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.     

An elasto-plastic finite element for steel pipelines

An efficient finite element for the modeling of inelastic behaviour of three-dimensional pipe systems is presented. The formulation is based on a two-node pipe element with 12 degrees of freedom. The element consists of an elastic portion and two potentially plastic 3D hinges of zero-length lumped at both nodes. The behaviour of the plastic hinges is characterized using recently derived and experimentally validated plastic interaction relations for pipe sections. The normality condition of plasticity is applied to the analytically derived yield hyper-surface at the stress resultant level in order to approximately simulate material elasto-plastic behaviour. The element models shear deformation effects both in the elastic and plastic ranges. Thus, it is suitable for predicting pipe behaviour subjected to high shearing forces. The model captures the essential features of pipe behaviour using a remarkably small number of degrees of freedom and is particularly suited for the analysis of long pipeline systems. Solutions for simple problems are provided and compared to several other well-established elements in the ABAQUS library in order to assess the validity of the results and demonstrate their scope of applicability.     

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.     

Effect of reinforcement on plastic limit loads of branch junctions

This paper provides effects of reinforcement shape and area on plastic limit loads of branch junctions under internal pressure and in-plane/out-of-plane bending, via detailed three-dimensional finite element limit analysis assuming elastic-perfectly plastic material behaviour. It is found that reinforcement is most effective when (in-plane/out-of-plane) bending is applied to the branch pipe. When bending is applied to the run pipe, reinforcement is less effective when bending is applied to the branch pipe. The reinforcement effect is the least effective for internal pressure.     

Experimental investigation of stresses in cold-bent pipes due to internal pressure and in-plane bending

Experimental measurements have been made of stresses in out-of-round pipe bends under internal pressure and in-plane bending. This paper describes the results of tests on one new and one ex-service pipe bend under the two loadings and compares these results with various theoretical predictions. For the pressure case the original formula due to Haigh² with modifications to take into account thickness variations and pipe bend radius, is reasonably accurate and for bending loads the recent formulation by Spence and Boyle¹² is a reasonable approximation. The code method of combining peak stresses by addition is confirmed in this case. The results of the tests have assisted designers in reviewing allowable limits on the ovality of manufactured pipes and in placing realistic limits on the cold springing of pipes to overcome erection tolerances.     

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

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

Cyclic behavior of a pipe section subjected to bending, ovalization or torsion loads in the case of a perfectly plastic material

The work presented is a stage in the development of a global inelastic calculation method for thin pipes and includes an incremental formulation for handling nonmonotonic bending, ovalization and torsion loads in piping in the case of a perfectly plastic material. Each load is dealt with separately and the global variables used are moments and curvatures.     

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.     

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.     

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.     

Limit loads for pipe bends under combined pressure and in-plane bending based on finite element limit analysis

Approximate plastic limit load solutions for pipe bends under combined internal pressure and bending are obtained from detailed three-dimensional (3-D) FE limit analyses based on elastic-perfectly plastic materials with the small geometry change option. The FE results show that existing limit load solutions for pipe bends are lower bounds but can be very different from the present FE results in some cases, particularly for bending. Accordingly closed-form approximations are proposed for pipe bends under combined pressure and in-plane bending based on the FE results.     

Limit loads for piping branch junctions under internal pressure and in-plane bending—Extended solutions

The authors have previously proposed plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on finite element (FE) limit loads resulting from three-dimensional (3-D) FE limit analyses using elastic–perfectly plastic materials [Kim YJ, Lee KH, Park CY. Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending. Int J Press Vessels Piping 2006;83:645–53]. The solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and for the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0. Moreover, the solutions considered the case of in-plane bending only on the branch pipe. This paper extends the previous solutions in two aspects. Firstly, plastic limit load solutions are given also for in-plane bending on the run pipe. Secondly, the validity of the proposed solutions is extended to ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0. Comparisons with FE results show good agreement.     

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.     

Glass reinforced composites of mixed wall construction

Strain gauge results are presented for three glass reinforced plastic (GRP) straight pipes subjected separately to pressure and bending moment. Tests under pressure were continued to destruction and failure test results are given. The pipes were of E-glass and polyester resin and were of 250 mm inside diameter but the wall constructions had glass provided in different combinations of chopped strand mat (CSM) and woven roving (WR). When in the linear regime under pressure, outer surface strains were lower than inside strains, and significantly so for the pipe with the greatest proportion of woven rovings. No satisfactory explanation is given at the moment in spite of extensive analytical efforts which include modelling as a thick-walled cylinder made up of a series of transversely isotropic laminae. Three-dimensional analysis was used throughout and is presented, for general interest, in a form suitable for implementation on a computer. Results are compared with those using simpler thick-cylinder theory where the wall is not of laminated construction.     

Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending

The present work presents plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic–perfectly plastic materials. To assure reliability of the FE limit loads, modelling issues are addressed first, such as the effect of kinematic boundary conditions and branch junction geometries on the FE limit loads. Then the FE limit loads for branch junctions under internal pressure and in-plane bending are compared with existing limit load solutions, and new limit load solutions, improving the accuracy, are proposed based on the FE results. The proposed solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0.     

Determination of flexibility factors in curved pipes with end restraints using a semi-analytic formulation

Piping systems are structural sets used in the chemical industry, conventional or nuclear power plants and fluid transport in general-purpose process equipment. They include curved elements built as parts of toroidal thin-walled structures. The mechanical behaviour of such structural assemblies is of leading importance for satisfactory performance and safety standards of the installations. This paper presents a semi-analytic formulation based on Fourier trigonometric series for solving the pure bending problem in curved pipes. A pipe element is considered as a part of a toroidal shell. A displacement formulation pipe element was developed with Fourier series. The solution of this problem is solved from a system of differential equations using mathematical software. To build-up the solution, a simple but efficient deformation model, from a semi-membrane behaviour, was followed here, given the geometry and thin shell assumption. The flexibility factors are compared with the ASME code for some elbow dimensions adopted from ISO 1127. The stress field distribution was also calculated.     

Assessment of the flexural capacity of corroded steel pipes

Flexural capacity of corroded pipes can be determined analytically assuming a full plastic failure mode for the pipe. A set of generalized solutions for flexural capacity of the pipe can be developed if the shape of the corrosion is known a priori. The generalized solutions derived in this paper are able to account for the simultaneous action of internal pressure and axial force. For practical purposes, the generalized solutions thus derived are simplified into approximate closed-form equations using three idealized corrosion shapes, namely, constant-depth, elliptical, and parabolic corrosions. Numerical examples indicate that the closed-form approximate solutions provide good comparison with the generalized solutions. The closed-form approximate solutions are subsequently compared to experimental results from full-size tests of pipes with different corrosion depth and width. Parameter study conducted as part of this paper indicates that the shape of a corrosion defect has significant influence on the flexural capacity of the corroded pipes.     

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

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

Theoretical analysis of local indentation on pressured pipes

A quasi-static analysis is presented in this paper for in-service pressurised pipelines subjected to an external impact. Based on the assumed simple rigid, perfectly plastic deformation model, a simple relationship is obtained between the external denting force F and the maximum dent depth δ₀. Results from the theoretical analysis are in reasonable agreement with results from finite element analyses. These show that the pressure p=p_in−p_out has a large influence on the pipe resistance to the indentation, where p_in and p_out are the internal and external pressure, respectively. For the same dent depth, a higher external denting force is required for pipes with higher pressure, p. The difference of the required force between a lowly pressurised pipe and a highly pressurised pipe increases with increasing denting depth.     

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.