Axial Through-wall Cracks Research Articles

Plastic collapse moment equations of throughwall axially cracked elbows subjected to in-plane bending moment

A throughwall axial crack may develop in an elbow or pipe bend due to service related degradation mechanism. It is very important to know the plastic collapse moment (PCM) of an elbow in the presence of a throughwall axial crack. The existing PCM equations of throughwall axially cracked (TAC) elbows are based on very few test data points of Griffiths without detailed analyses and also the range of applicability of their proposed equations are limited. Further, they do not differentiate between closing and opening modes of bending although deformation characteristics under these two modes are completely different. Therefore, the present study has been undertaken to investigate through 3D elastic–plastic finite element analysis. A total of 84 elbows with various sizes of axial cracks ( a/ D m = 0–1), different wall thickness ( R/ t = 5–20), different elbow bend radii ( R b/ 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. Both geometric and material non-linearity are considered in the analysis. Crack closing is observed in most of the cases. To capture the crack closure effect, contact analysis has been performed. Plastic collapse moments have been evaluated from moment–end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate plastic collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations are compared with the test data available in the literature. Matching between predictions and experimental results is found to be satisfactory.

Determination of failure pressure for tubes with two non-aligned axial through-wall cracks

The 40% of wall thickness criterion which has been used as a plugging rule is applicable only to a single cracked steam generator tubes. In the previous studies performed by authors, several failure prediction models were introduced to estimate the plastic collapse pressures of steam generator tubes containing two adjacent collinear or parallel axial through-wall cracks. The objective of this study is to examine the failure prediction models and propose optimum ones for two non-aligned axial through-wall cracks in steam generator tubes. In order to determine the optimum ones, a series of plastic collapse tests and finite element analyses were carried out for steam generator tubes with two machined non-aligned axial through-wall cracks. Thereby, either the plastic zone contact model or COD based model was selected as the optimum one according to axial distance between two cracks. Finally, the optimum failure prediction model was used to demonstrate the conservatism of flaw characterization rules for multiple cracks having equal lengths according to ASME code.

Assessment of Steam Generator Tubes with Dual Axial Through-Wall Cracks

In this paper, conservatisms of current plugging criteria on steam generator tubes are reviewed and six new failure prediction models for dual through-wall cracks are proposed. In order to determine the optimum ones among these local or global failure prediction models, a series of plastic collapse tests and corresponding finite element analyses are carried out with respect to two adjacent axial through-wall cracks in thin plates. Then, reaction force model, plastic zone contact model and COD (Crack Opening Displacement) base model were selected as the optimum ones for integrity assessment of steam generator tubes with dual cracks.

Coalescence evaluation of collinear axial through-wall cracks in steam generator tubes

To maintain the structural integrity of steam generator tubes, usually, 40% of wall thickness plugging criterion has been adopted. However, since the criterion is applicable only for the steam generator tube containing a single crack, the interaction effect of multiple cracks cannot be considered. In this paper, the coalescence pressure of tube with dual cracks is evaluated based on detailed three-dimensional elastic–plastic finite element analyses. In terms of the crack configuration, collinear axial through-wall cracks with various length, distance and ratio between individual cracks are selected. The applicability of failure pressure prediction models recently proposed by the authors was verified by comparing the finite element analyses results with corresponding experimental data for tubes with two identical cracks. Further, in order to quantify the effect of crack length ratio on failure behavior, the failure pressure prediction model was used expansively for tubes containing different-sized cracks and a coalescence evaluation diagram was developed.

