This paper describes the analytical model for complex shaped axial defects. The model is based on classical lower bound limit load theorem of theory of plasticity, and consists in construction of statically admissible solution (distribution of stress which satisfies to equilibrium equations). Its main advantage is the possibility to explicitly take into account a lot of geometrical (complex shape) and physical parameters (additional axial loading, variance of material properties along the axis), — while still retaining its relatively simple application and appearance. So, contrary to other approaches, the formula for rectangular defect here is only a particular case of application of the general procedure. The main focus of the paper is description and justification of numeric algorithm of this general procedure (named here as O-procedure) for axial complex defect in pipe under internal pressure, which in fact is an optimization process to get the most favorable stress distribution.

Four different approaches for complex shaped defect are compared. First, ASME (named here as A-) rectangular defect formula combined with RSTRENG (named here as R) procedure, i.e., A-R approach. Second, PCORRC (P-) formula with R-procedure, P-R approach. Third, Orynyak (O-) rectangular formula with R-procedure, O-R approach. Fourth, our universal procedure (as goal of the paper), O-procedure. The comparison is performed as for some artificial complex defects, for example, two interacting rectangular defects, as well as for known full scale test performed in Waterloo University. Further considerations as to enhancing of the theory and its experimental verification are made.

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