Net-section limit moments and approximate J estimates for circumferential cracks at the interface between elbows and pipes

This paper firstly presents net-section limit moments for circumferential through-wall and part-through surface cracks at the interface between elbows and attached straight pipes under in-plane bending. Closed-form solutions are proposed based on fitting results from small strain FE limit analyses using elastic–perfectly plastic materials. Net-section limit moments for circumferential cracks at the interface between elbows and attached straight pipes are found to be close to those for cracks in the centre of elbows, implying that the location of the circumferential crack within an elbow has a minimal effect on the net-section limit moment. Accordingly it is also found that the assumption that the crack locates in a straight pipe could significantly overestimate the net-section limit load (and thus maximum load-carrying capacity) of the cracked component. Based on the proposed net-section limit moment, a method to estimate elastic–plastic J based on the reference stress approach is proposed for circumferential cracks at the interface between elbows and attached straight pipes under in-plane bending.     

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.     

J-integral and local damage fracture analyses for a pump casing containing large weld repairs

Three-dimensional J-integral and two-dimensional Local Approach finite element studies are described for postulated crack-like defects in a large repair weld to the casing of a light water reactor circulation pump. The repair weld residual stress field is simulated and plant operating pressure and thermal transient loads are applied. Crack tip constraint effects are quantified through detailed analysis of the cracked structure and compact tension fracture toughness specimens. Fracture initiation crack sizes are shown to be larger than conceivable fabrication defects that are detectable using modern ultrasonic inspection techniques. The Local Approach study demonstrates the benefits of quantifying crack tip constraint conditions, compared with conventional J-estimation schemes and cracked body J-integral analysis. The method of introducing the crack into the finite element model is shown to have a large effect on calculated crack tip fracture parameters; a slowly developing crack in the residual stress field being more benign.     

Predictions for fatigue crack growth life of cracked pipes and pipe welds using RMS SIF approach and experimental validation

The objective of the present study is to understand the fatigue crack growth behavior in austenitic stainless steel pipes and pipe welds by carrying out analysis/predictions and experiments. The Paris law has been used for the prediction of fatigue crack growth life. To carry out the analysis, Paris constants have been determined for pipe (base) and pipe weld materials by using Compact Tension (CT) specimens machined from the actual pipe/pipe weld. Analyses have been carried out to predict the fatigue crack growth life of the austenitic stainless steel pipes/pipes welds having part through cracks on the outer surface. In the analyses, Stress Intensity Factors (K) have been evaluated through two different schemes. The first scheme considers the ‘K’ evaluations at two points of the crack front i.e. maximum crack depth and crack tip at the outer surface. The second scheme accounts for the area averaged root mean square stress intensity factor (K_RMS) at deepest and surface points. Crack growth and the crack shape with loading cycles have been evaluated. In order to validate the analytical procedure/results, experiments have been carried out on full scale pipe and pipe welds with part through circumferential crack. Fatigue crack growth life evaluated using both schemes have been compared with experimental results. Use of stress intensity factor (K_RMS) evaluated using second scheme gives better fatigue crack growth life prediction compared to that of first scheme. Fatigue crack growth in pipe weld (Gas Tungsten Arc Welding) can be predicted well using Paris constants of base material but prediction is non-conservative for pipe weld (Shielded Metal Arc Welding). Further, predictions using fatigue crack growth rate curve of ASME produces conservative results for pipe and GTAW pipe welds and comparable results for SMAW pipe welds.     

Finite element calculation of contour integral parameters for cracked P91 pipe weld

Abstract

This paper reports the results of elastic–creep finite element (FE) analyses of a P91 steel pipe weld with two external ‘type IV’ circumferential cracks, subjected to internal pressure and end (system) load using creep properties obtained at 650°C. Numerical contour integral calculations have been performed to obtain both transient and stationary high temperature fracture mechanics parameters. A mesh sensitivity analysis was performed in order to ensure the accuracy of FE analyses in the transient creep stage. The effects of load magnitude, the material mismatch near the crack surfaces and the crack depth on the stationary creep C* contour integrals have been investigated, and corresponding analytical correlations are presented.     

