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Nuclear power plant piping systems frequently encounter complex loads due to factors like internal pressure, self-weight, structural supports, and operational conditions. Within these systems, pipe bends play a crucial role in releasing energy through deformation. Cracks pose a risk to the integrity of the system, necessitating the calculation of the plastic collapse load for cracked pipe bends. This study presents estimations for the plastic collapse load of cracked pipe bends under pure out-of-plane bending moments and simultaneous in-plane and out-of-plane bending moments. Cracks located in the intrados, extrados, and crown of pipe bends were considered. The estimations for plastic collapse load are proposed based on the observed similarity between plastic collapse load and plastic deformation under both in-plane and out-of-plane bending conditions. For combined in-plane and out-of-plane bending moment conditions, circular and parabolic relationships have been proposed for a straightforward plastic collapse load prediction. Additionally, the estimations for plastic collapse loads were derived from the results of finite element analysis conducted on crack-free pipe bends, demonstrating its applicability to cracked pipe bends as well. • Plastic collapse load estimates for cracked pipe bends under combined loads, including out-of-plane bending, were studied. • Yield loci were compared with plastic collapse loads of cracked pipe bends under combined in-plane and out-of-plane bending. • Plastic collapse load estimates for crack-free and cracked pipe bends under combined in-plane and out-of-plane bending are proposed. [ABSTRACT FROM AUTHOR]

This study aims at investigating the effects of local wall thinning on the cyclic plasticity behaviours of 90° back-to-back pipe bends, which are commonly utilised in flexible piping systems within plant facilities. Over time, the prolonged operation of these pipe bends may lead to wall thinning and a deterioration of their structural integrity. To understand the effects of such wall thinning, a 3D finite element analysis is conducted. Load interaction diagrams are generated using the Linear Matching Method, which considers the cyclic plasticity behaviours of shakedown and ratcheting. The investigation includes pipe bends with three different locations of local wall thinning: intrados, extrados, and crown. The pipe bends are subjected to steady internal pressure and various cyclic bending moments, including in-plane closing, in-plane opening, and out-of-plane bending. Moreover, comprehensive parametric studies are carried out for the pipe bend structures, varying the wall thinning rates. Semi-empirical formulas are derived based on the study results, enabling the prediction of limit load, shakedown limit, and ratchet limit concerning the position of the local wall thinning. Results and discussions have demonstrated the most detrimental combination of wall thinning type and loading on the structural integrity of the pipe bends and have provided valuable insights into the problems associated with deteriorated pipe bends. • The effects of local wall thinning on the cyclic plasticity behaviours of 90° back-to-back pipe bends are investigated. • The pipe bends with three different locations of local wall thinning is considered: intrados, extrados, and crown. • Shakedown and ratchet limit boundaries are analysed using the Linear Matching Method. • Critical loading combinations and the specific wall thinning locations that may lead to adverse effects are identified. [ABSTRACT FROM AUTHOR]

Local wall-thinning of pipe is a common volume defect in application, which would cause pipeline leakage or rupture under complicated pipeline loads. The finite element analysis method was used to analyze the limit load of Pipe Bend with Local Wall-Thinning defect (PB LWT) under internal pressure, bending moment, torsion moment, axial force, and their combinations. The limit load empirical equations of PB LWT under single load and complex loads were fitted. According to the allowable pipeline load on equipment nozzles, the influences of torsion moment and axial force on the load bearing capacity of PB LWT were quantitatively analyzed. It is found that the load bearing capacity is reduced by an average of 1 % for medium and low-pressure equipment. For high-pressure equipment, the load bearing capacity is reduced by 10.07 %∼20.90 % under the influence of torsion moment. Under the effect of axial force, the load bearing capacity is reduced by 2.01 %∼12.40 %. • The limit loads of bends with extrados local wall-thinning defect are analyzed under internal pressure, bending moment, torsion moment, axial force, and their combinations. • Empirical equations for limit load of bend with defects are worked out for complex loads. • Torsion and tension can decrease the load-bearing capacity of bends by up to 10 %∼20 %. [ABSTRACT FROM AUTHOR]

