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.     

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.     

Predictions of displacements and stresses in cracked reinforced concrete containment vessels subjected to seismic loads

A three dimensional, nonlinear finite element analysis capability for analysis of cracked reinforced concrete nuclear containment vessels is described. A bilinear shear stress-shear strain model, based on experiments, is used to study the distribution of radial and tangential shear produced by horizontal seismic loading. Results show substantial redistribution of tangential shear, and significant increases in radial shear, peak bending stress, and vessel displacement, as compared to conventional linear analysis results.     

Crack growth and fracture behaviour of pipes with circumferential defects under internal pressure and superimposed alternating bending load

Pipes made of 20 MnMoNi 5 5 steel and an MnMoNiV special melt, with an external diameter of 800 mm, wall thickness of 47 mm and length of up to 5500 mm, were provided with circumferential defects of defined length and depth. The pipes were loaded by internal pressure and a superimposed alternating bending moment. During the tests, deformation and crack growth were determined in the wall thickness and circumferential direction, and these were compared with calculated values. Pipes with an outer diameter of 226 mm and a wall thickness of 20 mm were used to investigate the leak-before-break behaviour in the dynamic sphere. These pipes also were made of 20 MnMoNi 5 5 steel and an MnMoNiV special melt, and were loaded with internal pressure and an alternating bending moment. The excitation took place at the resonance frequency of the pipes. The pipes also contained circumferential defects of defined length and depth.     

Opening and extension of circumferential cracks in a pipe subject to dynamic loads

Nuclear power plants are presently designed to withstand instantaneous pipe severance in combination with the maximum seismic loads. The hypothetical combination of these two unlikely events leads to system designs which are very expensive and require dynamic event devices such as pipe whip restraints which have the potential for deleterious interaction with the piping system during normal operations. These present pipe rupture criteria are based on the a priori hypothesis that the instantaneous guillotine pipe break is possible, rather than from a consideration of the manner in which cracks might open or extend in a real piping system. The objective of this study is to help establish the basis for understanding how cracks which might exist in the primary piping of a pressurized water reactor (PWR) would open and extend so that improved criteria can be developed based on this information.One of the regions where loss of pressure boundary integrity must be postulated is the terminal end of the cold leg at the reactor vessel inlet nozzle. This region (including the effects of the reactor vessel and the primary pump) is modelled for analysis with the MARC general purpose finite element program. A circumferential crack, one-half circumference long, is considered to suddenly occur around the outside of the elbow when the pipe is at normal operating pressure. The most severe part of the safe shutdown earthquake (SSE) loading transient is applied simultaneously with the initiation of the crack.The plastic dynamic analysis of the crack opening effects in the discharge leg pipe is performed using the MARC program until the maximum opening occurs. The J-integral plastic crack extension criterion is computed for all times during the transient. The results indicate that none of the cracks will extend significantly and that the opening areas are small fractions of the flow area of the pipe.     

Comparison of critical circumferential through-wall crack lengths in welds between pieces of straight pipes to welds between straight pipes and bends, with and without internal pressure at force- and displacement-controlled bending load

In many research projects methods to calculate critical circumferential through-wall cracks have been developed and verified. During the last years, the differentiation between force- and displacement-controlled loading has been shown to be of significant importance. So it was looked at with more interest in new analytical methods to calculate the critical crack length. Most of the approaches applied in the safety analysis of piping systems assume defect at welds connecting pieces of straight pipes. But in nearly all cases in modern power plants the true position of the welds in the piping system is not correctly represented, as in those systems only few welds connect parts of straight pipes. Most of the connections are situated between pipes and bends, bends with elongated ends, nozzles or T-parts. This paper presents a non-linear finite element (FEM) study covering an essential part of the relevant piping parameters of nuclear power plants primary and secondary system. It compares defects in circumferential welds between straight pipes to those joining pipes to elbows. In the case of displacement controlled loading, e.g. as due to restrained thermal expansion, which is one of the most severe load cases for most of the welds, we find, that the calculated J-integral values, and so the critical crack length are of comparable size. At force-controlled loading the codes require stronger limitations to the allowable forces and moments. In the regime of allowable loads, we find that the critical crack sizes in welds near bends are not significantly longer than the ones connecting straight pipes. In the cases where we have to consider in the safety analysis of piping systems, it is a realistic approach to use the methods accepted for welds between pipes to calculate the critical crack length in welds near bends.     