An Internal Conical Mandrel Technique for Fracture Toughness Measurements on Nuclear Fuel Cladding

Abstract An understanding of the limiting stress level for crack initiation and propagation in a fuel cladding material is a fundamental requirement for the development of water reactor clad materials. Conventional tests, in use to evaluate fracture properties, are of limited help, because they are adapted from ASTM standards designed for thick materials, which differ significantly from fuel cladding geometry (small diameter thin-walled tubing). The Internal Conical Mandrel (1CM) test described here is designed to simulate the effect of fuel pellet diametrical increase on a cladding with an existing axial throughwall crack. It consists in forcing a cone, having a tapered increase in diameter, inside the Zircaloy cladding with an initial axial crack. The aim of this work is to quantify the crack initiation and propagation criteria for fuel cladding material. The crack propagation is monitored by a video system for obtaining crack extension δa. A finite-element (FE) simulation of the ICM test is performed in order to derive J integrals. A node release technique is applied during the FE simulation for crack propagation and the J-resistance curves (J-δa) are generated. This paper presents the test methodology, the J computation validation, and results for cold-worked stress relieved Zircaloy-4 cladding at 20° and 300°C and also for Al 7050-T7651 aluminum alloy tubing at 20°C.

06/01235 Optimum local failure model of steam generator tubes with multiple axial through-wall cracks: Moon, S. I. et al. Nuclear Engineering and Design, 2005, 235, (17–19), 2099-2108

06/01235 Optimum local failure model of steam generator tubes with multiple axial through-wall cracks: Moon, S. I. et al. Nuclear Engineering and Design, 2005, 235, (17–19), 2099-2108

An Automated System for Detection of Through-Wall Cracks in Racks in Steam Generator Tubes

Through-wall axial cracks occurred by primary water stress corrosion are one of the serious defects in steam generator (SG) tubes (made of alloy 600) in pressurized water reactors. Therefore, it is necessary to detect and size them by eddy current testing (ECT) conducted during in-service inspection of SG tubes. To address this issue, it has been recently proposed an effective method, namely „M-shape profile“ approach, which relies on the difference in the amplitude between the pancake and plus point coils in a MRPC probe. Even though the M-shape curve approach is straightforward in principle, it requires time-consuming data processing if performed by human operators. In order to get rid of this tedious task, an automated system is developed in the present work. This paper addresses the principle of the M-shape approach together with the automated system and its performances for the detection of natural axial cracks in SG tubes. The results observed in the present work demonstrate the high potential of the developed system as a very promising tool for detecting through-wall cracks in many practical field applications.

두 개의 비대칭 축방향 관통균열이 존재하는 증기발생기 세관의 소성붕괴압력 평가

The of wall thickness criterion which has been used as a plugging rule is applicable only to a single cracked steam generator tubes. In the previous studies performed by authors, several failure prediction models were introduced to estimate the plastic collapse pressures of steam generator tubes containing collinear or parallel two adjacent axial through-wall cracks. The objective of this study is to examine the failure prediction models and propose optimum ones for non-aligned two axial through-wall cracks in steam generator tubes. In order to determine the optimum ones, a series of plastic collapse tests and finite element analyses were carried out for steam generator tubes with two machined non-aligned axial through-wall cracks. Thereby, either the plastic zone contact model or COD based model was selected as the optimum one according to axial distance between two clacks. Finally, the optimum failure prediction model was used to demonstrate the conservatism of flaw characterization rules for various multiple flaws according to ASME code.

Optimum local failure model of steam generator tubes with multiple axial through-wall cracks

It is commonly required that steam generator tubes wall-thinned in excess of 40% should be plugged. However, the plugging criteria are known to be too conservative for some locations and types of defects and its application is confined to a single crack. In the previous study, a crack coalescence model applicable to steam generator tubes with two collinear axial through-wall cracks was proposed and a coalescence evaluation diagram was developed which can be used to determine whether the adjacent cracks detected by NDE coalesce or not. In this paper, a total of 9 local failure models including flow stress model, necking-based model, stress-based model, reaction force model and plastic zone contact model were introduced to determine the optimum local failure model. Plastic collapse tests and finite element analyses using thin plates with two collinear through-wall cracks were performed for the selection of the optimum local failure model. By comparing the test results with the prediction results obtained from local failure models, the reaction force model and plastic zone contact model were determined as the optimum local failure models.

