Hierarchical scaling model for size effect on tensile strength of polycrystalline rock

Abstract

Here, we proposed an analytical model for quantifying the intriguing size-dependent tensile strength of polycrystalline rock, i.e. first ascending then descending with the increase of specimen size. The meso‑structure of polycrystalline rock was firstly degraded to a hierarchical arrangement of regularly cuboid mineral grains. The tensile strength distribution of mineral grain interface (GI) is modeled by Weibull distribution, and the stress state near the failed GI is analytically calculated. Then a probabilistic analysis of the failure evolution in hierarchical mineral grain sets (sets of sets) was performed by considering the meso crack initiation at the GI to their propagation at macro scale, so that the tensile strength distribution and the meso crack accumulation in the rock specimen can be derived. The consistency between the model predictions and experimental results demonstrates the proposed model is valid. In addition, the results revel that the size effect trend, ascending or descending, is determined by the dispersion degree of structure strength distribution.