Analytical calculation of stress intensity factors for cracks emanating from a quasi-square hole in an infinite plane

A new conformal mapping is proposed in order to solve stress intensity factor (SIF) problem in an infinite plane containing a traction-free square hole with two unequal cracks, analytically. To this end, Schwarts-Christoffel integral is expanded as sum of finite term series through Newton's binomial formula to approximate the square hole to a rounded corner square one, which is called quasi-square. Next, the mapping function of cracked hole is expanded to a series of fractional expressions to combine with Muskhelishvili formulation. Finally, SIFs are presented for the remote tensile loading and the effects of crack length and radius of corners on the SIF are studied. To ensure the accuracy, results are compared to the available literature and FEM. Contrary to the previous researches, it was shown that the hole-shape had a considerable effect on the SIF for the small cracks though for large length cracks it is negligible.