Intrinsic Length Scales in Tool-Rock Interaction1

Indentation and cutting experiments in rocks reveal that the action of a tool can induce either ductile and/or brittle failure, with the ductile mode associated with damage of the rock and/or plastic flow, and the brittle mode with the propagation of cracks. In normal indentation, the development of a damaged zone precedes the initiation of tensile cracks; in cutting, the failure mechanism switches from a ductile to a brittle mode as the depth of cut is increased beyond a threshold value. In this paper, we first argue that these observations can be accounted for by introducing an intrinsic length scale ${\mathcal{l}}_m\sim {(K_{\mathrm{Ic}}∕{\sigma }_c)}^2$ in the rock description (with $K_{\mathrm{Ic}}$ denoting the toughness and ${\sigma }_c$ the compressive strength). Next, we report the results of numerical simulation of indentation and cutting tests with the discrete element method. After showing that the internal length scale ${\mathcal{l}}_m$ can be modified by the ratio of the shear to normal bond strength, we illustrate by numerical simulations that the selection of the failure mode can indeed be controlled by varying ${\mathcal{l}}_m$ .