Variational phase-field modeling of fracture and fatigue in shape memory alloys

TL;DR

This work introduces a variational phase-field framework for fracture and fatigue in pseudoelastic shape memory alloys within a 1D setting, anchored to the Auricchio–Petrini constitutive model. A key feature is a transformation-strain limit $\varepsilon_L$ that causes damage to diffuse over a fully transformed region, delaying fracture and enabling realistic fatigue predictions under cyclic loading. The model couples phase transformation and damage through damage-dependent SMA parameters, yielding a gradient-damage energy functional and an energy-balance–driven evolution. Validation against Ni-Ti multi-wire experimental data shows good agreement in fatigue life predictions and the ability to discriminate safe from critical loading conditions, highlighting the framework’s potential for SMA fatigue assessment and design optimization.

Abstract

We propose a novel variational phase-field model for fracture and fatigue in pseudoelastic shape memory alloys (SMAs). The model, developed in a one-dimensional setting, builds upon the Auricchio-Petrini constitutive formulation for SMAs and couples damage evolution with phase transformation. We study analytically and numerically the homogeneous and localization responses of a bar under both monotonic and cyclic loading, and we investigate various macroscopic behaviors by tuning the constitutive parameters. A key feature of the model is the introduction of a transformation strain limit, beyond which the material is fully martensitic and behaves elastically. This leads to a distinctive behavior in which the region of localized damage widens, yielding a delay of fracture. The capability of the model to predict the fatigue performance is demonstrated by simulating the uniaxial response of Ni-Ti multi-wire samples under different loading conditions. The results show promising agreement with experimental fatigue life data, enabling the discrimination between safe and critical loading scenarios.

Figures (17)

• Figure 1: Characteristic thermomechanical behavior of SMAs: (i) pseudoelasticity above the austenite finish temperature $A_f$ allowing large stress-induced strain recovery, and (ii) shape memory effect allowing the recovery of the original shape after deformation in the martensitic phase below the martensite finish temperature $M_f$.
• Figure 2: Homogeneous response for the E-T-D model under monotonically increasing strain: a) evolution of the forward transformation stress, damage stress, stress, transformation strain, and damage; b) forward transformation (red) and damage (green) yield surfaces with the evolution path depicted in blue.
• Figure 3: Homogeneous response for the E-T-TD model under monotonically increasing strain: a) evolution of the forward transformation stress, damage stress, stress, transformation strain, and damage; b) forward transformation (red) and damage (green) yield surfaces with the evolution path depicted in blue.
• Figure 4: Possible loading and unloading paths for the a) E-T-D model and b) E-T-TD model. The stress reached during loading for different final strains and the corresponding unloading curves are represented in blue and black, respectively. The value of the reverse transformation stress for the different paths is plotted in red. The figures in the upper right corners depict the evolution of the strain during loading (blue) and possible unloading (black).
• Figure 5: Localized response for the E-T-D model with $l=0.15$: a) stress-displacement diagram; b) energy diagrams; c) damage, d) transformation strain, and e) displacement profiles along the bar at different loading steps.