Modeling of Shape Memory Alloys Considering Rate-independent and Rate-dependent Irrecoverable Strains

Abstract

This dissertation addresses new developments in the constitutive modeling and structural analysis pertaining to rate-independent and rate-dependent irrecoverable inelasticity in Shape Memory Alloys (SMAs). A new model for fully recoverable SMA response is derived that accounts for material behaviors not previously addressed. Rate-independent and rate-dependent irrecoverable deformations (plasticity and viscoplasticity) are then considered. The three phenomenological models are based on continuum thermodynamics where the free energy potentials, evolution equations, and hardening functions are properly chosen. The simultaneous transformation-plastic model considers rate-independent irrecoverable strain generation and uses isotropic and kinematic plastic hardening to capture the interactions between irrecoverable plastic strain and recoverable transformation strain. The combination of theory and implementation is unique in its ability to capture the simultaneous evolution of recoverable transformation strains and irrecoverable plastic strains. The simultaneous transformation-viscoplastic model considers rate-dependent irrecoverable strain generation where the theoretical framework is modfii ed such that the evolution of the viscoplastic strain components are given explicitly. The numerical integration of the constitutive equations is formulated such that objectivity is maintained for SMA structures undergoing moderate strains and large displacements. Experimentally validated analysis results are provided for the fully recoverable model, the simultaneous transformation-plastic yield model, and the transformation-viscoplastic creep model.