Logarithmic singularity in an arc crack problem

This paper investigates an arc crack in an infinite plateunder antisymmetric loading on the crack faces. In other words,the tractions on the two crack faces are the same in magnitude and indirection. Complex variable method is used to solve theabove-mentioned problem. The stresses and the displacements are expressedthrough two complex potentials. After some manipulations, the problem isreduced to a Riemann-Hilbert problem for the complex variable functions,which can be solved in a closed form. The stress intensity factors at thecrack 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 tipis defined and evaluated, in a closed form.