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Application of failure assessment diagram methods to cracked straight pipes and elbows

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... Ainsworth`s 2016 presented assessments of the loads for ductile fracture which are initiated in 21 large-scale piping tests and consisting of 8 straight pipes and 13 elbows [10]. It has been shown that the use of modern solutions for stress intensity factor and limit load recently presented in the literature in conjunction with standard fracture assessment approaches [2], [8], [11]. ...
... The results show that the assessment points for the predicted loads lie on the failure assessment curve. It can be seen that the predicted initiation loads are close to the experimental loads, with the percentage differences and that ductile initiation occurs before plastic collapse [10]. ...
... Predicted and experimental initiation load points (∆a=0.2 mm) on FAD[10]. ...
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The failure assessment diagram (FAD) method has been widely accepted to evaluate the extent to which cracks may affect structural safety. The usage of this FAD method has been validated and included in [1]-[3]. The structure under investigation, described in four fully welded T-joint (BCC5) specimens, where these welded joints are a source of stress concentration and defects from which fatigue cracks can grow. The four specimens were modeled under different displacement loading using a finite element analysis program Ansys and SolidWorks software. In this work, the application of a FAD (Lr, Kr) using maximum stress, cumulative stress ranges, and the last half-cycle stress range was investigated. The results are showing that all the points were lying outside the FAD curve except for the BCC5D specimen point was inside FAD when using maximum stress. Conclusions made that the cumulative stress gives Lr and Kr are extremely large and hence predict failure too early. With the Crack Tip Opening Displacement (CTOD) of the test specimen assumed to be about 1mm rather than 0.1mm it was found that, if a FAD is to be used to indicate failure, then both Lr and Kr should be based on the maximum stress. It appears that the FAD methodology does help to predict the final failure (which is the usual application in such cases). This represents more effectively the structural behavior and would be more easily used by designers.
... The Notch Failure Assessment Diagram (NFAD) is frequently used to study the safety and for the fracture assessment of pipelines or elbows with different types of defects [39,41,[63][64][65][66][67][68][69][70][71][72][73][74][75][76]. It depends on the fracture toughness (K C ), defect size, i.e., defect depth ratio (d/t), and the internal loading -pressure (P) [69]. ...
... Numerous previous studies have shown that elbows are more vulnerable than straight pipes due to the more severe stress conditions of elbows with a defect, while assessment points for elbows are typically shifted in comparison with straight pipes and located in the brittle fracture domain of the FAD or NFAD (see subsection 3.3.) [17,52,[63][64][65]. ...
... A schematic representation of a typical NFAD with two characteristic polar angle values ( 1 and  2 ) that defined three typical domains (>  1 -brittle fracture,  1 > >  2 -elasto-plastic fracture, and <  2 -plastic collapse) is shown in Fig. 7. Failure happens if the assessment point (L r , K r ) is above the interpolation -failure curve K r = f (L r ) [84]. More details about polar angles definition, three typical domains, and the application of the NFAD are presented in numerous previously published works [12,39,41,[64][65][66][67][68][69][70][71][72][73][74][75]84,86]. somewhat higher than the critical semi-elliptical relative crack depth ratio (d/t= 0.28) in the pipe elbow obtained in our previous study [12]. ...
Article
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Pipe elbows (bends) are considered critical pressurized components in the piping systems and pipelines due to their stress intensification and the effect of bend curvature. They are prone and hence more exposed to different corrosion failure modes than straight pipes. Late detection of such elbow damages can lead to different dangerous and emergency situations which cause environmental disasters, pollution, substantial consumer losses and a serious threat to human life. A comprehensive safety and reliability assessment of pipe elbows, including usage of prediction models, can provide significant increases in the service life of pipelines. It is well known that the limit pressure is an important parameter to assess the piping integrity. In this paper, the integrity assessment of damaged pipeline elbows made of API 5L X52 steel was done within the framework of numerical modeling using the finite element method (FEM) and finite element analysis (FEA). The evaluation of numerically FEM modeled limit pressure in the corroded elbow containing a rectangular parallelepiped-shaped corrosion defect with rounded corners at the intrados section was done and compared to different codes for calculating limit pressure. Moreover, the area with the corrosion defects with different relative defect depth to wall thickness ratios was FEM modeled at the intrados section of the pipe elbow where the highest hoop stress exists. The results showed that the codes for straight pipes could not be applied for the pipe elbows due to the significantly higher error in the obtained limit pressure value compared with numerically FEM obtained results. However, the results for modified codes, adapted for the pipe elbow case using the Goodall formula for calculation of the hoop stress in pipe elbows with defects are pretty consistent with the numerical FEA results. The notch failure assessment diagram (NFAD) was also used for the straight pipe and pipe bends with different corrosion defect depth ratios, while the obtained critical defect depth ratios further highlighted the criticality of pipe elbows as an essential pipeline component.