This paper provides an engineering assessment of an oval-shaped clad pipes with a circumferential part-through surface crack subjected to bending moment based upon equivalent stress-strain relationship method (ESSRM) in conjunction with EPRI J -estimation procedure. Plastic limit load equations are developed specially to determine the equivalent stress-strain relationship of the welded clad pipe. Then, the conventional EPRI J -estimation procedure is extended to calculate J values of the equivalent configuration with oval cross-section converted from the welded clad pipe using the ESSRM. The validation of the ESSRM/EPRI estimation framework mentioned in the above is carried out by comparing with the results obtained from 3-D elastic-plastic finite element (FE) analysis. [ABSTRACT FROM AUTHOR]

In this study, the plastic influence functions, h 1 , for estimates of J -integral of a pipe with a complex crack were newly proposed based on the systematic 3-dimensional (3-D) elastic-plastic finite element (FE) analyses by using Ramberg-Osgood (R-O) relation, in which global bending moment, axial tension and internal pressure were considered as loading conditions. Based on the present plastic influence functions, the GE/EPRI-type J -estimation scheme for complex-cracked pipes was suggested, and the results from the proposed J -estimation were compared with the FE results using both R-O fit parameters and actual tensile data of SA376 TP304 stainless steel. The comparison results demonstrate that although the proposed scheme provided sensitive J estimations according to fitting ranges of R-O parameters, it showed overall good agreements with the FE results using R-O relation. Thus, the proposed engineering J prediction method can be utilized to assess instability of a complex crack in pipes for R-O material. [ABSTRACT FROM AUTHOR]

The plastic geometry factors, i.e. the η pl and γ pl factors, are needed to calculate the J -integral from the load vs. crack mouth opening displacement (CMOD) or load-line displacement (LLD) curve in the J–R curve test. In this study, we carry out a systematic investigation of the η pl factor for plane-sided and side-grooved SE(B) specimens with a wide range of crack depths ( a / W ranging from 0.3 to 0.7) and thickness-to-width ratios ( B / W equal to 0.5, 1 and 2) based on three-dimensional (3D) finite element analyses (FEA). To examine the accuracy of the η pl factors suggested in ASTM E1820, the corresponding estimated J value are compared with the J value obtained from the 3D FEA based on both the large-strain and small-strain formulations. The LLD- and CMOD-based plastic η pl factors corresponding to both the average J value over the crack front and the local J value at the mid-thickness of the crack front are evaluated. The main finding of this study is that besides the crack depth, both the thickness and side grooves of the specimens have observable impacts on the η pl factor. Based on the results of the 3D large-strain FEA, a set of expressions for the η pl and γ pl factors are proposed. The results of this study can improve the accuracy of the experimentally determined J–R curve and facilitate the use of non-standard medium-cracked (0.3 ≤ a/W < 0.45) SE(B) specimens for the J–R curves testing. [ABSTRACT FROM AUTHOR]

Most of the commonly used standards and codes for burst pressure prediction at a corrosion defect of steel pipelines generally just consider internal pressure alone. However, an actual oil/gas pipeline is usally subjected to external loads, such as axial compression/tension and bending moment, which may affect the burst capacity of the pipeline. In this study, a three-dimensional (3D) nonlinear finite element (FE) model validated by burst tests was developed to investigate the effect of bending moment and axial force on the burst capacity of corroded pipelines. Subsequently, the effects of external loads (i.e., bending moment, and axial force) and corrosion geometry features (involving corrosion depth, width, length, and clock position) on the pipe burst pressure were determined. Then, based on a series of FE cases, a new burst prediction model for corroded pipelines subjected to the combination loads of bending load and axial compressive force was fitted and developed. Finally, the effectiveness and reliability of the new proposed model were verified by extensive parametric FE analysis and burst test data. The results show that the prediction errors for the failure pressures between the proposed-model and the FEM were less than 10% for most 92.793% of the 222 cases. Moreover, the proposed model can also be applied to the condition that the pipeline is under single internal pressure, and its prediction accuracy is better than that of other seven well-known models of ASME B31G, Mod B31G (0.85 d L), Z662, DNV, PCORRC, CUP, and Shell-92. • Developed a finite element model for corrosion defect assessment on pipeline under bending moment and axial force. • Determined the effect of corrosion width on failure pressure of pipelines. • Considered the effect of clock position of corrosion defect on burst pressure of pipelines. • Proposed a novel burst capacity model for corroded pipelines under bending and axial compression loads. • Determined the effect of bending moment and axial force on failure pressure of corroded pipelines. [ABSTRACT FROM AUTHOR]

