Circumferential Through-wall Crack Research Articles

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

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 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 J-estimation 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.

Elastic–plastic fracture mechanics analyses of circumferential through-wall cracks between elbows and pipes

The present work proposes a method for elastic–plastic fracture mechanics analysis of the circumferential through-wall crack in weldment joining elbows and attached straight pipes, subject to in-plane bending. Heterogeneous nature of weldment is not explicitly considered and thus, the proposed method assumes cracks in homogeneous materials. Based on small strain finite element limit analyses using elastic–perfectly plastic materials, closed-form limit loads for circumferential through-wall cracks between elbows and straight pipes under bending are given. Then applicability of the reference stress-based method to approximately estimate J and crack opening displacement (COD) is evaluated. It was found that the limit moments for circumferential cracks between elbows and attached straight pipes can be much lower than those for cracks in straight pipes, particularly for a crack length of less than 30% of the circumference; this result is of great interest in practical cases. This result implies that, if one assumes that the crack locates in the straight pipe, limit moments could be overestimated significantly, and accordingly, reference stress-based J and COD could be significantly overestimated. For the leak-before-break analysis, accurate J and COD estimation equations based on the reference stress approach are proposed.

EVALUATION MODEL FOR RESTRAINT EFFECT OF PRESSURE INDUCED BENDING ON THE PLASTIC CRACK OPENING OF A CIRCUMFERENTIAL THROUGH-WALL CRACK

This paper presents a closed-form model for evaluating the restraint effect of pressure induced bending on the opening of a circumferential through-wall crack, which is considered plastic deformation behavior. Three-dimensional finite element analyses with different crack lengths, restraint conditions, pipe geometries, magnitudes of internal pressure, and tensile properties were used to investigate the influence of each parameter on the pressure-induced bending restraint on the crack opening displacement. From these investigations, an analytical model based on elastic-perfectly plastic material was developed in terms of the crack length, symmetric restraint length, mean radius to thickness ratio, axial stress corresponding to the internal pressure, and normalized crack opening displacement evaluated from a linear-elastic crack opening condition. Finite element analyses results demonstrate that the proposed analytical model reliably estimated the restraint effect of pressure-induced bending on the plastic crack opening of a circumferential through-wall crack and properly reflected the dependence on each parameter within the range over which the analytical expression was derived.

소성거동을 고려한 원주방향 관통균열 열림에 미치는 압력유기굽힘의 구속효과 평가 모델

This paper presents the model for evaluating restraint effect of pressure induced bending (PIB) on the circumferential through-wall crack opening displacement (COD), which considers plastic behavior of crack. This study performed three-dimensional elastic-plastic finite element (FE) analyses for different crack angle, restraint length, pipe geometry, stress level, and material conditions, and evaluated the influence of each parameter on the PIB restraint effect on COD. Based on these evaluations and additional perfectly-plastic FE analyses, a closed-form model to evaluate the restraint effect of PIB on the plastic crack opening of circumferential through-wall crack, was proposed as functions of crack angle, restraint length, radius to thickness ratio, axial stress corresponding to an internal pressure, and normalized COD evaluated from linear-elastic crack opening condition.

A Method of J Testing Based on Crack Opening Displacement for Circumferential Through-Wall Cracked Pipes under Combined Tension and Bending

Application of the leak-before-break concept to nuclear piping requires accurate fracture mechanics assessment on pipes with postulated circumferential through-wall crack subject to combined tension and bending. One important element is determination of relevant J-resistance curve for pipes under combined loading. This paper provides experimental J estimation method for the circumferential through-wall cracked pipe under combined tension and bending, based on the load-crack opening displacement (COD) record to estimate J-resistance curve. To give confidence in the proposed method, the J results from detailed elastic-plastic finite element (FE) analysis are also compared with estimated J based not only on proposed method but also on conventional method using load-load line displacement, which shows that estimated J based on the proposed method provides reliable J estimates regardless of analysis condition, on the other hand, the conventional method using the load-load line displacement record gives erroneous results for shallow cracks.

