Enhanced elastic stress solutions for junctions in various pipe bends under internal pressure and combined loading (90° pipe bend, U-bend, double-bend pipe)

Piping systems in nuclear power plants normally operate under high pressure and high temperature. To efficiently manage space within these systems, pipe bends are extensively used. However, the welded joints connecting these pipes may be susceptible to flaws due to weld residual stress, transient loads, and operating environments. When flaws are present in such areas, analytical evaluation of flaws is to be carried out based on fracture mechanics parameters such as stress intensity factor. To calculate the stress intensity factor, distributions of the elastic stress are required. Therefore, this paper presents closed-form approximations of elastic stress in the junction between a pipe bend and a straight pipe under internal pressure. Review of the existing elastic stress solutions for estimating the stresses in pipe bends was carried out analyzing their limitations. Based on those limitations elastic stress solutions for thick to thin wall pipe bends were proposed and were validated against finite element (FE) analysis for thick-wall to thin-wall pipe bends under internal pressure and combined loading (i.e. internal pressure, in-plane bending, out-of-plane bending inflicted simultaneously). $90°$ pipe bend, U-bend and double-bend pipe configurations were considered and showed good agreement with the FE results exhibiting less than 5.8 % discrepancies. The accuracy of the elastic stress solutions for pipe bends provided in the existing code are summarized and validated in the appendix as well.