Optimum Global Failure Prediction Model of Steam Generator Tube With Two Parallel Axial Through-Wall Cracks

The 40% of wall criterion, which is generally used for the plugging of steam generator tubes, is applied only to a single crack. In the previous study (Moon et al. (2002)), a total number of 9 failure models were introduced to estimate the local failure of the ligament between cracks and the optimum coalescence model of multiple collinear cracks was determined among these models. It is, however, known that parallel axial cracks are more frequently detected during an in-service inspection than collinear axial cracks. The objective of this study is to determine the plastic collapse model which can be applied to the steam generator tube containing two parallel axial through-wall cracks. Three previously proposed local failure models were selected as the candidates. Subsequently interaction effects between two adjacent cracks were evaluated to screen them. Plastic collapse tests for the plate with two parallel through-wall cracks and finite element analyses were performed for the determination of the optimum plastic collapse model. By comparing the test results with the prediction results obtained from the candidate models, a crack opening displacement (COD) base model was selected as an optimum model.

평행한 두 개의 균열이 존재하는 증기발생기 세관의 최적 광범위파손 예측모델 개발

The 40% of wall thickness criterion which has been used as a plugging rule of steam generator tubes is applicable only to a single cracked tube. In the previous studies performed by authors, several global failure prediction models were introduced to estimate the failure loads of steam generator tubes containing two adjacent parallel axial through-wall cracks. These models were applied for thin plates with two parallel cracks and the COD base model was selected as the optimum one. The objective of this study is to verify the applicability of the proposed optimum global failure prediction model for real steam generator tubes with two parallel axial through-wall cracks. For the sake of this. a series of plastic collapse tests and finite element analyses have been carried out for the steam generator tubes with two machined parallel axial through-wall cracks. Thereby, it was proven that the proposed optimum failure prediction model can be used as the best one to estimate the failure load quite well. Also, interaction effects between two adjacent cracks were assessed through additional finite element analyses to investigate the effect on the global failure behavior.

Elastic–plastic analysis of an elbow with a through-wall axial crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows under in-plane bending moment are not available in open literature. This paper presents the J-integral results for 90°, long radius elbows subjected to in-plane opening bending moment based on a large number of finite element analyses covering a wide range of standard geometries. The non-linear elastic–plastic finite element analyses were performed using WARP3D software. Both geometric and material non-linearity were considered in the study. The geometry considered were for R m/ t = 5, 6, 7.5, 9, 12, 15, 20 and 25 with crack angles of 9°, 18°, 27° and 36° and strain hardening exponent, ‘ n’ varied for 2, 3, 5, 7 and 10.

Elastic J-integral solution for an elbow with axial through-wall crack at crown under in-plane bending

Piping elbows under bending moment are vulnerable to cracking at crown. The structural integrity assessment requires knowledge of the J-integral. The J-integral values for axially through-wall cracked thick elbows are not available in the open literature over a certain range. This paper presents a closed form expression for elastic J-integral for 90°, long radius elbows subjected to bending moment. The expression is derived, based on the results of a large number of finite element analyses covering a wide range of standard geometries. The analyses were performed using WARP3D software. The present study enables the estimation of the elastic J-integral over a range of R m/ t from 5 to 25 ( R m/ t = 5, 6, 7.5, 9, 12, 15, 20 and 25) and thus extends the range of earlier solution towards the thicker elbows used in nuclear industry. The crack angles considered were 9°, 18°, 27° and 36°.