Recent results of fracture experiments on carbon steel welded pipes

Several pipe fracture experiments were conducted with circumferential cracks in the center of ferritic nuclear pipe welds. These experiments involved either submerged arc or shielded metal arc welds with either through-wall cracks or internal surface cracks. The pipe diameters varied from 940 mm (37 inches) to 152 mm (6 inches), and thickness from 10·9 mm (0·43 inches) to 86·6 mm (3·41 inches). Some of the through-wall and surface-cracked pipe experiments were conducted under constant internal pressure and four-point bending. The test temperature was 288°C (550°F). The results of these experiments are compared with limit-load analyses, the ASME, Section XI, article IWB-3650 criterion, and more elaborate elastic-plastic fracture mechanical analysis.     

Limit load and J estimates of a centre cracked plate with an asymmetric crack in a mismatched weld

The limit load and J estimates of a centre cracked plate with an asymmetric crack in the tensile properties mismatched weld were investigated. A limit load expression was derived on the basis of a simplified slip-line field. A good agreement between the predictions of the expression and finite element (FE) results was found for ratios of half-weld width to the crack ligament, H/l, of less than 0.5. The equivalent stress–strain relationship method (ESSRM) was used to predict elastic–plastic J values. Results from FE analyses show that the ESSRM is accurate for the crack with asymmetry in the mismatched weld provided an accurate theoretical or numerical value of the limit load of the same specimen is available. Defect assessment methods are discussed, and it is found that the failure assessment diagram (FAD) of an asymmetrically cracked mismatched weld can be constructed from the equivalent stress–strain relationship for the same mismatched geometry with a symmetric crack. The effect of an asymmetric crack on the FAD may then be covered by the limit load solution for the asymmetrically cracked mismatched weld.     

Relevance of plastic limit loads to reference stress approach for surface cracked cylinder problems

To investigate the relevance of the definition of the reference stress to estimate J and C* for surface crack problems, this paper compares finite element (FE) J and C* results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface cracks and finite internal axial cracks are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) a local limit load, (ii) a global limit load, (iii) a global limit load determined from the FE limit analysis, and (iv) the optimised reference load. It is found that the reference stress based on a local limit load gives overall excessively conservative estimates of J and C*. Use of a global limit load clearly reduces the conservatism, compared to that of a local limit load, although it can sometimes provide non-conservative estimates of J and C*. The use of the FE global limit load gives overall non-conservative estimates of J and C*. The reference stress based on the optimised reference load gives overall accurate estimates of J and C*, compared to other definitions of the reference stress. Based on the present findings, general guidance on the choice of the reference stress for surface crack problems is given.     

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part III: off-center cracks,restraint of bending,thickness transition and weld residual stresses

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers1, 2[Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.     

Approximate J-estimation methods for pipes with circumferential surface cracks in welds

Approximate J-estimation methods including the effects of weld mis-match, for a circumferentially surface-cracked pipe with an internal, constant-depth and finite-length surface flaw in pure bending are developed. The methods are based on principles described by Rahman and Brust. Closed-form J-solutions in terms of elementary functions are derived from classical beam theory combined with an equivalence criterion. Several numerical examples of welded joints are presented to verify the proposed methods.     

Influences of some materials on J-estimation methods for pipes with circumferential surface cracks

The approximate calculation methods (SC.ENG1 and SC.ENG2) for the J-integral for pipes with circumferential surface cracks are discussed and three-dimensional elastic–plastic finite element models for circumferentially surface-cracked pipe are conducted to evaluate the accuracy of these methods for different pipe materials used in China. The numerical studies verify that the SC.ENG2 method provides more accurate estimates of J than SC.ENG1. Based on three-dimensional elastic–plastic fracture analysis, the distribution of the local J-integral along the front of a circumferential constant-depth internal surface crack is investigated and the influences of different pipe materials with different yield plateaux on J-integral values are discussed. The validity of SC.ENG1 and SC.ENG2 J-integral estimation methods for pipe steel materials with different yield plateaux used in China are examined in detail and the SC.ENG2 method is found to provide reasonable estimates of J for materials with yield plateaux.     

