Fracture Mechanism of the Formation with a Natural Flaw Under a Single-Tooth Cutting

Abstract

The process of a single-tooth cutting formation is taken as the representative to analyze the fracture mechanism of the formation with natural flaws under the PDC drill bit. The modeling of the stress field distribution of the formation under a single tooth is proposed first. Subsequently, the modeling of the stress intensity factor K, T-stress and the initiation angle $$\theta $$ of the flaw under two far-field compressive loads in two cases are presented based on the mode-II fracture. Finally, the results of theoretical calculations and simulations are given and discussed. Based on the analysis undertaken, it can be concluded that the confinement ratio $$\lambda $$ applying on the flaw changes nonlinearly with the variation in $$\alpha +\varphi $$ . The relationship between the dimensionless ratio $$\beta _{{x}}/\beta _{{y}}$$ of T-stress and the rotational polar angle $$\varphi $$ is a parabola with an upward opening. When the direction of the cutting force is consistent with the flaw, the stress intensity factor K and the initiation angle $$\theta $$ at the tip of the flaw reach the maximum. In addition, the angle between the cutting force and the flaw weakens the T-stress and inhibits the crack initiation and propagation of the flaw. The results of numerical simulations show good agreement with theoretical calculations.