A Simple Model of Dynamic Cleavage Producing Constant Speed Crack Propagation in a Sample of Finite Width

A simple model of dynamic cleavage under longitudinal shear deformation is analyzed as an attempt to understand how ancient lapidaries might have produced smooth cleaved surfaces. Attention is concentrated on the time signature of the load applied to the specimen in order to maintain a constant stress intensity factor (or energy release rate) at the crack tip as it propagates away from the location of the applied load at a constant speed. The analysis is also applicable to situations in which fracture requires a time dependent energy release rate. An example of the cleavage of diamond is considered.