Fracture Mechanism of the Formation with a Natural Flaw Under a Single-Tooth Cutting
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ISSN 1860-2134
Fracture Mechanism of the Formation with a Natural Flaw Under a Single-Tooth Cutting Siqi Li1
Wei Li1
Tie Yan1
Fuqing Bi2
Huan Zhao1
Xin Ling1
1
( Institute of Petroleum Engineering, Northeast Petroleum University, Daqing 163318, Heilongjiang, China) (2 The Fifth Oil Production Plant of Daqing Oilfield, Daqing 163513, Heilongjiang, China)
Received 15 May 2019; revision received 25 March 2020; Accepted 30 March 2020 c The Chinese Society of Theoretical and Applied Mechanics 2020
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 θ 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 λ applying on the flaw changes nonlinearly with the variation in α + ϕ. The relationship between the dimensionless ratio βx /βy of T -stress and the rotational polar angle ϕ 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 θ 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.
KEY WORDS Single-tooth cutting, Stress field, Stress intensity factor, Initiation angle, Extended finite element
List of Symbols F Cutting force (N) α Force angle of cutting tooth (◦ ) ϕ Angle between the force and the flaw, namely rotational polar angle (◦ ) χ Stress function x, y Horizontal and vertical distances between the cutting force and the flaw (m) a Half-length of the flaw (m) θ Initiation angle of the flaw (◦ ) β Inclination angle of the flaw (◦ ) σx , σy Far-field normal stresses applying on the flaw along the x- and y-directions (MPa) KII Mode-II stress intensity factor at the tip of the flaw (MPa mm0.5 ) Tx , Ty T -stresses along the x- and y-directions (MPa) μ Coulomb friction coefficient
Corresponding author. E-mail: [email protected]
ACTA MECHANICA SOLIDA SINICA
λ rc
Confinement ratio Critical distance of crack initiation (m)
1. Introduction Rock mass is a kind of discontinuous medium with various flaws, such as cracks, joints and faults, which are the roots of new cracks. New flaws crack, propagate and continue to coalesce with the original and other new flaws under various external loads, which will eventually lead to volumetric damage of the rock [1, 2]. In fact, this behavior of rock fragmentation is of great significance in many engineering fields [3
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