Abstract: No experimental data exist within open literature, to the best knowledge of the author, for determining shakedown boundaries of 90° back-to-back pipe bends. Ninety degree back-to-back pipe bends are extensively utilized within piping networks of nuclear submarines and modern turbofan aero-engines where space limitation is considered a paramount concern. In the current research, the 90° back-to-back pipe bend setup analyzed is subjected to a spectrum of steady internal pressures and cyclic in-plane bending moments. A previously developed direct non-cyclic simplified technique for determining elastic shakedown limit loads is utilized to generate the elastic shakedown boundary of the analyzed structure. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Offshore pipelines are subjected to large plastic strain conditions, such as bending accompanied by high internal pressure, during the installation and operation processes. These pipelines are usually constructed by the girth welding method and weldments may contain naturally occurring surface and embedded planar and/or volumetric imperfections and/or defects. It is widely recognized that the existing fracture assessment procedures which are based on the load-controlled method, are not explicitly designed for situations with large plastic deformation. The main objective of the current paper is to find a routine to make fracture assessment for a pipeline subjected to plastic bending. In this paper, based on 3D elastic–plastic finite element analyses, the influences of various parameters on the fracture responses (CTOD) of the cracked pipelines are investigated and a CTOD estimation formula is proposed. Furthermore, comparison with fracture assessments made by BS7910:2005 code and finite element analyses indicates that the former gives over-conservative predictions. Based on the proposed formula, a failure assessment diagram (FAD) for strain-based fracture, is presented for the specific geometry and material properties of the particular pipe with semi-elliptical surface cracks under large plastic bending, where the global strain is up to 3%. [Copyright &y& Elsevier]

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

Structural integrity analysis of pipe elbows is of critical significance because they not only withstand the internal or external pressure but also absorb the bending moment in a pipeline system. While the burst capacity of pipe elbows under internal pressure only have been extensively investigated in the literature, the study on the burst capacity of pipe elbows under combined internal pressure and bending moment is still limited. In this paper, the effect of bending on the burst capacity of thin-walled defect-free and local wall-thinning (LWT) elbows subjected to combined internal pressure and bending moment is systematically investigated. A correction factor is defined to quantify the bending effect on the burst capacity; extensive parametric finite element analysis (FEA) is carried out to analyze the dependence of the correction factor on the bending mode and magnitude, elbow size and steel grade, and LWT size and location. The results indicate that as the magnitude of the bending increases, the burst capacity of both the defect-free and LWT elbows generally deceases. For the defect-free elbows, the elbow steel grade has a significant influence on the correction factor while the influence of the elbow geometry is marginal. For the LWT elbows, the correction factor depends markedly on the LWT location and bending mode. • Employ FEA to investigate the bending effect on burst capacity of pipe elbows. • Consider three bending modes: in-plane closing and opening, and out-of-plane. • Consider wide ranges of elbow dimensions and steel grade for defect-free elbows. • Consider various sizes and locations of local-wall thinning (LWT) defects on elbows. [ABSTRACT FROM AUTHOR]

Based on the conservation law and bending theory, a technique to determine complicated stress intensity factors on three-dimensional components is proposed, A series of closed form expressions of stress intensity factor are derived for cracked shells under different loads, such as bending, tension. The method requires the geometric relationship between multiple singular stress fields from the crack section, and the relationship between the stress at different crack tips can be estimated. In the expression of the stress intensity factor K, K is proportional to the stress σ at the crack tip, and we can get the supplementary equation of between different stress fields K according to the ratio of the stress at the crack tip, then use the J -integral method to calculate the stress intensity factors of different stress fields. In order to verify the feasibility of this method, a cracked R-fluted shells model was constructed. Under the action of the bending moment, the corner crack propagation is simulated through the reserved corner crack, and two crack tips with different stress fields are generated during the simulation. The research result indicates that the proposed method is effective for cracked R-fluted shells, and has universal applicability for solving complex stress intensity factors on three-dimensional components. • J2-integral can estimate the different SIFs of complex stress fields under bending. • The geometric relationship of the crack tip can express the relationship between the stress intensity factors of the crack tip. • Simplifies the calculation of stress intensity factors for complex cracks. • Deduced the calculation process of the stress intensity factor at the crack tip under complex loads. [ABSTRACT FROM AUTHOR]