... Sahu et al. (2015) worked on determination of fracture toughness curve using R-6 failure assessment method. Fracture assessments of large-scale straight pipes and elbows of various pipe diameters and crack sizes is reported by (Ainsworth et al., 2016). Orrock (2018) investigated the effects that scaling has on key structural integrity concepts, namely, stress fields, stress intensity factors and the J-integral. ...
... The (FAD) from Eq. (29) (KIII) by (Ocejo et al., 1997;Ainsworth, 1993;May, 2002;MacLennan, 1996;Schaser, 1994;Sanderson et al., 2015;Ainsworth et al., 2016;Amann, 2017;Orrock, 2018;Meek, 2017;Amara et al., 2018;Fuentes et al., 2018;Hassani et al., 2018;Hoh et al., 2018;Mai, 2018;Montassir et al., 2020) is compared with the unified Persian curve (PSU) in Fig. 8. The lifetime is mapped onto the state variable as (Lr = 2.25 ξ). ...
Article
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A conventional tool for assessing the integrity of structures containing flaws is, the Failure Assessment Diagram (FAD). The (FAD) is a combination of the limiting conditions for load, the flaw size and fracture toughness or yielding stress. The abscissa is the load ratio and the ordinate is the toughness ratio. The toughness ratio is defined as a function of the load ratio. Three options are available for this function. The (FAD) drive is based on parameters of fracture mechanics. Classical fracture mechanics contains epistemic uncertainty and is unreliable. As a result, the state of the art for the (FAD) is also unreliable. The present authors' team, conducted an extensive investigation in the past two decades, which led to the birth of the change of state philosophy that is digested in the Persian Curve. In the present paper the Persian Curve is used for development of a reliable (FAD). The validity of the work is verified via concise mathematical logics and comparison of the results with those of the others.
... The Failure assessment diagram method is not limited applicable for steel walled pressured equipment problem, several non-pressurized equipment problem that was assessed using FAD method, they are, FAD use to estimate the initiating of brittle fracture at the end of structural CJP groove welded joint with defect due to post earthquake Kobe 1995 [17], failure assessment structural square hollow section with crack at T-joint [18], validation of BS7910:2005 assessment procedure for structural square hollow section with crack at T-, Yand K-Joints [19], failure assessment of cracked X and K joints of structural circular hollow section [20], study on development of deformation limit using FAD method for fatigue-cracked X-joint of structural hollow section subjected in-plane flexure [21], Extensive assessment of notched structural steel component [22], Assessment of aero-engine turbine disk beyond normal operation condition [23], an extensive failure and fatigue assessment for component subjected with rolling contact using FAD method with varies variable [24]. Non-steel walled equipment that was assessed using FAD method, they are, Failure assessment on Zr-2.5Nb alloy material pressure tube used in the Canadian Deuterium Uranium (CANDU) heavy water reactor due to delayed hydride cracking [25], failure assessment for 316H stainless steel containing creep crack [26], assessment of Ti-6Al-4V titanium alloy laser welded plate containing undercut defect [27], fracture assessment of notched short glass fibre reinforced polyamide 6 (SGFR-PA6) [28], failure assessment of nuclear steam generator tubes (SGTs) made of Inconel 690 and incoloy 800 [29], extensive assessment of additively manufactured (AM) specimen containing noctes [30], strength analysis of lithium hydride ceramic subjected thermal stresses during sintering process [31]. ...
Article
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Failure assessment include fatigue assessment was performed for an in-service pressurize equipment utilized to support hydrocarbon proceesing activity as the response of crack-like flaw finding during phase array scanning inspection. The assessment required to ensure the integrity and the safety in the operation of deteriorated pressure vessel. The fitness-for-service assessment in this study are consist of failure assessment using Failure Assessment Diagram (FAD) and the fatigue assessment based on API 579-1/ASME FFS-1. The assessment has demonstrated that the current condition of the equipment was pass the assessment requirement and still has adequate strength and the fatigue damage due to actual operation pressure is an insignificant factor affecting the life of the equipment. This study also investigates the correlation between the geometry of the flaw and the stress increase ratio that is expressed in the exponential function as σC/σR = 4.18e0.82(LD/T^2)
... As in Section 6, corrections were made for the SENT specimen limit loads. TWC pipes were also simulated under limit load which according to the experimental data from [41] was load at fracture for 8-inch TWC pipes subjected to bending moment, while 16-inch pipes failed at L r < 1.0. ...
