无限大平面中斜裂纹的压剪断裂分析

根据Muskhelishvili的复势理论,结合裂面边界条件和位移单值条件,将无限大平面受压应力作用的裂纹问题转化为对应的Hilbert问题,并运用复变函数法分别给出了在伪集中力作用下,不同裂面形态的基本解。对不同裂面形态的摩擦力大小和分布进行了详细分析,建立了新的摩擦力计算模型。采用“伪力法”和叠加原理,结合所求的基本解,给出了含中心斜裂纹的岩石类材料在压缩荷载作用下的应力强度因子(SIF)的解法。研究表明:裂面状态对KⅠ的大小没有影响,而对KⅡ的影响却很大,相同应力条件下,裂面状态会影响裂纹的开裂角和开裂方式。

COMPRESSION AND SHEAR FRACTURE ANALYSIS OF SLANTING CRACKS IN INFINITE PLANES

Based on Muskhelishvili’s complex potential theory and using the boundary conditions on crack faces and the single value condition of displacement in an infinite plane, the crack problem under compressive loadings is transformed into a Hilbert problem and the fundamental solutions for cracks with different surface patterns due to concentrated pseudo-tractions are derived. For different surface patterns, the value and the distribution condition of the shear stress are analyzed in detail, and a new computing model is developed. With the aid of the pseudo-traction method, the superposition technique and the presented fundamental solutions, a method to obtain the stress intensity factors (SIFs) for materials such as rock with central inclined cracks under compressive loading is proposed. The study indicates that the surface pattern has no effect on KI , but has obvious effect on KII. Under the same condition, both the breaking angle and the breaking mode of cracks are affected by different surface patterns.