On the link between fracture toughness, tensile strength, and fracture process zone in anisotropic rocks

This paper presents experimental results on the anisotropy of the fracture toughness, Brazilian tensile strength, and the fracture process zone (FPZ) in granodiorite samples. The fracture toughness is measured using semi-circular bending tests, while Brazilian disk tests were conducted to measure the tensile strength indirectly. Digital image correlation (DIC) was employed to obtain full-field surface deformation associated with the fracture propagation and identify the FPZ. An averaging scheme is proposed to determine the length and width of the FPZ from the strain field. The DIC results confirm a semi-elliptical FPZ developing ahead of the crack tip, with an average length-to-width ratio of approximately two. The results also indicate that the theoretical models such as Irwin and strip-yield with uniform traction, which are based on plastic deformation near the crack tip, underestimate the extent of the inelastic zone, while the stripyield model with a linear cohesion stress distribution overestimate the length of the process zone. The anisotropy ratio of the FPZ length obtained from the models, however, agrees very well with the ratio obtained from the DIC measurements. This evidence supports the basis of the theoretical models that predict the FPZ length to be proportional to the square of fracture toughness over tensile strength.