Multi-crack analysis of hydraulically pumped cone fracture in brittle solids under cyclic spherical contact

The evolution of surface damage in bilayers due to cyclic spherical indentation in the presence of incompressible lubricant is studied using an all-transparent glass/polycarbonate system as a model for more practical applications such as dental crowns and rolling contact fatigue. In situ observations and post-mortem material sectioning reveal that inner cone cracks evolve sequentially from the contact edge inward by slow growth in a process controlled by stress shielding from preceding cracks. The embryonic cracks are then accelerated by the action of fluid pressure into the flexural tensile stress at the lower part of the coating, where crossover fracture leading to delamination between the coating and substrate may ensue. A consistent FEM brittle fracture analysis incorporating multiple cracks, rate-dependent toughness and liquid pressure is used to follow the damage evolution in the coating. Crack trajectories are determined incrementally under the dual constraint K_I=K_II=0, which maximize the tension at the crack tip upon the application of fluid pressure. The latter, evaluated at each increment with the aid of a fluid entrapment model, helps drive the leading crack past the compression zone beneath the contact via a hydraulic pump like action. In the early stages of fracture, the liquid pressure is reasonably well approximated by the Hertzian radial surface stress at the crack mouth. Fluid trapped in secondary cracks accentuate the compression beneath the contact. This helps squeeze more liquid into the tip of the leading crack in a zipping like action, which further enhance the crack driving force in the far field. The analytic predictions generally collaborate well with the tests.