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.     

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.     

Determination of equivalent single crack based on coalescence criterion of collinear axial cracks

In a nuclear power plant the steam generator tubes cover a major portion of the primary pressure-retaining boundary. Thus, very conservative approaches have been taken in the light of steam generator tube integrity. According to the present criteria, tubes wall-thinned in excess of 40% should be plugged whatever the cause. However, many analytical and experimental results have shown that no safety problems exist even with thickness reductions greater than 40%. The present criterion was developed about 20 years ago when wear and pitting were dominant causes for steam generator tube degradation, and it is based on tubes with single cracks regardless of the fact that the appearance of multiple cracks is more common in general. The objective of this study is to review the conservatism of the present plugging criteria of steam generator tubes and to propose a new coalescence model for two adjacent through-wall cracks existing in steam generator tubes. Using the existing failure models and experimental results, we reviewed the conservatism of the present plugging criteria. In order to verify the usefulness of the proposed new coalescence model, we performed finite element analysis and some parametric studies. Then, we developed a coalescence evaluation diagram.     

Vessel behavior following a through-wall crack

A fracture mechanics model has been developed to predict the behavior of a reactor pressure vessel following the occurrence of a through-wall crack during a pressurized thermal shock event. This study has been coordinated with the Integrated Pressurized Thermal Shock (IPTS) Program at Oak Ridge National Laboratory. The fracture mechanics model uses as inputs the critical transients and probabilities of through-wall cracks from the IPTS Program. The model has been applied to predict the modes of failure for plant specific vessel characteristics. A Monte Carlo type of computer code has been written to predict the probabilities of alternate failure modes. This code treats the fracture mechanics properties of the various welds and plates of a vessel as random variables. The computer code also calculates the crack driving force as a function of the crack length and the internal pressure for critical times during the transient. The fracture mechanics model has been applied in calculations that simulate the Oconee-1 reactor pressure vessel. The model predicted that about 50% of the through-wall axial cracks will turn and follow a circumferential weld giving a potential for missiles. Missile arrest calculations predict that vertical as well as all potential horizontal missiles will be arrested and will be confined to the vessel enclosure cavity. In future work, plant specific analyses will be continued with calculations that simulate Calvert Cliff-1 and H.B. Robinson-2 reactor vessels.     

A theoretical procedure for detection of simulated cracks in a pipe by the direct current–potential drop technique

Based on the direct current–potential drop (dc–pd) technique, an efficient theoretical detection procedure is developed to identify the existence of simulated cracks in a pipe. By this procedure, the electric potential on a ‘pseudo’ perfect pipe needs to be calculated in advance by finite element method. The proposed defect influence factor, which is defined as the ratio of the electric potential of the defective pipe divided by that of the ‘pseudo’ perfect one, is then employed to reveal the effect of cracks on the electric potential. By depicting the contours of the defect influence factor with sufficient resolution, not only the position, but also the shape and length size of cracks in the pipe can be identified accurately by the detection criterion devised in this work. The types of detectable through-wall cracks include circumferential crack, inclined crack, and multiple cracks. Good detection results show the merits of the procedure developed for the identification of the simulated cracks as described above in the pipe structure.     

Influence of flow stress choice on the plastic collapse estimation of axially cracked steam generator tubes

The influence of the choice of flow stress on the plastic collapse estimation of axially cracked steam generator (SG) tubes is considered. The plastic limit and collapse loads of thick-walled tubes with external axial semi-elliptical surface cracks are investigated by three-dimensional non-linear finite element (FE) analyses. The limit pressure solution as a function of the crack depth, length and tube geometry has been developed on the basis of extensive FE limit load analyses employing the elastic–perfectly plastic material behaviour and small strain theory. Unlike the existing solutions, the newly developed analytical approximation of the plastic limit pressure for thick-walled tubes is applicable to a wide range of crack dimensions. Further, the plastic collapse analysis with a real strain-hardening material model and a large deformation theory is performed and an analytical approximation for the estimation of the flow stress is proposed. Numerical results show that the flow stress, defined by some failure assessment diagram (FAD) methods, depends not only on the tube material, but also on the crack geometry. It is shown that the plastic collapse pressure results, in the case of deeper cracks obtained by using the flow stress as the average of the yield stress and the ultimate tensile strength, can become unsafe.     

