Controlled fracture in a finite geometry body as a stone shaping tool

A stone cutting technique capable of manufacturing curved shell sections from rectangular stone slabs has been recently proposed. Initially the rectangular slap of stone is prestressed by means of metal stamp pads which are rubber lined to prevent damage to the stone. Knife edges are then applied to the prestressed system at some fixed distance from the pads. As the load on the knives reaches a critical value, the stone fractures underneath the knife edges. The resulting crack propagation is curved and symmetric. Experiments with a limited number of different stones have shown that the initial angle of crack propagation is practically independent of the type of stone being cut. The purpose of this paper is to perform a preliminary analysis of this fracture process and to quantify such values as the initial angle of crack propagation and the critical knife-to-stamp load ratios producing fracture. Assuming the stone to be homogeneous, isotropic, linearly elastic and brittle, a two-dimensional plane model with an appropriate fracture condition is employed. The analysis shows that the conditions under which fracture occurs are material dependent in a small region about the knife location, but are independent of material properties outside this region. Further, the initial angles of crack propagation predicted by the analytical model are found to be in very good agreement with the experimental data.