Plastic limit pressures for cracked pipes using finite element limit analyses

Based on detailed finite element (FE) limit analyses, the present paper provides approximations for plastic limit pressure solutions for plane strain pipes with extended inner axial cracks; axi-symmetric (inner) circumferential cracks; axial through-wall cracks; axial (inner) surface cracks; circumferential through-wall cracks; and circumferential (inner) surface cracks. In particular, for surface crack problems, the effect of the crack shape, semi-elliptical or rectangular, on the limit pressure is quantified. Comparisons with existing analytical and empirical solutions show a large discrepancy for short circumferential through-wall cracks and for surface cracks (both axial and circumferential). Being based on detailed 3D FE limit analysis, the present solutions are believed to be accurate, and thus to be valuable information not only for plastic collapse analysis of pressurised piping but also for estimating non-linear fracture mechanics parameters based on the reference stress approach.

Investigation on the interaction effect of two parallel axial through-wall cracks existing in steam generator tube

It is commonly required that steam generator tubes wall-thinned in excess of 40% should be plugged. However, the plugging criterion is known to be too conservative for some locations and types of defects and its application is confined to a single crack. In the previous study, the conservatism of the present plugging criterion of steam generator tubes was reviewed and a crack coalescence model applicable to steam generator tubes with two collinear axial through-wall cracks was proposed. Since parallel axial cracks are more frequently detected during in-service inspections than collinear axial cracks, the studies on parallel axial cracks spaced in circumferential direction are necessary. The objective of this paper is to investigate the interaction effect between two parallel axial through-wall cracks existing in a steam generator tube. Finite element analyses were performed and a new failure model of the steam generator tube with these types of cracks is suggested. Interaction effects between two adjacent cracks were investigated to explain the deformation behavior of cracked tubes.

Leak-Before-Break: What Does It Really Mean?

Leak-before-break (LBB) is a term that has been used for decades in reference to a methodology that means that a leak will be discovered prior to a fracture occurring in service. LBB has been applied to missile casings, gas and oil pipelines, pressure vessels, nuclear piping, etc. LBB also has several technical definitions. For instance, LBB can occur for an axial flaw in a pipe where the penetration of the wall thickness will result in a stable axial through-wall crack. This is LBB under load-controlled conditions. LBB could also occur for a circumferential crack in a pipe with high thermal expansion stresses. This might be LBB under compliant displacement-controlled conditions. Finally, LBB might occur when the flaw is stable under normal operating conditions and remains stable when there is a sudden dynamic event (i.e., seismic loading). This might be a time-dependant inertial LBB analysis. These analyses are deterministic, and could be extended to probabilistic evaluations as well. This paper describes some of the technical LBB approaches, applications, and significance of the methodology used in the applications. [S0094-9930(00)01603-6]

Leak-before-break qualification of primary heat transport piping of 500 MWe Tarapur atomic power plant

The advent of Leak-Before-Break (LBB) concept has now replaced the traditional design basis event of the Double-Ended-Guillotine-Break (DEGB) to design the Primary Heat Transport (PHT) system piping of the Pressurised Heavy Water Reactor (PHWR) and Pressurised Water Reactor (PWR). This approach is being adopted to design the PHT system piping of 500 MWe Indian PHWR to be built at Tarapur (Tarapur Atomic Power Plant 3 and 4). The LBB concept basically demonstrates through fracture mechanics analysis that there is negligible chance of any catastrophic break of PHT pipes without prior indication of leakage. There are several steps in this work of LBB qualification, namely, evaluation of loads on the piping components, generation of tensile and fracture properties of PHT pipe base and weld material, determination of leakage size crack (LSC) and the elastic–plastic fracture mechanics (EPFM) and limit load analysis of the piping components with postulated LSC to evaluate the critical load at unstable ductile tearing and the limit load, respectively. The paper deals with the fracture analysis of the straight pipes and elbows of three pipe lines in the PHT system of TAPP 3 and 4. Three crack configurations are considered in the analysis. These are throughwall circumferential crack at the weld location of straight pipe and extrados of the elbow and throughwall axial crack at the elbow crown. In all the cases, necessary factor of safety with respect to the anticipated safe shutdown earthquake (SSE) load and LSC are shown to be more than the minimum required values for LBB qualification.

