Thermodynamically consistent non-isothermal phase-field modelling of elastocaloric effect: indirect vs direct method

Abstract

Modelling elastocaloric effect (eCE) is crucial for the design of environmentally friendly and energy-efficient eCE based solid-state cooling devices. Here, a thermodynamically consistent non-isothermal phase-field model (PFM) coupling martensitic transformation with mechanics and heat transfer is developed and applied for simulating eCE. The model is derived from a thermodynamic framework which invokes the microforce theory and Coleman-Noll procedure. To avoid the numerical issue related to the non-differentiable energy barrier function across the transition point, the austenite-martensite transition energy barrier in PFM is constructed as a smooth function of temperature. Both the indirect method using isothermal PFM with Maxwell relations and the direct method using non-isothermal PFM are applied to calculate the elastocaloric properties. The former is capable of calculating both isothermal entropy change and adiabatic temperature change (∆T ad ), but induces high computation cost. The latter is computationally efficient, but only yields ∆T ad . In a model Mn-22Cu alloy, the maximum ∆T ad (∆T max ad ) under a compressive stress of 100 MPa is calculated as 9.5 and 8.5 K in single crystal (3.5 and 3.8 K in polycrystal) from the indirect and direct method, respectively. It is found that the discrepancy of ∆T max ad by indirect and direct method is within 10% at stress less than 150 MPa, confirming the feasibility of both methods in evaluating eCE at low stress. However, at higher stress, ∆T max ad obtained from the indirect method is notably larger than that from the direct one. This is mainly attributed to that in the non-isothermal PFM simulations, the relatively large temperature increase at high stress could in turn hamper the austenite-martensite transition and thus finally yield a lower ∆T ad . The results demonstrate the developed PFM herein, combined with both indirect and direct method for eCE calculations, as a practicable toolkit for the computational design of elastocaloric devices.