Article
Commonly, fracture toughness tests on deeply cracked specimens are used to assess defects in large-scale components. The paper presents a method for selection of test specimen type, size and crack length in order to obtain fracture toughness estimates relevant to defects in cracked pipes. The method uses available closed-form T-stress, stress intensity factor and limit load solutions to determine the required specimen dimensions. The paper reports elastic–plastic finite element analyses for single edge notched bend (SENB) and single edge notched tension (SENT) specimens and cracked pipes which demonstrate good agreement of the matching approach, although care is needed in selecting the appropriate limit load solution for SENT geometries.
... Limiting the defect size by conventional workmanship criteria increases unnecessary weld repairs, leads to additional costs and may defer the project completion. The limiting criteria recommended by common pipeline codes [4,5] on the allowable flaw size become increasingly challenging to comply with the common adoption of corrosion resistance alloy (CRA) material and pipelines designed for large plastic deformations [6,7]. These drive for a pressing demand to optimize the allowable welding flaws using engineering critical assessment (ECA) based on the fitness-for-service (FFS) codes [8][9][10], which requires a detailed understanding of the crack driving force and the near tip constraints for coplanar cracks in pipelines. ...
Article
The presence of coplanar or multiple cracks emerges as a common problem in many engineering structures, e.g., at the toe of circumferential welds of pipelines subjected to cyclic actions and in other piping systems for the nuclear power plants. The failure assessment diagram provides a convenient means to examine the competing failure between the fracture failure and plastic collapse failure, often for structural components with a single crack. The existing failure assessment diagram relies on the leading term characterizing the near-tip stress solutions, and ignores the geometry or plasticity-induced constraint variations. This paper aims to integrate the crack interaction effect between two coplanar cracks, measured by a constraint-based crack interaction factor, into the option 3 failure assessment curve in the engineering standard. This study examines three types of circumferential coplanar cracks in a pipe: two coplanar embedded cracks; two coplanar surface cracks; and a surface crack interacting with an embedded crack. Using a modified J solution based on a proposed crack interaction factor, this investigation quantifies the plasticity-driven increase in the near-tip opening stress for coplanar cracks. The stress field estimated based on this modified J solution agrees closely with the numerically computed stress field near the coplanar crack tips at large deformation levels. This work subsequently integrates the modified J solution into the failure assessment diagram. The failure assessment diagram based on the equivalent crack size recommended in BS7910 appears to be un-conservative for a number of coplanar cracks considered in this study.
... One of the difficulties with the approach described above is that a number of different specimens or defect sizes are required at step 5 in order to generate the function of step 6, which is used to construct the constraint modified FAD. More recently, therefore, alternative approaches have been suggested [8,9], which are targeted at the use of specimens which more closely match the specific constraint level of interest in the component being assessed. The steps in an alternative constraint approach are as follows. ...
Article
Mind the gap' in Fitness-for-Service (FFS) assessment procedures was a workshop held at The University of Manchester in June 2015. The goal of the workshop was firstly to identify 'knowledge gaps' or areas for improvement in FFS assessment procedures and, secondly, to present methodologies that have been developed to narrow these gaps. It was intended that identification of these 'gaps' would allow an understanding of the current development needs for defect tolerance arguments in the FFS assessment procedures. The following questions were addressed: 1) What are the main 'knowledge gaps' in current FFS assessment procedures and methodologies? 2) What are the main barriers that need to be overcome in order to narrow these 'gaps'? 3) What are the current procedures (if any) and why are these not useful, over-or under-conservative and what needs to be improved? 4) What research is currently ongoing in order to narrow the gaps? This paper summarises the presentations and discussions at the workshop on subjects such as environmentally assisted cracking mechanisms, creep, welding residual stresses and fracture mechanics.
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A pressurized gas separator vessel was scanned to detect the possible discontinuities using a Phased Array Ultrasonic Testing (PAUT) device. Ultrasonic results from Hydrogen-Induced Cracks (HICs) at different depths were considered to represent the evaluation procedure. Final results were then generated for implementing Fitness-for-Service (FFS) procedure. After considering FFS procedures, it was found that some of the discontinuities are not acceptable due to their sizes or locations. Based on the simulated model results, including fracture analysis of cracks and generating Failure Analysis Diagrams (FAD), it can be inferred that the vessel is not acceptable to be in the current service operation condition and should be replaced.
