The cyclic and evolutionary response to approach the attraction loops under stress controlled isothermal conditions for a multi-mechanism based multi-axial SMA model

• Evolutionary cyclic responses of shape memory alloys were investigated.
• Inelastic hardening mechanisms were used to regulate the energy storage and dissipation.
• Pseudoelastic and pseudoplastic regimes under uni- and multi-axial loading were considered.
• Model predictions were compared to typical experimental data available in the literature.
• Both stress mean and amplitude have significant effect on the evolutionary response.

The main focus in the present work has been on studying the evolutionary responses of Shape Memory Alloy (SMA) materials under isothermal, cyclic loading conditions. To this end, predictions of a recently-developed SMA material model by the authors is used here to carry out the qualitative comparisons to some of the available experimental results in the literature for SMA material responses under different uniaxial and multi-axial conditions of stress-control, both in the pseudoelastic and the pseudoplastic regimes. In the formulation of this model, the significant roles played by the internal state variables, underlying the inelastic mechanisms in the model to regulate the material’s evolutionary response under extended cycles, are emphasized. The results presented have led to a number of important conclusions. First, the evolutionary character for pseudoelasticity is markedly different from that occurring in the pseudoplastic regime. Second, the virgin material response under minor loop cycles is dramatically different from its pre-cycled counterpart for which a prior major loop was established. Third, the careful selection of the loading-control variable such as magnitudes of the mean stress and stress amplitude plays a major role in dictating the amount of strain and detailed shapes of the saturated stress–strain loop achieved, as well as the number of cycles required to reach the saturation. Lastly, multi-axial load cycling under conditions of combined tension/compression/shear leads to a faster approach to the saturated states compared to the uniaxial load condition.