Abstract
A crack extension problem based on the fracture mechanics is solved to estimate the length of downward extension of a crack and the upper limit of depth of cut preventing its extension in orthogonal cutting of ceramics. To solve the problem evidently in conjection with mechanical properties of the work, the stress field of the expansion of a cylindrical tube is successfully applied to the elasto-plastic tensile stress field in the work by the tool progress. It is shown that the length of the crack extension is uniquely determined by the combination among the depth of cut, the fracture toughness and the yield strength. The upper limit of depth of cut is found to be proportional with square of the ratio of the fracture toughness for micro crack-to-the yield strength. The estimated value of the upper limit of depth of cut coincides approximately with that of experiment for alumina ceramics and soda-lime glass.
