Extension of micromechanics model and micro-macro description to shape memory effect of NiTi SMAs

Abstract

In this article, we presented an important extension of the micromechanics model and the micro-macro approach proposed by Gall et al. to the prediction of the shape memory effect (SME) of polycrystalline shape memory alloys (SMAs). In the constitutive model for a single crystal, the volume fractions of the 24 martensite variants (MVs) are taken as the internal variables, and the interaction between the MVs is considered. The constitutive description for polycrystalline SMAs was obtained by assembling the single crystals with different orientations using finite element method (FEM). The constitutive description for SME was derived by introducing the volume fraction of the detwinned-martensite and assuming that the mechanism of detwinning is identical with that of the phase transformation, incorporating the refined stress-temperature phase diagram. The corresponding numerical algorithm was developed, in which a special treatment is introduced to get rid of the contribution from the MVs that might be irrationally activated during computations, which could directly reduce the dimension of the Jacobian and effectively enable the convergence and stability of the numerical implementation, especially in the cases of complex nonproportional deformation. A thin-walled cylindrical tube model was used for FE simulations of the SMEs under biaxial tensile-shear deformations, in which the texture microstructure in the materials formed during the cold drawn process could be considered. The SMEs of some typical NiTi SMAs under uniaxial and multiaxial nonproportional loadings were simulated and compared with experimental results, and the satisfactory agreement demonstrates the validity of the developed approach.