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.     

A review of literature for the structural assessment of mitred bends

This paper presents a state-of-the-art review of literature available for the structural assessment of all types of mitred pipe bends. Compared with smooth bends, the volume of literature available for mitres is less extensive and its scope is not as wide. Historically, this reflects a reduced application level, as well as a less demanding range of applications, such as non-high temperature use. There is also the issue that an analysis of a mitred bend is complicated by discontinuity stresses, as well as those due to cross-section ovalisation. This fact delayed the development of non-linear analysis of mitred bends. Nevertheless, there is now a substantial body of work on mitred bends. This review tabulates and characterises all publications to date in chronological order. The details of experimental specimens are highlighted, with a view to these perhaps providing useful verification data for any future finite element analysis for example. Issues of particular interest to pipework designers are discussed, including the effects of combinations of loading, out-of-circularity, tangent pipe length and flanges. Failure characteristics and loads are discussed where relevant. Topics for further research are also noted. For example, comprehensive design curves do not exist for the elastic and plastic behaviour of all mitre types, over a practical range of geometry and loading parameters. Similarly, there is still scope for further work on the effect of combined loading, end effects and out-of-circularity. Limit, collapse and burst loads are not yet available across the entire spectrum of bends and loading parameters either. Creep and optimisation represent virgin territory as far as mitred bends are concerned and given that unforeseen vibration is a common source of high-cycle fatigue failure in pipework, there must also be scope for vibration-induced fatigue studies.     

Limit and plastic collapse loads for un-reinforced mitred bends under pressure and bending

Approximate limit and plastic collapse load solutions for un-reinforced mitred bends under internal pressure and under bending are proposed in this paper, based on three-dimensional finite element analysis and approximate solutions for smooth bends. Solutions are given for single- and multi-mitred bends (mainly for single and double segmented bends) with the pipe mean radius-to-thickness ratio (r/t) ranging from r/t = 5 to r/t = 50, and the bend radius-to-mean radius ratio (R/r) from R/r = 2 to R/r = 4. Internal pressure, in-plane bending and out-of-plane bending loads are considered, but not their combination. It is found that the essential features of limit and plastic collapse loads for mitred bends are similar to those for smooth bends, and thus existing solutions for smooth elbows can be used to construct limit loads and plastic collapse for mitred bends.     

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.     

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

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

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.     

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.     

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.     

Limit loads of circumferentially flawed pipes and cylindrical vessels under internal pressure

Published limit load formulae for circumferential defects overestimate the burst pressure for penetrating defects in pipes by the factor two in the short crack limit, because they only consider axial stress. Therefore, a class of limit load solution is discussed which takes the triaxial state of stress into account. The solutions for pressure loaded crack faces are improved analytically. Primal–dual limit analysis with the finite element method is used to adjust all solutions to numerical results. Limit loads are obtained for circumferential cracks of all sizes in thick-walled cylinders.     

Analysis and experiments on the plastic limit pressure of elbows

This paper discusses the plastic limit pressure of elbows without defects and with local thinned area in the extrados. Finite element analysis (FEA) and experiments have been used. The results of FEA show that the limit load of elbows under internal pressure increases with increasing wall thickness and bend radius of the elbow. The results are consistent with the calculated results by the Goodall formula, the maximum error is 6.58%. By data fitting of FEA, an empirical formula for the limit load of elbows with local thinned area in the extrados has been proposed, which is validated by experiments.     

