The Formation of Chips in the Penetration of Elastic-Brittle Materials (Rock)

Abstract

An analysis is presented for the formation of chips in a two-dimensional, isotropic, elastic-brittle solid, due to the penetration of a rigid wedge. The analysis can be viewed in three parts. It is first necessary to obtain the static stress field due to a prescribed traction on the boundary. An integral method is used for this which is particularly convenient for the present problem. With the stresses known the field is searched to determine where fracture is initiated. Fracture is assumed to satisfy a Coulomb-Mohr fracture criterion. It is found that for certain realistic parameter ranges fracture initiation is somewhat insensitive to the details of traction distribution and wedge angle but is dependent on the material parameters. An approximate fracture path is proposed for stable fracture growth based on a certain fracture function. It is further proposed that the transition from stable to unstable fracture growth takes place at the inflection point of the fracture function versus fracture path length plot. Arguments are based on the Griffith theory of fracture and experimental data on crack velocity. Ratios of chip formation wedge forces to incipient fracture wedge forces are calculated from the theory and are of the order of 4. The results appear to be in reasonable quantitative agreement with some wedge penetration experiments on charcoal grey granite.