New CMOD based η-factor equations considering R-O strain hardening for circumferential through-wall cracked pipe under bending moment

Abstract

The fracture study of circumferential through-wall cracked (CTWC) pipe under bending load is of interest for integrity assessment of conventional piping system and especially important for Leak-Before-Break (LBB) analysis of primary heat transport piping system of nuclear power plants (NPP). The fracture study in the elastic-plastic regime needs to obtain material J-resistance curve where J-integral is usually calculated from test data using the η-factor methodology. The evaluation of J-R curve for CTWC pipe is also important for study of transferability of material fracture resistance data from small specimen to full scale components. Further, η-factor to evaluate J-integral may be based on either load-lone-displacement (LLD) or crack mouth opening displacement (CMOD). The conventionalη-factor equations for CTWC pipe are LLD based and derived based on the assumption that the material is elastic perfectly plastic. However, use of LLD based η-factor needs to subtract no-crack displacement which poses additional difficulty and real materials always show some form of strain hardening. Therefore, an effort has been made in this paper to obtain the CMOD based η-factor for CTWC pipe considering material strain hardening as per the Ramberg-Osgood (R-O) relation. In the present study, plastic η-factor (ηpl) has been evaluated by elastic-plastic finite element analyses (FEA) over a wide range of crack angles (2θ = 30°–150°) and R-O strain hardening exponent (n = 2–7) for three R/t ratios (5, 10 and 20). To capture the ovalization of pipe cross section during deformation, geometric non-linearity is also considered in FEA. Based on these FEA, new ηpl equations are proposed by 2-D surface curve fitting for different R/t ratios. For validation of FE model, a separate set of geometrically linear FEA was also carried out for comparison of FE J-integral with EPRI Handbook solutions. Further, semi-analytical η-factor derived from EPRI relations of J-integral and CMOD were also compared with the present (geometric-linear) finite element results. In both the cases, the matching was very good.