Determination of plastic, shakedown and elastic limit loads of 90°pressurized pipe bends with shape imperfections

This study determines the plastic, shakedown and elastic limit loads and the corresponding regimes of 90 degrees pressurized pipe bends with shape imperfections subjected to cyclic in-plane closing bending moment. Three dimensional FE analyses with small strain formulation was performed. The induced shape imperfections are ovality and thinning, which were varied from 0% to 20% with a 5% increment at every step. Plastic limit load was determined from the moment rotation curve while shakedown and elastic limit loads were determined by using Abdalla's simplified technique (ST). The analysis indicates that the presence of ovality produces considerable effect on plastic limit loads. Thinning alters plastic limit loads only for long bend radius models with no ovality when normalised internal pressure ratio is unity and in other cases its effect is minimal. Presence of ovality and thinning has a remarkable effect on shakedown and elastic limit loads and their regimes though the thinning effect is insignificant at higher ovality (10%-20%). Bree diagram was constructed for the reference pipe bend models. It was observed that the failure of pipe bends is due to either reversed plasticity or ratcheting. Mathematical equations are proposed to express the generated plastic, shakedown and elastic limit moment boundaries for the analyzed pipe bend models.