Mechanism Analysis and Mathematical Modeling of Brittle Failure in Rock Cutting with a Single Sharp Cylinder-Shaped PDC Cutter

Abstract

Summary The drilling efficiency of a polycrystalline diamond compact (PDC) bit plays a vital role in oil and gas exploration, which is greatly affected by the rock-cutting performance of a single PDC cutter. Although many research efforts have been put in, the rock-cutting mechanism of a single PDC cutter is still indistinct. In this work, the rock-cutting process of a single sharp cylinder-shaped PDC cutter was captured using a high-speed camera. The brittle failure mode mechanism in the rock cutting of the PDC cutter was thus revealed by this real-time observation combined with the findings in previous publications. The brittle rock-cutting failure zones in front of the cutter were separated into three different zones: crushing zone, plastic flow zone, and rock chipping zone. The crushing zone grew while the cutter cut forward and generated a plastic flow zone. When the crushing zone was large enough, a tensile crack would tear apart the rock, forming the rock chip. Based on this rock-cutting mechanism, a new mathematical model of brittle failure in rock cutting of PDC cutter was developed, considering the rock properties and cutting parameters. The boundary geometry of the crushing zone was calculated using elastoplastic theory and the Mohr-Coulomb criterion. All forces on the boundaries of these three failure zones were calculated and combined into the tangential and normal forces in the 3D mathematical model. Furthermore, a new parameter, named as crescent area, was proposed in the mathematical model. When compared to previous publications, the newly developed mathematical model had no variables that needed to be calibrated with experimental data fitting. Moreover, a series of single PDC cutter cutting tests were carried out at various depths of cut (DOCs) and backrake angles to validate the mathematical model. The results showed that the model-predicted forces basically matched the experimental data. The modeling and experimental results shared the same trend for both tangential and normal cutting forces. The experimental phenomena could be well explained by the developed mathematical model. For example, the cutting forces increase with increasing DOC and backrake angle, which is caused by the changing of the crescent area of the rock-cutter interaction. All resultant forces have almost the same inclination angle to the horizontal plane because of the almost constant boundary shape of the crushing zone. The differences between modeling and experimental results could be attributed to several reasons, one of which was the oversimplified plastic flow zone. This work presents a mathematical model that can guide the PDC bit design at different formation properties.