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

2012 ◽  
Vol 78 ◽  
pp. 63-68 ◽  
Author(s):  
Rakesh Dhote ◽  
Hector Gomez ◽  
Roderick Melnik ◽  
Jean Zu
Keyword(s):  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Isogeometric Analysis ◽  
Field Model ◽  
Phase Field Model ◽  
Higher Order ◽  
Martensitic Phase Transformations

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.

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

2015 ◽  
Author(s):  
Rakesh Dhote ◽  
Kamran Behdinan
Keyword(s):  
Shape Memory ◽  
Phase Transformations ◽  
Phase Field ◽  
Isogeometric Analysis ◽  
Domain Walls ◽  
Landau Theory ◽  
Phase Field Model ◽  
Diffuse Interface ◽  
Free Energy Function ◽  
Martensitic Phase Transformations

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.

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