Modelling fracture process zone width and length for quasi-brittle fracture of rock, concrete and ceramics

The crack-tip fracture process zone (FPZ) length with distributed cohesive stresses is commonly modelled for quasi-brittle fracture of heterogeneous solids. This study highlights the crack-tip blunting effect from FPZ width since FPZ(W) > FPZ(L) at the peak fracture load. Both FPZ width and length are linked to the microstructure (grain size for rock and ceramics, aggregate size for concrete, atomic diameter for single crystal silicon), providing a fresh perspective on quasi-brittle fracture phenomena. Importantly, FPZ(W) at the peak fracture load bridges the gap between the fracture toughness K-IC and tensile strength f(t), i.e. K-IC <-> FPZ(W) <-> f(t). The influence of a blunt notch on quasi-brittle fracture can also be explained by a widened FPZ(W). A closed-form model containing both FPZ(W) and FPZ(L) (approximately FPZ(W)/FPZ(L) approximate to 2 at the peak fracture load) is used to analyse experimental data of rock, concrete and ceramic with macro-/micro-sized FPZ, and single crystal silicon with FPZ-like critically stressed atomic bonds in front of atomic scale defects.