Crack opening displacement of a through-wall crack in a plate subjected to bending load

This study was performed in order to clarify crack opening displacement (COD) of through-wall cracks in a plate subjected to bending load. The former COD evaluation methods were mainly developed corresponding to tensile load, but there has been nothing that has been developed corresponding to bending load. Therefore, the authors evaluated CODs of the through-wall cracks in plates which were subjected to a bending load using finite element method (FEM) analyses, and proposed a simplified COD evaluation method accounting for both tensile and bending loads. The proposed method is useful for leakage evaluation at a crack opening of an elbow crown or in the vicinity of the coolant surface of a vessel in which the bending stress is relatively large.     

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.     

Short circumferential through-wall cracked pipes subjected to stretch-bending load

The methods for assessment of elastic–plastic fracture behaviour of cracked components include the net section plastic collapse concept, the J-integral approach, and the two-parameter R-6 failure assessment diagram, Revision 3. These failure assessment methods are usually used to obtain fracture behaviour prediction with a reasonable degree of accuracy without carrying out complicated full-length numerical fracture analysis. In the current work, fracture experiments on stainless steel pipes with short circumferential through-wall cracks under stretch-bending load were conducted. Stretch-bending load refers to the loading situation where axial load is generated that is proportional or related to the applied bending load. The J-integral values derived from the experimental load-point load–displacement data under stretch-bending and pure bending conditions are compared to investigate the effect of axial load on the J–resistance curves. The results show clear dependence of crack resistance force on axial load for short circumferential cracks. Crack resistance force decreased noticeably for increased stretch-bending loading compared to pure bending loading.     

动态载荷下奥氏体不锈钢管道LBB环向贯穿裂纹稳定性实验及理论分析方法研究

管道环向贯穿裂纹是否稳定是评判管道是否满足破前漏（LBB）设计准则的标准之一,为确保LBB技术安全可靠,对管道环向贯穿裂纹在动态载荷下的稳定性进行实验研究。采用水平冲击机对含环向贯穿裂纹的管道依次进行加载速度为1.22、2、3、4 m/s的高温不带运行压力的冲击实验,以获得各应变率下的实验极限载荷值,并与工程理论分析计算结果进行比较。分析表明:奥氏体不锈钢管道环向贯穿裂纹在动态载荷下的失效模式为塑性失稳;经实验验证,在工程中对承受动态载荷的奥氏体不锈钢管道进行LBB分析时,采用美国核管会标准审查大纲3.6.3破前漏评估程序（SRP 3.6.3）中的极限载荷理论分析方法具有较高的工程安全性,若同时选用准静态下的材料力学性能,则工程安全性更高。      

Development of the evaluation method for crack propagation due to thermal striping

The evaluation code “THERST” was developed to estimate the fatigue crack propagation behavior under thermal stresses due to high-frequency temperature fluctuations, called “thermal striping”. This paper presents fundamental formulations of the evaluation method and verifications of the evaluation method by FEM analyses. Experimental data were obtained in high cycle thermal fatigue tests and the effect of a multiple crack which is characteristic for a crack under thermal stress is discussed in addition to the results of the FEM analyses. A modification of the evaluation method was performed to take multiple crack effects into account.     

Effects of off-centered cracks and restraint of induced bending caused by pressure on the crack-opening-area analysis of pipes

Current models for the crack-opening-area analysis of pipes with circumferential through-wall cracks are based on various idealizations or assumptions which are often necessary to simplify the mathematical formulation and numerical calculation. This paper focuses on the validity of two such assumptions that involve off-centered cracks and the restraint of induced bending caused by pressure, and quantifies their effects on the crack-opening area analysis of pipes. Finite element and/or simple estimation methods were employed to compute the center-crack-opening displacement and crack-opening shape for a through-wall-cracked pipe, considering off-centered cracks and the restraint of induced bending caused by pressure. The results of the analyses show that, for both cases, the crack-opening area can be reduced significantly. For pipes with off-centered cracks, the crack-opening area can be evaluated from analyses of symmetrically centered cracks and assuming elliptical profile. For pipes with complete restraint of the induced bending caused by pressure, the reduction in crack-opening area depends on the crack size. When the crack size is small, the restraint effects can be ignored. However, when the crack size is large, the restrained crack opening can be significantly smaller than the unrestrained crack opening, depending on the length of pipe involved; hence, it may be important for the crack-opening-area and leak-rate analyses.     