Elastic fracture properties of all-steel gas cylinders with different axial crack types

All steel cylinders are being used for on-board storage of compressed natural gas in vehicles. Typical maximum fill pressure for these cylinder is 25.85 MPa (3750 psi). These cylinders are subjected to fluctuating pressures, due to the refueling operation. In order to establish a relevant test method to ensure leak before break failure performance in the event of a through-wall cracking, the finite element stress analysis of the design containing various defects has to be firstly carried out to get some theoretical basis for the establishment of the test method. External and internal axial semi-elliptical surface cracks are modeled. Crack front regions are modeled using singular elements, whereas the rest of the cylinder is modeled using twenty-node hexahedron elements. Not only the cylindrical body but also the neck and transition areas of the cylinder are considered in the modeling. Slender cracks with approximately 10 times the wall thickness of the cylinder, which often appear in the engineering application of all steel gas cylinders, are considered. The crack depths varied from 25% to 100% of the wall thickness. Analysis is also carried out for the cylinder with through-wall axial cracks, which have similar crack lengths with external and internal surface cracks. The cylinders are assumed to be in the elastic deformation state. Stress intensity factor, K I, and crack mouth opening displacement, C MOD, as the functions of internal pressure, crack size, location (external verdus internal) and shape (elliptical versus straight-fronted), are established. Calculated results are compared with published results. Deep axial external cracks are found to be more severe than axial internal surface cracks having similar crack lengths. Crack driving force for a semi-elliptical through-wall crack is found to be significantly less than that of a straight-fronted through-wall cracks, which have the same crack length. So, the establishment of a relevant test method to ensure leak before break failure performance in the event of through-wall cracking is of high practical value for the engineering design and application of these cylinders.

Reliability of Steam Generator Tubes With Axial Cracks

An approach for estimating the failure probability of tubes containing through-wall axial cracks has already been proposed by the authors. It is based on probabilistic fracture mechanics and accounts for scatter in tube geometry and material properties, scatter in residual and operational stresses responsible for crack propagation, and characteristics of nondestructive examination and plugging procedures (e.g., detection probability, sizing accuracy, human errors). Results of preliminary tests demonstrated wide applicability of this approach and triggered some improvements. The additions to the model are extensively discussed in this paper. Capabilities are demonstrated by results of analysis of steam generator no. 1 in Slovenian nuclear power plant located in Krsˇko after the 1992 inspection and plugging campaign. First, the number of cracked tubes and the crack length distribution were estimated using data obtained by the 100-percent motorized pancake coil inspection. The inspection and plugging activities were simulated in the second step to estimate the efficiency of maintenance in terms of single and multiple-tube rupture probabilities. They were calculated as a function of maximum allowable crack length. The importance of human errors and some limitations of present nondestructive examination techniques were identified. The traditional wall thickness and crack-length-based plugging criteria are compared. The crack-length-based criterion is shown to be more efficient and more safe, especially because of strong suppression effect on probability of multiple-tube rupture. The results are considered to be important for safety and maintenance of existing plants and for further research.

Sensitivity and response surface analysis of cracked tube parameters in elastoplastic domain

A pressure piping system made of a few thousands tubes is considered; in these tubes through-wall axial cracks are studied. Considering a particular crack in the piping system tube two significant data are in our case very important: (1) critical pressure which predicts a nonstable crack growth or tube rupture, and (2) crack leak rate. The present work discusses the effects of geometric and material cracked tube parameters as variables in their tolerance range on the crack opening area and critical pressure. A sensitivity analysis of the mentioned tube parameters on crack opening and bulging was made. The most influencing tube parameters were selected and a crack opening area and critical pressure response surface was built. The fundamental calculations were made by a finite element method with respect to geometric and material nonlinearity. Some of the calculated results were compared with the results derived from experimental measurements and elastoplastic fracture mechanics calculations.