New plastic collapse moment equations of defect-free and throughwall circumferentially cracked elbows subjected to combined internal pressure and in-plane bending moment

Closed-form plastic collapse moments (PCM) equations were earlier proposed for throughwall circumferentially cracked (TCC) elbow subjected to pure in-plane bending moment. However, an elbow is often subjected to combined internal pressure and bending moment in actual service condition. Therefore, the present study investigates the effect of internal pressure on the in-plane PCM of a TCC elbow. The PCM of a cracked elbow is usually expressed as a product of two parameters: PCM of a defect-free elbow multiplied by a weakening factor due to the crack. Therefore, the present study also includes analysis of defect-free elbows. Elastic–plastic finite element analysis is employed for the present analysis. A total of 396 cases of elbows with various sizes of circumferential cracks (2 θ = 0–150°), different wall thickness ( R/ t = 5–20), different levels of normalized internal pressure ( p = PR/( tσ y) = 0–1), different elbow bend radii ( R b/ R = 2,3) and two different bending modes, namely closing and opening are considered in the analysis. Elastic–perfectly plastic stress–strain response of material is assumed. The load in the elbows is split in two components: a constant internal pressure applied initially followed by in-plane bending moment monotonically increasing in definite steps. PCM are evaluated from moment—end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate PCM of TCC and defect-free elbows subjected to combined internal pressure and in-plane closing/opening bending moment. Attempt has been made to compare the predictions of the proposed equations with the available experimental/numerical results and to rationally explain the behaviour where no experimental/numerical data is available for comparison.

관통균열 세관의 파열압력 예측을 위한 탄소성 파괴역학 해석

The structural and leakage integrity of steam generator tubes should be sustained all postulated loads with appropriate margin even if a crack is present. During the past three decades, for effective integrity evaluation, several limit load solutions have been used world-widely. However, to predict accurately load carrying capacities of specific components under different conditions, the solutions have to be modified by using lots of experimental data. The purpose of this paper is to propose a new burst pressure estimation scheme based on fracture mechanics analyses for steam generator tube with an axial or circumferential through-wall crack. A series of three dimensional elastic-plastic finite element analyses were carried out and, then, closed-form estimation equations with respect to both J-integral and crack opening displacement were derived through reference stress method. The developed engineering equations were utilized for structural integrity evaluation and the resulting data were compared to the corresponding ones from experiments as well as limit load solutions. Thereafter, since the effectiveness was proven by promising results, it is believed that the proposed estimation scheme can be used as an efficient tool for integrity evaluation of cracked steam generator tubes.

Limit Moments for Pipes with Circumferential Through-Wall Cracks: Experimental Verification

Experiments on copper tubes with simulated cracks and slots in them are used to provide justification of the classical approach to assessing the limit moment carrying capacity of cracked tubular components.

05/00629 Development of circumferential through-wall crack K-solutions for control rod drive mechanism nozzles

05/00629 Development of circumferential through-wall crack K-solutions for control rod drive mechanism nozzles

P112 影響関数法による配管の周方向貫通き裂の応力拡大係数の解析とその応用(信頼性,ポスター講演3)

P112 影響関数法による配管の周方向貫通き裂の応力拡大係数の解析とその応用(信頼性,ポスター講演3)

Closed-Form Collapse Moment Equations of Throughwall Circumferentially Cracked Elbows Subjected to In-Plane Bending Moment

A large throughwall circumferential crack in an elbow subjected to in-plane bending moment can significantly reduce its collapse load. Therefore, it is very important to know the collapse moment of an elbow in the presence of a throughwall circumferential crack. The existing closed-form collapse moment equations of throughwall circumferentially cracked elbows are either too conservative or inadequate to correctly quantify the weakening effect due to the presence of the crack, especially for opening mode of bending moment. Therefore, the present study has been carried out to investigate through elastic-plastic finite element analysis the effect of a throughwall circumferential crack on the collapse moment of an elbow under in-plane bending moment. A total of 72 cases of elbows with various sizes of circumferential cracks (2θ=0–150 deg), different wall thickness (R/t=5–20), different elbow bend radii Rb/R=2,3 and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Collapse moments have been evaluated from moment-end rotation curves by twice-elastic slope method. From these results, closed-form expressions have been proposed to evaluate collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations have been compared with 8 published elbow test data and are found to be within ±11% variation except for one case.

