Finite Strain Constitutive Modeling of Shape Memory Alloys Incorporating Transformation-Induced Plasticity under Cyclic Loading

Abstract

Shape Memory Alloys (SMAs), as a subgroup of active materials, provide remarkable advantages working as solid-state actuators in terms of the trade-offs between structure overall weight and functionality, thus gaining tremendous application interests in various industries such as biomedical, aerospace, and civil engineering. However, the majority of constitutive models for SMAs are developed based on small strain theory which are inaccurate in the case of large deformations. Besides, applications involved with cyclic loading require SMAs experiencing repeated phase transformations, during which permanent deformations are developed due to transformation-induced plasticity (TRIP) at an effective stress level much lower than the material yielding point. Moreover, realistic applications also need SMA-based actuators subjected to multiaxial stress state originated from geometry complexities or installment required discontinuities such as notches and holes, where the non-uniform stress field has shown to have a significant impact on the multiaxial TRIP evolution during thermomechanical loading cycles. To meet the above modeling challenges, this work aims to address the following objectives. First, a three-dimensional finite strain constitutive model is proposed for polycrystalline SMAs to account for the large deformations (including large strains and rotations) that SMA components may undertake. Furthermore, the model is extended to incorporate the multiaxial TRIP evolution under non-uniform stress fields. A detailed implementation of the proposed model is presented through a user-defined material subroutine within a numerical environment for solving different bound value problems. Finally, the predicted cyclic pseudoelastic and actuation responses for a wide range of SMA material systems under both uniaxial and multiaxial loading conditions are compared against experimental results to validate the proposed modeling capabilities.