Article

Study of Thermoelastic Martensitic Transformations Using a Phase-Field Model

Metallurgical and Materials Transactions A (Impact Factor: 1.73). 01/2011; 42(5):1154-1164. DOI: 10.1007/s11661-010-0526-6

ABSTRACT The mechanisms of face-centered cubic (fcc)Û \Leftrightarrow 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 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 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 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 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 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 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 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. experimental observation of thermoelastic MTs.

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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.
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