A phase-field length scale insensitive micropolar fatigue model

Abstract

This article proposes a novel micropolar phase-field model for size-dependent fatigue failure in solids under mechanical loading. To develop the proposed model that can capture experimentally observed size effects in brittle materials, we employ micropolar theory in a phase-field length scale-insensitive framework and address the limitations of classical phase-field fatigue models. A key advantage of the proposed model is its ability to eliminate artificial nonlocal effects introduced by the phase field length scale while preserving the physical size effects dictated by the material microstructure. In the proposed model, we introduce micro-rotation as an additional kinematic variable and derive the governing partial differential equations by invoking the principle of virtual power. The constitutive relations are established in accordance with thermodynamic laws, enabling the incorporation of dissipative effects whenever required. To make the proposed model insensitive to the phase-field length scale and thus eliminate artificial nonlocal effects, we incorporate a fatigue-related parameter that defines the fatigue threshold energy as a function of the material fracture strength. We demonstrate the efficacy of the proposed model through numerical simulations on a set of benchmark two- and three-dimensional problems that include three-point bending tests, single-edge notched plates, etc., and provide a qualitative experimental validation against the results available in the literature. The numerical results show a significant influence of the micropolar parameters on fatigue behavior, emphasizing the necessity of the proposed formulation for materials that exhibit pronounced nonlocal effects. We demonstrate the insensitivity of the proposed model to the phase-field length scale using plots of consistent crack growth versus the number of cycles for different values of the phase-field length scale. For the numerical implementation of the proposed model, we use an open-source finite element library called Gridap, available in Julia, a recently developed high-performance programming language. The availability of open-source codes ensures transparency, reproducibility, and ease of verification, setting a high standard for open-source computational tools in scientific research. The numerical findings validate the robustness of the proposed model, establishing its suitability for accurately simulating size-dependent fatigue behavior in materials.