Process zone and size effect in fracture testing of rock

Fracture of rock involves formation of a localized region of damage or cohesive process zone, which controls size effects on strength and stability. Therefore, any attempt in predicting size of process zone is of prime importance in fracture study of quasi-brittle materials. In this paper, an approximate theoretical relationship between size of process zone and specimen size is proposed. The appropriateness of this relationship is examined by conducting a discrete element analysis of rock fracture. A softening contact bond model is used to study the process zone around a notch tip in three point bending tests. The numerical analysis is utilized to obtain the nominal tensile strength, apparent fracture toughness, and width of process zone. It is shown that the apparent fracture toughness is a function of the specimen size, and that the change in nominal tensile strength with specimen size can be captured by Bazant's size effect law. In addition, both the theoretical arguments and the numerical results suggest that the inverse of width of the crack tip process zone has a linear relationship with the inverse of specimen size. The numerical results indicate a stronger relationship between width of process zone and specimen size for a material with a larger value of characteristic size. On the other hand, for a brittle material, specimen size has a small or no impact on the size of the process zone.