A Discrete Element Model for Damage and Fatigue Crack Growth of Quasi-Brittle Materials

Xiaofeng Gao,Cyrille Chazallon,Georg Koval

doi:10.1155/2019/6962394

Abstract

The repeatedly applied low-intensity loads would lead to the damage and fatigue crack growth of mechanical structures made of quasi-brittle materials. In numerical modelling, these two mechanisms are normally treated differently and separately; the damage is usually associated with nonlocal approaches, while the fatigue crack growth is related to the local stress intensity range at the crack tip. In this study, a discrete element model for damage and fatigue crack growth of quasi-brittle materials is proposed, which is able to model the damage and fatigue crack growth simultaneously in one single model. The proposed model achieves the implementation of a continuum damage model in a discrete element code, which is a helpful enrichment of this numerical method. The evaluation method of the stress intensity range during the damage evolution provides a way to couple both failure mechanisms. This feature allows crack initiation to be induced by localized damage and a progressive transition to a fracture behaviour with the crack propagation. Independent parameters for the fatigue damage model and fatigue crack growth model are admitted without any previous calibration. The numerical results are in good agreement with the theoretical predictions of damage and fracture mechanics, and intact and precracked samples are analysed under fatigue loading to show the consistent coexistence of fractured and damaged zones in a single model.

Highlights

Academic Editor: Pasquale Gallo e repeatedly applied low-intensity loads would lead to the damage and fatigue crack growth of mechanical structures made of quasi-brittle materials
A discrete element model for damage and fatigue crack growth of quasi-brittle materials is proposed, which is able to model the damage and fatigue crack growth simultaneously in one single model. e proposed model achieves the implementation of a continuum damage model in a discrete element code, which is a helpful enrichment of this numerical method. e evaluation method of the stress intensity range during the damage evolution provides a way to couple both failure mechanisms. is feature allows crack initiation to be induced by localized damage and a progressive transition to a fracture behaviour with the crack propagation
Independent parameters for the fatigue damage model and fatigue crack growth model are admitted without any previous calibration. e numerical results are in good agreement with the theoretical predictions of damage and fracture mechanics, and intact and precracked samples are analysed under fatigue loading to show the consistent coexistence of fractured and damaged zones in a single model

Summary

Damage and Fatigue Crack Growth Models

Evolution of damage (local version of the model) is controlled by the strain state of the material by a scalar equivalent strain, which can be written as follows:. Paris’ Law. Fatigue crack growth in a wide variety of brittle and quasi-brittle materials [50,51,52] is described well by the well-known Paris (or Paris–Ergodan) law [49], which relates the stress intensity factor range ΔK to the crack growth rate da/dNc via a power law, with ΔK Kmax − Kmin. Paris’ law works for sufficiently large cracks, where ΔK is higher than the fatigue threshold ΔKth, and the maximum value of the stress intensity factor Kmax remains below the material fracture toughness Kc. 3. This direct relationship can be found in [56, 61]

De nition of Strain and Stress in a Discrete Medium

Discrete Element Fatigue Damage Model

Coupled DEM Model for Damage and Fatigue Crack Growth

Numerical Modelling Results for a Center Cracked Plate