Development of circumferential through-wall crack K-solutions for control rod drive mechanism nozzles

The US Nuclear Regulatory Commission (USNRC) has undertaken a program to assess the integrity of control rod drive mechanism nozzles in existing plants that are not immediately replacing their reactor pressure vessel heads. This paper summarizes some of the efforts undertaken on behalf of the USNRC for the development of circumferential crack-driving force solutions to be used in probabilistic determinations of the time from detectable leakage to failure. Detailed three-dimensional elastic–plastic finite element analyses of these nozzles were conducted to determine the effects of operating conditions, tube-to-head interference fit, tube yield strength, and nozzle-to-head angle on the crack-driving force. Three major observations to date are: • Conducting simple tube-only analyses can severely overpredict the actual crack-driving force in the control rod drive mechanism nozzles. • The crack-driving force is a strong function of the nozzle yield strength, nozzle-to-head angle, interference fit, and weld residual stress; and • In many cases, when the crack is made to be perpendicular to the wall of the nozzle, the operating conditions and residual stresses appear to create some crack closure along the crack faces, suggesting that cracks in service will grow at an angle through the thickness.

관통균열이 존재하는 증기발생기 전열관의 파열압력 평가

Operating experience of steam generators shows that the tubes are degraded by stress corrosion cracking, fretting wear and so on. These defected tubes could stay in service if it is proved that the tubes have sufficient structural margin to preclude the risk of tube bursting. This paper provides detailed plastic limit pressure solutions for through-wall cracks in the steam generator tubes. These are developed based on three dimensional(3D) fmite element analyses assuming elastic-perfectly plastic material behavior. Both axial and circumferential through-wall cracks in free span and in u-bend regions are considered. The resulting limit pressure solutions are given in a polynomial form, and thus can be simply used in practical integrity assessment of the steam generator tubes.<br/>

Evaluation of restraint effect of pressure induced bending on the elastic–plastic crack opening behaviour

The present study investigated the effect of restraint of pressure induced bending (PIB) on the elastic–plastic crack opening behaviour of a circumferential through-wall crack in a pipe. Elastic and elastic–plastic finite element analyses were performed to estimate the crack opening displacement (COD) for various restraint conditions and circumferential crack angles. The results showed that the restraint of PIB decreased the crack opening at a specific crack angle and magnitude of internal pressure, and the decrease in crack opening was considerable for larger crack angles with short restraint length. Also, the restraint effect was more significant in elastic–plastic analysis than linear elastic analysis. In the elastic–plastic analysis, the increasing internal pressure enhanced the restraint effect of PIB, and its effect was dependent on the circumferential crack angle. Additionally, it was observed that the restraint effect on COD is governed by the shorter restraint length rather than the overall restraint length when a cracked pipe is restrained non-symmetrically.

Crack opening displacement of circumferential through-wall cracked cylinders subjected to tensile and through-wall bending loads

This study is concerned with crack opening displacements (CODs) of cylinders with a circumferential through-wall crack which is subjected to tensile and through-wall bending loads. A series of FEM analyses were performed in various scaled cylinders, and then the present results on the CODs were compared with the previous studies. Especially, the crack opening behaviors of the large scaled cylinders under a membrane stress and a through-wall bending stress were characterized evidently in this study. The present results are expected to be valid for the leakage evaluation of structures which is subjected to internal pressure and thermal distribution.

