A phenomenological approach to fatigue with a variational phase-field model: The one-dimensional case

A framework to model the fatigue behavior of brittle materials based on a variational phase-field approach

“…To introduce the fatigue effects, we propose to modify the fracture energy density similarly to [36] as follows…”

“…In the present paper we propose a novel approach to model the fatigue behavior of brittle materials based on variational phase-field modeling of fracture. The first 1-D investigation has been reported in [36] and the existence of quasi-static evolutions with a vanishing viscosity approach studied in [37]. As in [36] we modify the free energy potential of the monotonic case introducing a suitable fatigue history variable and a fatigue degradation function that modifies the rate of the dissipated energy accounting for the fatigue loading history.…”

“…The first 1-D investigation has been reported in [36] and the existence of quasi-static evolutions with a vanishing viscosity approach studied in [37]. As in [36] we modify the free energy potential of the monotonic case introducing a suitable fatigue history variable and a fatigue degradation function that modifies the rate of the dissipated energy accounting for the fatigue loading history. The proposed approach aims at linking regularized monotonic fracture mechanics to fatigue crack growth establishing a framework suitable for any type of (brittle) materials.…”

On phase field modeling in the context of cyclic mechanical fatigue

“…To handle this issue in [4] and [5] fatigue crack growth was simulated by a degradation of the critical energy release rate once an accumulated strain measure or the fatigue damage, respectively, increases. As mechanisms of the fatigue phenomenon occur already at comparatively very low load levels, a minimizer for (1) will not include a decrease of s at any location even if huge cycle numbers are simulated.…”

Phase field modeling of chemomechanical fracture of intercalation electrodes: Role of charging rate and dimensionality

“…These models have been validated by theoretical analyses [24] and comparisons of predicted and observed crack paths in non-trivial geometries [25]. They have been used to reproduce complex experimental observations in brittle fracture including thin-film fracture [26], thermal fracture [20], mixed mode fracture [27], dynamic fracture [27,28,29], fracture in colloidal systems [30], ductile fracture [31,32,33,34], and fatigue fracture [35,36,37]. Given their potential over the past few years, researchers have extended the use of these models to chemo-mechanical fracture in battery particles [38,39,40,41].…”