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.     

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.     

Assessment of the integrity of a pipe under combined load and displacement controlled loading

A pipe containing a circumferential part penetrating defect in the heat affected zone of a weld is analysed under a combination of load and displacement induced tension-bending. The defect tolerance for the pipe is estimated using a novel procedure for the assessment of the integrity of components containing defects — the Method of Real Elements (MeReEl). The proximity of service conditions to the limiting state conditions was assessed in terms of the lateral displacement of the end of the pipe (the deformation parameter which governs its loading) and, for the purpose of comparison, in terms of the bending moment in the section containing the defect. The results obtained were compared with the results of conventional limit analysis. The adequacy of using the dominant parameter (displacement) for the estimation of the safety margins was substantiated. The advantages and limitations of the proposed method are discussed.     

Finite element based stress concentration factors for pipes with local wall thinning

Based on detailed three-dimensional elastic FE analysis, the present work compiles the elastic stress concentration factor for a pipe with local wall thinning. To cover practically interesting cases, a wide range of pipe and defect geometries are considered, and both internal pressure and global bending are considered. Resulting values of stress concentration factors are tabulated for practical use, and the effects of relevant parameters such as pipe and defect geometries on stress concentration factors are discussed.     

Plastic limit load of cylindrical shells with cutouts subject to pure bending moment

In this paper, the results of limit analyses of thin-walled cylindrical shells with a circular hole under the action of a pure bending moment are presented in dimensionless form for a wide range of geometric parameters. Analytical estimation of lower bound limit load is carried out using the feasible sequential quadratic programming (FSQP) technique. The finite element calculations of limit load consist of elastic–plastic and lower and upper bound predictions by elastic compensation methods. A testing device was made to perform experiments to obtain limit bending moment of cylinders with circular openings. The analytical and finite element calculations are compared with experimental results and their correlation is discussed. The finite element calculation results were found to be in good agreement with lower bound estimations by the nonlinear mathematical programming (FSQP) method and the formula proposed by Shu.     

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.     

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.     

Reference stress method for evaluation of failure assessment curve of cracked pipes in nuclear power plants

In order to obtain a precise failure assessment curve (FAC) in the R6 defect assessment procedure, it is necessary to evaluate the J-value of cracked components. The reference stress method can be used for estimating J-values. However, the accuracy of estimation depends on the limit load used for evaluating the reference stress. In this study, the applicability of several limit load solutions was investigated through comparison with the results of elastic-plastic finite element analyses (FEA). A pipe containing a circumferential surface crack was analyzed under pure bending load. Six materials used in nuclear power plants were assumed. It was shown that the reference stress method is valid for FAC evaluation. The maximum non-conservativeness caused by using the reference stress method is less than 20% compared to the results obtained by FEA.     

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.     

Experimental study of low-cycle fatigue of pipe elbows with local wall thinning and life estimation using finite element analysis

Low-cycle fatigue tests were conducted using elbow specimens with local wall thinning. Local wall thinning was machined on the inside of the elbow in order to simulate metal loss from erosion corrosion. The local wall thinning was located in three different areas known as the extrados, crown and intrados. The elbow specimens were subjected to cyclic in-plane bending under displacement control without internal pressure. In addition, three-dimensional elastic-plastic analyses were also carried out using the finite element method. As a result, the crack penetration area and the crack growth direction were successfully predicted by the analyses. The fatigue lives estimated by the analyses were close to those obtained by the experiments.     

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.     

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.     

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.     

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.     

Cross-sectional flattening of pipes subjected to bending

Pipes subjected to bending may fail by cross-sectional flattening due to a plastic hinge mechanism occurring at the mid-section. In this paper the relationship between the applied bending moment and the stresses and strains at the neutral axis is calculated, using a power law stress-strain relationship. As a tentative failure criterion, a critical local bending radius of the pipe wall was selected. It can be expected that failure by the flattening mechanism occurs in the medium range of wall thickness to pipe radius ratio. For smaller ratios buckling on the compressive side—and, for larger ratios, fracture on the tensile side—of the pipe is shown to be the failure mechanism.     

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.     

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.     

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.     

Failure pressure of straight pipe with wall thinning under internal pressure

The failure pressure of pipe with wall thinning was investigated by using three-dimensional elastic–plastic finite element analyses (FEA). With careful modeling of the pipe and flaw geometry in addition to a proper stress–strain relation of the material, FEA could estimate the precise burst pressure obtained by the tests. FEA was conducted by assuming three kinds of materials: line pipe steel, carbon steel, and stainless steel. The failure pressure obtained using line pipe steel was the lowest under the same flaw size condition, when the failure pressure was normalized by the value of unflawed pipe defined using the flow stress. On the other hand, when the failure pressure was normalized by the results of FEA obtained for unflawed pipe under various flaw and pipe configurations, the failure pressures of carbon steel and line pipe steel were almost the same and lower than that of stainless steel. This suggests that the existing assessment criteria developed for line pipe steel can be applied to make a conservative assessment of carbon steel and stainless steel.     

Stress concentration factors for intersecting cylindrical shells under mechanical loading

Based on an efficient finite element algorithm for the calculation of the stress field at the intersection region of rotationally symmetric component shells, the case of circular cylindrical shells intersecting at arbitrary inclination angles are considered under conditions of general mechanical loading upon the branch pipe.

As examples, stress concentration factors are calculated and presented for different diameter and thickness ratios of two cylindrical shells intersecting at 30° and 90° angles under an axial force, and in- and out-of-plane bending moment loadings acting on the intersecting cylinder.