Shakedown and limit analysis of 90° pipe bends under internal pressure,cyclic in-plane bending and cyclic thermal loading

The Linear Matching Method is used to create the shakedown limit and limit load interaction curves of 90° pipe bends for a range of bend factors. Two load cases are considered i) internal pressure and in-plane bending (which includes opening, closing and reversed bending) and ii) internal pressure and a cyclic through wall temperature difference giving rise to thermal stresses. The effects of the ratios of bend radius to pipe mean radius (R/r) and mean radius to wall thickness (r/t) on the limit load and shakedown behaviour are presented.     

Pressure of Newtonian fluid flow through curved pipes and elbows

Under conditions of high temperature and high pressure, the non-uniformity of pressure loads has intensified the stress concentration which impacts the safety of curved pipes and elbows. This paper focuses on the pressure distribution and flow characteristic in a curved 90 o bend pipe with circular cross-sections, which are widely used in industrial applications. These flow and pressure characteristics in curved bend pipes have been researched by employing numerical simulation and theoretical analysis. Based on the dimensionless analysis method a formula for the pressure of Newtonian fluid flow through the elbow pipes is deduced. Also the pressure distributions of several elbows with different curvature ratio R/D are obtained by numerical methods. The influence of these non-dimensional parameters such as non-dimensional curvature ratio, Reynolds number and non-dimensional axial angle α and circumferential angle β on the pressure distribution in elbow pipes is discussed in detail. A number of important results have been achieved. This paper provides theoretical and numerical methods to understand the mechanical property of fluid flow in elbow pipes, to analyze the stress and to design the wall thickness of elbow pipes.     

Life estimation of pressurised pipe bends using steady-state creep reference rupture stresses

Steady-state reference rupture stresses were obtained for a range of 90° pipe bends, subjected to internal pressure only, using simplified 2D axisymmetric finite element (FE) models. The bends were considered to be circular in shape and not include any ovality. Creep damage FE analyses were performed to obtain realistic failure lives and to determine the skeletal point rupture stresses, using the material properties, obtained at 640 °C, for a service-exposed CrMoV pipe steel. The effects of the normalised pipe bend dimension on the reference rupture stresses are presented. The results obtained confirm the validity of the use of the steady-state reference rupture stress in life estimation for a wide range of pressurised pipe bend geometries. The life predictions were compared with those of the corresponding straight pipes and their relevance considered.     

Stress analysis of smooth curved tubes with flanged end constraints

A detailed experimental stress analysis programme is described on smooth pipe bends with flanged end constraints loaded under in-plane bending. A 335·6 mm (14 in) diameter steel pipe bend with special adjustable flange type constraints was extensively strain gauged and complete stress distributions were obtained for flanged bend angles of 90° and 180°. Two smaller 114·3 mm ($\text{4}\text{1}\text{2}\text{in}$) diameter flanged steel bends of 90° and 180° but different curvature were also tested.A theoretical development for the stresses in bends bounded by rigid flanges is described and results given for a complete range of geometries. Detailed comparisons are made between the theory and experiments and the agreement is good.     

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.     

Measurement of leak-rate through fatigue-cracks in pipes under four-point bending and BWR conditions

Leak-rate tests were performed using 114 mm and 165 mm (4 and 6 in) diameter, schedule 80 pipes made of austenitic stainless steel SUS304 and carbon steel STS42. Each pipe contained a through-wall fatigue crack and was mounted on a four-point bending machine of 400 kN maximum loading. Tests were done under a pressure of 7 MPa, with a subcooling temperature. The leak rate was measured by a Venturi flow meter and a differential pressure transducer attached to the pressure vessel. Comparisons of the effect of pipe material, diameter and crack angle were made. This paper shows that from a Leak-Before-Break viewpoint, the stainless-steel pipe is superior to the carbon-steel one, and that the pipe with the larger diameter is better than the one with the smaller diameter. No unstable fracture was observed in the tests.     

