This article discusses the scale dependence of the mode $$\mathrm {I}$$ I fracture toughness of rocks measured via the semi-circular bend (SCB) test. An extensive set of experiments is conducted to scrutinise the fracture toughness variations with size for three distinct rock types with radii ranging from 25 to 300 mm. The lengths of the fracture process zone (FPZ) for different sample sizes are measured using the digital image correlation (DIC) technique. A theoretical model is also established that relates the value of fracture toughness to the sample size. This theorem is based on the strip-yield model to estimate the length of FPZ, and the energy release rate concept to relate the FPZ length to the fracture toughness. This theoretical model does not rely on any experimental-based curve-fitting parameter, but only on the tensile strength of the rock type as well as the fracture toughness at a specific sample size. The size effects predicted by the theoretical model is in a good agreement with the experimental data on both fracture toughness and the FPZ length. Finally, theoretical correction factors are introduced for various geometrical configurations of the SCB specimen, using which a scale-independent mode $$\mathrm {I}$$ I fracture toughness of the rock material can be estimated from the results of experiments performed on small samples.

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This paper presents the analytical solution of the crack tip fields as well as the crack parameters in an infinitely large composite plate with a central crack subjected to pure shear loading. To this end, the complex variable method is employed to formulate an asymptotic solution for the crack tip fields in an anisotropic plane. Using a stress-based definition of the crack tip modes of loading, only the mode II crack parameters are found to be non-zero under pure shear load. Special focus is given to the determination of the higher order parameters of the crack tip asymptotic field, particularly the first non-singular term, ie, the T-stress. Unlike the isotropic materials, in which the T-stress is zero under pure shear, it is found that the T-stress is non-zero for the case of anisotropic materials, being the only material-dependent crack tip stress parameter. The veracity of our exact crack tip fields is assessed and verified through a comparison made with respect to the finite element (FE) solution. Finally, we demonstrate the significance of the T-stress on stresses near the crack tip in composite plates under pure shear loads.

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