Logarithmic singularity in an arc crack problem
圆弧形裂纹问题中的应力对数奇异性

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.