A nonlinear 3D model for iron-based shape memory alloys considering different thermomechanical properties for austenite and martensite and coupling between transformation and plasticity

The paper presents a 3D macroscopic constitutive model for Iron-based shape memory alloys (Fe-SMAs) that uses different thermomechanical properties for austenite and martensite, and considers nonlinear coupling effects between phase transformation and plasticity. The constitutive equations are derived from a potential comprising the Voigt mixture of the free energies of the two phases adapted from the ZM model, and a new interaction energy term. The loading conditions for phase transformation and plastic deformation are obtained by requiring the governing thermodynamic forces to derive from an appropriate dissipation potential, in which a quadratic plasticity-dependent term has been introduced to account for its suppressive effect on forward transformation. The model is implemented in ABAQUS through a user defined material subroutine (UMAT), validated against experimental data taken from the literature, and used to simulate partial unloading and investigate the influences of interaction parameters. Finite element analysis of a precracked compact tension sample is then carried out under both plane stress and plane strain (nonproportional stress fields with strong gradients). The results show highly heterogeneous stress distribution in the specimen. The inelastic strain singularity at the crack front is a consequence of pure phase transformation at low temperature, pure plasticity at high temperature, and a mix of both at intermediate temperatures. During unloading, the crack front accommodates the compression of the surrounding material by undergoing cyclic phase transformation and/or reversed plasticity, which, in turn, induces partial crack closure. If the mechanical loading cycle is operated at low temperature then heating leads to complete crack closure due to martensite→ austenite transformation, while if it is operated at elevated temperature, heating leads to further but not complete crack closure as a result of the thermal-induced plasticity.