A macroscale phase-field model for shape memory alloys with non-isothermal effects: Influence of strain rate and environmental conditions on the mechanical response

Abstract

A Ginzburg–Landau model for the macroscopic behaviour of a shape memory alloy is proposed. The model is essentially one-dimensional, in that we consider the effect of the martensitic phase transition in terms of a uniaxial deformation along a fixed direction and we use a scalar order parameter whose equilibrium values describe the austenitic phase and the two martensitic variants. The model relies on a Ginzburg–Landau free energy defined as a function of macroscopically measurable quantities, and accounts for thermal effects; couplings between the various relevant physical aspects are established based on thermodynamic principles. The theoretical model has been implemented within a finite-element framework and a number of numerical tests are presented which investigate the mechanical behaviour of the model under different conditions; the results obtained are analyzed in relation to experimental evidence available in the literature. In particular, the influence of the strain rate and of the ambient conditions on the response of the model is highlighted

NiTi‐Based Elastocaloric Cooling on the Macroscale: From Basic Concepts to Realization

“…Key parameters for cooling are the local temperature evolution combined with the local stress–strain behavior, which include amongst others the phase front formation and the thermal conductivity. Some models use a localization effect and a non‐local extension in order to recreate the localized phase transformations and continuous transitions between austenitic and martensitic regions …”

“…Therefore,l ocal effects are important to calculatet he exact absorbed heat and with this the cooling efficiency of material and devices.K ey parameters for cooling are the local temperature evolution combined with the local stressstrain behavior, which include amongst others the phase front formationa nd the thermal conductivity.S ome models use al ocalizatione ffect and an on-local extension in order to recreatet he localized phase transformations and continuous transitions between austenitic and martensitic regions. [18,60,[97][98][99] Thermomechanically coupledf inite element simulations based on an extended version of the 1D Müller-Achenbach-Seelecke( MAS)m odel [91,92] have been conducted on actuator wires, [100] superelastic wires, [101] and beams. [55,102] Other1 D simulations of actor wires [18,103] have been based on the approach proposed by Shaw and co-workers.…”

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

“…Now, we summarize all the governing partial differential equations and constitutive relations for the above model as along with the boundary conditions (refer to Fig. 3 for the boundary nomenclature) n n n · ∇φ Γ Γ Γ = 0, u u u Γ 1 = 0 0 0, n n n · ∇σ σ σ Γ 2,3 = 0, n n n · ∇σ σ σ Γ 4 =σ σ σ, n n n · ∇θ Γ Γ Γ = h(θ − θ ext ), (28) where h is the heat transfer coefficient and θ ext is the external environment temperature. The initial conditions are defined as…”

“…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.…”

“…The model is now studied here by incorporating the full thermo-mechanical coupling and phase evolution equations. In addition, the model is simulated with the material properties of the Ni 55 Ti 45 specimen [38,28].…”