Crack initiation, crack growth and fracture behaviour of large diameter pipes with circumferential defects under internal pressure and superimposed alternating bending load

Pipes made of steel 20 MnMoNi 5 5 and MnMoNiV-special melt having an external diameter of 800 mm, wall thickness of 47 mm, and length of up to 5500 mm were provided with circumferential defects of defined length and depth. They were loaded by internal pressure and a superimposed alternating bending moment. During the tests deformation and crack growth were determined in the wall thickness and circumferential direction. Pipes with an outer diameter of 226 mm and a wall thickness of 20 mm were used to investigate the leak-before-break behaviour in the dynamic sphere. These pipes were also made of steel 20 MnMoNi 5 5 and a MnMoNiV-special melt and were loaded with internal pressure and an alternating bending moment. The excitation took place at the resonance frequency of the pipes. The pipes also contained circumferential defects of defined length and depth.     

Elasto-plastic behavior of pipe subjected to steady axial load and cyclic bending

The elasto-plastic behavior of a pipe subjected to a steady axial force and a cyclic bending moment is studied. By using two parameters c and d, which describe the elasto-plastic interfaces of beam cross-section, the boundary curve equations between various types of elasto-plastic behavior, such as shakedown, plastic fatigue, ratcheting, and plastic collapse, are derived. The results are applicable for beams of any cross-section with two orthogonal axes of symmetry. As a result, the load regime diagram for a pipe is obtained, which gives an intuitive picture of the elasto-plastic behavior of the pipe under a given combination of constant axial load and cyclic bending moment.     

Evaluation of ductile tearing in cracked pipes and elbows under bending

A major project was launched in France to develop leak-before-break methods applicable to the primary circuit of pressurized water reactors. An important aspect is to be able to calculate the resistance strength of piping components (tube or elbow) that contain a through-wall circumferential crack. This paper presents details of the development of an experimental method that can be used to define J-R curve, using experiments performed on cracked tubes and elbows at room temperature. Applications for components made from ferritic steel and austenitic steels are described. It is concluded that the procedure could be effective for characterizing the real behaviour of cracked pipes or elbows.     

Comparison of stress intensity factor solutions for cylinders with axial and circumferential cracks

Numerous stress intensity factor solutions have been proposed so far depending on the objects of evaluation including the variations of structures, cracks, and applied loads. In applying the flaw evaluation methodology to components of nuclear power plants, the use of reliable stress intensity factor solutions is essential. In this study, cracked cylinders were focused on as one of the typical configurations in actual plants. Existing stress intensity factor solutions for cracked cylinders were reviewed, and the accuracy of these solutions was investigated thorough the comparison with each other. Specific solutions were then recommended for cylindrical structures. Approximate expressions were newly derived for axially through-wall cracked cylinder subjected to linear stress distribution and for circumferentially through-wall cracked cylinder subjected to bending to realize simple evaluation of stress intensity factor. Considering that the cylindrical structures are often replaced with flat plates in the evaluation of actual components, the propriety of the replacement was also studied.     

Dynamic behaviour of thin cylindrical shells subjected to impulsive bending moments along their tips

The dynamic behaviour of thin cylindrical shells with concentrated masses at their tips is investigated when they are subjected to impulsive bending moments at their tips. The relationships between the dimensions of a cylinder, concentrated mass and maximum values of dynamic stresses are obtained. The fundamental equation of motion is solved by the Laplace transformation method. From the results of the theoretical analysis, it became evident that impulsive stresses become much larger than static ones. For the case where bending moments are applied statically, the fundamental equations are also derived, taking into account the effect of shearing force.     

Fracture behavior of carbon steel pipe with local wall thinning subjected to bending load

To evaluate the structural integrity of power plant piping, monotonic bending tests are conducted on 4- and 3.5-in. diameter full-scale carbon steel pipe specimens with local wall thinning. The local wall thinning is simulated as erosion/corrosion metal loss. The eroded area of the wall thinning is subjected to tensile or compressive stress by applied bending moment. The deformations or fracture behaviors at maximum moments are found to be classified into three types. When the eroded area is subjected to tensile stress, ovalization or crack initiation/growth occurs at the maximum moment. When an eroded area is subjected to compressive stress, ovalization or local buckling occurs. The occurrence of ovalization, crack initiation/growth, or local buckling depends on the initial size of local wall thinning. From the relationships among ovalization, crack growth and local buckling, allowable sizes for local wall thinning are proposed.     

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.     

