Circumferential Through-wall Crack Research Articles

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.

The effect of crack-system compliance on the leakage area for a circumferentially cracked pipe subjected to combined axial and bending loadings

When formulating a leak-before-break case for circumferentially cracked steel piping, a key requirement is an estimate of the size of through-wall circumferential crack that will give a measurable leakage for normal operating conditions, and this requires a knowledge of the crack opening area. Calculation of this area is usually performed using the stresses at the assumed cracked section, with these stresses being determined via a purely elastic analysis for the piping system and assuming the system to be uncracked. However, a piping system is restrained, i.e. it is built-in at its ends into a larger component, and also because a cracked section is associated with an effective rotational discontinuity, this simple procedure overpredicts the crack opening area and therefore has the potential to jeopardise any leak-before-break argument. The present paper employs a simple analytical procedure for the general situation where the stresses at an assumed cracked section are a combination of bending and axial tensile loadings, thereby generalizing earlier studies which were focused on these loadings considered separately. The conclusion that arises from the study is that, for most practical situations, the overestimation of the crack opening area introduced by inputting the uncracked system stresses into the methodology, should be sufficiently small that it can be disregarded.

Determination of critical circumferential through-wall crack sizes regarding load reduction by increased flexibility in piping systems

Piping systems in power stations are not only loaded by the system pressure and force controlled bending moments e.g. due to the weight of the system, but also by additional bending moments caused by the thermal expansion of the hot system and prescribed motions, as in the case of an earthquake, resulting in displacement controlled moments. To determine critical circumferential through-wall crack sizes in pipes, a method based on the J-integral has been developed, which takes into account the load reduction due to the increased flexibility of a flawed section. The method is presented and compared with results by the finite element method and experimental data.

Analytical and experimental fracture assessment of carbon steel piping with circumferential through-wall cracks under bending

In this paper the true stress-strain curves of carbon steel pipes are described by a three-segment fitting method rather than the Ramberg-Osgood relation for their yield plateau characteristics. Failure assessment curves for carbon steel piping containing circumferential through-wall cracks were obtained by different options in the CEGB R6 approach. The J-integral was calculated using a new expression proposed by the authors. Initiation and maximum moments of piping under bending were predicted by several methods and measured by experiments. Calculated moments were quite close to test results.

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.

J integral estimation fracture analysis for circumferentially cracked carbon steel piping

The three-segment fitting method is presented to describe the material stress-strain curves with yield plateaus. A J integral estimation approach for carbon steel piping with circumferential through-wall cracks was developed. Failure assessment curves obtained using three options in the CEGB R6 approach were proposed for GB20 carbon steel piping under bending. The initiation and maximum moments predicted by the J estimation approach presented in this paper are quite close to the experimental values.

Leak-before-break: estimating the leakage area associated with a through-wall circumferential crack in a steel piping system

A key element in the development of a leak-before-break case for circumferentially cracked steel piping is an estimation of the size of through-wall circumferential crack that will give a measurable leakage under normal operating conditions. This estimation is usually made by calculating the stresses at the assumed crack section via a purely elastic analysis for the piping system, but assuming that the system is in fact uncracked. However because a piping system is built-in at its ends into some large component, and because the crack's presence is associated with an effective kink (rotational discontinuity) at the cracked section, this procedure will underpredict the crack size associated with a specified leakage area, and this has the potential to jeopardise the leak-before-break case. The present paper addresses this problem, and presents a very simple analysis which suggests that, for actual piping systems, the error is very small when one uses a methodology based on the uncracked piping stress to calculate the measurable leakage crack size.

