Influence of material heterogeneities on crack propagation statistics using a Fiber Bundle Model

The problem of damage in heterogeneous materials has received particular attention in recent years. The numerical models currently used in the simulation of damage require an internal length that is not currently related to a characteristic length of the material components. However, understanding damage regarding the size of the heterogeneities of the material is of crucial importance, particularly in civil engineering. The Fiber Bundle Model has been widely used to qualitatively address the issue of damage in heterogeneous media by studying the statistics of failure events during damage. The so-called ZIP model derives from Fiber Bundle Model to mimic crack propagation. In this work, a spatial correlation of tensile strength of fibers is added to the ZIP model to highlight the role of heterogeneity size in statistics of failure events during crack propagation. The addition of spatial correlation into the ZIP model modifies the distribution of failure events. Indeed, for a simulated material without spatial correlation, failure events follow two regimes. By adding a spatial correlation to the material, a transitional regime appears. The influence of spatial correlation on fiber rupture avalanche strongly depends on the ratio between the sizes of the shapes of the stress field and of the heterogeneities.