In this two-part paper, guidance for assessing plates containing embedded elliptical cracks under complex loading conditions is developed, based on the fracture mechanics validation of the limit load solutions using the finite element (FE) J solutions. In Part I of this paper, elastic-plastic 3D FE analyses are performed for plates with embedded off-set elliptical cracks under combined biaxial stresses and through-thickness bending for developing a FE J database containing 612 cases. Totally 18 cracked plate models are created. For each cracked plate, 17 load combinations are considered and two material strain hardening exponents are analysed. The obtained plastic J solutions are correlated as the EPRI type fully-plastic J factor h 1. The effect of the applied normal stress parallel to the crack plane, σ 2 , on the elastic-plastic J behaviour is investigated and it is found that the EPRI linear addition J estimation scheme may not describe the elastic-plastic J behaviour very well for cases under combined bending moment and σ 2. The limit load validation using the FE J solutions is detailed in Part II of this paper. • Embedded off-set elliptical cracks in plates under complex loading. • Elastic-plastic 3D FE J database developed containing 612 cases. • Fully-plastic FE J solutions provided as EPRI h 1 factor. • Effect of stress parallel to the crack plane on elastic-plastic J investigated. [ABSTRACT FROM AUTHOR]

Theoretical analysis based on the finite element (FE) method for plastic collapse of metallic single mitred pipe bends of various geometries, subject to in-plane bending moment, were carried out using both ABAQUS and ANSYS structural FE programs covering both linear small displacement and non-linear large displacement analysis. Parametric surveys presented interesting features including an increase in plastic collapse in-plane bending moments after mitre angles of around 40°. Results obtained using either ANSYS or ABAQUS could not be compared against any available experimental data as they differ significantly in areas like strain hardening and other features of a real material that did not exist in the FE modelling. However, single case comparison with the only reported experimental work, known to the author, showed that large displacement FE analysis led to more realistic predictions. It is, therefore, concluded that despite complex behaviour of a real material as compared to material models available in FE analysis, effective plastic collapse moments can be predicted using the small displacement FE analysis. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

The present study addresses outcomes of extensive nonlinear finite element analyses concerning a diverse geometric spectrum ranging from 30° to 180° pipe bend configurations accounting for the initial geometric deformations of the cross-sections resulting from the bending fabrication process. Pipe bends are modeled with the realistic and accurate cross-section by incorporating initial ovality and thinning/thickening (together called initial geometric imperfection) up to 20%. The modeled pipe bends are loaded by in-plane opening moment and internal pressure, considering material models of elastic-perfectly-plastic (EPP) and strain-hardening (SH). The detailed finite element results show that the presence of initial imperfection has a pronounced impact on the plastic collapse moment. At the lower magnitude of applied pressure, the initial imperfection decreases collapse moment of deformed pipe bends significantly as compared to that of circular cross-sectioned pipe bends. At the higher pressure values, the negative effect of initial imperfection decreases with increased pressure for thinner pipe bends. Based on the results of the conducted finite element analyses, governing empirical equations are formulated to predict the collapse moments of pressurized 30° to 180° thin-walled pipe bends with more realistic cross-section employing EPP and SH models. • Nonlinear analysis of 30°to 180°pipe bends with initial geometric imperfection. • Elastic-perfectly plastic and strain-hardening materials are used for analysis. • The initial geometric imperfection produces negative effect on collapse moment. • Collapse moment equations are proposed for 30°to 180°pressurized pipe bends. [ABSTRACT FROM AUTHOR]

Buried pipes suffer from various natural and human-related phenomena leading to the bending forces on such structures. The analytical models face obstacles such as the complications in modeling material behavior and the local stress concentration due to the appearance of defects are combined. This causes the accumulative over and under-estimation of pipe capacity due to the idealizations of full plastic stress distribution and location of defects at the most dangerous area, respectively. Consequently, such models are not appropriate in the case that defects are not located on the bending plane. The Finite Element, FE, approach is used to overcome these difficulties with the appearance of defects is randomly propagated around the pipe. Additionally, the bilinear material model is also applied accounting for the shape of actual stress-strain curves in a simplified manner. Various Finite Element Analyses are conducted consequently to have an extensive FE database with 772 samples labeled by the bending capacity of the corresponding pipe. To avoid the difficulties for users due to the requirement of coding skill, statistics, and advanced mathematics knowledge, and the implicit appearance of the conventional data-driven models, an empirical model, which can be explicitly expressed, has been developed. The main process of developing such a model is to optimize the design variables in the reduction factors. The objective function is chosen as the Mean Absolute Error of the predicted versus simulated reduction factor. The proposed model has been validated with the high accuracy of R-square at 0.9929 on the test set reveals an improvement compared to other available models. • Various FE models including the differences in material models and failure criteria have been investigated. • An extensive FE database with 772 samples generated for predicting Moment capacity of the defected pipe. • Accounting to the effect of bidirectional bending moment, axial forces in the bending pipe, the effects of out-of-bending plane defects are observed along with other inputs. • Development of engineering applicable empirical model with R2 up to 0.9929. [ABSTRACT FROM AUTHOR]