Crack resistance of austenitic pipes with circumferential through-wall cracks

For a monotonously increasing load the correct evaluation of the crack resistance properties of a structure is essential for safety analyses. Considerable attention has been given to the through-wall case, this is generally believed to be the controlling case with regard to complete pipe failure. The maximum load conditions for circumferential crack growth in pipes under displacement-controlled loading has been determined. The need for crack resistance curves, measured on circumferentially through-wall cracked straight pipes of austenitic stainless steel 316 L under bending, is emphasized by the limitation in the data range from small specimens and by the differences in the fracture mechanics procedures. To address these issues and to improve calculational methods a joint fracture mechanics programme is being performed by Electricité de France, Novatome and Siemens-Interatom. The working programme contains experimental and theoretical investigations on the applicability of small-specimen data to real structures.

Crack growth resistance methodologies for austenitic stainless steels

The paper reviews the methodologies that are being used to quantify the effect of cracks in austenitic stainless steel structures. As a framework for discussion, these methodologies, i.e. net-section stress and tearing modulus, used to describe respectively the onset of crack extension and crack stability, are considered with regard to the behaviour of a circumferential through-wall crack in a piping system.

COD of off-centred cracks in pipes under bending load: a geometrical solution

Leak before break analyses require the knowledge of the crack shape and the effect of the acting load. In this paper a very simple but effective model to determine the crack opening displacement (COD) profiles for a circumferential through-wall crack in a pipe under off-centred bending load is proposed. The analytical solution presented allows for calculation of the leakage area, for a given crack length and off-centre angle, on the base of geometrical considerations. The solution proposed can be easily extended to the coupled case of bending and internal pressure loads. The general validity of the proposed model has been verified with an extensive finite element simulation.

Elastic-Plastic Analysis of Small Cracks in Tubes

Analytical methods for predicting the elastic or elastic-plastic behavior of large circumferential through-wall cracks in tubes subjected to bending, tension, or combined bending and tension are well developed. Gilles and Brust (1991) and Gilles et al. (1991) summarize five such methods and provide a number of comparisons between analytically predicted results and experimental data. These techniques consist of developing a method for estimating the value of the J-integral. Classical J-tearing theory is utilized for the analyses. A method has also been recently developed to estimate J for a through-wall crack in a pipe weld (Rahman et al., 1991; Rahman and Brust, 1992). Unfortunately, the ability of these J-estimation techniques to predict the crack growth behavior for small cracks ({<=} 12 percent of the circumference) has not been established, even though such small cracks are often the concern in practical structures. Indeed, the finite element solutions compiled in the GE/EPRI handbook (Kumar et al., 1984) appear quite inadequate for small-size cracks (Gilles and Brust, 1991; Gilles et al., 1991). This paper presents the results of a series of finite element solutions for small cracks tabulated in the spirit of the handbook (Kumar et al., 1984). The theoretical background for the developmentmore » and use of simplified elastic-plastic fracture methods is fully discussed in Gilles and Brust (1991). Here, the authors provide the solutions for J-integral and the crack opening displacements for small crack problems under pure bending. Ongoing work will complete these solutions for tension and for combined tension-bending loads.« less

Limit load analysis and safety assessment of an elbow with a circumferential crack under a bending moment

The use of the leak-before-break concept in the design of a Primary Heat Transport (PHT) piping system for nuclear power plants requires postulation of the largest credible flaws at highly stressed points and demonstration of system stability under the most severe loading conditions. In the PHT piping system, the elbows and branch tees are normally found to be among the most highly stressed piping components. This necessitates detailed flaw evaluation of these components. In the present paper, safety assessment of a pump discharge elbow of 500 MWe Indian PHWR with a throughwall circumferential crack under a bending moment is carried out using the R6 approach. The stress intensity factors (SIF) have been computed by using a database of SIF for elbows with cracks which was generated in one of our recent studies. Limit loads at plastic collapse have been evaluated by carrying out non-linear finite element analysis. Finally, the safety assessment of the pump discharge elbow is performed by doing a sensitivity study on crack length, applied moment and material fracture toughness.

