Elastic–plastic J and COD estimation schemes for 90° elbow with throughwall circumferential crack at intrados under in-plane opening moment

Abstract

Leak-before-break (LBB) assessment of primary heat transport piping of nuclear reactors involves detailed fracture assessment of pipes and elbows with postulated throughwall cracks. Fracture assessment requires the calculation of elastic-plastic J -integral and crack opening displacement (COD) 1 for these piping components. Analytical estimation schemes to evaluate elastic-plastic J -integral and COD simplify the calculations. These types of estimation schemes are available for pipes with various crack configurations subjected to different types of loading. However, such schemes for elbow (or pipe bend), which is one of the important components for LBB analyses, is very meager. Recently, elastic-plastic J and COD estimation scheme has been developed for throughwall circumferentially cracked elbow subjected to closing bending moment. However, it is well known that the elbow deformation characteristics are distinctly different for closing and opening bending modes because the ovalisation patterns of elbow cross section are different 1 COD varies along the crack length. It is zero at the crack tips and maximum at the middle. Throughout this paper, COD denotes the maximum crack opening displacement at the middle of crack length. under these two modes. Development of elastic-plastic J and COD estimation scheme for an elbow with throughwall circumferential crack at intrados subjected to opening bending moment forms the objective of the present paper. Experimental validation of proposed Jestimation scheme has been provided by comparing the crack initiation, unstable ductile tearing loads and crack extension at instability with the test data. The COD estimation scheme has been validated by comparing the COD of test data with the predictions of the proposed scheme.Keywords J -Estimation scheme · J -Integral · Crack opening displacement · Elbow · Pipe bend · Crack · GE-EPRI Nomenclature a Semi-crack length D o Outer diameter of elbow cross section E Young's modulus h = t R b /R 2 Elbow factor or pipe bend characteristics h 1 Plastic influence function to calculate plastic J -integral (Eqs.10, 18, 19) h 2 Plastic influence function to calculate plastic COD (Eqs.11, 22, 23) J J -integral J avg Average J -integral across the thickness J e , J p Elastic, Plastic J -integral (J i ) SZW Initiation toughness obtained from stretched zone width 123 228 Chattopadhyay et al. J in , J mid , J out J -integral at inside, middle, outside surface J p 1 Plastic J −integral evaluated at M = M L using Eq. 18 J p 1.2 Plastic J -integral evaluated at M = 1.2 × M L using Eq. 19 K Stress intensity factor M Moment M 0 Plastic collapse moment of defectfree elbow M L Plastic collapse moment of cracked elbow n Ramberg-Osgood hardening exponent (Eq. 2) R Mean radius of elbow cross section R b Mean bend radius of elbow at crown or flank t Wall thickness t av Average wall thickness of elbow at crack plane V 2Elastic influence function to calculate elastic COD (Eq. 7) X Weakening factor w.r.t. defect-free elbow collapse moment (Eq. 12)Greek Symbols α Ra...

Linear and Non-Linear Analyses of Pressure Pipe Elbows

“…We note that an increase in this ratio results in a decrease in the h(n) function. It should be noted, however, that this behavior is similar to that found in another study using a wall of constant thickness (Chattopadhyay et al 2007, Kim et al 2005. The results shown in these figures make it possible to determine for each pressure applied the value of the function h(n) whatever the size of the crack to calculate the J integral.…”

“…J. Chattopadhyay et al (2007) conducted experiments on elbows (TWC) 200-400 mm in diameter with circular cracks, subjected to bending loading. Liamani, S et al (2021) analyzed the presence of a horizontal crack in an HDPE pipe using finite element analysis (FEA) under patch-corrected internal loading.…”

Reference stress based J and COD estimation of circumferential through-wall cracked elbows under in-plane bending

“…Full-scale pipe test data for circumferential through-wall cracked elbows under in-plane bending were taken from the published works by an Indian research group [13][14][15][16][17][18][19][20]; the pipe test set-up is schematically illustrated in Fig. 13.…”

“…For comparison, predictions made by an Indian research group, taken from Refs. [15,19], are also listed in Table 1.…”

“…On the other hand, despite its common use in power plants, published works on LBB analysis for through-wall cracked elbows are still limited. Most of the existing works on elastic-plastic J and COD estimation methods for elbows have been done by an Indian research group [13][14][15][16][17][18][19][20]. Using extensive elastic-plastic finite element (FE) solutions, they developed an engineering estimation method, similar to the GE/EPRI approach [18,20], to estimate elastic-plastic J and COD for http://dx.doi.org/10.1016/j.engfracmech.2015.06.022 0013-7944/Ó 2015 Elsevier Ltd. All rights reserved.…”