Article
The failure assessment diagram (FAD) is the most widely used method for analyzing the reliability of structure containing crack defect. In practical engineering, the failure assessment point (FAP) and failure assessment curve (FAC) are impossible to be determined accurately. Therefore, an interval failure assessment diagram (IFAD) method is proposed in this paper to analyze the reliability of structure containing crack defect when the FAP and FAC cannot be obtained accurately. Firstly, based on the interval method and FAD method, an interval failure assessment diagram (IFAD) model is established by considering the FAP and the failure critical point (FCP) as interval variables. And then the FAP and FCP intervals are converted into the normalized region to design the IFAD reliability index [Formula: see text] according to the relationship between the limit state function and the normalized region. The structural arbitrary state can be described by the IFAD reliability index [Formula: see text]. In addition, 10 cases are given as examples to clearly expound the IFAD method, and the analysis results are compared with the FAD method, which confirms that the IFAD method is feasible and valid to analyze the structural reliability with the bounds of FAP and FCP. Finally, the IFAD reliability analysis of a certain propellant storage tank ellipsoidal bottom containing surface crack is taken as an application example to verify the practicability of the proposed method. And the results show that the IFAD reliability index can be obtained without the exact value of parameters.
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This paper proposes a ductile tearing assessment diagram to assess the evolution of load resistance versus stable tearing in material and structural components. This approach extends beyond the failure assessment diagram documented in engineering standards and allows the assessment for the tearing process in a cracked structural component through a single assessment curve derived from the experimental records of a fracture specimen. The validation of the proposed approach utilizes two types of specimens: (1) material fracture specimens, made of HY-80 steel and aluminum alloy 6061-T6511; and (2) welded structural components including the S355 steel welded pipes and the S690 steel welded tubular joint. The proposed method predicts the load resistance versus crack extension relation for a structural component with an extending crack, which translates the tearing assessment into a load level assessment. The load resistance at different crack extension, estimated from the tearing assessment curve developed from fracture specimens, remains within 10% compared to the experimental results for welded structural components presented in this study.
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Pipes are widely applied across many industries such as the automotive, aerospace and air conditioning industries. With the development of industrial technology, various pipe materials and various pipe shapes are produced according to the purpose. Many researchers have been studied pipe bending technology to meet these diverse needs, and among them, the long-type elbow is a typical one that changes the moving direction of fluid or gas among various pipe types. Many researchers work on the pipe segment. In-process push-bending used in pipe bending is a bending process where a cut pipe is inserted into a die. Push-bending is effective for reducing the weight of parts that do not induce material loss, but the process is more complicated than the draw-bending process. In this study, we proposed an analytical model for a push-bending process in which a joint type mandrel was added to a long-type elbow made of C1220 material for weight reduction. The forming analysis is to verify the experiment by comparing the analysis result and the experimental result through the forming analysis software DEFORM to confirm the change of the wrinkle and the thickness of the bent pipe. In addition, we confirmed the wrinkling of the bent pipe and the die non-contact phenomenon depending on the angle and position of the joint mandrel and presented the optimum angle and center of gravity position of the joint mandrel using the experimental design method.
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Determination of fracture toughness, J-R curve from experimental test results requires certain geometry factors such as η and γ. These expressions of geometry factors are available for standard geometries and loading configurations. However, these expressions are not available in open literature for complex geometries and loading configurations. R6 Failure Assessment Diagram (FAD) methodology is used for assessment of failure in the failure regime of cleavage fracture, ductile crack initiation and plastic collapse. Recently, one load based approach was proposed for calculation of fracture toughness by R6 using experimental load vs. crack extension data. On comparison with already reported J-R curves calculated using conventional η -factor approach, predicted results were showing good match for some cases while for few cases it became significantly non-conservative. In this paper, the load based approach is modified to displacement based approach and instead of load vs. crack extension data, displacement vs. crack extension data is used for calculation. The calculated fracture properties using displacement based approach show a marked improvement over results using load based approach while comparing with the conventionally calculated J-R curves. The problem of non-conservatism of predicted fracture properties by load based approach is also resolved by the proposed displacement based approach.
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An Elbow is one of the major component that make up the piping system of a nuclear power plant and chemical plant facilities. In general, the elbow is made by welding a straight pipe and bend part. So, periodic welding inspection is required due to the potential defects in weld zone. Recently, the application of induction heating pipe bend is increasing in order to reduce this problem. Pipe bend made by induction heating band is not necessary welding process because it is made by bending a straight pipe but the intrados thickness and the extrados thickness are different. On the other hand, J-integral is widely used to evaluate a structural integrity (to check crack stability) but the J estimation of pipe bend with un-uniform thickness is very difficult because of the thickness differences in each locations.