Plastic limit pressures for cracked pipes using finite element limit analyses

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

Finite element simulation of welding residual stresses in martensitic steel pipes

Abstract

Finite element (FE) simulations of the welding of two high grade steel pipes are described. The first is a P91 steel pipe welded with a similar P91 weld consumable, and the second is a P92 steel pipe welded with dissimilar nickel–chromium based weld consumables. Both welds are multipass circumferential butt welds, having 73 weld beads in the P91 pipe and 36 beads in the P92 pipe. Since the pipes and welds are symmetric around their axes, the FE simulations are axisymmetric, allowing high FE mesh refinement and residual stress prediction accuracy. The FE simulations of the welding of the P91 and P92 pipes comprise thermal and sequentially coupled structural analyses. The thermal analyses model the heat evolution produced by the welding arc, determining the temperature history throughout the FE models. Structural analyses use the computed temperature history as input data to predict the residual stress fields throughout the models. Post-weld heat treatment (PWHT) of both pipes has also been numerically simulated by assuming that the FE models obey the Norton creep law during the hold time period at 760°C. The residual stresses presented here have all been validated by corresponding experimental measurements. Before PWHT, it has been found that, at certain locations in the weld region and heat affected zone (HAZ) in the pipes, tensile hoop and axial residual stresses approach the tensile strength of the material, presenting a high risk of failure. It has also been found that PWHT substantially reduces the magnitude of residual stresses by varying degrees depending on the material.     

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

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

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part I: analytical models

Leak-before-break (LBB) analyses for circumferentially cracked pipes are currently being conducted in the nuclear industry to justify elimination of pipe whip restraints and jet impingement shields which are present because of the expected dynamic effects from pipe rupture. The application of the LBB methodology requires calculation of leak rates. The leak rates depend on the crack-opening area of the through-wall crack in the pipe. In addition to LBB analyses which assume a hypothetical flaw size, there is also interest in the integrity of actual leaking cracks corresponding to current leakage detection requirements in NRC Regulatory Guide 1.45, or for assessing temporary repair of Class 2 and 3 pipes that have leaks, as are being evaluated in ASME Section XI. The objectives of this study were to review, evaluate, and refine current predictive models for performing crack-opening-area analyses of circumferentially cracked pipes. A three-phase effort was undertaken to accomplish this goal. It is described here in a series of three papers generated from this study. In this first paper (Part I — Analytical models), a comprehensive review is performed to determine the current state-of-the-art in predicting crack-opening displacements for circumferentially cracked pipes under pure bending, pure tension, and combined bending and tension loads. Henceforth, new and improved analytical models and some preliminary results are presented for cases where current methods are inadequate or there are no available methods. Also, based on this review, a number of appropriate predictive models are identified for a systematic evaluation of their accuracy. The results of their evaluations will be presented and examined in the forthcoming companion papers (Part II — Model validations [1] and Part III — Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) [2].     

Creep crack growth data and prediction for a P91 weld at 650 °C

Creep crack growth tests have been carried out on compact tension (CT) specimens machined from a P91 weldment. Four of these specimens were cut from the parent material side of the weld and another seven specimens were cut across the weld. For the cross-weld specimens, starter cracks were positioned into (or close to) the Type IV region. The creep tests were carried out under constant loads, at 650 °C. The results obtained showed that, the creep crack growth rates for parent material specimens are about ten times lower than those for the cross-weld specimens and that the scatter in the data is relatively high. In this respect, the accuracy of the crack tip location, in the cross-weld CT specimens, plays an important role. Finite Element (FE) analyses were carried out, on notched bar and CT models, using damage mechanics material behaviour models. These analyses were used to estimate the triaxial stress factor, α, for the parent material (PM), the weld metal (WM) and the heat affected zone (HAZ). FE analyses were then used to predict the creep crack growth in the CT specimens. Results from the FE analyses for both the PM and the cross-weld CT specimens were in good agreement with the corresponding experimental results. The effect of the potential drop versus crack length calibration on the calculated C* values was also investigated.     

Creep crack growth in welds: a damage mechanics approach to predicting initiation and growth of circumferential cracks

The results of damage mechanics finite element analyses have been used to estimate the initiation and growth of type IV cracks in a series of internally pressurised circumferential pipe welds, in main steam pipelines made of 1/2CrMoV steel. The material properties used, for the various zones of new, service-aged and repaired welds, were produced from creep test data at 640°C. Damage distributions and accumulation with time within the HAZ are presented, from which the crack initiation times and positions for these welds, under a closed-end condition, and with additional axial (system) loading, were identified. By investigating the propagation of damage through the wall thickness, the remaining lives of the various weld types were estimated. The method provides a means for predicting the initiation and growth of type IV cracks in these CrMoV weldments, and for estimating the length of time a weld can safely be left in service, after damage, or type IV cracking, is identified during inspection.     

