Mathematical model of the stress-strain behaviour of central three-dimensional defect

The authors consider a mathematical model concerning breaking hoop stress for thin-walled pipes with the central elliptical part-through crack. On the basis of a certain theoretical analysis by Kolosov-Muskhelishvili's method the analytical solution is obtained. Two rapture criteria are used. The first criterion is based on critical displacement of crack borders. The second criterion considered the stress existing in the ligament near the moment of rapture, which is considered to be equal to material yield stress. Obtained formulas are generalizing previously existing formulas for linear crack.