Analytical Limit Load Procedure for the Axial Complex Shaped Defect in a Pressurized Pipe

The paper is devoted to elaboration of the analytical O-procedure for the limit load analysis of complex shaped axial defect in a pressurized pipe. It is based on the classical lower bound theorem of the theory of plasticity, and consists in construction of the statically admissible solution, where distribution of stress satisfies to the equilibrium equations and strength conditions. O-procedure is an optimization process to get the most favorable stress distribution for providing the maximal pressure. It allows to explicitly account for the variable geometrical and physical parameters. Contrary to other approaches, the derived formula for rectangular defect is only a particular case of the general procedure application. Four different methods for the complex defects are compared. They are: first, ASME, A-, rectangular defect formula combined with RSTRENG, R-, procedure, i.e., A–R approach; second, PCORRC, P-, formula with R-procedure, P–R approach; third, Orynyak's, O-, formula with R-procedure, O–R approach; and fourth, our universal O-procedure. The verification begins for rectangular defects where both theoretical and experimental comparison is performed for A-, P-, and O- formulas. The difference between them is small, provided that all three employ the same characteristic of material, here the ultimate strength. Then theoretical comparison for A–R, P–R, O–R approaches and O-procedure is performed for the artificial complex defects, for two symmetrical rectangular defects, for triangular defect. Experimental comparison between four methods is made based on the well-known University of Waterloo full scale tests.