KINETIC INSTABILITIES DURING THE PROPAGATION OF A BRANCH CRACK - EFFECTS OF LOADING CONDITIONS AND INTERNAL-PRESSURE

In order to understand the physical processes controlling the formation of various branch features stemming from pre-existing defects in rocks, this paper presents a model based on fracture mechanics concepts. We examine the consequences of the elastic stress field around an open oblique elliptical defect subjected to constant uniaxial or biaxial stress on the kinetics of the classical branch crack. Assuming that propagation does not fundamentally change the elastic stress field, the strain energy release rate, G, is computed for each branch crack length, L, by integrating the values of the principal stress acting perpendicular to the stress trajectory of the other principal stress, starting exactly from the point of maximum tensile stress at the edge of the elliptical defect. The propagation regime depends on the slope of the G(L) curve and on its position with respect to the equilibrium value G(o) and the critical value G(c), for which catastrophic rupture occurs. Without internal pressure, the unimodal curves predict three possible successive propagation regimes: (1) stable propagation with increasing velocity; (2) catastrophic propagation with velocity jump and associated acoustic emission; and (3) stable propagation with decreasing velocity. The catastrophic regime is limited to high load values. Experimentally, the triggering of the propagation can be very difficult to predict, as it depends on slight variations in the length of pre-existing microcracks stemming from the elliptical defect at the root of the branch crack path. With internal pressure, the stress field is modified so that the maximum tensile stress is present at some distance from the edge of the elliptical defect. This can result in a change in the shape of G(L) curves which indicates that two independent velocity jumps may occur: the first one is mainly linked to the local influence of the defect, the second (leading to a large extension) is due to the general influence of the internal pressure.