Isogeometric Analysis of 3D Dynamic Thermo-Mechanical Phase-Field Model for Cubic-to-Tetragonal Phase Transformations in Shape Memory Alloys

In this paper, we study the dynamic thermo-mechanical behaviors of 3D shape memory alloy (SMA) nanostructures using the phase-field (PF) model. The PF model is based on the Ginzburg-Landau theory and requires a non-convex free energy function for an adequate description of the cubic-to-tetragonal martensitic phase transformations. We have developed a model that includes domain walls, treated as a diffuse interface, which leads to a fourth-order differential equation in a strain-based order parameter PF model. Arising numerical challenges have been overcome based on an isogeometric analysis (IGA) framework. Microstructure morphology evolution and consequent thermo-mechanical properties have been studied on SMA nanostructures of different geometries. The numerical results are in agreement with experimental observations. The developed coupled dynamic model has provided a better understanding of underlying microstructures and behaviors, which can be used for development of better SMA-based devices.Copyright © 2015 by ASME