A microplane constitutive model for shape memory alloys considering tension-compression asymmetry

Shape memory alloys are a group of advanced materials that have found several industrial applications due to their interesting mechanical properties including a shape memory effect and superelasticity. In order to optimize the use of such materials in manufacturing different devices, appropriate advanced constitutive models are required. Recent experiments show that shape memory alloys exhibit an asymmetric response during tension and compression loading. In this paper, a new three-dimensional constitutive law is proposed based on microplane theory with the purpose of describing the tension-compression asymmetry. The model utilizes an equivalent stress on the foundation of second and third invariants of the deviatoric stress tensor in combination with two internal variables to distinguish between martensite volume fraction as well as martensite elastic modulus during tension and compression. The proposed model is then used to simulate uniaxial tension-compression loading in superelasticity as well as ferroelasticity regimes. The simulation results are compared with the corresponding results obtained by experiment and previous models reported in the literature, and a good agreement is observed. In addition, a four-point bending test is simulated for NiTi tubes in several cases. The predicted moment-curvature response and variations in the position of the neutral axis correlate fairly well with the experimental findings reported in the literature.