An Asymmetric Elasto-Plastic Phase-Field Model for Shape Memory Effect, Pseudoelasticity and Thermomechanical Training in Polycrystalline Shape Memory Alloys

We propose an elasto-plastic phase-field model (PFM) to conduct the first microscopic computational study of shape memory effect (SME), pseudoelasticity, stress assisted two-way memory effect (SATWME), and thermomechanical training of CuAlBe shape memory alloy (SMA). This non-isothermal PFM model considers the effects of temperature dependent properties, latent heat, grain boundaries, and asymmetric transformation and plasticity. PFM simulations demonstrate the capacity of our model to capture the thermomechanical and purely mechanical shape recovery in the SMA. When considering transforming grain boundaries, grain refinement generates a higher transformation stress, a steeper transformation hardening, and smaller hysteresis loops for both SME and pseudoelasticity. The results also point out slightly higher transformation stress when geometrical grain boundaries are used. The simulations of SATWME highlight an augmentation of the residual martensite as the hold stress increases, which is consistent with experimental observations. This is the first PFM that can mimic the thermal training within several SATWME cycles, showing an asymptotic increase of plastic strain and the related retained transformation strain until the fourth cycle, and their stabilization thereafter. The activation of plasticity occurs always after initiation of phase transformation. Although plasticity results in more stress relaxation, it deteriorates the shape recovery for both SME and pseudoelasticity by hindering the reverse transformation. Comparison between tension and compression demonstrates the capacity of this PFM to account for, for the first time, the nonsymmetrical transformation and plastic responses of SMAs.