Study of Thermoelastic Martensitic Transformations Using a Phase-Field Model

Metallurgical and Materials Transactions A (Impact Factor: 1.73). 05/2011; 42(5):1154-1164. DOI: 10.1007/s11661-010-0526-6


The mechanisms of face-centered cubic (fcc)face-centered tetragonal (fct) thermoelastic martensitic transformations (MTs) in Mn-rich Mn-Cu alloys were studied using a phase-field model. In this article, a phase-field model describing the martensitic transformation was developed with the capability of treating continuously varying temperatures under two boundary conditions. The analysis of various energies during the microstructural evolution reveals that the elastic strain energy is a resistant force in the forward MT, but it becomes a driving force in the reverse MT. The feature of self-accommodation in forward MT is revealed by comparing the elastic strain energy of two martensitic variants with three martensitic variants. The simulated microstructural evolution demonstrates that the plate of polytwinned martensite shrinks with increasing temperature, and during the sequent cooling, the plate of polytwinned martensite grows and almost retraces to its original state. This reversibility of MTs is in good agreement with the reported experimental observation of thermoelastic MTs.

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    • "Yamanaka et al. (2008) introduced an elastoplastic phase field model based on Guo et al. (2005) to investigate cubic to tetragonal transformation, their model confirmed that plastic accommodation largely reduces the elastic strain energy during the formation of the tetragonal phase because of both selfand plastic accommodations. Man et al. (2011) presented a phase field model to study forward and reverse proper MPT with capability of treating continuously varying temperature. Recently, Yeddu and Malik have extensively studied the austenite to martensite transformation in steel. "
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    ABSTRACT: Martensitic tetragonal-to-monoclinic transformation in zirconia is a “double-edged sword”, enabling transformation toughening or shape memory effects in favorable cases, but also cracks and phase degradation in undesirable scenarios. In stressed polycrystals, the transformation can burst from grain to grain, enabling stress field shielding and toughening in an autocatalysis fashion. This transformation strain can be recovered by an adequate thermal cycle at low temperatures (when monoclinic is stable) to provide a shape memory effect, or by unloading at higher temperatures (when tetragonal is stable) to provide pseudoelasticity. We capture the details of these processes by mining the associated microstructural evolutions through the phase field method. The model is both stress and temperature dependent, and incorporates inhomogeneous and anisotropic elasticity. Results of simulations show an ability to capture the effects of both forward (T→M) and reverse (M→T) transformation under certain boundary conditions.
    Full-text · Article · Sep 2014 · International Journal of Plasticity
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    • "Moreover, most models assume isothermal conditions, which neglects the thermo-mechanical coupling of SMAs, a significant modeling limitation. The nucleation and growth of martensitic transformations have been widely studied by using the kinetic time-dependent Ginzburg-Landau models [18] [19] [21] [22] [23] [24] [16] [25] [26]. Using the strain-based OP PF models, the temperature-and stress-induced phase transformations have been studied for SMAs [27] [14]. "
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    ABSTRACT: The paper focuses on numerical simulation of the phase-field (PF) equations for modeling martensitic transformations in shape memory alloys (SMAs), their complex microstructures and thermo-mechanical behavior. The PF model is based on the Landau-Ginzburg potential for the 3D cubic-to-tetragonal phase transformations in SMAs. The treatment of domain walls as diffuse interfaces, leads to a fourth-order differential equation in a strain-based order parameter PF model. The fourth-order equations introduce a number of unexplored numerical challenges because traditional numerical schemes have been primarily applied to second-order problems. We propose isogeometric analysis (IGA) as a numerical formulation for a straightforward solution to the fourth-order differential PF equations using continuously differentiable non-uniform rational B-splines (NURBS). We present microstructure evolution in different geometries of SMA nanostructures under temperature-induced phase transformations to illustrate the geometrical flexibility, accuracy and robustness of our approach. The simulations successfully capture the dynamic thermo-mechanical behavior of SMAs observed experimentally.
    Full-text · Article · Mar 2014 · Computers & Structures
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    • "The influence of different strain rates on microstructure and mechanical response of FePd samples on temperature-and stress-induced PTs was examined using the isothermal model. Other 3D PF models have reported morphological evolution in spinodal decomposition [39], thermoelastic transformations [40] and decomposition of the supersaturated binary solid solution [41]. "
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    ABSTRACT: 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 effects is essential to capture inherent thermo-mechanical behavior in SMAs. In this paper, we propose a new fully coupled thermo-mechanical 3D phase-field model that accounts for two-way coupling between mechanical (or structural) and thermal physics. The 3D model provides a realistic description of the properties of SMAs nanostructures. 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 sensitive dependence of different boundary conditions on the microstructure morphology has been examined energetically. The tensile tests on a 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, result in high yield stress and phase transformations occur at higher stress during dynamic axial loading. The simulation results using the developed model are in qualitative agreement with the numerical and experimental results from the literature.
    Full-text · Article · Mar 2014
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