rate. Fracture toughness enhancement associated with transformation dissipation is observed and its sensitivity on the variation of key characteristic non-dimensional parameters related to the constitutive response is investigated. Moreover, the effect of the dissipation due plastic deformation on the fracture resistance is analyzed by using a Cohesive Zone Model (CZM). The effect of thermo-mechanically-induced transformation on the driving force for crack growth is analyzed in an infinite center-cracked SMA plate subjected to thermal actuation under isobaric mode I loading. The crack-tip energy release rate is identified as the driving force for crack growth and is measured over the entire thermal cycle by means of the VCCT. A substantial increase of the crack-tip energy release rate – an order of magnitude for some material systems – is observed during actuation as a result of phase transformation, i.e., martensitic transformation occurring during actuation causes anti-shielding that might cause the energy release rate to reach the critical value for crack growth. A strong dependence of the crack-tip energy release rate on the variation of the thermomechanical parameters characterizing the material response is examined. Therefore, it is implied that the actual shape of the strain- temperature curve is important for the quantitative determination of the change of the crack-tip energy release rate during actuation