Relationship between fracture and friction for brittle rocks

We fit a recently proposed failure criterion to experimental data for fracture and friction strength of various rocks. The criterion rests on the Cardano condition for the existence of three real-valued eigenvalues of the characteristic equation of the stress tensor and specifically addresses the non-linear dependence of fracture and friction on increasing mean stress. The approach provides a theoretical link between macroscopic fracture of a continuum and sliding friction on a pre-existing interface. The criterion rests on three fit parameters whose physical meaning is investigated by fitting previously published data of rocks characterized by differences in composition, porosity, and grain size. In all investigated cases the friction characteristics predicted from the fit of fracture strength data excellently fit independent experimental friction data. Of the three fit parameters, one appears to be determined by the stress concentrations associated with pores and an intrinsic, composition-dependent strength parameter of the constituents, such as mineral-hardness. The second parameter scales inversely with grain size and represents the tensile strength of the polycrystalline aggregates. Mostly owing to the lack of explicit tensile strength or extension data, the third parameter quantifying the pressure-dependence at very low mean stresses remains poorly constrained. It appears affected by composition or the geometric distribution of phases. Fitting macroscopic failure accompanied by pressure-insensitive, crystal plastic deformation mechanisms, such as mechanical twinning in marbles, requires much lower values of the third parameter than purely brittle deformation.