Geometrical deviations in the manufacture and assembly of mechanical products often result in non-parallel bearing surfaces in the bolted joint. To reveal the influence of the non-parallel bearing surface on the loosening of the bolted joint, the paper proposes a non-parallel bearing surface anti-loosening analysis model, revealing the anti-loosening mechanism of the non-parallel bearing surface, and found that the non-parallel bearing surface will introduce additional contact pressure and contact friction torque. Within a certain range, the contact pressure and the contact friction torque increase as the inclination angle of the non-parallel bearing surface increases, and the thread anti-loosening performance is improved. A parametric finite element model is further established to verify the existence of additional contact pressure and contact friction torque, and the slip factor is introduced to evaluate the loosening. Finally, the anti-loosening analysis model and the finite element model are validated by the loosening experiment of the non-parallel bearing surface. The research result provides a new idea for the anti-loosening control of bolted joints. • The non-parallel bearing surface creates a bending moment on the bolt joint that causes the threads to be subjected to the lateral force, and the nut moves laterally, pressing the thread contact pairs to create additional contact forces and contact friction torques. • The additional contact force and the contact friction torque increase the bolt's anti-loosening properties. • The anti-loosening ability of the non-parallel bearing surface is affected by the inclination angle, and the bigger the inclination angle, the stronger the anti-loosening ability. • In the simulation process, combined with the slip factor, the influence of non-parallel bearing surface is further revealed, and the relevant laws are consistent with the theory and experiment. [ABSTRACT FROM AUTHOR]

This paper is dedicated to providing a detailed limit load analysis for 180° pipe bends under bending moment using three dimensional finite element (FE) method considering geometric nonlinearity. Results show that FE results for 180° pipe bends are all lower compared to those for 90° pipe bends, especially for pipe bends with thin wall and small bend radius (R / r = 1.5, r / t = 50). However, for pipe bends with thick wall and large bend radius (R / r = 4, r / t = 5), results seem very close. New predicted equations are proposed based on the FE results. If the geometric nonlinearity effect is considered, when the material parameters of yield strain ε s = 0, results still obey the estimating solutions without geometric nonlinearity considered. But the geometry change should have some significant influence on the failure with the material's behavior changing. With the applied bending load increasing, the ovalization parameter C will also continue to increase. The change of the parameter C is significant for the thin pipe bends (r / t = 50), while is not obvious for thick pipe bends (r / t = 5). The influence of the bend radius on the parameter C is not significant. Geometric effect is significant for a high yield strain value that the pipes will have enough ability to be deformed. • Three-dimensional non-linear finite element method considering geometric nonlinearity is used. • Limit loads are analyzed for 180° pipe bends under bending moment. • Parameter r / t is the main factor affecting the limit load of the pipe bends. [ABSTRACT FROM AUTHOR]

The present study determines the effect of shape imperfections on the B 2 index of pipe bends subjected to in-plane opening moment using 3D nonlinear finite element (FE) methodology. The analysis considers the large strain formulation option and the material behavior is elastic-perfectly plastic. The reaction moment versus angular rotation curves are plotted for all the simulated pipe bends and the plastic collapsing moments are determined using Twice-elastic slope technique as recommended in ASME B&PV, section III (clause NB-3213.25). The B 2 stress index was computed for each model from their respective collapse moment. The variable wall thickening in the pipe bend's cross section yields negligible effect and the presence of ovality has a momentous effect on B 2 stress indices. A mathematical equation is suggested to compute B 2 stress index for pipe bends with ovality subjected to in-plane opening bending moment. • Non-linear finite element analysis was performed on pipe bends under in-plane opening moment. • The B 2 stress index was evaluated in the pipe bends having shape imperfections. • Presence of ovality in the pipe bends cross section produces significant effect. • The effects of thinning on B 2 stress index are minimal. • Closed form solution is proposed to compute B 2 stress index of pipe bends with ovality. [ABSTRACT FROM AUTHOR]