R. Dhote

Isogeometric Analysis of Coupled Thermo-mechanical Phase-field Models for Shape Memory Alloys Using Distributed Computing☆

A variational formulation and numerical implementation of the phase-field models for shape memory alloys using distributed computing are reported in the paper. The numerical implementation is based on the isogeometric analysis framework, constituting the rich NURBS basis functions. The phase field models are developed using the strain based order parameter and the Ginzburg-Landau theory. The fourth order fully coupled thermo-mechanical 2D and 3D models are solved with the isogeometric finite element methodology in the distributed computing environment. The weak scaling performance studies on the 2D model demonstrate current challenges and open a way for future improvements.

Shape memory alloy nanostructures with coupled dynamic thermo-mechanical effects

Abstract Employing the Ginzburg–Landau phase-field theory, a new coupled dynamic thermo-mechanical 3D model has been proposed for modeling the cubic-to-tetragonal martensitic transformations in shape memory alloy (SMA) nanostructures. The stress-induced phase transformations and thermo-mechanical behavior of nanostructured SMAs have been investigated. The mechanical and thermal hysteresis phenomena, local non-uniform phase transformations and corresponding non-uniform temperatures and deformations’ distributions are captured successfully using the developed model. The predicted microstructure evolution qualitatively matches with the experimental observations. The developed coupled dynamic model has provided a better understanding of underlying martensitic transformation mechanisms in SMAs, as well as their effect on the thermo-mechanical behavior of nanostructures.

Effect of Aspect Ratio and Boundary Conditions in Modeling Shape Memory Alloy Nanostructures with 3D Coupled Dynamic Phase-Field Theories

The behavior of shape memory alloy (SMA) nanostructures is influenced by strain rate and temperature evolution during dynamic loading. The coupling between temperature, strain, and strain rate is essential to capture inherent thermomechanical behavior in SMAs. In this paper, we propose a new 3D phase-field model that accounts for two-way coupling between mechanical and thermal physics. We use the strain-based Ginzburg-Landau potential for cubic-to-tetragonal phase transformations. The variational formulation of the developed model is implemented in the isogeometric analysis framework to overcome numerical challenges. We have observed a complete disappearance of the out-of-plane martensitic variant in a very high aspect ratio SMA domain as well as the presence of three variants in equal portions in a low aspect ratio SMA domain. The dependence of different boundary conditions on the microstructure morphology has been examined energetically. The tensile tests on rectangular prism nanowires, using the displacement based loading, demonstrate the shape memory effect and pseudoelastic behavior. We have also observed that higher strain rates, as well as the lower aspect ratio domains, resulting in high yield stress and phase transformations occur at higher stress during dynamic axial loading.

Phase Field Dynamic Modelling of Shape Memory Alloys Based on Isogeometric Analysis

Shape Memory Alloys (SMAs) exhibit complex behaviors as a result of their constituent phases and microstructure evolution. In this paper, we focus on the numerical simulations of microstructure evolution in SMAs using a phase-field model for the two dimensional square-to-rectangular martensitic phase transformations. The phase-field model, based on the Ginzburg-Landau theory, has strong non-linearity, thermo-mechanical coupling, and higher-order differential terms and presents substantial challenges for numerical simulations. The isogeometric analysis, developed in this paper using the rich NURBS basis functions, offers several advantages in solving such complex problems with higher-order partial differential equations as the problem at hand. To our best knowledge, we report here for the first time the use of the new method in the study of microstructure evolution in SMAs. The numerical experiments of microstructure evolution have been carried out on the FePd SMA specimen. The results are in good agreement with those previously reported in the literature.

Temperature Induced Cubic-to-Tetragonal Transformations in Shape Memory Alloys Using a Phase-Field Model

Shape memory alloys (SMAs) exhibit hysteresis behaviors upon stress- and temperature-induced loadings. In this chapter, we focus on numerical simulations of microstructure evolution of cubic-to-tetragonal martensitic phase transformations in SMAs in 3D settings under the dynamic loading conditions. A phase-field (PF) model has been developed to capture coupled dynamic thermo-mechanical behavior of such SMA structures and the system of governing equations have been solved numerically using the isogeometric analysis. Temperature induced reverse and forward transformations have been applied to a cubic SMA specimen, starting with evolved accommodated martensitic microstructure. We have observed that during the forward transformation, the martensitic variants nucleate abruptly. The transient microstructures are aligned along \(\left[ 110 \right]\) planes, which is in accordance with the crystallographic theory and experimental results.

Dynamic Thermo-Mechanical Properties of Shape Memory Alloy Nanowires Upon Multi-Axial Loading

In this paper, we study the behavior of shape memory alloy (SMA) nanowires subjected to multi-axial loading. We use the model developed in our earlier work to study the microstructure and mechanical properties of finite length nanowires. The phase field model with the Ginzburg-Landau free energy is used to model the phase transformation based on the chosen order parameter. The governing equations of the thermo-mechanical model are solved simultaneously for different loading cases. We observe that nanowire behaves in a stiff manner to axial load with complete conversion of the unfavorable martensite to the favorable one. The bending load aids the phase transformation by redistributing the martensitic variants based on the local axial stress sign. The nanowire behavior to multi-axial (axial and bending together) is stiffer axially than the axial loading case. The understanding of the behavior of nanowire to multi-axial loading will be useful in developing better SMA-based MEMS and NEMS devices.Copyright

Microstructures of Constrained Shape Memory Alloy Nanowires Under Thermal Effects

In this paper, martensitic transformations in constrained Fe-Pd nanowires are studied using a mesoscopic model analyzed in detail numerically in our earlier papers. The dynamics of square-to-rectangular transformation is modeled by using the modified Ginzburg-Landau theory. The simulations are performed accounting for the thermal effects using the coupled equations of non-linear thermoelasticity. Up to date, these effects have typically been neglected in modeling microstructures at the scales of interest considered here. Nanowires of length 2000 nm and widths ranging from 200 nm to 50 nm are simulated to study the effect of size on the microstructure evolution. There exists a critical width below which the size effect is prominent. We present a series of numerical results demonstrating this phenomenon. We also have carried out the study of variations in values of bulk, shear, and Landau constants to understand the difference in evolved microstructure in the coupled and uncoupled physics.Copyright

Dynamic multiaxial behaviors of 3D shape memory alloy nanowires: A phase-field study

ABSTRACT This article focuses on the dynamic multiaxial behaviors of shape memory alloy (SMA) rectangular prismatic nanowires. A strain-based order parameter 3D phase-field model is used to study microstructure evolution and consequent thermo-mechanical behaviors in the cubic-to-tetragonal transformations in SMA nanowires. The FePd nanowire is subjected to axial-transverse and axial-torsion loadings paths. The numerical results demonstrate the strong influence of multiaxial loadings on microstructures and thermo-mechanical response. The variation of thermo-mechanical response stems from the nucleation of energetically favorable martensitic variants to the applied loading. The understanding of multiaxial thermo-mechanical response of nanowires is essential in developing better SMA-based devices.

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

Nanostructures with shape memory effect: Modelling coupled dynamics

In this contribution we apply a phase-field (PF) modeling approach for the analysis of properties of shape-memory alloy (SMA) nanostructures, focusing on their complex microstructures and thermo-mechanical behavior. 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 the isogeometric analysis (IGA). Microstructure evolutions for different geometries of SMA nanostructures under temperature-induced phase transformations have been studied and some typical examples are presented here.