Modeling of bulk and porous shape memory alloys

Abstract

The unique properties of shape memory alloys (SMAs), including shape memory effect and superelasticity, have found applications in an increasing number of industries and engineering branches. A porous structure made of an SMA can offer the benefits associated with both porous metals and SMAs. With the recent progress in additive manufacturing technologies, it is now easier to produce lattice structures with customized unit cell geometries in order to meet certain mechanical requirement. A notable application for custom-designed porous SMA is in the field of human implants, where a biocompatible bone implant can be produced that has closer mechanical behavior to the bone, along with better bonding to the surrounding tissue. A fundamental step in designing a porous SMA is the process of modeling and simulation of the part in order to predict its behavior. This includes material modeling of the SMA and reproducing its stress-strain behavior, as well as predicting the macroscopic response of the porous structure made of the SMA. In the first part of this thesis, five different superelastic unit cells with porosities ranging from 0 to 90% were analyzed using FEM. The geometries were created and then analyzed under uniaxial tensile loads using Ansys APDL with its superelastic material model. Four major mechanical characteristics, namely, apparent reversible strain, apparent elastic modulus, volume fraction of transformed material, and strain energy absorption/dissipation were calculated. As a result, the dependency of these mechanical characteristics upon porosity and geometry of the unit cells were laid out. The procedures and methodology used for generating these data can be used as a framework that can also be expanded into a wider range of unit cell types and loading conditions. In the second part, the accuracy of Auricchio’s SMA material model implemented in the current FE programs such as Ansys and Abaqus was investigated. A series of experimental tests were performed on superelastic thin-walled tube samples made of NiTi. Uniaxial, as well as multiaxial path-varying loads were applied to characterize mechanical behavior of the NiTi samples. The experimental tests demonstrated a distinct path-dependent behavior Under multiaxial load cases. To validate the Auricchio’s model, the test sample geometry was created and analyzed in Ansys under the load cases similar to the experimental tests. It was shown that while this material model was able to closely reproduce the uniaxial response of the SMA, it was not able to predict the multiaxial and path-dependent behavior of NiTi samples accurately. In the third part, Likhachev’s model was investigated as an alternative SMA material model that has the potential to provide a better prediction of the SMA response under multiaxial loading conditions. By implementing this model in Matlab, it was shown that, under multiaxial load cases, Likhachev’s model could predict the SMA behavior more closely to the experimental curves, compared to the Auricchio’s model. To adapt this model for FE implementation, two strain-driven formulations of Likhachev’s model were proposed. The first one was a non-iterative reformulation with short calculation time that was limited to 1D loadings only. The second one was an iterative scheme with a PID control concept for achieving convergence, which was functional in all load cases. An attempt was made to derive the tangent modulus numerically, but it did not produce consistent results. As a future work, it will be valuable to devise an analytical formulation of the tangent modulus for this model.

Date	11 Feb 2020
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Patrick Terriault (Supervisor)