圆弧形裂纹问题中的应力对数奇异性

研究了无限大板上的一条圆孤形裂纹, 又在裂纹表面作用有反对称载荷. 换言之, 裂纹两侧表面的载荷是大小相等方向相同的. 上述问题可用复变函数方法来解决. 应力和位移分量通过两个复位函数来表示. 经过一系列推导, 此问题可归结为复变函数的黎曼-希尔巴德(Riemann-Hilbert) 问题, 并且可用闭合形式得出解答. 裂纹端的应力强度因子用通常方法定出. 在裂纹端邻域, 得到的复位函数中有对数函数部分. 由这个对数函数部分, 可以定义和得出裂纹端的对数奇异性, 此对数奇异性系数用闭合型式得出.

Logarithmic singularity in an arc crack problem

This paper investigates an arc crack in an infinite plate under antisymmetric loading on the crack faces. In other words, the tractions on the two crack faces are the same in magnitude and in direction. Complex variable method is used to solve the above-mentioned problem. The stresses and the displacements are expressed through two complex potentials. After some manipulations, the problem is reduced to a Riemann- Hilbert problem for the complex variable functions, which can be solved in a closed form. The stress intensity factors at the crack tips can be determined as usual. At the vicinity of the crack tips, the logarithmic terms can be found from the obtained complex potentials, From the logarithmic terms, the logarithmic singularity at the crack tip is defined and evaluated, in a closed form.