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Accurate prediction of burst pressure plays a central role in engineering design and integrity assessment of oil and gas pipelines. Theoretical and empirical solutions for such prediction are evaluated in this paper relative to a burst pressure database comprising more than 100 tests covering a variety of pipeline steel grades and pipe sizes. Solutions considered include three based on plasticity theory for the end-capped, thin-walled, defect-free line pipe subjected to internal pressure in terms of the Tresca, von Mises, and ZL (or Zhu-Leis) criteria, one based on a cylindrical instability stress (CIS) concept, and a large group of analytical and empirical models previously evaluated by Law and Bowie (International Journal of Pressure Vessels and Piping, 84, 2007: 487–492). It is found that these models can be categorized into either a Tresca-family or a von Mises-family of solutions, except for those due to Margetson and Zhu-Leis models. The viability of predictions is measured via statistical analyses in terms of a mean error and its standard deviation. Consistent with an independent parallel evaluation using another large database, the Zhu-Leis solution is found best for predicting burst pressure, including consideration of strain hardening effects, while the Tresca strength solutions including Barlow, Maximum shear stress, Turner, and the ASME boiler code provide reasonably good predictions for the class of line-pipe steels with intermediate strain hardening response.
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A large throughwall circumferential crack in an elbow subjected to in-plane bending moment can significantly reduce its collapse load. Therefore, it is very important to know the collapse moment of an elbow in the presence of a throughwall circumferential crack. The existing closed-form collapse moment equations of throughwall circumferentially cracked elbows are either too conservative or inadequate to correctly quantify the weakening effect due to the presence of the crack, especially for opening mode of bending moment. Therefore, the present study has been carried out to investigate through elastic-plastic finite element analysis the effect of a throughwall circumferential crack on the collapse moment of an elbow under in-plane bending moment. A total of 72 cases of elbows with various sizes of circumferential cracks (20=0-150 deg), different wall thickness (R/t=5-20), different elbow bend radii (R-b/R=2,3) and two different bending modes, namely closing and opening have been considered in the analysis. Elastic-perfectly plastic stress-strain response of material has been assumed. Collapse moments have been evaluated from moment-end rotation curves by twice-elastic slope method. From these results, closed-form expressions have been proposed to evaluate collapse moments of elbows under closing and opening mode of bending moment. The predictions of these proposed equations have been compared with 8 published elbow test data and are found to be within +/- 11 % variation except for one case.
Article
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The elastic T-stress is a parameter used to define the level of constraint at a crack tip. It is important to provide T-stress solutions for practical geometries to apply the constraint-based fracture mechanics methodology. In the present work, T-stress solutions are provided for circumferential through-wall cracks in thin-walled cylinders. First, cylinders with a circumferential through-wall crack were analyzed using the finite element method. Three cylinder geometries were considered; defined by the mean radius of the cylinder (R) to wall thickness (t) ratios: R/t=5, 10, and 20. The T-stress was obtained at eight crack lengths (θ/π=0.0625, 0.1250, 0.1875, 0.2500, 0.3125, 0.3750, 0.4375, and 0.5000, θ is the crack half angle). Both crack face loading and remote loading conditions were considered including constant, linear, parabolic and cubic crack face pressures and remote tension and bending. The results for constant and linear crack face pressure were used to derive weight functions for T-stress for the corresponding cracked geometries. The weight functions were validated against several linear and non-linear stress distributions. The derived weight functions are suitable for T-stress calculations for circumferential cracks in cylinders under complex stress fields.
Chapter
Description Highlights include: • A Framework for Quantifying Crack Tip Constraint • Constraint and Toughness Parameterized by T • An Experimental Investigation of the T Stress Approach • Statistical Aspects of Constraint with Emphasis on Testing and Analysis of Laboratory Specimens in the Transition Region • Predictions of Specimen Size Dependence on Fracture Toughness for Cleavage and Ductile Tearing
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A series of cracked specimen configurations have been tested to correlate the geometry dependence of crack tip constraint and fracture toughness in full plasticity. Specimens with through cracks included a range of edge-cracked bend bars, compact tension specimens, and center-cracked panels. Surface-cracked panels were tested in tension to produce resistance curves. The geometry dependence of ductile crack extension in plane strain has been correlated with crack tip constraint as parameterized by the T stress, which indicates the nature of the development of higher order terms in the nonlinear asymptotic crack tip expansion.
