A Probabilistic Approach to Investigate the Size and Boundary Condition Effects on the Fracture Response of Brittle Materials Loaded in Diametral Compression

Abstract

The focus in this work is toward an investigation of the fracture response of brittle materials with different specimen size loaded in diametral compression using different boundary conditions. The compacted zone underneath the loading points is assumed to be limited and only responsible for the load transition to the rest of the material. Therefore, the theory of elasticity is used to define the stress state within a circular specimen. A tensile failure criterion is used, and the final load capacity is related to the formation of a subsurface crack initiated in a probabilistic manner in a region in the vicinity of the loaded diameter of the specimen. This process is described by Weibull theory, and it is assumed here that the growth of the subsurface crack occurs in an unstable manner. Therefore, the assumption in Weibull theory that the final failure occurs as soon as a macroscopic fracture initiates from a microcrack is fulfilled. The concept of disk effective volume used in Weibull size effect is presented in a convenient way that facilitates the application of the model to transfer the tensile strength obtained from different methods such as three point bending and Brazilian test. The experimental results for Brazilian test on a selected hard rock are taken from the literature and a fairly close agreement is obtained with the model predictions.