The avalanche process of the fiber bundle model with defect

In order to explore the impacts of defect on the tensile fracture process of materials, the fiber bundle model with defect is constructed based on the classical fiber bundle model. In the fiber bundle model with defect, the two key parameters are the mean size and the density of defects. In both uniform and Weibull threshold distributions, the mean size and density all bring impacts on the threshold distribution of fibers. By means of analytical approximation and numerical simulation, we show that the two key parameters of the model have substantial effects on the failure process of the bundle. From macroscopic view, the defect described by the altering of threshold distribution of fibers will has a significant impact on the mechanical properties of the bundle. While in microscopic scale, the statistical properties of the model are still harmonious with the classical fiber bundle model.