A non-isothermal phase-field model for shape memory alloys: Numerical simulations of superelasticity and shape memory effect under stress-controlled conditions

Abstract

A phase-field–based model has been employed for numerical tests on the mechanical response of a shape memory alloy. The model consists of a time-dependent Ginzburg–Landau equation for a scalar order parameter describing the local phase of the material (austenite or martensite), coupled with the balance of linear momentum and the heat equations; the mechanical effect of the martensitic phase transition is described in terms of a uniaxial deformation strain along a fixed direction, making the model suited for predictions over monodimensional specimens. A number of numerical simulations under stress-controlled conditions have been performed to investigate the mechanical behaviour of the model; the results obtained are analysed in relation to the experimental evidences available in the literature and previous investigations under strain-controlled conditions.

A three-dimensional non-isothermal Ginzburg–Landau phase-field model for shape memory alloys

“…The area under the σ 11 -ǫ 11 curve remains constant. These results are consistent with the results reported in the literature [38,28,37].…”

“…Thus the constitutive equations not only relate the σ σ σ and ǫ ǫ ǫ, but also the φ. The common methodology to achieve this is to decompose strain into the elastic and phase transformation components [14,19,20,21,23,28,37]. We too follow this methodology, however, we allow to account the different forms of dependencies of compliance on φ and σ σ σ.…”

“…We assume the plane stress formulation with a consideration that the thickness is small as compared to the other dimensions. For simplicity, we adopt the quasistatic approximation under the assumption that the timescales of thermal dynamics and phase evolution phenomenon are larger than the stress wave time scale [28,37]. We neglect the non-linear effect of λ λ λ 3 and λ λ λ 4 compliance tensors.…”

“…A point to be noted in Eq. ( 9) that the phase transformation is governed by the stress tensor σ σ σ as opposed to the transformation strain tensor described, e.g., in [14,19,20,21,23,28,37].…”

Atomistic simulation of shape memory effect (SME) and superelasticity (SE) in nano-porous NiTi shape memory alloy (SMA)

“…Numerical modeling of SMAs, based on the phenomenological constitutive relation are reported in the literature [18][19][20][21][22][23]. Other mesoscopic/ microscopic models for porous NiTi include those reported in [24,25], and some of them are developed from phase-field theory [26,27]. Significant level of experimental studies [28][29][30][31] are also reported that explore the phase transformation and superelasticity property of SMA, under a wide range of constant and gradient porosity.…”