Approximate elastic–plastic J estimates of cylinders with off-centred circumferential through-wall cracks

This paper provides approximate J estimates for off-centred, circumferential through-wall cracks in cylinders under bending and under combined tension and bending. The proposed method is based on the reference stress approach, where the dependence of elastic and plastic influence functions of J on the cylinder/crack geometry, the off-centred angle and strain hardening is minimised through the use of a proper normalising load. Based on published limited FE results for off-centred, circumferential through-wall cracks under bending, such normalising load is found, based on which the reference stress based J estimates are proposed for more general cases, such as for a different cylinder geometry and for combined loading. Comparison of the estimated J with extensive FE J results shows overall good agreements for different crack/cylinder geometries and for combined tension and bending, which provides sufficient confidence in the use of the proposed method for fracture mechanics analyses of off-centred circumferential cracks. Furthermore, the proposed method is simple to use, giving significant merits in practice.

Reference stress based fracture mechanics analysis for circumferential through-wall cracked pipes: experimental validation

This paper presents experimental validation of the reference stress based J estimates for circumferential through-wall cracked (TWC) pipes, recently proposed by the authors. Using the pipe test data for circumferential TWC pipes given in the Pipe Fracture Encyclopedia [Pipe Fracture Test Data, vol. 3, Battelle, 1997], the predicted fracture initiation and instability loads according to the proposed reference stress method are compared with experimental ones as well as predictions according to the reference stress method embedded in R6. The results show that both the R6 method and the proposed method give conservative estimates of initiation and maximum moments for circumferential TWC pipes, compared to experimental data. For longer cracks, the proposed method reduces the conservatism embedded in the estimated J according to the R6 method, and the resulting predictions are less conservative, compared to those from the R6 method. For shorter cracks, on the other hand, the proposed method reduces possible non-conservatism embedded in estimated J according to the R6 method, and the resulting predictions are slightly more conservative.

비대칭 원주방향 관통균열 배관의 탄소성 J-적분 계산식

This paper provides approximate J estimates for off-centred, circumferential through-wall cracks in cylinders under bending and under combined tension and bending. The proposed method is based on the reference stress approach, where the dependence of elastic and plastic influence functions of J on the cylinder/crack geometry, the off-centred angle and strain hardening is minimised through the use of a proper normalising load. Based on published limited FE results for off-centred, circumferential through-wall cracks under bending, such normalising load is found, based on which the reference stress based J estimates are proposed for more general cases, such as for a different cylinder geometry and for combined loading. Comparison of the estimated J with extensive FE J results shows overall good agreements for different crack/cylinder geometries and for combined tension and bending, which provides sufficient confidence in the use of the proposed method to fracture mechanics analyses of off-centred circumferential cracks. Furthermore, the proposed method is simple to use, giving significant merits in practice.

On the Assessment of Through-Wall Circumferential Cracks in Steam Generator Tubes With Tube Supports

The assessment of steam generator tubes with defects is of great importance for the life extension of steam generators. Circumferential through-wall cracks are the most severe of all tube circumferential defects, and usually require plugging of the affected tubes. The assessment of the tubes with through-wall circumferential cracks or cracks projected to become through-wall can be conducted using the failure assessment diagram (FAD) approach. This approach requires the calculation of the stress intensity factor and the limit load. The available stress intensity factor and limit load solutions for cracked tubes do not include the constraining effect of the tube supports. In the present paper, it is shown that this can be overly conservative. Solutions for stress intensity factors and limit loads are presented for tubes with circumferential through-wall cracks including the effect from the tube support plates. Different values of support spacing are considered. Based on these solutions, the assessment of a typical steam generator tube is demonstrated.

Evaluation of leak-before-break assessment methodology for pipes with a circumferential through-wall crack. Part III: estimation of crack opening area

Evaluation of the crack opening area (COA) plays a central role in the evaluation of the critical crack length for a detectable leak for piping systems. Simplified evaluation methods for the COA for a circumferential through-wall crack in a pipe subjected to axial and bending loading or their combination is reviewed in this paper. Elastic solutions are compared and recommendations are given. Plastic solutions by the reference stress method are compared with nonlinear finite element solutions. The reference stress method tends to overestimate the COA for medium or large crack angles. Considerable improvement is achieved by making empirical modifications to the limit load expressions used in the calculation of the reference stress.