Plastic collapse moment of 90° long radius elbows with internal circumferential surface crack at intrados under in-plane bending

Piping elbows under in-plane bending moment are vulnerable to cracking. The crack initiates at the surface and eventually reaches through the thickness and may lead to failure. The structural integrity assessment requires knowledge of the limit load. Limit load solutions for elbows with through-wall crack configurations are available in the open literature. But solutions for surface crack are not available. This paper presents a closed form expression for the plastic collapse moment (PCM) of 90°, long radius elbows with circumferential surface cracks at the intrados, under in-plane bending moment. The expression is derived, based on the results of non-linear (geometric and material) FE analyses covering a wide range of geometries and crack sizes. These plastic collapse moments evaluated herein will help in structural integrity assessment.     

Plastic collapse of pipe bends under combined internal pressure and in-plane bending

Plastic collapse of pipe bends with attached straight pipes under combined internal pressure and in-plane closing moment is investigated by elastic–plastic finite element analysis. Three load histories are investigated, proportional loading, sequential pressure–moment loading and sequential moment–pressure loading. Three categories of ductile failure load are defined: limit load, plastic load (with associated criteria of collapse) and instability loads. The results show that theoretical limit analysis is not conservative for all the load combinations considered. The calculated plastic load is dependent on the plastic collapse criteria used. The plastic instability load gives an objective measure of failure and accounts for the effects of large deformations. The proportional and pressure–moment load cases exhibit significant geometric strengthening, whereas the moment–pressure load case exhibits significant geometric weakening.     

A global limit load solution for plates with surface cracks under combined end force and cross-thickness bending

A global limit load solution for rectangular surface cracks in plates under combined end force and cross-thickness bending is derived, which allows any combination of positive/negative end force and positive/negative cross-thickness moment. The solution is based on the net-section plastic collapse concept and, therefore, gives limit load values based on the Tresca yielding criterion. Solutions for both cases with and without crack face contact are derived when whole or part of the crack is located in the compressive stress zone. From the solution, particular global limit load solutions for plates with extended surface cracks and through-thickness cracks under the same loading conditions are obtained. The solution is consistent with the limit load solution for surface cracks in plates under combined tension and positive bending due to Goodall & Webster and Lei when both the applied end force and bending moment are positive. The solution reduces to the limit load solution for plain plates under combined end force and cross-thickness bending when the crack vanishes.     

Fracture response of pipelines subject to large plastic deformation under bending

Demand for long-distance offshore pipelines is steadily increasing. High internal pressure combined with bending/tension, accompanied by large plastic strains, along with the potential flaws in girth welds make the structural integrity of pipelines a formidable challenge. The existing procedures for the fracture assessment of pipelines are based on simplified analytical methods, and these are derived for a load-based approach. Hence, application to surface cracked pipes under large deformation is doubtful. The aim of this paper is to understand and identify various parameters that influence the fracture response of cracks in pipelines under more realistic loading conditions. The evolution of CTOD of a pipeline segment with an external circumferential surface crack is investigated under pure bend loading as well as bending with internal pressure. Detailed 3D elastic–plastic finite element simulations are performed. The effects of crack depth, crack length, radius-to-thickness ratio and material hardening on fracture response are examined. The results show that at moderate levels of CTOD, the allowable moment capacity of the pipe decreases significantly with increase in internal pressure. Further, the variation of CTOD with strain can be well approximated by a simple linear relationship.     

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.     

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.     

Shakedown limit loads for elbows under internal pressure and cyclic in-plane bending

This paper presents elastic, shakedown and plastic limit loads for 90° elbows under constant internal pressure and cyclic in-plane bending, via finite element (FE) analysis. Effects of the elbow geometry (the bend radius to mean radius ratio and the mean radius-to-thickness ratio) and of the large geometry change are systematically investigated. By normalizing the in-plane bending moment by the plastic limit load solution of Calladine, the shakedown diagram is found to be close to unity up to a certain value of normalized pressure (normalized with respect to the limit pressure) and then to decrease almost linearly with increasing normalized pressure. The value up to which shakedown limit loads remain constant depends on the elbow geometry and the large geometry change effect. Effects of the elbow geometry and the large geometry change on shakedown diagrams are discussed.     

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.     