Experimental calibration of stress intensity factor for piping with circumferential through-wall crack

A survey of the literature shows that the existing stress intensity factor solutions for circumferential through-walled cracks in piping may be classified into three categories. One category is based on Sanders' analytical results for long pipe cracks, with various corrections in the short crack range and different curve-fitting formulae to give convenient closed form expressions. The second category consists of various independent finite element solutions. Each of these solutions is for a discrete pipe geometry and crack length and so is not practical to be used in fracture mechanics analysis. Lastly there is Kanninen & Zahoor's solution, derived independently of Sanders' results. Comparison showed that the results from the first two categories roughly agreed but were vastly different from Kanninen & Zahoor's results. Experimental calibration using the strain gauge method and the fatigue crack growth rate back-tracking method has been carried out. The experimental results agreed with the family of solutions derived from Sanders' work. Details about this experimental calibration are presented.

Experimental and analytical fracture assessment of 165-mm diameter AISI 304 seamless piping containing a circumferential through-wall crack

Field engineers often face the need to assess the residual strength and remnant life of cracked components within a limited time. A number of engineering methods for the assessment of elastic-plastic fracture behaviour of cracked components proposed in the past decade may be used for this purpose. These include the net section plastic collapse method, the J- integral estimation method and the R6 (Revision 3) failure assessment method. The primary aim of these methods is to obtain fracture behaviour prediction with a reasonable degree of accuracy without resorting to a complicated full-length numerical elastic-plastic fracture mechanics analysis. Systematic comparison of these different methods for assessing the relative degrees of accuracy and conservatism based on experimental results are still very limited. In the current work, some fracture experiments on 165-mm diameter piping with through-wall cracks were conducted. Based on these data, the predictive capabilities of the three engineering assessment methods are compared. The relative merits and limitations of each method are discussed in the light of these evaluations. The results suggest that the J- integral method has the best overall accuracy but requires the most detailed baseline material properties data. The R6 Revision 3 method offers a number of choices which vary in complexity and amount of data needed; this method tends to give relatively more conservative results than the J- estimation method. The net section method is the simplest among the three and gives reasonable predictions of maximum load in the current case.

A database to evaluate stress intensity factors of elbows with throughwall flaws under combined internal pressure and bending moment

The advent of the leak-before-break (LBB) concept has widely replaced the traditional design basis event of a double-ended guillotine break (DEGB) in the design of primary heat transport (PHT) piping. The use of the LBB concept requires postulation of the largest credible cracks at highly stressed locations and demonstration of their stability under the maximum credible loading conditions. Stress analysis of PHT piping in nuclear power plants shows that the highly stressed piping components are normally elbows and branch tees. This necessitates detailed fracture mechanics evaluation of such piping connections by computing their stress intensity factors (SIF) and/or J-integral. Simple analytical solutions for evaluation of the SIF and J-integral for cracks in straight pipes are readily available in the literature. However the same type of solution for elbows and tees is limited in the open literature. In the present work a database is generated to evaluate the SIF for throughwall circumferential and longitudinal cracks under combined internal pressure and bending moment. Different parameters used to characterise a cracked elbow are pipe factor ( h), pipe bore radius to thickness ratio ( r t ) and crack length. Another parameter (ϱ) is used to consider the relative magnitude of stresses due to internal pressure and remote bending moment. This database has been used to derive closed-form expressions to evaluate the SIF for elbows with cracks in terms of the aforementioned parameters.

Numerical analysis of IPIRG cracked pipe experiments subjected to dynamic and cyclic loading

