Constitutive Response of Precipitation Hardened Ni-Ti-Hf Shape Memory Alloys through Micromechanical Modeling

Shape memory alloys (SMAs) are unique materials with the ability to generate and recover moderate to large inelastic deformations. Due to their aforementioned ability, SMAs are suitable for applications in aerospace, oil and gas and automotive industries, where compact actuators with high actuation energy density are required. The current work presents a modeling framework that links the heat treatment of SMAs with their effective response and aims to accelerate the discovery of new high temperature SMAs with optimal performance. Thus a finite element based, multi-field micromechanical framework is developed to capture the constitutive response of precipitation hardened Ni-Ti-Hf SMAs. A representative volume element of precipitated polycrystalline SMAs is considered which contains randomly distributed non-overlapping precipitates, while periodic boundary and geometric conditions are maintained. The SMA matrix is assumed to behave isotropic as a result of random texture while the precipitates are considered as linear elastic solids. The effect of the lattice mismatch between the precipitates and the matrix, and the effect of the Ni and Hf depletion during precipitation on the thermo-mechanical response of the material are taken into consideration. The Fickian diffusion law is used to predict the Ni and Hf concentration field in the vicinity of the precipitates, which results in substantial SMA transformation temperature shifts. Finally, the predictive capability of the developed framework is assessed through correlations with experimental results.