Analysis of the contact forces on a blunt PDC bit

Drilling with drag bits (PDC bits) simultaneously involves fragmentation of rock by the cutters and frictional contact on the cutter wear flats. While there is reasonable understanding of the forces arising from the cutting process, knowledge of the factors affecting the contact forces on the wear flats is still fragmentary. This paper focuses on determining the parameters that influence the mean normal stress σ on the cutter wear flats, and on mapping the dependence of a on these parameters, by analyzing the idealized problem of a slightly inclined rigid slider moving on the surface of a Mohr-Coulomb elastoplastic half-plane. Reminiscent of the problem of a blunt indenter, a continuous range of solutions from elastic to rigid-plastic contact exists. The number η = E'tan β/q (where E' is the plane strain modulus, q is the unconfined compressive strength, and β denotes the inclination of the slider) essentially controls the nature of the solution: elastic contact if η is small, rigid-plastic if η is large, and elastoplastic between these two limiting behaviors. The dependence of the scaled contact stress II = σ/q on η is determined by numerical simulations using the code FLAC. The theoretical results are broadly consistent with experimental data obtained with blunt cutters; in particular the inverse dependence of II on the friction coefficient at the wear flat/rock interface.