Crack originating from a corner of a square hole

Abstract A crack originating from a corner of a square hole is analyzed as a plane elastic problem. Muskhelishvili's method and the rational mapping function of the sum of fractional expressions are used. A closed solution is obtained. Stress distributions and stress intensity factors are investigated for some angles of the corner of the hole and crack lengths. The T -shaped crack is analyzed as a special case. The stress intensity at the opposite corner to the corner with the crack is investigated. Three loading states of uniform tension in the direction of the x and y axes and pure shear are considered.