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Global limit load solutions for thick-walled cylinders with circumferential internal/external surface and through-wall defects under combined positive/negative axial force, positive/negative global bending moment and internal pressure are derived based on the von Mises yield criterion and the net-section collapse principle. Solutions for cases both with/without considering crack face contact when all or part of the crack is located inside the compressive stress zone are obtained. For some limiting cases, the solutions are compared with available solutions and with some published finite element (FE) data, showing good agreement. Systematic validation of the solutions using a wide range of elastic-perfectly plastic 3-D FE data is described in Part II.
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Global limit load solutions for thick-walled cylinders with circumferential internal/external surface and through-wall defects under combined positive/negative axial force, positive/negative global bending moment and internal pressure have been developed in Part I of this paper. In this Part II, elastic-perfectly plastic 3-D finite element (FE) analyses are performed for selected cases, covering a wide range of geometries and load combinations, to validate the developed limit load solutions. The results show that these limit load solutions can predict the FE data very well for the cases with shallow or deep and short cracks and are conservative. For the cases with very long and deep cracks, the predictions are reasonably accurate and more conservative.
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Analytical solution of limit load for a defect-free pipe elbow is obtained under internal pressure using GM (geometric midline), in which the strain hardening effect has been taken into account. The limit load is a function of ratio of thickness to radius t0/r0, strain hardening exponent n, curvature influence factor m and ultimate tensile strength. Comparison with FE and analytical results of other investigators was performed. Although the limit loads calculated by GM criterion are little higher than the traditional analytical results, the GM results are in good agreement with FE results. Besides, the effect of different criteria, strain hardening exponent, ratio of thickness to radius, as well as curvature influence factor on the limit loads are also discussed systematically.
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The combined effect of ovality and thinning/thickening on collapse load of pipe bends under in-plane opening bending moment was investigated using finite element limit analysis considering large geometric change effect. The material is assumed to be elastic-perfectly plastic. Twice-elastic-slope method is used to obtain collapse moment from moment–rotation curves drawn for each bend. Variation of thickness due to thinning in the cross section of pipe bend produces negligible effect on collapse load. The effect of ovality is significant except for pipe ratio 20 with λ = 0.5. A new closed-form solution is proposed to determine collapse moment of pipe bends with ovality and it is validated with existing experimental data.
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In this research, burst tests were conducted on real-scale elbow specimens, each with an artificial local wall-thinning defect, under combined internal pressure and constant in-plane bending load, as well as under simple internal pressure, to evaluate the effect of load-controlled bending load on the failure pressure of locally wall-thinned pipe elbows. Ninety-degree, 65A Schedule 80 elbows, with wall-thinning defects in the intrados and extrados, were used as specimens. The bending loads were in-plane opening- and closing-mode bending, applied in load-control mode. The results clearly indicated that a load-controlled in-plane bending load reduced the failure pressure of wall-thinned pipe elbows, in contrast to observations previously made under displacement-controlled bending conditions. The effect of the bending load was more significant for opening-mode than for closing-mode bending, regardless of the wall-thinning location in the elbow. Also, the effect was greater when the wall-thinning defect was located in the intrados region of the elbow, rather than the extrados region. Existing models that have been proposed to evaluate the failure of wall-thinned elbows under simple internal pressure conservatively predicted the failure pressure of elbows subjected to a combined internal pressure and load-controlled bending load.
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The influence of internal pressure and shape imperfections of pipe bends on collapse load was investigated under in-plane closing bending moment using finite element limit analysis based on elastic-perfectly plastic material considering geometric nonlinearity. Twice-elastic-slope method was used to obtain the collapse load. For each model, at a certain internal pressure, the collapse moment was found to be the same for the pipe bends with oval and circular cross sections, at any other pressure the effect of ovality is significant. The thinning produces negligible effect on collapse load. Closed-form solutions are proposed to determine the collapse moment of pipe bend.
Article
The effect of ovality and variable wall thickness (thickening at intrados and thinning at extrados) on the collapse loads in pipe bends subjected to in-plane bending moment that tend to close the bend was investigated using finite element limit analyses based on elastic-perfectly plastic material with large geometry change option. The collapse moments were obtained from load–deflection curves of the models with circular (uniform wall thickness) and irregular cross sections and compared. The presence of ovality in the pipe bends significantly affects the collapse loads while thinning produce very less effect. Based on finite element collapse load (twice-elastic-slope) results, a mathematical equation is proposed to include the effect of ovality.
Article
This paper presents closed-form approximations to elastic stresses in thick- and thin-walled elbows with attached straight pipes under internal pressure, based on three-dimensional elastic finite element analysis. Elastic stresses in the centre of an elbow are found to be close to an existing closed-form solution, suggesting that the hoop stress varies with the longitudinal position. The FE results indicate that the hoop stress varies linearly with the longitudinal position. Moreover, stresses in the junction of an elbow and straight pipe are shown to be the average of those in the centre of the elbow and in the straight pipe.
