Lower bound limit load of a circumferentially cracked pipe under combined mechanical loading

In a study on extension of the reference stress method, for J simplified assessment, to a three dimensional (3D) configuration under combined loading, lower bound limit analysis has been developed by J. Desquines. In the present paper the limit load for cracked pipe, with a 3D circumferential flaw, under pressure, tension and bending is detailed. The limit load is explicitly defined as a yield surface is the 3D space loading. A simple algorithm is proposed to solve the non linear problem associated to the reference stress calculation. Moreover, the lower bound solution is compared with Elastic Compensation Method (ECM) results computed on a 3D finite element mesh of the cracked pipe. The lower bound yield surface underestimates the numerical limit loads with a discrepancy lower than 20%.