Mechanism Of Rock Cracking Under Indentation And Primary Investigation On Spacing Optimization

Experiments have indicated that when brittle materials are under indentation,various forms of cracks including median crack, ring crack, Hertzian crack and side(lateral) crack nucleate leading to the fragmentation. The lateral cracking underindentation can be attributed to unloading and plays a crucial role in formation ofchips. Based on the mechanism of the lateral cracking, we have investigated a pennyshaped crack parallel to surface under indentation with unloading. To tackle theproblem, cavity expansion model has been adopted to characterize the inelasticdeformation under the indentation while the unloading process has been assumed toinduce only elastic deformation and can be characterized as the reverse process ofHertzian contact. The problem of lateral cracking can then be simplified as a pennyshaped crack under the traction due to cavity expansion and unloading in a half space.The boundary value problem via integral transformation can be routinely reduced tothe solution of a system of Cauchy singular integral equations. The stress intensityfactors (SIFs) and the energy release rate haven been calculated. It has been found thatthere exists a crack size at which both SIF and the energy release rate attainsmaximum values. Relationship between the indentation force and that crack size hasbeen obtained numerically. The influences of the dilatancy angle and unloading havebeen also demonstrated. With the optimum design of cutter in mind, we have studiedthe conditions under which the minimum of specific energy is achieved and henceestimated the optimum spacing. Slight difference of the optimum spacing has beendemonstrated between a conical indenter and a spherical indenter.It is known that rock is a kind of porous material, based on the theory of porouselastic medium, we have considered the saturated elastic porous half space under aspherical indenter. Using the Laplace-Hankel integral transform, the indentationproblem can be reduced to the solution of a set of dual integral equations, theload-displacement relation and stress distribution have been calculated so as toestimate the possible damage induced.