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 loadi ng at the crack tip. This geometry change introduces a nonlinear effect and has significant influence on the phenomenon. The nonlinear effect was demo nstrated by incorporating it into an analytical model for a crack propagati ng along an interface parallel to the free surface. A finite-element analys is was then conducted to examine the crack trajectory formed in a homogeneo us material. This numerical analysis showed that the crack reaches a maximu m depth, and then deviates back to the free surface to form a spall. The fo rm of this trajectory results from the additional bending moment acting at the crack tip induced by the bending of the chip and the consequent displac ement of the applied load. The length of the spall was found to be approxim ately proportional to the square root of (E) over cap d(5/2)/K-IC, where K- IC is the fracture toughness of the material, (E) over cap is the appropria te modulus of the material, and d is the depth over which the edge load is applied.