Stress distribution and flexibility of the suction bend of the primary sodium pump—LMFBR-SNR 300

Hydrodynamic aspects lead to the design of a special smooth suction bend for the LMFBR-SNR 300 primary sodium pump. This bend is built up from two symmetrical halves, formed from plates by explosive forming.For the nuclear piping system design, the ASME Boiler and Pressure Vessel Code —Section III¹ gives formulae for the simplified stress analyses by using the stress indices and flexibility factors. The application of these formulae to the prediction of the stresses and flexibility of the suction bend considered does not guarantee the reliability of the results. To achieve a more accurate prediction of the bend's stresses and flexibility linear stress analyses are carried out based on two different methods.In the first method the bend is schematised by various toroidal segments with bend parameter λ ranging from 0·049 to 0·22. Each segment is analysed as described below.Internal pressure: Stress analyses are carried out using the KSHEL computer program developed by Kalnins and based on his theory.²In- and out-of-plane bending: Based on the energy equations of von Karman³ and Vigness,⁴ a theoretical solution was developed by Rodabaugh and George.⁹ Applying the principle of least work gives the following equation: $\text{[D(λ,r,p,n,E)]{c}{}_{\mathrm{n}}\text{} = {?3,0,0,0,…}}{}^{\mathrm{T}}$ where D is a symmetrical band matrix and c_n is the modified unknown coefficient of the trigonometric series of the displacement field. The stresses and flexibility could be determined by substituting c_n in the appropriate equations. The membrane circumferential stress distribution obtained by Rodabaugh and George was modified by Dodge and Moore⁶ based on Gross's solution.⁸The computer program PIPEBEND, based on the above-mentioned solutions, is developed for calculating the stresses and flexibility of each toroidal segment.The second method deals with three-dimensional stress analysis. This is necessary in order to investigate the influence of change of curvatures and cross-sections (neglected in the first method). Modelling is carried out for the symmetry of half of the complete suction bend, applying the thick shell element QUABC9 of the ASKA system. Application of this element for thin shell problems requires the reduction of the number of integration points. For the considered model, a $\text{2 × 2}$ reduced integration scheme is chosen for the transverse shear component only.The results of both methods were compared and it was concluded that, for internal pressure and pure—or nearly pure—bending load, adequate prediction of the stresses and flexibility can be obtained by the first method.     

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.     

Experimental determination of stress corrosion crack rates and service lives in a buried ERW pipeline

Threshold stresses and crack growth rates for in-service stress corrosion cracking (SCC) of two electrical resistance weld (ERW) seam welded pipes from two 45-year-old oil pipelines were experimentally assessed. Seventeen high-pH SCC tests were carried out, in both base and ERW weld metals, at two temperatures (73 and 45 °C). Tapered specimens were used for base metal, and constant section specimens were developed for ERW tests, in which original surface conditions were preserved. It was found that susceptibility of the ERW seam welds is much higher than for base materials, so that the welds define the length of the pipe that is susceptible to SCC. Threshold pressure estimates for SCC initiation were defined from tests at elevated temperature, service temperature, and literature correlations. Fabrication residual stresses were also measured and taken into consideration. SCC threshold pressures for these lines are controlled by the ERW welds; the pipe tracts that are considered to be susceptible to SCC are those that undergo a service pressure of at least 2.4 MPa. For the case under study, this represents about 70% of the length of the pipeline.     

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.     

Large-scale experimental investigation of the effect of biaxial loading on the deformation capacity of pipes with defects

This paper presents results from large-scale four-point bending tests of 12″ X65 seamless pipes with circumferential defects subjected to different levels of internal pressure. The aim of the tests has been to investigate the effect of biaxial loading on the strain capacity of the pipes. The results from the tests show a significant effect of the biaxial loading. For cases without internal pressure, the pipes fail due to local buckling on the compression side of the pipe. Upon application of internal pressure the failure mode shifts to fracture from the defect on the tension side. The failure bending strain levels for these cases were 1.5–2.25%, whereas the local buckling occurred at strain levels in the range of 3.5–4%. The main reason for this appears to be that the biaxial loading increases the crack driving force for a given applied strain level. No significant effect of the biaxial loading on the ductile tearing resistance was observed. The results are of great importance for fracture assessment of pressurised pipelines loaded into the plastic region, as the biaxial loading effect observed is not accounted for in current fracture assessment procedures.     

