An analysis of chipping in brittle materials

The chipping process in a brittle material subjected to a uniformly applied edge load has been investigated. The present analysis extends earlier work by recognizing that as the chip is formed it may bend and change the loading at the crack tip. This geometry change introduces a nonlinear effect and has significant influence on the phenomenon. The nonlinear effect was demonstrated by incorporating it into an analytical model for a crack propagating along an interface parallel to the free surface. A finite-element analysis was then conducted to examine the crack trajectory formed in a homogeneous material. This numerical analysis showed that the crack reaches a maximum depth, and then deviates back to the free surface to form a spall. The form of this trajectory results from the additional bending moment acting at the crack tip induced by the bending of the chip and the consequent displacement of the applied load. The length of the spall was found to be approximately proportional to the square root of Êd/KIC , where KIC is the fracture toughness of the material, Ê is the appropriate modulus of the material, and d is the depth over which the edge load is applied.