Volume 19, Issue 11 (November 2019)                   Modares Mechanical Engineering 2019, 19(11): 2771-2780 | Back to browse issues page

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Mirzakhani S, Javanbakht M. Finite Element Analysis of Phase Field Equations for Martensitic Phase Transformations at the Nanoscale. Modares Mechanical Engineering 2019; 19 (11) :2771-2780
URL: http://mme.modares.ac.ir/article-15-18439-en.html
1- Mechanical Engineering Department, Isfahan University of Technology, Isfahan, Iran
2- Mechanical Engineering Department, Isfahan University of Technology, Isfahan, Iran , javanbakht@cc.iut.ac.ir
Abstract:   (2623 Views)
In the present work, the nonlinear finite element method is used to solve the phase field equations for phase transformations at the nanoscale. In the phase field theory, the evolution of a martensitic nanostructure is described in terms of several order parameters and the Ginzburg-Landau equation is a linear relationship between the of the change rate of an order parameter and the thermodynamic forces which are the variational derivative of the free energy of the system with respect to the order parameter. Since the free energy includes nonlinear terms of the order parameter, the thermodynamic forces are nonlinear functions of the order parameter. Therefore, the phase field equations are solved using the nonlinear finite element method and the self-developed code. The studied transformation is the conversation of cubic to tetragonal phase in NiAl by temperature changes and neglecting the mechanical effects. Therefore, the transformation is the induction temperature type and is defined using only one order parameter. To validate the numerical work, the profile, width, energy, and velocity of the austenite- martensite interface were calculated and compared to the previous works and a very good agreement is found between them. Also, various physical problems such as plane interface propagation, martensitic nucleation, and propagation undercooling, and reverse phase transformation under heating are simulated. The obtained results present a proper tool to solve more advanced phase field problems for phase transformations at the nanoscale including mechanics effects and complex initial and boundary conditions.
Full-Text [PDF 1056 kb]   (1745 Downloads)    
Article Type: Original Research | Subject: Metal Forming
Received: 2018/04/4 | Accepted: 2019/05/21 | Published: 2019/11/21

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