Fracture strength and behavior of carbon steel pipes with local wall thinning subjected to cyclic bending load

The power plant piping is designed to withstand seismic events using the design fatigue curve. However, the fatigue strength of a pipe with local wall thinning caused by erosion/corrosion is not clear. To evaluate the fatigue strength of pipes with local wall thinning, low cycle fatigue tests were conducted on 100A carbon steel pipes with local wall thinning. In load controlled tests on these pipes, ratcheting deformation was observed, and the fatigue strength became lower than that of cracked pipes. In displacement controlled tests, the fatigue strength of eroded pipes with 100 mm in eroded axial length, 0.5 in normalized eroded depth and 90° in eroded angle was almost equal to that given by the design fatigue curve in ASME B&PV Code Sec. III. To evaluate the local strain range in the maximum wall thinning area, the finite element analysis was conducted on the eroded pipes in the displacement controlled tests. It is concluded that the Mises strain range in the maximum wall thinning area and the low cycle fatigue curve can be used to conservatively estimate the low cycle fatigue life of an eroded pipe and the validity of estimated results can be confirmed experimentally.     

Investigation of the structural behaviour of nuclear spent fuel reprocessing plant components subjected to dynamic loads

In the planned reprocessing plant for spent nuclear fuel elements in Germany components and systems, which form a process-technical unit are integrated in a steel structure called a “module”. In the present paper, the stability and strength of two representative modules under dynamic loading due to earthquake are investigated. Since full scale models of the modules exist, both analytical and experimental investigations are possible. The results of the two investigation methods are in good agreement. Both modules withstand the earthquake loadings with only minor modifications.     

Approximate evaluation method for ductile fracture analysis of a circumferentially through-wall-cracked pipe subjected to combined bending and tension

To estimate the structural integrity of the Light Water Reactor piping, combined loading consists of a tensile load due to internal pressure and a bending load under seismic conditions should be considered as a basic loading mode. However, theoretical investigation on the methodology to evaluate ductile fracture behavior is not adequate to date. In this study, an approximate evaluation method, ‘LBB.ENGC’, for ductile fracture analysis of a circumferentially through-wall-cracked pipe subjected to combined bending and tension was newly developed. This method can explicitly incorporate the contribution of both tension and bending. The effect of growing crack is also considered in the method. The LBB.ENGC was then applied to the full-scale pipe fracture tests. Based on the comparison with experimental results as well as finite element calculations, it could be ascertained that the LBB.ENGC could well predict ductile fracture behavior under combined loading. The effect of combined loading on ductile fracture was sensitivity-studied using the LBB.ENGC. As a result, it was quantitatively found that the superposition of longitudinal stress reduced the maximum bending load of cracked pipe.     

Current state of knowledge on the behavior of steel liners in concrete containments subjected to overpressurization loads

In the US, concrete containment buildings for commercial nuclear power plants have steel liners that act as the internal pressure boundary. The liner abuts the concrete, acting as the interior concrete form. The liner is attached to the concrete by either studs or by a continuous structural shape (such as a T-section or channel) that is either continuously or intermittently welded to the liner. Studs are commonly used in reinforced concrete containments, while prestressed containments utilize a structural element as the anchorage. The practice in some countries follows the US practice, while in other countries the containment does not have a steel liner. In this latter case, there is a true double containment, and the annular region between the two containments is vented.This paper will review the practice of design of the liner system prior to the consideration of severe accident loads (overpressurization loads beyond the design conditions).An overpressurization test of a 1:6 scale reinforced concrete containment at Sandia National Laboratories resulted in a failure mechanism in the liner that was not fully anticipated. Post-test analyses and experiments have been conducted to understand the failure better. This work and the activities that followed the test are reviewed. Areas in which additional research should be conducted are given.     

Analytically predicted versus measured response of a free-standing steel containment vessel subjected to safety-relief valve discharge loads

Following the actuation of safety-relief valves in BWR nuclear power plants, first water then air and steam are cleared from the discharge lines through quencher devices into a suppression pool. This clearing results in water spike, air bubble, and condensation pressure loads applied to structures in the pool, and the surrounding containment vessel.The Leibstadt Nuclear Power Plant has the only free-standing steel Mark III containment vessel in the world. All other steel Mark III containment vessels have concrete backing in the suppression pool region, which dampens clearing load responses. As such, it is of interest to note how this steel vessel responds to discharge pressures, and compare these responses to analytically predicted results.The purpose of this paper is to compare the analytical results used to design the steel containment vessel with the responses measured during in-plant testing. The analytical methods considered the effects of fluid-structure interaction. The test program included initial and consecutive actuations of a single valve, and initial actuation of multiple (four) valves. The conclusion of the comparison is that, in general, there are large conservatisms in the analytical predictions versus measured responses.