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.     

Limit load solutions of thick-walled cylinders with fully circumferential cracks under combined internal pressure and axial tension

Limit load solutions for thick-walled cylinders with fully circumferential inner/outer cracks under combined internal pressure and axial tension are derived, considering the elastic-perfectly plastic material properties and von Mises yield criterion. The solutions are consistent with the thin-walled solution when the walls of the cylinders become thin compared with their radii. Elastic-perfectly plastic finite element (FE) analyses are performed to validate the solution. The results show that the solutions obtained in this paper agree reasonably well with the FE results and are conservative.     

Thermal shock experiments on cracked cladded plates

To investigate the effect of the cladding on the behaviour of postulated near surface cracks in the wall of a nuclear pressure vessel under thermal shock transients, two model experiments on cladded plates with artificially introduced cracks were performed. In numerical finite element analyses temperatures and stresses as well as crack driving force for different parts of the crack front were calculated for the applied loads. The results were used to verify analytical defect assessment methods and to analyse the crack behaviour. A comparison of observed crack initiation and arrest events for a subclad and for a surface crack experiment with results of analytical and FE analyses shows good agreement.     

含整圈周向裂纹厚壁圆筒在内压和轴力共同作用下的极限载荷-简化滑移线场解

采用简化的滑移线场理论,推导出了含整圈环向裂纹厚壁圆筒在内压和轴力共同作用下的理想弹塑性材料极限载荷表达式,并采用有限元方法进行了验证.结果表明,对于含内表面裂纹的圆筒,其极限载荷解可由基于简化滑移线场的极限载荷解与无裂纹圆筒极限载荷解共同确定.有限元验证结果显示,理论解与有限元结果非常一致,且偏于保守.对含外表面裂纹的圆筒,其基于简化滑移线场的极限载荷解只适用于非常深的裂纹.其它情况建议使用基于Mises准则的解.     

Restraining effect of support plates on the limit loads for circumferential cracks in the steam generator tube

The steam generator in a nuclear power plant is a large heat exchanger that uses heat from a reactor to generate steam to drive the turbine generator. Rupture of a steam generator tube can result in release of fission products to environment outside. Therefore, an accurate integrity assessment of the steam generator tubes with cracks is of great importance for maintaining the safety of a nuclear power plant. The steam generator tubes are supported at regular intervals by tube support plates and rotations of the tubes are restrained. Although it has been reported that the limit load for a circumferential crack is significantly affected by boundary condition of the tube, existing limit load solutions do not consider the restraining effect of tube support plate correctly. In addition, there are no limit load solutions for circumferential cracks in U-bend region with the effect of tube support plate. This paper provides detailed limit load solutions for circumferential cracks in top of tube sheet and the U-bend regions of the steam generator tube with the actual boundary conditions to simulate the restraining effect of the tube support plate. Such solutions are developed based on three-dimensional (3-D) finite element analyses. The resulting limit load solutions are given in a polynomial form, and thus can be simply used in practical integrity assessment of the steam generator tubes.     

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.     

Mechanical integrity analysis of TMI-1 OTSG unplugged tubes

Small I.D. circumferential defects have been identified in many steam generator tubes. The origin of the cracks is known to be chemical, not mechanical. A fracture mechanics evaluation has been conducted to ascertain the stability of tube cracks under steady-state and anticipated transient conditions. A spectrum of hypothetical crack sizes was interacted with tube stresses derived from the load evaluation using the methods of linear elastic fracture mechanics (LEFM). Stress intensities were calculated for part-through wall cracks in cylinders combining components due to membrane stress, bending stress, and stresses due to internal pressure acting on the parting crack faces as the loads are cycled.The LEFM computational code, “BIGIF”, developed for EPRI, was used to integrate over a range of stress intensities following the model to describe crack growth in INCO 600 at operating temperature using the equation (ΔK)^3.5.The code was modified by applying ΔK_Th, the threshold stress intensity range. Below ΔK_Th small cracks will not propagate at all. Appropriate R ratio values were employed when calculating crack propagation due to high cycle or low cycle loading.Cracks that may have escaped detection by ECT will not jeopardize tube integrity during normal cooldown unless these cracks are greater than 180° in extent. Large non-through-wall cracks that would jeopardize tube integrity are not expected to evolve because in axi-symmetric tensile stress fields, cracks propagate preferentially through the tube wall rather than around the circumference. Tube integrity can be demonstrated for mid-span tube regions and for the transition region as well.The as-repaired transition geometry is a design no less adequate than the original. The as-repaired condition represents an improvement in the state of stress due to mechanical and thermal loads as compared to the original.     

