Theoretical aspects of edge singularity at surface cracks

Abstract

回顾和探讨了位于三维裂纹前沿和固体自由表面交叉点附近的被称作复杂尖端奇异性的问题 .结果表明 ,自由面上的裂纹边界点并不具有传统裂纹尖端应力场r- 0 .5阶的奇异性 (其中r为从裂纹尖端量起的距离 ) ,而是应该采取rλ 阶的形式 .其中指数λ是关于破裂模式 (即模式I、II或III) ,裂纹前沿在自由面的倾角 β ,破裂面与固体表面的夹角γ以及材料泊松比的函数 .这一问题只对极个别情况存在解析解 ,而绝大多数已知结果都是通过高精度有限元、有限差分方法和强奇异积分方程得到的 .尽管尖端奇异性问题对工程应用极其重要 ,但在应力场强度系数手册中并无现成结果 The complicated issue of the so-called vertex singularity near the corner point of the intersection of a three-dimensional crack front and the free surface of the solid are reviewed and discussed. It was discovered that classical stress singularity near a crack front of r-0.5 （where r is the distance measure from the crack tip） does not hold at the edge of the crack at the free surface, but instead of the form rλ. The exponent λ is a function of mode of cracking （i.e. mode I, II or III）, the inclination angle β of the crack front at the free surface, the inclination angle γ of the crack plane with the solid surface and the Poisson’s ratio of the solid. Analytical results exist only for very special cases, whereas most existing results were obtained through the use of very fine mesh finite element method, finite difference and hypersingular integral equation. Although the vertex singularity is of paramount importance in engineering application, these results were not readily available in the handbooks of stress intensity factor. Therefore, the main purpose of this paper is to summarize this importance results in a form that can be easily used by engineers and scientists.