Modelling the mechanical behavior of shape memory alloys under variant coalescence

In shape memory alloys (SMA) reorientation of crystallographic variants upon stressing takes place in a temperature regime fewer than the martensite finish temperature M(f), a process which is denoted as variant coalescence (VC). The macroscopic deformation behavior of a polycrystalline Cu-Al-Ni shape memory alloy under VC is modelled by utilizing a combined computational micromechanics and continuum-thermodynamics framework. The kinematical description of the reorientation process is based on the crystallography of the beta(1) --> gamma'(1) martensitic transformation in Cu-Al-Ni. A thermodynamic field concept for VC is followed by introducing a Gibbs free energy formulation for the polycrystalline mesodomain and the derivation of a criterion for the thermodynamic admissibility of the reorientation process considering the stored elastic energy due to reorientation-induced microstresses and the energy dissipation due to the movement of boundaries between the martensitic variants. The reorientation process on the size scale of self-accommodating plate groups is formulated by the use of simple microscale constitutive assumptions. The reorientation process is the subject of a micromechanical simulation. By checking the thermodynamic admissibility of any small increment of the reorientation process the corresponding required magnitude of externally applied tensile stress can be calculated and the related overall mechanical behavior results with the stress-strain curve. The micro-macro transition is performed by an averaging procedure for each crystallite and a finite element based periodic microfield approach. VC is studied with respect to the mobility of the intervariant boundaries and energy dissipation due to interfacial motion. The effect of the volume change associated with the beta(1) --> gamma'(1) martensitic transformation in Cu-Al-Ni and the difference in the mechanical behavior in uniaxial tension and compression is quantified.