Engineering estimate of plastic collapse loads for cracked pipe bends under in-plane and out-of-plane bending

Nuclear power plant piping systems frequently encounter complex loads due to factors like internal pressure, self-weight, structural supports, and operational conditions. Within these systems, pipe bends play a crucial role in releasing energy through deformation. Cracks pose a risk to the integrity of the system, necessitating the calculation of the plastic collapse load for cracked pipe bends. This study presents estimations for the plastic collapse load of cracked pipe bends under pure out-of-plane bending moments and simultaneous in-plane and out-of-plane bending moments. Cracks located in the intrados, extrados, and crown of pipe bends were considered. The estimations for plastic collapse load are proposed based on the observed similarity between plastic collapse load and plastic deformation under both in-plane and out-of-plane bending conditions. For combined in-plane and out-of-plane bending moment conditions, circular and parabolic relationships have been proposed for a straightforward plastic collapse load prediction. Additionally, the estimations for plastic collapse loads were derived from the results of finite element analysis conducted on crack-free pipe bends, demonstrating its applicability to cracked pipe bends as well.