Model of shape memory alloy deformation with resistance asymmetry | Mekhanika | kompozitsionnykh | materialov i konstruktsii

Model of shape memory alloy deformation with resistance asymmetry


Shape memory alloys (SMA) behavior essentially depends on the type of stress-strain state. For example, under active tension and compression of initially chaotic martensite, the martensitic inelasticity curves differ both in absolute values and in shape. A flat slope section of the curve like yield plateau is present under tension and is absent in case of compression. The intensity of inelastic deformations caused by tension and compression stresses with the same intensity can be twice as much. Reversing and cyclic tension-compression curves have parts with similar differences. A nonlinear model of polycrystalline SMA phase-structural transformation is proposed using hypothesis of heterogeneous strain hardening of a representative volume and analogue of incremental plasticity theory with isotropic and translational hardening to describe the structural transformation. Two dimensionless parameters proportional to the ratio of deviator third invariant to the cube of intensity of inelastic deformation tensor and active stress (or inelastic deformation increment) tensor respectively are introduced to take into account the type of stress and strain state. The parameter of martensitic volume isotropic hardening is lifetime maximum of the ratio of inelastic deformation intensity to its limit value corresponding to the current strain state type. The material function of translational hardening depends on the full stress intensity and stress state type. The test modes of SMA loading to determine functions used in the model are described. The requirements to these functions related to solution uniqueness, dissipation, and cross hardening are formulated. Special cases of SMA martensitic inelasticity in a homogeneous stress state and corresponding simplifications of the basic equations are considered. The first case relates to the proportional loading of a specimen, the second one relates to the axial tension-compression and torsion of a thin-walled cylindrical beam. The results of numerical calculations in the framework of proposed model demonstrating resistance asymmetry of the material are presented.