A MICROCRACK MODEL OF ROCK INELASTICITY PART II: PROPAGATION OF MICROCRACKS

The second stage of inelasticity-kinking and propagation of secondary (dilatant) microcracks-is considered in the framework of the model introduced in Part I (Kachanov, this issue). Three-dimensional problem of branched penny-shaped crack is treated as a set of two-dimensional cross-sections. On the basis of the analysis of results for a kinked crack, modified with account of pressure, normal to the kink, simple expressions for the microstrains associated with a propagation of a branched crack are derived. The macroscopic stress strain relations obtained by averaging over the crack orientations provide a description of many inelastic effects. Association of the onset of dilatancy with the onset of microcrack propagation allows one to estimate fracture toughness of the material: the estimates of K(IC) thus obtained are in a reasonable agreement with the commonly accepted values. However. dilatancy. predicted by the model, is much lower than the experimentally observed values. A modified version of the model, incorporating uplifting at asperities as an additional mechanism of dilatancy. is introduced. It provides a generally satisfactory description of experimental data. It should be noted that this version introduces an uncertainty at,out the first stage of inelasticity (Part I) and the association of the onset of dilatancy with initiation of crack growth.