Validation of simplified fracture mechanics methods by testing of real components

The evaluation of integrity of structural components is often based on the proof of leak-before-break (LBB). Leak-before-break behaviour in piping constitutes a fail-safe condition. Which means that, during multiplied loading conditions, a defect results at first in a leakage. The crack length which leads to the leakage is smaller than the critical through-wall crack length. Simplified fracture mechanics concepts are used for the demonstration of LBB. For this the conservative, safe calculation of the critical through-wall crack length for ductile failure is necessary. To validate simplified calculation methods for circumferential cracks (flow stress concept (FSC); plastic limit load (PLL)) and for axial cracks (Battelle approach (BMI); Ruiz approach (RUIZ)) all available experiments on real structural components, especially on pipes, were analysed and evaluated by the mentioned simplified methods (approximately 460 experiments). The methods were adapted by application of correction factors, mainly on the flow stress, to result in conservative (safe) and realistic (as near as possible to the experiments) predictions. Depending on method (FSC, PLL, BMI, RUIZ), crack orientation (circumferential and axial cracks) and type of material (ferritic and austenitic material) different definitions of flow stresses were established.     

压力管道“先漏后破”评定的准则研究

以弹塑性断裂力学为基础,分别建立了轴向表面裂纹和周向表面裂纹韧带的极限失稳压力Pu和穿透裂纹的起裂压力Pc的表达式,提出了一种压力管道的"先漏后破"缺陷评定准则:即若管道表面裂纹韧带的极限失稳压力Pu低于相应穿透裂纹的起裂压力Pc,则管道会泄漏失效;若管道表面裂纹韧带的极限失稳压力Pu等于或大于相应穿透裂纹的起裂压力Pc,则管道会爆破失效.该准则得到了一些文献提供的试验数据的验证.     

Failure and fracturing analysis of concrete structures

Some aspects of fracture analysis of concrete structures are discussed in this article. In particular it is shown that when localized failure occurs (by macrofracture propagation or localization of strain) structural size effects come into play. Mesh dependent finite element solutions are then observed unless size effects are correctly accounted for.Tensile fracture is examined first. The “classical” discrete and smeared crack approaches are reviewed and their extension to nonlinear fracture models like the fictitious crack model and the crack band model is illustrated. The smeared crack approach coupled first with a tensile strength criterion, second with a linear elastic fracture mechanics criterion is then applied to the failure mode analysis of a PCRV.Plastic fracturing with localization into shear bands, strain softening, mesh dependence and its correction are examined next. The use of plasticity for tensile fracture simulation is also discussed.Finally numerical difficulties inherent to the modeling of softening behavior are investigated.     

Elastic-plastic finite element analyses of stable crack growth and fracture instability in a girth welded pipe

Detailed elastic-plastic finite element fracture mechanics analyses were conducted on a 16 inch diameter Type 304 stainless steel pipe containing a circumferential through-wall crack located in a girth weld. Calculations were performed to analyze the welded pipe treated as (1) a monolithic pipe entirely composed of the base metal, and (2) a composite of base metal and weldment. In the latter, each constituent was assigned distinct mechanical and fracture properties. In both solutions applied J values were calculated for a fixed axial load combined with a monotonically increasing applied bending moment. The material J-resistance curves appropriate for the two problems were each used to initiate and grow the initial crack in a stable manner until fracture instability occurred under load control. It was found that the extent of stable crack growth and the applied loads at fracture instability are distinctly different in the two analyses. It is concluded that more precise fracture mechanics approaches than those now in current use are required for accurate assessments of weld cracking problems.     