The effect of a superimposed compressive load on the failure of a stainless steel pipe containing a through-wall circumferential crack : Part I: Bending deformation is load-controlled

A net-section stress failure criterion is currently used to determine the critical size of circumferential crack for austenitic stainless steel as used in nuclear reactor piping systems. The acceptable crack size for prescribed applied loadings is determined by assuming that failure occurs when the stress across the net-section (that is the pipe cross-section area reduced by the crack area) attains a critical value, the stress at the cracked section being calculated on the basis of the undeformed pipe configuration. However, an axial compressive load can give an increased bending moment if the stress calculation is based on the deformed pipe configuration. This paper therefore examines the effect of an axial compressive load, superimposed upon a bending load, on the failure of piping due to the presence of a through-wall circumferential crack. The results show that the failure assessment should be based on the deformed configuration even when the axial load is only a small fraction of the pipe's Euler critical load, or otherwise the net-section stress approach can give non-conservative failure predictions.     

Stress intensification factors in elbows subjected to in-plane bending moments at elevated temperature

This paper reports the results of a static stress analysis in piping elbows, either with or without stiffening effects due to the sectional ovalization restraint provided by tangent straight pipes. The physical and geometrical aspects together with the loading conditions used in this study are typical of those of pipings for main cooling systems of Liquid Metal Fast Breeder Reactors (LMFBR). The aim of the study is directed towards comparing stress intensification factors in elbows subjected to pure in-plane bending moments obtained by experimental, analytical (using the ASME Section III Subsection NB 3685 detailed analysis procedures) and numerical tests. The numerical calculation was performed taking into account some nonlinearity effects due to the particular geometry of sections or load-induced phenomena, and neglecting the plastic response of the material (elastic behaviour).     

Limit moment of local wall thinning in pipe under bending

In engineering practice, pipe containing local wall thinning may be subjected to bending load. The existence of local wall thinning on pipe surface impairs the load-carrying capacity of pipe. In order to maintain the integrity of the pipe containing local wall thinning, it is very important to develop a method to evaluate such a pipe with local wall thinning under bending. In this paper, the limit moment of local wall thinning pipe under pure bending is computed employing 3D elastic–plastic finite element analysis. The results show that the limit moment of pipe is affected not only by the width of defect but also by the longitudinal length of defect. When the longitudinal length of defect overpasses some critical value, the results from net-section collapse criterion (NSC) are in very reasonable agreement with the results from finite element analysis. Therefore, the NSC formula can conservatively be used to assess the limit load-carrying capability of local wall thinning pipe under bending.     

Parametric survey of upper and lower bound limit in-plane bending moments for single mitred pipe bends of various geometries

The problem of limit analysis for a cylinder–cylinder intersection forming a single mitred pipe bend subject to in-plane bending has been investigated. Lower bound analysis with new equations of force and moment equilibrium together with a higher number of parameters resulted in more stability as compared to a previous analysis of the same problem [PhD Thesis, The University of Manchester, 1991]. Concurrently, abaqus finite element plastic collapse moments were obtained as upper bounds to the problem. Two sets of results were compared, showing good agreement with each other. It could be finally concluded that the true limit moments are bounded in between.     

Net-section limit load approach for failure strength estimates of pipes with local wall thinning

The net-section limit load approach is typically used in assessment of pipes with local wall thinning, based on which a maximum load carrying capacity is easily estimated from one equation that includes two terms associated with the effect of the defect geometry and the material's resistance (strength). To better understand the applicability of the net-section limit load approach to pipes with local wall thinning, four different limit load expressions for pipes with local wall thinning under pure bending are considered, together with two different definitions of the material's resistance. Estimated failure moments are then compared with full-scale pipe test data. It is found that the use of an appropriate limit load solution reduces not only the degree of conservatism but also the dependence of the assessment results on the wall thinning geometry, and thus gives the best results. Therefore, finding such solutions for pipes with local wall thinning is an important issue.     

Fracture behaviour of stainless steel pipes containing circumferential cracks at room temperature and 280°C

The paper presents the experimental results of a research programme on fracture behaviour of austenitic stainless steel and TIG welds in pipes containing circumferential through-wall cracks at room temperature and 280°C. Pipes were loaded in pure bending using a four-point bend test method. The diameter of the pipes under investigation was 168 mm and 324 mm, with a thickness varying from 10 to 17 mm.

As opposed to the behaviour of carbon steel pipes, it is found that the Net Section Collapse (NSC) criterion predicts the moment of instability. Crack mouth opening displacements (COD) and collapse moments calculated using the GE-EPRI engineering approach show a rather high scatter with respect to experimental results.     