This report contains results of a finite element study aiming to identify the influence of loading history and geometry for cracked pipes subjected to complex loading. The experiments have been performed within the International Piping Integrity Research Group (IPIRG) Program. The majority of the numerically analyzed experiments were conducted on straight pipes with an outside diameter of 168 mm and containing a large circumferential through-wall crack. The considered pipes were loaded in four-point bending under displacement control and at a temperature of 288°C. The types of loading were combinations of either quasi-static or dynamic and also monotonic or cyclic loading with different loading ratios R. Some analyses were also performed on surface-cracked pipes subjected to slow, monotonic loading. In the finite element study, 20-node solid elements were used for the through-wall cracked pipes and a combination of shell and non-linear line spring elements for the surface-cracked pipes. Stable crack growth was simulated by gradual node relaxation and crack closure is accounted for by using simple contact elements. The J- integral for a remote contour is calculated and used as a characterizing fracture parameter although the cyclic loading violates the theoretical basis for this procedure. The near-tip J can not be used for growing cracks because of the weak energy singularity. The results of the numerical study confirm the trends from the experiments in that a high loading rate has a negative influence on the fracture properties of the studied carbon steel and that large cyclic loading, especially at R = −1, lowers the apparent J R-curve for both carbon and stainless steels. To some extent geometry effects appear to be present when comparing the results from pipes containing surface cracks and through-wall cracks with results from CT specimens. These effects are more pronounced for large amounts of stable crack growth than at initiation.

Computation of leak areas of circumferential cracks in piping for application in demonstrating leak-before-break behaviour

This paper presents a simplified engineering method to evaluate lower bounds of leak areas for circumferential through-wall cracks in view of their application in demonstrating the Leak-Before-Break behaviour of pipes. Starting from the simple elastic solution in a flat plate, bulging and plasticity correction factors are applied to determine leak rates in pipes. An amplification factor due to bulging is based on Sanders' shell solutions while, for plasticity, the Dugdale-Barenblatt model is used, introducing the reference-stress concept. The method is thus applicable for a large range of diameter-to-thickness ratios and for non-uniform applied loading situations. The method is tested against a number of results obtained either numerically (finite-elements analysis) or experimentally. The results are also compared with other known simplified methods used in the USA and FRG. The simplified approach presented here, to evaluate the crack leak areas in circumferential through-cracks, has been validated on a large range of diameter-to-thickness ratios and for non-uniform applied loads. The method seems promising for demonstration of Leak-Before-Break behaviour of pipes.

A circumferential throughwall crack in a pipe subjected to combined bending and axial loading

A J- resistance curve solution is developed for a circumferential throughwall crack in a pipe under combined bending and tension. The J solution can be applied with load-displacement-crack extension data from one pipe test. Material resistance curves are developed for throughwall cracks in Type-304 stainless steel and SA333 Gr6 carbon steel base materials. The effect of loading type on the J- resistance curve is shown to be insignificant. Post-test tearing instability analyses are performed to assess the accuracy of J- estimation scheme solutions and conservatism associated with the use of a specimen J- resistance curve.

Ductile fracture analysis of carbon steel pipe with a circumferential through-wall crack

It is necessary to make clear the pipe fracture conditions based on elastic-plastic fracture mechanics to assess the leak before break situation of carbon steel pipes for LWR plants. The aim of the present work is to discuss the effects of pipe size, initial crack length and fracture toughness on the estimated fracture load and mode of carbon steel pipes with a circumferential through-wall crack. As an analytical method, the R6-Rev.3 approach was applied to the pipe fracture analyses considering its simplicity in the application. The results indicate that the net-section collapse attainment becomes difficult with increasing diameter and decreasing thickness of carbon steel pipes. The degree of the net-section collapse attainment decreases with increasing crack length up to some critical size and then increases. The predicted fracture load is more sensitive to the material's J– R curve than to the elastic-plastic fracture toughness J IC . And a simple limit load analysis based on the yield stress is appropriate to evaluate the fracture load, as long as a proper margin was included.

Fracture margin of pipe with detectable crack by leakage

This paper describes a theoretical method for calculating a detectable crack size by leak detection systems in BWR plants. Crack opening areas for carbon steel pipes of various diameters containing circumferential through-wall cracks are analyzed. It was shown that large diameter pipes have a much higher safety margin, and that the 0.1 A Criterion (10% of pipe cross-section) for postulated leak cross-sections gives a conservative estimate.