Study of Thermoelastic Martensitic Transformations Using a Phase-Field Model

Abstract

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.

Effect of variant strain accommodation on the three-dimensional microstructure formation during martensitic transformation: Application to zirconia

“…For instance, within the Ginzburg-Landau theory [32], the primary order parameters may be used to describe either some components of the strain tensor or atomic shuffles. In the first approach, the free energy density is a polynomial in terms of strain components [33][34][35][36][37][38], while in the second approach, the free energy is a Landau polynomial in terms of atomic shuffles plus a linear or quadratic term which couples order parameters and the strain tensor [19,[39][40][41][42][43][44][45][46]. A third approach may be worth mentioning here, which uses the same order parameters as in the aforementioned second approach, but it couples the strain tensor components to the order parameter(s) through a 2-3-4 or higher-order polynomial [47][48][49][50][51][52].…”

3D coupled thermo-mechanical phase-field modeling of shape memory alloy dynamics via isogeometric analysis

“…(23). Additionally, they showed that conditions (24) and (26) for accuracy and stability will still hold true (condition (25) does not apply to the first-order problem because when the Y Y Y variables are dropped, the parameter β plays no role in the algorithm). The generalized-α algorithm permits optimal high-frequency dissipation by parameterizing α m and α f in terms of the spectral radius of the amplification matrix as ∆t → ∞, namely ̺ ∞ .…”

“…(23). Additionally, they showed that conditions (24) and (26) for accuracy and stability will still hold true (condition (25) does not apply to the first-order problem because when the Y Y Y variables are dropped, the parameter β plays no role in the algorithm).…”

“…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].…”

Shape memory alloy nanostructures with coupled dynamic thermo-mechanical effects

“…However, the influence of different strain rates on microstructure and mechanical response of FePd samples on temperature-and stress-induced PTs was examined by using exclusively 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].…”