Hydraulically pumped cone fracture in brittle solids

An analysis of inner cone cracks in brittle solids subject to cyclic indentation in liquid is presented. These inner cone cracks, so named because they form well within the maximum contact circle, are postulated to be driven by a hydraulic pumping mechanism. Unlike their more traditional outer cone crack counterparts, inner cones do not appear in monotonic loading or even cyclic loading in the absence of liquid. According to the hydraulic pumping postulate, an expanding contact engulfs surface fissures or flaws, closing the crack mouths and squeezing entrapped liquid toward the subsurface tips, thereby enhancing downward penetration. Finite element modeling is used to analyze the stress and displacement fields in the vicinity of the growing cracks and to compute stress-intensity factors, using soda-lime glass loaded by a spherical indenter in water as a case study. A stepwise incrementing procedure determines the inner cone crack evolution, i.e., crack depth c as a function of number of indentation cycles n, for this system. The predicted c(n) response reproduces essential features of experimentally observed behavior, relative to companion outer cone cracks: notably, a sluggish start in the initial regions, where Hertzian stresses govern, followed by rapid acceleration as hydraulic pumping activates, ultimately dominating in the steady-state far-field.