Phase-field modeling of cyclic behavior in quasi-brittle materials: a micromechanics-based approach

TL;DR

The paper addresses fatigue and cyclic failure in quasi-brittle materials by extending a micromechanics-based phase-field framework to capture ratcheting-driven cyclic plasticity within a thermodynamically consistent variational formulation. It introduces a three-field model coupling displacement, crack phase-field $\alpha$, plastic strain $\bm{\varepsilon}^{\mathrm{p}}$, and ratcheting strain $\bm{\varepsilon}^{\mathrm{r}}$, with a free energy that distinguishes open vs closed microcracks and a non-associated plastic flow that explicitly accounts for ratcheting. Key contributions include the incorporation of fatigue via a history-dependent degradation function $h(\mathcal{F})$ and two fatigue laws (asymptotic and logarithmic), a regularized, mode-sensitive fracture energy $G_c$ across $\mathrm{tr}(\bm{s}^{\mathrm{p}})$, and a robust dissipation framework that preserves thermodynamic admissibility. The approach is validated through monotonic and cyclic three-point bending, high-cycle fatigue of a single element to produce $S$-$N$ curves, and material-point and perforated-specimen simulations illustrating ratcheting behavior and damage localization, demonstrating the model’s versatility for design under complex cyclic loading.

Abstract

In this paper, we extend the micromechanics-based phase-field modeling of fatigue fracture to capture cyclic plasticity with ratcheting. This mechanism is particularly important for low-cycle fatigue, where the accumulation of inelastic strains plays an important role in the progression to final failure. The ratcheting contribution is formulated through the evolution of ratcheting strain, which accumulates over loading cycles and captures the inelastic strain growth characteristic of cyclic plasticity in a thermodynamically consistent manner. The extended plastic potential allows independent control over deviatoric and volumetric ratcheting components. Numerical simulations are performed to evaluate the model under both monotonic and cyclic loading and to assess the influence of ratcheting on material response.

Figures (18)

• Figure 1: Schematic representation of the continuum solid (left), the RVE consisting of a matrix-inclusion system with microcracks (middle), and the orientation of a penny-shaped microcrack (right) (adapted from Ulloa et al. ulloa2022a).
• Figure 2: 1D rheological representation of elastoplastic-ratcheting model
• Figure 3: Asymptotic degradation function () and logarithmic degradation functions for $k=1$ (), $k=0.5$ () and $k=0.2$ ().
• Figure 4: Regularized fracture energy.
• Figure 5: Boundary conditions of a centrally notched concrete beam subjected to three-point bending.