Application of first and second order reliability methods in the safety assessment of cracked steam generator tubing

The First- and Second Order Reliability Methods (FORM and SORM) have been applied in the safety assessment of steam generator tubes with through-wall axial stress corrosion cracks. The underlying probabilistic fracture mechanics model takes into account the scatter in tube geometry, material properties and stable crack propagation. Also, the effect of the maintenance strategy has been considered. A realistic numerical example has been given to compare the failure probabilities calculated by FORM and SORM to those obtained by different versions of Monte Carlo simulations. The relative errors of the numerical methods employed have been analysed, which has shown that FORM performs in an acceptable and SORM in an excellent manner. Some changes in failure surface properties, caused by different maintenance strategies, are indicated and a sensitivity analysis of influencing parameters is made. The results obtained demonstrate the applicability of FORM and SORM in the safety assessment of stress corrosion cracked steam generator tubing.     

Simulation of the fracture behavior of Zircaloy-4 cladding under reactivity-initiated accident conditions with a damage mechanics model combined with fuel performance codes FEMAXI-7 and RANNS

A continuum damage mechanics model using FEM calculations was proposed to be applied to an analysis of the fuel failure due to pellet cladding mechanical interaction (PCMI) under reactivity-initiated accident conditions. The model expressed ductile fracture via two processes: damage nucleation related to void nucleation and damage evolution related to void growth and linkage. The boundary conditions for the simulations were input from the fuel performance codes FEMAXI-7 and RANNS. The simulation made reasonable predictions for the cladding hoop strain at failure and reproduced the typical fracture behavior of the fuel cladding under the PCMI loading, characterized by a ductile shear zone in the inner region of the cladding wall. It was shown that occurrence of a through-wall crack is determined at an early stage of crack propagation, and the rest of the through-wall penetration process is achieved with a negligible increment in strain. The effect of a local temperature rise in the cladding inner region on the failure strain was found to be less than 5% for the conditions investigated. Failure strains predicted under a plane strain loading were smaller by 20%–30% than those predicted under equibiaxial tensions between the hoop and the axial directions.     

Approximate fracture methods for pipes — Part II: Applications

In the part I paper entitled “Approximate fracture methods for pipes — Part I, Theory” [4], five different J-estimation schemes for through-wall cracked pipes were presented. The (i) GE.EPRI method utilizes a compilation of finite-element solutions. The (ii) Paris/Tada and (iii) LBB.NRC methods utilize an interpolation between the linear elastic and rigid plastic solutions, (iv) the LBB.GE method also uses numerical solutions, and (v) the LBB.ENG uses an equivalent area method to estimate J. All five methods are very simple to use and all five give reasonable predictions of crack growth and failure in pipes. The present paper provides a comparison of some of the methods to full-scale finite-element analyses. In addition, predictions for actual pipe experiments compared to experimental data are also provided.     

Elastic-plastic analysis of small cracks in tubes under internal pressure and bending

Elastic-plastic finite element analyses were conducted to generate new solutions of J-integral and crack-opening displacement (COD) for short through-wall cracks in pipes subjected to combined bending and tension loads. The results are presented in terms of the well-known GE/EPRI influence functions to allow comparisons with some limited results in the literature. Two different pipe pressures with values of 7.24 MPa (1050 psi) and 15.51 MPa (2250 psi) simulating BWR and PWR operating conditions, respectively, were used to evaluate the effects of pressure on J and COD. Pipes with various radius-to-thickness ratios, crack sizes, and material parameters were analyzed. Limited analyses were also performed to evaluate the effects of hoop stresses in pipes under pure pressure loads. The results suggest that the fracture response parameters can be significantly increased by pressure-induced axial tension for larger crack size, material hardening constant, and radius-to-thickness ratio of the pipe. The presence of pressure-induced hoop stresses also increases the fracture response, but in low-hardening materials their effects are insignificant due to small plastic-zone size that was expected for the intensity of pipe pressure and crack size considered in this study. However, for high-hardening materials when the plastic-zone size is not negligible, the hoop stresses can moderately increase J and COD.