Effect of vibration loading on the fatigue life of part-through notched pipe

A systematic experimental and analytical study has been carried out to investigate the effect of vibration loading on the fatigue life of the piping components. Three Point bend (TPB) specimens machined from the actual pipe have been used for the evaluation of Paris constants by carrying out the experiments under vibration + cyclic and cyclic loading as per the ASTM Standard E647. These constants have been used for the prediction of the fatigue life of the pipe having part-through notch of a/t = 0.25 and aspect ratio (2c/a) of 10. Predicted results have shown the reduction in fatigue life of the notched pipe subjected to vibration + cyclic loading by 50% compared to that of cyclic loading. Predicted results have been validated by carrying out the full-scale pipe (with part-through notch) tests. Notched pipes were subjected to loading conditions such that the initial stress-intensity factor remains same as that of TPB specimen. Experimental results of the full-scale pipe tests under vibration + cyclic loading has shown the reduction in fatigue life by 70% compared to that of cyclic loading. Fractographic examination of the fracture surface of the tested specimens subjected to vibration + cyclic loading have shown higher presence of brittle phases such as martensite (in the form of isolated planar facets) and secondary micro cracks. This could be the reason for the reduction of fatigue life in pipe subjected to vibration + cyclic loading.     

Influence of geometry change on creep failure life of 90° pressurised pipe bends with no initial ovality

The influence of the geometry change during creep on the failure life of 90° pipe bends, subjected to internal pressure, was investigated using finite element creep damage analyses. The bends were considered to be circular in shape with no initial ovality. The failure lives obtained using the material properties for a CrMoV pipe steel at 640 °C clearly show a significant life reduction when the geometry change is included. In the range of the pipe bend dimension ratios investigated, it was found that the failure lives could be reduced to between 65 and 78% of those obtained from constant geometry cases, indicating that the influence of geometry change may need to be appraised for detailed numerical analysis. The results were compared with those of the corresponding straight pipes and their relevance considered. It has been shown that under constant geometry conditions, the failure life for pipe bends is about 30% lower than that for the straight pipes.     

Effects of attached straight pipes on finite element limit analysis for pipe bends

The effect of the length of an attached straight pipe on the plastic limit load of a 90° pipe bend under combined pressure and bending is quantified, based on finite element (FE) limit analyses using elastic–perfectly plastic materials with the small geometry change option. Systematic FE limit analyses of pipe bends with various lengths of the attached pipe are performed. It is shown that the effect of the length of the attached straight pipe on plastic limit loads can be significant, and the limit loads tend to decrease with decrease of the length of the attached straight pipe. In the limiting case of no attachment, the limit loads are found to be close to existing analytical solutions.     

Stresses in a pipe bend of oval cross-section and varying wall thickness loaded by internal pressure

The types of geometrical irregularity arising from the production of pipe bends are briefly discussed and formulae are presented which facilitate the calculation of stresses caused by each individual irregularity, when the pipe is subjected to internal pressure.The individual formulae are combined to enable the stress distribution to be calculated in a pipe bend under internal pressure with all the irregularities discussed. Results given from the formulae for a typical pipe bend are compared with results obtained by the finite element method.The requirements and limitations of British Standards are discussed in comparison with the predictions of the formulae derived in this paper.     

Moment resistance of steel pipes subjected to combined loads

The first part of this paper provides a review of recent investigations on steel pipes subjected to combined loads. Attention is given to studies involving both numerical and experimental components aimed at quantifying the modified moment resistance of pipes subjected to internal pressure and axial force. The comparison of experimental and finite element results indicate that the nonlinear shell finite element analysis is a reliable tool for predicting moment capacities of pipes. The second part of the paper reports two additional full-scale tests recently conducted at the University of Ottawa aimed at expanding the existing experimental database to pipes subjected to more complex load combinations involving twisting moment and shear (in addition to axial force, internal pressure, and bending). The finite element analysis for both tests is shown to provide excellent predictions of pipe moment capacity. The third part of the paper is a systematic parametric study based on the FEA model verified in previous and present investigations, aimed to assess the ability of pipe sections to attain their modified elastic and/or plastic moment resistance as predicted by analytically derived interaction equations. The parameters investigated are the applied torsion, internal pressure, axial force, and the diameter-to-thickness ratio of the pipe.     

Creep crack growth of seam-welded P22 and P91 pipes with artificial defects. Part I. Experimental study and post-test metallography

