A Three-Dimensional Constitutive Model for Polycrystalline Shape Memory Alloys Under Large Strains Combined With Large Rotations

Abstract

Shape Memory Alloys (SMAs), known as an intermetallic alloys with the ability to recover its predefined shape under specific thermomechanical loading, has been widely aware of working as actuators for active/smart morphing structures in engineering industry. Because of the high actuation energy density of SMAs, compared to other active materials, structures integrated with SMA-based actuators has high advantage in terms of tradeoffs between overall structure weight, integrity and functionality. The majority of available constitutive models for SMAs are developed within infinitesimal strain regime. However, it was reported that particular SMAs can generate transformation strains nearly up to 8%–10%, for which the adopted infinitesimal strain assumption is no longer appropriate. Furthermore, industry applications may require SMA actuators, such as a SMA torque tube, undergo large rotation deformation at work. Combining the above two facts, a constitutive model for SMAs developed on a finite deformation framework is required to predict accurate response for these SMA-based actuators under large deformations. A three-dimensional constitutive model for SMAs considering large strains with large rotations is proposed in this work. This model utilizes the logarithmic strain as a finite strain measure for large deformation analysis so that its rate form hypoelastic constitutive relation can be consistently integrated to deliver a free energy based hyper-elastic constitutive relation. The martensitic volume fraction and the second-order transformation strain tensor are chosen as the internal state variables to characterize the inelastic response exhibited by polycrystalline SMAs. Numerical experiments for basic SMA geometries, such as a bar under tension and a torque tube under torsion are performed to test the capabilities of the newly proposed model. The presented formulation and its numerical implementation scheme can be extended in future work for the incorporation of other inelastic phenomenas such as transformation-induced plasticity, viscoplasticity and creep under large deformations.