Three-Dimensional Modeling of Rate-Dependent Deformation in Shape Memory Alloys at High Temperatures

Abstract

Active structures composed of Shape Memory Alloys (SMAs) and High Temperature SMAs (HTSMAs) continue to be developed for applications that benefit from solid-state actuation. The need to account for the response of these materials under non-conventional loading paths that include elevated temperature conditions has become important. Conventional SMAs are exposed to such temperatures during processing, including final shape-setting. HTSMAs, by virtue of their title, are exposed to such high temperatures during transformation. This work addresses new developments in the constitutive modeling and numerical analysis pertaining to irrecoverable inelasticity in SMAs at high temperatures, where this behavior becomes rate-dependent. The description of such behavior requires the development of a theoretical framework able to capture the coupling between the rate-independent transformation and the rate-dependent creep. The proposed phase transformation-viscoplastic model is based on continuum thermodynamics; here the elastic relations, the inelastic evolution equations, and the transformation criteria are summarized. The evolution equation for the viscoplastic strain is non-homogeneous in time, and thus rate-dependency results. The viscoplastic parameters are generally assumed to exhibit a strong dependence on temperature. The rate-independent and rate-dependent constitutive equations that comprise the full 3-D model are numerically integrated using a scheme that accounts for both transformation and viscoplastic deformation in a coupled manner. The implementation allows for 3-D analysis of SMA bodies using an FEA framework that includes Abaqus and an associated user material subroutine. Example analyses are discussed, including shape-setting in a conventional SMA and experimentally validated structural analysis of an HTSMA specimen.