Article
Using finite element analysis, this paper extends elastic stress solutions for 90° pipe elbows under in-plane bending, given in Marie et al. (2007) [1], to cases of mean pipe radius-to-thickness ratio up to 50. It is found that for 90° elbows an in-plane bending moment produces not only an axial membrane stress component but also axial and hoop bending stress components. Furthermore, the magnitudes of these stress components depend strongly on the mean radius-to-thickness ratio, the circumferential location and the longitudinal location. Maximum stresses tend to occur in the centre of the elbow at or near the crown.
Article
In this paper, information on plastic limit loads and both elastic and elastic-plastic fracture mechanics parameters is given for cracked thick-walled pipes with mean radius-to-thickness ratios ranging from two to five. It is found that existing limit load expressions for thin-walled pipes can be applied to thick-walled pipes, provided that they are normalized with respect to the corresponding un-cracked thick-walled pipe values. For elastic fracture mechanics parameters, FE values of the influence functions for the stress intensity factor and the crack opening displacement are tabulated. For elastic-plastic J, it is shown that existing reference stress based J estimates can be applied, provided that a proper limit load for thick-walled pipes is used.
Article
This paper compares published experimental plastic collapse loads for 90° elbows with existing closed-form solutions. A total of 46 experimental data are considered, covering pure bending (in-plane closing, in-plane opening and out-of-plane bending) and combined pressure and bending loads. The plastic collapse load solutions considered are from the ASME code, the Ductile Fracture handbook of Zahoor, by Chattopadhyay and co-workers, and by Y.-J. Kim and co-workers. Comparisons with the experimental data shows that the ASME code solution is conservative by a factor of 2 on collapse load for in-plane closing bending, 2.3 for out-of-plane bending, and 3 for in-plane opening bending. The solutions given by Kim and co-workers give the least conservative estimates of plastic collapse loads, although they provide slightly non-conservative estimates for some data.
Article
Closed form stress intensity factor (K//1) expressions are presented for cracks in pipes subjected to a variety of loading conditions. The loadings considered are: 1) axial tension, 2) remotely applied bending moment, and 3) internal pressure. Expressions are presented for circumferential and axial cracks, and include both part-through and through-wall crack geometries. The closed form K//1 expressions are valid for pipe radius to wall thickness ratio between 5 and 20.
Article
Integrity assessment of piping components is very essential for safe and reliable operation of power plants. Over the last several decades, considerable work has been done throughout the world to develop a system oriented methodology for integrity assessment of pipes and elbows, mainly for application to nuclear power plants. However, there is a scope of further development/improvement of issues, particularly for pipe bends, that are important for accurate integrity assessment of pipings. Considering this aspect, a comprehensive Component Integrity Test Program was initiated in 1998 at Reactor Safety Division (RSD) of Bhabha Atomic Research Centre (BARC), India in collaboration with MPA, Stuttgart, Germany through Indo-German bilateral project. In this program, both theoretical and experimental investigations were undertaken to address various issues related to the integrity assessment of pipes and elbows. The important results of the program are presented in this two-part paper. In the part I of the paper, the theoretical investigations are discussed. Part II will cover the experimental investigations. The theoretical investigations considered the following issues: new plastic (collapse) moment equations of defect-free elbow under combined internal pressure and in-plane closing/opening moments; new plastic (collapse) moment equations of throughwall circumferentially cracked elbow, which are more accurate and closer to the test results; new ‘ηpl’ and ‘γ’ functions of pipes and elbows with various crack configurations under different loading conditions to evaluate J–R curve from test data; and the effect of deformation on the unloading compliance of TPB specimen and throughwall circumferentially cracked pipe to measure crack growth during fracture experiment. These developments would also help to study the effect of stress triaxiality in the transfer of material J–R curve from specimen to component.
Article
This paper provides tabulated solutions of elastic stress intensity factors and crack opening displacements for circumferential through-wall cracked elbows under internal pressure and under in-plane bending, based on extensive three-dimensional elastic finite element analyses covering a wide range of crack lengths and elbow/pipe geometries. The effect of crack length and elbow/pipe geometry on the results is discussed, with particular emphasis on the crack closure behaviour under in-plane bending.
