Influence of cluster shaped defects on fracture process of fiber bundle

Abstract

Defects that exist inside composites have an important effect on the tensile fracture properties of composites. The fiber bundle model is a theoretical model commonly used to study the tensile fracture properties of disorder materials. Existing work on fiber bundle models with single fiber defects shows that after single fiber defects are introduced into the fiber bundle model, the defects have a significant effect on the tensile fracture properties of the model. Since there are more complex microscopic defect structures in actual materials, such as voids, gaps, impurities, dislocations, micro-cracks, etc, it is necessary to build a multi-size defect model. In order to study the defects of different sizes and damage degrees existing in actual materials, the spatial size of the defect, the degree of defect and the distribution of fiber damage levels within the defect and other influencing factors are introduced to construct an extended fiber bundle model with cluster shaped defects. For the model, it is first assumed that the degree of defect of the fiber inside each cluster decays linearly from the center to the outside in two spatial attenuation forms: exponential decay and constant degree of defect. In the fiber bundle model of this cluster-shaped defect, the two most important factors are the number of defects <i>α</i> and the upper limit of defect size <i>β</i>. The numerical simulation method is used to analyze the influence of the number of defects, the upper limit of defect size, and spatial distribution of degree of defective fibers inside defect on the macroscopic mechanical properties and statistical properties of fracture when the model is subjected to quasi-static load borne under the nearest neighbor stress redistribution. Through the simulation analysis, it is found that owing to the overlapping competition mechanism of the defect spatial distribution, when the upper limit <i>β</i> of the defect size is large, the influence of the number of defects on the system load capacity trends to saturation. Since the defect degree of the defect center fiber is proportional to the defect size, with the upper limit <i>β</i> of the defect size increasing, its influence on the load capacity of the model becomes more and more significant. When large size defects exist, even if the number of defects is small, the load bearing performance of the material will be significantly reduced. The spatial distribution function of the damage degree of fiber inside the defect has no substantial influence on the above rules, and only changes the specific value of each fracture property. The simulation analysis results in this paper have certain theoretical significance in improving the mechanical properties of composite materials.