A finite-strain thermomechanical behavior model for iron-based shape memory alloys accounting for coupling between phase transformation and plastic slip

Shape Memory Alloys (SMAs) have the main interesting property to recover an inelastic strain induced by martensitic transformation. The initial shape can be recovered directly after unloading or with the application of an additional heating. Iron-based SMAs (Fe-SMAs) are characterized by a high coupling between phase transformation and plastic slip at low temperatures under small stress levels. Thermomechanical constitutive models describing such coupling developed based on small-strains are not suitable for higher loading levels. This motivates the proposed development of a finite-strain constitutive model for Fe-SMAs considering thermomechanical coupling between phase transformation and plastic slip, and by extending the small-strain model within a finite-strain thermodynamical framework in order to describe large strains mainly induced by plastic hardening in Fe-SMA material point. The model here has two internal variables (volume fraction of martensite and the accumulative plastic strain). It is based on the assumption of the local multiplicative split of the deformation gradient into elastic and inelastic parts with a total Lagrangian formulation. The inelastic deformation gradient splits also into a transformation and a plastic parts. The developed model is implemented into the commercial software Matlab. The results obtained for thermomechanical loadings are discussed and, a good agreement with experimental results is also observed.