This paper describes the experimental work conducted on creep and fatigue crack growth behaviour in axially-notched, seam-welded pipes. The key objective of this work is to examine how the results from feature tests compare with standard laboratory specimen data using different European high temperature assessment methods, the final aim being to contribute towards the development and validation of a unified European procedure for estimating crack growth behaviour and remaining life of high temperature components. Within the context of this work, two steels P22 (2 1/4Cr1Mo) and P91 (9Cr1MoVNb) were studied at 565 and 625 °C, respectively.Two pipes were tested for each material; one pipe was subjected to a constant gas pressure (SP) and the other was tested under low cyclic pressure (CP) (10⁻⁴ Hz). Each pipe contained three axially machined notches, one in the heat affected zone (HAZ) and two in the base metal. The direct current (DC) potential drop (PD) technique was successfully applied to monitor crack growth during the tests. In both steels, the defect situated in the HAZ exhibited a higher crack growth rate, confirming that the HAZ is more vulnerable to crack initiation and propagation than the parent metal. Post-test metallography analysis showed that creep cavitation damage is the main mechanism governing the crack propagation. In the case of the cyclic tests for which the selected frequency was close to, or slightly higher than, the frequencies encountered in high temperature plants, metallographic observations showed no noticeable effect of cyclic loading in terms of transgranular crack growth.The data analysis of the experimental data obtained in this work are presented in Part II of this paper [Creep Crack Growth of Seam-welded P22 and P91 Pipes with Artificial defects—Part II. Data analysis. Second International HIDA Conference, Advances in Defects Assessment in High Temperature Plant, MPA, Stuttgart, Germany, 4–6 October, 2000].     

Calculation of the ultimate plastic state of thick-walled pipe bend in the circumferential direction

An engineering approach to determine the ultimate state of pipe bend in the circumferential direction is proposed. The essence of the approach is in the realization of several sequential steps. At the first stage, a separate action of certain groups of external loads by means of the semi-inverse method of Saint Venant is considered. Then, a reduction coefficient for internal moments is determined in the case of the simultaneous action of external bending moments and internal pressure. Finally, a general approach is proposed to the calculation of the ultimate state at the prescribed point of the bend section for the resulting system of internal force factors: the bending moment and tensile force in the circumferential direction, longitudinal and tangential forces. The possibility is indicated for the use of the results obtained to take into account cracks and three-dimensional defects available in the pipe bend.     

Transferability of specimen J–R curve to straight pipes with throughwall circumferential flaws

The stress triaxiality is an important parameter in explaining the geometry dependence of J–R curves. By comparing the stress triaxiality across the ligament of a specimen and a cracked component, it is possible to assess whether the cracked component exhibits similar fracture behaviour to the specimen. In the present investigation, fracture experiments have been carried out on throughwall circumferentially cracked 8-in. diameter pipes under four point bending load and three point bend bar (TPBB) specimens machined from the same pipe. Subsequently, 3-D elastic–plastic finite element analyses have been carried out on cracked pipes and TPBB specimens to determine the stress triaxiality across the ligament. It is found that the stress triaxiality conditions across the ligament are similar for the specimen and the cracked pipes. Therefore, the specimen fracture parameters can be transferred to these cracked components. It is also verified from the experimental results that the specimen J–R curves also fall within the acceptable band of component J–R curves. These investigations emphasise the role of stress triaxiality in selecting the specimen type for transferring fracture parameters under large scale yielding.     

Fracture mechanics analysis of stable crack growth under sustained load and instability of circumferential cracks in straight water-steam pipes

In order to determine the component behaviour of pipes made from X 20 CrMoV 121 steel for the water-steam circulation system of a helium-cooled high-temperature reactor component, tests were carried out under load conditions similar to the case of emergency cooling. The aim of the tests was to determine the stable and unstable crack growth in the less tough weld filler metal of girt-welded pipes of 18·5 mm wall thickness and 400 mm inside diameter. The tests were carried out with weld filler metals of two different toughnessesSuch stable crack growth could be of particular importance in the case of residual heat removal. For this reason two tests were carried out on pipes with a circumferential crack under sustained load.In the second part of the test programme pipes with defects were loaded under sustained internal pressure, and additionally an increasing bending moment was applied. The aim of this investigation was to determine the boundary conditions for failure occurring by leak or by fracture with regard to the different toughness of the weld filler metal.The fracture mechanics analysis was carried out using a modified version of the flow-stress criterion for circumferential cracks (Batelle approach) and using also the so-called ‘effective fracture toughness’ $\text{K}{}_{\mathrm{<mtext>eff</mtext>}}$.The investigation has revealed that the component toughness is adequately high and component failure by fracture is not expected. The experimental results can be described theoretically using either the Battelle approach or the formulae of linear-elastic fracture mechanics if the data obtained in the test characterising component behaviour (flow stress or effective toughness) are used as a basis. The results show that an evaluation of component behaviour using $\text{K}{}_{\mathrm{<mtext>Jo</mtext>}}$ values determined by CT specimens according to the $\text{J}$ integral procedure is too conservative.