Life Time Estimation for Cladding Tube Cracking Caused by Absorber Swelling of PWR RCCA Rodlets

Intergranular cracks of cladding tubes had been observed at the tips of the rodlets of PWR rod cluster control assemblies (RCCAs). Because RCCAs are important core components, an investigation was carried out to estimate their service life time.

(1) As it is essential to know the effect of slumping of the neutron absorber for the life time estimation, tests on absorber material were carried out. Both the dynamic and static stresses of the absorber are sufficiently small compared with its mechanical characteristics and it is concluded that slumping does not occur.

(2) The crack was initiated at the inner surface of the cladding tubes and Sipush et al. obtained an intergranular fracture surface in tensile tests of similar material at a very slow strain rate in an argon gas atmosphere. Therefore the mechanism of the intergranular crack of the cladding tube is not IASCC but irradiation assisted cracking (IAC) caused by an increase in hoop strain due to the swelling of the absorber and a decrease in elongation due to neutron irradiation.

(3) The crack initiation limit of cylindrical shells made of low ductile material and subjected to internal pressure is determined in relation to the uniform strain of the material and is in accordance with that of the RCCA rodlets in an actual plant.

From the above investigation, the method of estimating the life time and countermeasures for its extension are obtained.     

An elasto-plastic fracture mechanics based model for assessment of hydride embrittlement in zircaloy cladding tubes

This paper describes a finite element based fracture mechanics model to assess how hydrides affect the integrity of zircaloy cladding tubes. The hydrides are assumed to fracture at a low load whereas the propagation of the fractured hydrides in the matrix material and failure of the tube is controlled by non-linear fracture mechanics and plastic collapse of the ligaments between the hydrides. The paper quantifies the relative importance of hydride geometrical parameters such as size, orientation and location of individual hydrides and interaction between adjacent hydrides. The paper also presents analyses for some different and representative multi-hydride configurations. The model is adaptable to general and complex crack configurations and can therefore be used to assess realistic hydride configurations. The mechanism of cladding failure is by plastic collapse of ligaments between interacting fractured hydrides. The results show that the integrity can be drastically reduced when several radial hydrides form continuous patterns.     

Prediction of crack coalescence of steam generator tubes in nuclear power plants

Prediction of failure pressures of cracked steam generator tubes of nuclear power plants is an important ingredient in scheduling inspection and repair of tubes. Prediction is usually based on nondestructive evaluation (NDE) of cracks. NDE often reveals two neighboring cracks. If the cracks interact, the tube pressure under which the ligament between the two cracks fails could be much lower than the critical burst pressure of an individual equivalent crack. The ability to accurately predict the ligament failure pressure, called “coalescence pressure,” is important. The failure criterion was established by nonlinear finite element model (FEM) analyses of coalescence of two 100% through-wall collinear cracks. The ligament failure is precipitated by local instability of the ligament under plane strain conditions. As a result of this local instability, the ligament thickness in the radial direction decreases abruptly with pressure. Good correlation of FEM analysis results with experimental data obtained at Argonne National Laboratory’s Energy Technology Division demonstrated that nonlinear FEM analyses are capable of predicting the coalescence pressure accurately for 100% through-wall cracks. This failure criterion and FEA work have been extended to axial cracks of varying ligament width, crack length, and cases where cracks are offset by axial or circumferential ligaments.     

Investigation on constraint effect of reactor pressure vessel under pressurized thermal shock

In recent years, the integrity of reactor pressure vessels (RPVs) under pressurized thermal shock (PTS) accident has been treated as one of the most critical issues. Under PTS condition, the combination of thermal stress due to a steep temperature gradient and mechanical stress due to internal pressure causes considerable tensile stress inside the RPV wall. As a result, cracks on the inner surface of RPVs can experience elastic-plastic behavior that can be explained using the J-integral. In such a case, however, the J-integral may possibly lose its validity due to the constraint effect. The degree of constraint effect is influenced by the loading mode, the crack geometry and the material properties. In this paper, three-dimensional finite element analyses are performed for various surface cracks to investigate the effect of clad thickness and crack geometry on the constraint effect. A total of 36 crack geometries are analyzed and results are presented by the two-parameter characterization based on the J-integral and the Q-stress.     

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.     

