PDC钻头单齿切削天然裂缝地层断裂机理

Fracture mechanism of formation with natural flaws under a single tooth cutting of PDC drill bit

为研究PDC钻头作用下地层断裂机理,以单齿切削含有天然裂缝地层为研究对象,基于弹性力学理论,建立单齿切削下地层应力分布模型,作为裂缝的远场应力;结合切削齿作用力角度和旋转极角,确定作用于裂缝表面的正应力和裂缝倾角,以Ⅱ型起裂方式为断裂模式,给出在两种裂缝表面正应力条件下裂缝尖端的应力强度因子和起裂角模型;通过扩展有限元数值模拟,分析单齿切削下裂缝尖端的起裂特征。结果表明:作用于裂缝的远场应力比例因数随作用力角度和旋转极角之和呈抛物线形式变化;当切削齿作用力方向与地层裂缝方向一致时,裂缝尖端的应力强度因子最大;裂缝尖端的起裂角也随旋转极角变化呈抛物线形式变化。数值模拟结果与理论计算结果有较好的一致性。

In order to study the fracture mechanism of the formation under the action of PDC drill bit,a single tooth cutting the formation containing a natural flaw is taken as the research object in this paper.Based on the theory of elastic mechanics,the stress distribution model of the formation under a single tooth cutting which is taken as the far-field stress of the crack is proposed.The normal stress on the crack surface and the tip of crack are determined combined with the angle of cutting force and rotational polar angle.Then,the stress intensity factor and the initiation angle at the tip of the flaw under two normal stress conditions on the crack surface are presented based on the modeⅡfracture.Finally,the initiation characteristics of the crack under a single tooth cutting are analyzed through numerical calculation and extended finite element simulations.The research results show that the ratio coefficient of the far-field stress changes in a parabolic shape with the variation ofα+φ.When the direction of the cutting force is consistent with the flaw,the stress intensity factor at the tip of the flaw reach the maximum.The initiation angle also changes in a parabolic shape with the variation ofφ.The numerical simulation results are in good agreement with the theoretical calculation results.