Constitutive modeling of porosity and grain size effects on superelasticity of porous nanocrystalline NiTi shape memory alloy

Porous nanocrystalline NiTi shape memory alloy (SMA) benefit from a combination of the smart responses of nanograined SMA and the characteristics of porous materials, showing great potential in the high-tech field. Porosity and grain size exert an influence on the microstructure evolution during phase transformations, thus possessing the ability to alter the transformation characteristics of NiTi SMA. To investigate the porosity and grain size-dependent superelastic behaviors of porous nanocrystalline NiTi, the constitutive model incorporating grain size effects and tensile-compressive asymmetry for dense nanocrystalline NiTi is first developed. Based on the dense SMA model, porous nanocrystalline NiTi SMA is regarded as a composite material consisting of the void phase and the SMA matrix phase. The voids are treated as inclusions embedded in the SMA matrix composed of grain core and grain boundary. Tensile-compressive asymmetry, transformation hardening modulus associated with intrinsic length scale and grain size are incorporated into the modified Gurson-Tvergaard-Needleman potential function, leading to the construction of constitutive model for porous nanocrystalline NiTi SMA. Simulated results demonstrate that the proposed model is capable to describe the characteristics of porous nanocrystalline NiTi SMA, such as grain size and porosity dependent superelasticity and tensile-compressive asymmetry. Using the developed model, the combined effects of porosity and grain size on the critical transformation stresses, strain hardening, peak stresses, tensile-compressive asymmetry behaviors and the superelastic stress-strain hysteresis loop are analyzed.