On the anisotropy of shear fracture toughness in rocks

Highlights

• We experimentally analyse the anisotropy of true mode II fracture toughness in rocks.

• Shear fracture toughness is shown to follow a sinusoidal variation.

• A simplified relationship between fracture toughness and fracture energy is presented.

• True mode II fracture toughness is noticeably greater than mode I fracture toughness.

• The fracture process zone of a true mode II crack is of a semi-elliptical shape.

Abstract

Experimental and theoretical analyses are presented that assess true mode II fracture toughness, $K_{\mathrm{IIc}}$, fracture energy, ${\mathcal{G}}_{\mathrm{IIc}}$, and associated fracture process zone (FPZ) in anisotropic rocks. The term true signifies the type of mode II crack that grows in a self-planar manner as a result of shear stresses, and thus differentiates it from a generic mode II crack that often extends by forming a tension-induced kink. We give the theoretical basis for the sinusoidal variation of $K_{\mathrm{IIc}}$, and present simplified relations for the direction dependence of the ${\mathcal{G}}_{\mathrm{IIc}}$ in an anisotropic plane. Our experimental data on anisotropic Grimsel Granite validate this theoretical model, thereby providing supporting evidence that $K_{\mathrm{IIc}}$ of this rock type indeed follows a sinusoid function. This model takes only two principal values of $K_{\mathrm{IIc}}$ to characterise fracture toughness and energy in any direction within an anisotropic plane. Our analyses also show that the values of $K_{\mathrm{IIc}}$ and ${\mathcal{G}}_{\mathrm{IIc}}$ are noticeably higher than the ones of mode I, and one must distinguish between these toughness values when formulating growth criteria in rocks. Lastly, a thorough analysis of the strain localisation obtained from the digital image correlation data gives insight on the nature of the FPZ, and demonstrates that the FPZ of a true mode II crack is of a semi-elliptical shape and has a comparable size with the one of a mode I crack.