Transverse flexural fracture of a plate containing an arc crack

In this paper, the transverse flexural fracture of a plate weakened by a circular arc crack is studied. The flexural loads of out-of-plane bending, twisting, and shearing are assumed to act upon the plate edge at infinity. On the basis of the complex variable approach for first boundary condition problems, a new conformal mapping is proposed to transform the contour surface of a circular arc crack into a unit circle. General formulations for transverse loading were applied to derive the governing boundary equation. By taking the Cauchy integral for each term of the boundary equation, the complex stress functions corresponding to the flexural loads are formulated. Also, corresponding stress intensity factors are given through a coordinate transformation followed by taking a limiting process. In addition, for the transverse flexural fracture, the mutual weakening between both crack tips is investigated.