Article
Closed-form plastic collapse moments (PCM) equations were earlier proposed for throughwall circumferentially cracked (TCC) elbow subjected to pure in-plane bending moment. However, an elbow is often subjected to combined internal pressure and bending moment in actual service condition. Therefore, the present study investigates the effect of internal pressure on the in-plane PCM of a TCC elbow. The PCM of a cracked elbow is usually expressed as a product of two parameters: PCM of a defect-free elbow multiplied by a weakening factor due to the crack. Therefore, the present study also includes analysis of defect-free elbows. Elastic–plastic finite element analysis is employed for the present analysis. A total of 396 cases of elbows with various sizes of circumferential cracks (2θ = 0–150°), different wall thickness (R/t = 5–20), different levels of normalized internal pressure (p = PR/(tσy) = 0–1), different elbow bend radii (Rb/R = 2,3) and two different bending modes, namely closing and opening are considered in the analysis. Elastic–perfectly plastic stress–strain response of material is assumed. The load in the elbows is split in two components: a constant internal pressure applied initially followed by in-plane bending moment monotonically increasing in definite steps. PCM are evaluated from moment—end rotation curves by twice-elastic slope method. From these results, closed-form equations are proposed to evaluate PCM of TCC and defect-free elbows subjected to combined internal pressure and in-plane closing/opening bending moment. Attempt has been made to compare the predictions of the proposed equations with the available experimental/numerical results and to rationally explain the behaviour where no experimental/numerical data is available for comparison.
Article
Fracture assessment of pipe bends or elbows with postulated through wall crack is very essential for leak-before-break qualification of primary heat transport system piping of nuclear power plants. The methodology for fracture assessment of cracked elbows is still in developing stage. Any new development in theoretical aspect requires experimental validation. However, fracture test data on cracked elbows is not so abundant as straight pipes. The earlier experiments on cracked elbows were focused mainly on the determination of limit load. Other fracture parameters e.g. crack growth, crack initiation load or crack opening displacement were not reported in the open literature. Against this backdrop, a comprehensive experimental and theoretical program on component integrity has been initiated at Reactor Safety Division (RSD) of Bhabha Atomic Research Center (BARC), India. Under this program, a number of fracture tests have been carried out on elbows with through wall circumferential/axial cracks subjected to in-plane closing/opening bending moment. These test data are then thoroughly analysed numerically through non-linear finite element analyses, analytically through limit load comparison and also through comparison of crack initiation loads by finite element and R6 methods. These test data may be utilized in future for validation of new theoretical developments in the integrity assessment of through wall cracked elbows.
Article
This paper proposes plastic loads (limit load and twice-elastic-slope (TES) plastic load) for pipe bends with circumferential through-wall and part-through surface cracks under in-plane bending, based on three-dimensional FE limit analyses. The material is assumed to be elastic–perfectly plastic, and both the geometrically linear (small strain) and nonlinear (large geometry change) effects are considered. Regarding a crack location, both extrados and intrados cracks are considered. Based on the FE results, closed-form approximations of limit and TES plastic loads are proposed for practical applications, and compared with corresponding solutions for straight pipes.
Article
Transferability of the specimen J–R/J–T curve to the component level is an important issue in the field of fracture mechanics. Towards this goal, fracture experiments have been carried out on three point bend (TPB) specimen and throughwall circumferentially cracked straight pipe of 219 and 406 mm outer diameter under four point bending load. The pipe material is SA333Gr6 and TPB specimens are machined from pipes. The image processing technique has been used to measure the crack growth and crack opening displacement in pipes. Component J–R curves have been generated from the load-deflection and load-crack growth data of pipe fracture experiments. These are compared with the TPB specimen J–R curves. Power law and second order polynomial fitting are done on the specimen and component J–R curves and J–T curves are generated. Specimen and component J–T curves are compared. Maximum moments in the pipe fracture experiments are also compared with the critical moments predicted by the ‘G factor’, ‘Z factor’ and limit approach.
Guide to methods for assessing the acceptability of flaws in metallic structures
BS 7910:2013þA1:2015. Guide to methods for assessing the acceptability of flaws in metallic structures. London, UK: British Standard Institution; 2016. Incorporating Corrigenda 1 and 2.
In-service inspection rules for the mechanical components of PWR nuclear islands. Appendix 5.4 e analytical methods for calculating stress intensity Factors and J Integral
  • Rse-M Code
RSE-M Code. In-service inspection rules for the mechanical components of PWR nuclear islands. Appendix 5.4 e analytical methods for calculating stress intensity Factors and J Integral, 2010 edition. Paris: AFCEN; 2010.
Review of limit loads solutions for defective pipe bends
  • Y Lei
Lei Y. Review of limit loads solutions for defective pipe bends. Report E/REP/ BBGB/0060/GEN/09 Revision 000. Gloucester, UK: EDF Energy Nuclear Generation; 2011.