Secondary cracking in hydrided Zr-2.5 Wt% Nb alloys

The occurrence of secondary cracking in cold-worked, hydrided Zr-2.5 wt% Nb pressure tube material has been studied. The results indicate that the secondary cracking can occur during three different modes of propagation of the primary crack, i.e. dynamic fatigue, hydrogen-induced delayed cracking, and ductile fracture. Metallographic studies revealed that the secondary and primary crack planes are approximately perpendicular, and, moreover, the secondary crack path lies either through the brittle zirconium hydride precipitates or the hydride-matrix interface. Evidence is presented to show that the secondary cracks nucleate and propagate within the plastic zone of the primary crack as a result of the transverse (through thickness) component of the triaxial stress at the crack tip. During hydrogen-induced delayed cracking, the secondary cracks either propagated with the primary stable crack, causing pronounced cusping of the crack front, or more typically growth of the secondary cracks terminated at an early stage, and the main crack broke away from the secondary cracks. This difference in behaviour is thought to be related to the degree of hydride continuity and alignment in the matrix.     

Failure assessment of RPV nozzle under loss of coolant accident

In case of a postulated loss of coolant accident (LOCA) of a reactor pressure vessel (RPV), the nozzle region experiences higher stresses and lower temperatures than the remaining part of the RPV. Thus, the nozzle is to be considered in the RPV safety assessment. For a LOCA event, three-dimensional elastic–plastic finite element calculations of stresses and strains in the intact RPV were performed. Using the substructure technique, fracture mechanics analyses were then carried out for several postulated cracks in the nozzle corner and in the circumferential weld below the nozzle. For different crack geometries and locations, the J-integral and the stress intensity factor were calculated as functions of the crack tip temperature. Based on the K_IC-reference curve and the J_R curve, both brittle and ductile instability of the postulated cracks were excluded. In order to reduce the expenses of three-dimensional finite element analyses for various crack geometries, an analytical procedure for calculating stress intensity factors of subclad cracks in cylindrical components was extended for cracks in the nozzle corner.     

Fracture mechanics analysis of iodine-induced crack growth in Zircaloy-4 tubing between 500 and 700°C

Low ductility failure of zircaloy tubing due to iodine-induced stress corrosion cracking (SCC) can occur up to about 700°C. The time-to-failure behavior of Zircaloy-4 cladding tubes containing iodine has been described by the elastic-plastic fracture mechanics model CEPFRAME for the temperature region 500 to 700°C. The model includes an empirically-determined computation method for the incubation period of crack formation, as a portion of the time-to-failure, as well as an elastic-plastic model for describing crack growth due to iodine-induced SCC. The total life time of the cladding tube is obtained by adding the crack initiation and crack propagation periods. The incubation period is a temperature-dependent function of both the depth of surface damage (both fabrication pits and machined notches) and the applied load, and is 40 to 90% of the time-to-failure. The elastic-plastic crack growth model is a modified version of the stress intensity K_I-concept of linear-elastic fracture mechanics. The extensions of this concept take into account a plastic strain zone ahead of the crack tip, which effectively increases the crack depth, and in addition, a dynamic correction factor for the crack geometry which is essentially a function of the effective crack depth. Unstable crack growth is predicted to occur when the residual cross section reaches plastic instability.Model results show good agreement with experimental data of tube burst tests at 500, 600, and 700°C. The crack growth velocity at all three temperatures is a power function of stress intensity ahead of the crack tip; the exponent is 4.9. The model can estimate time-to-failure of as-received cladding tubes containing iodine within a factor of 2. Application of the model to temperatures below 500°C is possible in principle. Due to the increasing scatter in experimental data, the structural transformation of the cladding by recrystallization, and the growing importance of creep strain, CEPFRAME has an upper temperature limit of approximately 650°C. The model is suitable for use in computer codes describing LWR fuel rod behavior during reactor transients and accidents.     

Leak-before-break and plastic collapse behaviour of statically indeterminate pipe system with circumferential crack

Much research has been carried out on Leak-Before-Break (LBB) behavior of pipes with cracks. However, most studies have been made on statically determinate pipe systems. Few studies have been made on LBB behavior of statically indeterminate pipe systems. Most pipe systems in nuclear power plants have supports and restraints, thus they can be considered as statically indeterminate pipe systems. From above points of view, LBB and plastic collapse behaviors of statically indeterminate pipe with circumferential crack and compliance were studied in this paper. A new method is proposed to analyze and evaluate the LBB and plastic collapse behavior of a statically indeterminate structure. The pipe system of which one end is clamped and the other is supported with compliance was analyzed. The main results obtained are as follows: (1) By combining the limit analysis theory and elastic–plastic fracture mechanics, the effects of crack size, compliance and fracture toughness on load deflection behaviors to failure and structural integrity of statically indeterminate pipe system have been analyzed quantitatively and easily. (2) When a crack grows in a statically indeterminate pipe before plastic collapse, load drop conditions can be derived quantitatively, as a function of J_IC, dJ/da, flow stress, crack size, pipe span length, compliance and flexural rigidity of the pipe. (3) The analytic method developed in this research is useful and convenient to evaluate the LBB and tearing instability behavior of a statically indeterminate pipe system. (4) LBB resolves easily for statically indeterminate pipes with a crack, even when it does not resolve for statically determinate pipes with the same crack. That results from the fact that bending moment redistribution during the fracture process occurs easily for statically indeterminate pipe systems, and its redistribution restrains plastic deformation of the cracked weak section.     