Nonlinear analysis and plastic deformation of pipe elbows subjected to in-plane bending

The purpose of this study is to investigate the large strain and stress analysis for pipe elbows subjected to in-plane bending moments. A finite element model for the bend was constructed and loaded taking geometric and material nonlinearities into account using (ABAQUS) nonlinear finite element code. The initiation of yielding for the opening and closing cases appears at the inside surface of the elbow crown. However, further loading causes a significant difference in strain distribution and deformed shapes. The limit moment for the opening cases is higher than that for closing due to the geometric stiffening effects.     

The interaction of pressure, in-plane moment and torque loadings on piping elbows

This study concerns the load interaction behaviour of 90° smooth piping elbows with circular cross-section and long straight tangent pipes. The finite element method is used for stress analysis of elbows having a wide range of bend and pipe factors. The main aim of the study is to establish the first yield interaction behaviour when an elbow is subjected to a combination loading of in-plane bending, torsion and internal pressure. The study shows that load interaction is influenced by pipe factor, bend radius and load coupling effect, with thinner elbows being affected to a larger degree.     

Derivation of ‘γ’ parameter from limit load expression of cracked component to evaluate J–R curve

Experimental evaluation of the J-integral requires the ‘η_pl’ function, proposed by Rice et al. [Progress in flaw growth and fracture toughness testing (1973) 231], to multiply the area under the load vs. plastic load-line-displacement curve. However, the J-integral, thus evaluated, requires modification if crack growth occurs. A ‘γ’ term was proposed by Hutchinson and Paris [Elastic–plastic fracture (1979) 37] and later generalised by Ernst et al. [Fracture mechanics (1979) 581] and Ernst and Paris [Techniques of analysis of load–displacement records by J-integral methods (1980)] to correct the J-integral to account for crack growth. The η_pl and γ functions are available for very few geometries under specific loading conditions. A limit load-based general expression of η_pl was given by Roos et al. [Int J Pres Ves Piping 23 (1986) 81], but no such expression is available for γ functions. The advantage of having limit load-based general expressions for η_pl and γ functions is that the limit load for a particular geometry subjected to a specific loading condition is easily available in the open literature. In the present paper, a limit load-based general expression for the γ function is derived. The general expression is then validated by deriving the known γ functions of various geometries subjected to various loading conditions, which are available in the open literature. The general expressions are then used to derive new η_pl and γ functions for same pipe and elbow geometries with various crack configurations under different loading conditions, for which no solutions are available in the open literature. Finally, experiments have been carried out on 200 mm nominal bore (NB) elbows with throughwall circumferential cracks under in-plane bending moment. The proposed new expressions of η_pl and γ functions for this geometry are used to obtain the J–R curve from the experimental load vs. load-line-displacement and load vs. crack growth data.     

Plasticity around an axial surface crack in a cylindrical shell

This paper presents a plasticity model for deep axial surface cracks in pressurised pipes. The model is used in an investigation of the relative merits of fracture criteria based on COD and plastic instability.Recent investigations have shown that the inconsistency of the singular bending stress field in an axially cracked cylindrical shell arising from use of classical eighth order shallow shell theory is removed when use is made of a tenth order shell theory which accounts for transverse shear deformations. Although the membrane stresses are only moderately affected, the influence on the bending stresses is considerable. In the case of surface cracks moments are induced due to the eccentricity of the crack and transverse shear effects should therefore be included.A plasticity model for a rectangular axial surface crack is developed. Like a previous surface crack model by Erdogen and Ratwani,^3–5 it generalises Dugdale's assumption of a concentrated yield zone in the plane of the crack but, contrary to that model, transverse shear effects are included and a continuous stress distribution is assumed in the yield zone. The inherent difficulties arising from the use of shell theory to model a three-dimensional problem can be overcome when the crack is sufficiently deep and the material is so ductile that full yield of the section around the crack develops before failure. In that case the calculations confirm the initial assumption of separation of the crack surfaces and the sides of the yield zone.The model is used to analyse published test data on surface cracked pressurised pipes. The analysis consists in COD evaluation and estimate of failure as a consequence of plastic instability. A method is proposed which deals with the problem by simultaneous analysis of a number of cracks with increasing depth. The method avoids iterations and enables, for any load and crack length, calculation of the smallest crack depth which would cause instability.     

French experimental studies of circumferentially through-wall cracked austenitic pipes under static bending

This paper describes experimental studies performed on cracked pipes made of austenitic steel and subjected to a bending load. The studies concern the characterization of conditions for which an initial crack (fatigue precracked) initiates and then propagates along the circumference of the tube. The influences of different parameters were obtained: crack length, crack tip radius, tube geometry (radius, thickness), temperature and weldment. The predictive criteria checked in these studies are limit analysis (or net-section stress criterion) and J estimation.     

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.