Thermodynamic rationale for transformation-induced dislocations in shape memory alloys

Abstract

Shape Memory Alloys (SMAs) undergo stress-induced martensitic phase-transformation affording a “superelastic” behavior with functional applications. Such behavior is undermined by the formation and accumulation of irreversible residual strains in each cycle. These residual strains arise from transformation-induced dislocation-emission and current understanding has postulated the microstructural role of emitted dislocations to accommodate lattice-mismatch while also observing a preference to occur during reverse-transformation. This study develops a thermodynamic framework to offer a causal explanation for dislocation-emission from Gibbs’ free energy considerations. Superelastic stress-strain curves for a reversible pathway without emitted-dislocations and for an irreversible pathway with emitted-dislocations are derived. The role of emitted-strain in relaxing the transformation-strain of the martensitic-inclusion and in accruing residual strain is proposed. It is shown that both pathways obey the first law of thermodynamics but it is the second law of thermodynamics that dictates the path preference. It is shown that the irreversible path achieves the critical condition for spontaneous reverse-transformation at a higher stress-level than the reversible path. Thus, the irreversible pathway initiates earlier during unloading and is thermodynamically selected during reverse-transformation. The driving-forces associated with the irreversible pathway are analyzed to establish the cause of emitted-dislocations and why it is thermodynamically preferred despite offering a higher lattice-friction barrier. Consequently, a new approach to target fatigue-resistant SMA properties is offered, focusing on the interplay of the individual driving-forces coming from the elastic strain-energy, work-interaction, and lattice-friction, as revealed by the thermodynamic framework.