The expansion of a cylinder under conditions of finite plane strain

The problem of the expansion of an initially thick-walled cylinder due to an internal pressure under conditions of plane strain is considered. The cylinder is composed of an elasto-plastic, Tresca material with an associated flow rule. No restriction is placed on the magnitude of the deformation or on the magnitude of the material parameters. Solutions are presented for a particular initial (stress free) geometry and it is shown that the maximum value of the internal pressure is a function of the deformation to strength parameter ratio.     

On the dynamic response of EBR-II ducts to pressure pulses

An important consideration for the continued irradiation of experiments to and beyond pin failure in EBR-II is the response of the duct to a pressure pulse that may result from the rapid release of gas from a failed pin. Although all fuel element failures to date in EBR-II have been benign, typically pjn-holes or hairline cracks, the possibility of cladding bursts during transients cannot be precluded. Thus, the EBR-II project has performed numerous pressure pulse tests on subassembly duct and is continuing with analytical studies as well as additional testing. Investigations are being conducted within the fail-safe analysis framework. Correlation of the duct test results yielded an empirical relationship between the permanent deformations of a duct, and the pressure and volume of the fission gas in the fuel element. Results of the correlation are given for a number of variables including the type of gas, the cladding and duct material, the presence of internal restriction to gas flow, and whether predefected tubes of rupture discs are used to produce the pressure pulse.Preliminary dynamic stress analyses have been conducted using the one-dimensional finite element code, STRAW (Report ANL-8065, June 1974). A comparison of analytical predictions of maximum permanent duct deflection between flats and test results is presented in this paper. The analytical results are shown only for the deflection of a single flat. Since the analysis assumes an axisymmetric pressure pulse, opposing flats have equal deformation. However, in the tests the duct flat closest to the opening in the pressurized tube experienced the largest deformation. Parametric analyses have been conducted to study the influence of pulse shapes and material properties on duct deformation. Initial studies using a triangular pulse have shown that the pulse decay time and plastic hardening slope of the material have negligible influence on duct deformation. Consequently, subsequent studies used a constant decay time of 2 msec and a slope of 80 psi. Among the results discussed in the paper are the influence of peak pressure and yield strength on duct deformation for two rates of pressure rise and the influence of non-uniform pressure on duct deformation. The pressure is assumed to vary linearly from the middle of the flat to the corner. A pressure increase from a uniform 200 to 300 psi at the middle of a flat, increases the deformation by only 14 mil. These results demonstrate the importance of the pulse shape and its distribution over the duct and the material properties of the latter.Additional parametric investigations of duct deformation and dynamic stresses are being conducted. Two-dimensional finite element codes are being employed to study the fracture resistance of irradiated ducts.     

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.     

Buckling sensitivity analysis of cracked thin plates under membrane tension or compression loading

Thin-walled structural components such as plates and shells are commonly used in practical applications such as aerospace, naval, nuclear power plant, pressure vessels, mechanical and civil engineering structures and so on, and the safety assessment of such structures must carefully consider all the phenomena which can decrease the bearing capacity of such elements. Among them, the presence of cracks in thin-walled structures can heavily affects their safety factor with respect to the more common modes of failure such as buckling or fracture. For very thin plate, buckling collapse under compression or even under tension, apart fracture or plastic failure in this last case, can easily take place: the presence of flaws such as through-the-thickness cracks can sensibly modify such ultimate loads. In the paper the effects of cracks’ length and orientation on the buckling loads of rectangular elastic thin-plates - characterised by different boundary conditions and by various Poisson's ratio - under tension and compression, is considered. For tensioned flawed plates a fracture-buckling and a plastic-buckling collapse maps are obtained. After a short explanation of the buckling phenomena in plates, several FE numerical parametric analyses results are presented in terms of critical load multiplier in compression or in tension in cracked plates. The obtained results are discussed and some interesting and useful conclusions regarding the sensitivity to cracks’ presence of buckling loads of thin plates under compression or tension (or fracture in this last case) are explained. The interesting case of tensioned cracked plates is considered by studying the easiest collapse between fracture, plastic flow and buckling: in such cases some failure-type maps are finally determined.