A three-dimensional macroscopic fully thermomechanically coupled constitutive model for shape memory alloy under thermomechanical cyclic loading

NiTi Shape memory alloy (SMA) is a nearly equiatomic alloy of nickel and titanium. It is widely used in various industries such as automotive, aerospace, civil and bioengineering. In most of the applications, the NiTi component is under thermomechanical cyclic loading and, therefore, susceptible to fatigue failure. Fatigue of NiTi shape memory alloys is a key issue that should be solved in order to promote their engineering applications and utilize their unique shape memory effect and superelasticity more sufficiently. In this work, a three-dimensional macroscopic fully thermomechanically coupled constitutive model reproducing the behaviors of the shape memory alloy under thermomechanical cyclic loading is presented. This new model is an extension of the Saint-Sulpice et al. [1-2] model. If the SMA is subjected to thermomechanical cyclic loading, the permanent inelastic strain increases up to it reaches a stable value after a certain number of cycles. This procedure is at the origin of fatigue effect in SMA by introducing a residual strain which evolves with the cycles. The origin of the residual strain produce during a cyclic loading process is one of the most important problems facing for the modeling of the cyclic behavior and fatigue of SMAs. So, it is important to predict its evolution correctly with models to improve the reliability of SMA devices and to propose the well adapted fatigue criteria. These criteria should be based on the indicators of the cumulated residual strain. In this study, based on the observations and using a measurement approach such as electric resistance variation, the origin of the residual strain is investigated and the progressive increase of residual strain with the increased cycle number is assumed to be a consequence of the progressive increase of residual martensitic volume fraction upon the cyclic effects. This model is shown to give good results for the prediction of residual strain that produced under thermomechanical cyclic loading for NiTi shape memory alloy. [1] Saint-Sulpice, L., Arbab Chirani, S., Calloch, S., 2009. A 3D super-elastic model for shape memory alloys taking into account progressive strain under cyclic loadings. Mechanics of Materials 41, 12-26. [2] Saint-Sulpice, L., Arbab Chirani, S., Calloch, S., 2012. Thermomechanical cyclic behavior modeling of Cu-Al-Be SMA materials and structures. International Journal of Solids and Structures 49, 1088-1102.