Crack-opening-area analyses for circumferential through-wall cracks in pipes—Part II: model validations

This is the second paper in a series of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. This paper (Part II—Model Validations) focuses on the evaluation of current analytical models, discussed in the first paper (Part I—Analytical Models) as well as finite element models for conducting crack-opening-area analyses of pipes with circumferential through-wall cracks. The evaluation was performed by direct comparisons of the predicted results with the test data from full-scale pipe fracture experiments. The results from 25 full-scale pipe fracture experiments, conducted in the Degraded Piping Program, the International Piping Integrity Research Group Program and the Short Cracks in Piping and Piping Welds Program, were used to verify the analytical models. The main objective was the evaluation of engineering analysis procedures (estimation methods) as well as the ability of the finite element method to predict crack-opening displacements and shapes in pipes with circumferential through-wall cracks. Statistics were developed to quantify the accuracy of the current predictive models. A wide variety of pipe fracture tests involving cracks in base metals, weld metals and bimetallic weld metals were analyzed. Pipes containing both simple through-wall cracks and complex cracks were evaluated.     

Elasto-plastic fracture properties of an all-aluminium gas cylinder with different cracks

All-aluminium cylinders are used for on-board storage of compressed natural gas in vehicles. Besides being subjected to the maximum fill pressure, these cylinders are subjected to fluctuating pressures, due to refuelling operations. In order to establish a relevant test method to ensure leak before break failure performance, elasto-plastic finite element stress analysis of the design containing various defects was carried out to obtain a theoretical basis for the establishment of the test method. Axial semi-elliptical cracks in the central portion of the cylinder and circumferential cracks in the bottom of the cylinder are modelled using 20-node hexahedron elements. Not only the cylindrical body but also the neck and transition areas of the cylinder are considered in the modelling. Slender cracks with lengths approximately five times the wall thickness of the cylinder, which often appear in applied all-aluminium gas cylinders, are considered. Crack depths varied from 22.5% to 100% of the wall thickness. Through discussions about the calculated J-integral and crack mouth opening displacement (CMOD) of the axial and circumferential cracks, the effects of the different cracks on all-aluminium cylinders in the elasto-plastic deformation state are made clear. The analyses show that under the elasto-plastic deformation state, axial cracks in the centre of the cylinder are more dangerous for the cylinder than circumferential cracks in the bottom of the cylinder, if these are of the same size and under the same conditions. The axial external crack is found to be most severe among these different crack types. Finally, the CMOD of cylinders with an axial external crack have been measured by the experimental method and a good agreement between the calculated CMOD and the tested CMOD was reached.     

Static and impact crack properties of a high-strength steel welded joint

In order to gain the benefits of weldable high-strength steels in pressurized equipment applications, satisfactory toughness and crack properties of the welded joint, both in the weld metal and the heat-affected –zone (HAZ), are required. Experimental investigations of toughness and crack resistance parameters through static and impact tests of a high-strength, low-alloy steel (HSLA) with a nominal yield strength of 700 MPa and its welded joint, were performed on Charpy-sized specimens, V-notched and pre-cracked, of the parent metal, weld metal and HAZ. The selected electrode produced slight undermatching and enabled the welded joints to be manufactured without cold cracks. The impact energy and its parts responsible for crack initiation and propagation were determined by toughness evaluation. Crack sensitivity, defined as the ratio of the impact energy for V-notched and for pre-cracked specimens, enabled a comparison of the homogeneous microstructure of the parent metal and the weld metal, and of the heterogeneous microstructure of the heat-affected-zone (HAZ), which indicated a better crack toughness behaviour of the HAZ. The results obtained showed that the toughness and crack resistance of the weld metal were significantly lower than those of the parent metal and the HAZ. The fracture mechanics parameters, J_Ic integral, and plane strain fracture toughness, K_Ic, as well as J resistance curves expressed the degradation less.