Improved integrity assessment equations of pipe bends

Pipe bend or elbow is one of the important components in any piping system. Accurate integrity assessment of these pipe bends is very important for reliable operation of all types of plants including nuclear plants. While considerable research has been done in the last few decades to develop accurate integrity assessment procedures of straight pipe with or without cracks, similar efforts were missing for pipe bend or elbow. Reactor Safety Division, Bhabha Atomic Research Centre in collaboration with MPA, University of Stuttgart had embarked upon a comprehensive component integrity test program (CITP) in around 1998 to develop improved integrity assessment methods of piping components in general and elbow in particular. As a part of this program, detailed analytical, numerical and experimental investigations for so many years have generated large number of new equations for improved integrity assessment of elbows. Mainly three aspects of the integrity assessment procedure are focused – development of improved plastic collapse moment equations, proposing new elastic–plastic J-integral and crack opening displacement (COD) estimation schemes to simplify leak-before-break (LBB) analysis and presenting new eta and gamma expressions to evaluate J–R curve from test data. All these newly proposed equations have been validated with the findings of the test data, generated as a part of the CITP. A reasonably good to excellent matching between predictions of the newly proposed equations and test results have been observed in all the cases. The present paper enumerates these research findings in a consolidated yet brief manner.     

A practical application of an evaluation model for the restraint effect of pressure-induced bending on a plastic crack opening

This paper presents an evaluation model for the restraint effect of pressure-induced bending (PIB) on the opening of a circumferential through-wall crack (TWC) and a result of its application to the calculation of crack-opening displacement (COD) of postulated cracks for a practical leak-before-break (LBB) analysis. Three-dimensional finite element analyses with different crack lengths, restraint conditions, pipe geometries, magnitudes of internal pressure, and material tensile properties were used to investigate the influence of each parameter on the PIB restraint for the plastic COD. From these investigations, we proposed an evaluation model based on elastic–perfectly plastic behavior. Comparison with finite element analysis results demonstrated that the proposed model reliably estimated the PIB restraint effect on the plastic crack opening of a circumferential TWC and properly reflected the effect of each parameter within the range over which the analytical expression was derived. The model was then used to calculate restrained CODs of postulated cracks for a practical LBB analysis. When plastic crack behavior was considered, the PIB restraint effect was considerable for some LBB analysis cases of the primary piping systems in a typical nuclear power plant. This effect was estimated to be negligible by existing linear elastic-based models.     

Ratchetting and ratchetting boundary study of pressurized straight low carbon steel pipe under reversed bending

With a quasi-three point bending apparatus, ratchetting and the ratchetting boundary were studied experimentally for a pressurized low carbon steel pipe under reversed bending. The ratchetting strain occurs mainly in the hoop direction. Multi-step bending revealed that the ratchetting rate increases with increasing loading level but reduces or even vanishes at a lower bending level imposed after a higher bending level. Ratchetting simulation was performed by elasto–plastic finite element analysis with ANSYS in which the Ohno–Wang model and some modified Ohno–Wang models were applied. By comparison with the experimental data, it is found that the Jiang–Sheitoglu model with a minor modification gives reasonable simulation. The ratchetting boundary was determined by the KTA/ASME, RCC-MR and C-TDF with the lightly modified Jiang–Sehitoglu model. By comparison with the experimental data range in this study, it is shown that the ratchetting boundary determined by the C-TDF method, with the lightly modified Jiang–Sehitoglu model, divides the shakedown region well.     

A comparative study of usefulness for pad reinforcement in cylindrical vessels under external load on nozzle

The main purpose of this paper is to perform a comparative study of strength behavior for cylindrical shell intersections with and without pad reinforcement under out-of-plane moment loading on nozzle. Three pairs of full-scale test vessels with different d/D ratios were designed and fabricated for testing and analysis. A three-dimensional nonlinear finite element numerical analysis was also performed. The maximum elastic stress for each vessel under per unit moment on nozzle is provided. The plastic limit moment on nozzle is obtained by load–displacement and load–strain curves for each test vessel. The results indicate that the effect of pad reinforcement on decreasing maximum elastic stress and increasing plastic limit load is obviously effective. The study results will serve as the available data for understanding the usefulness of pad reinforcements and as the basis for developing an advanced design method by limit analysis for pad-reinforced cylindrical vessels under external loads on nozzle.     

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.     

Stability and post-buckling response of sandwich pipes under hydrostatic external pressure

Sandwich pipe systems can be considered as potentially optimum design configurations for overcoming the shortfalls of single-walled pipes for deep-water applications. This potential design alternative has gained considerable attention in recent years. In this paper the stability of these systems is investigated. The possible equilibrium paths are evaluated and the effect of the various significant parameters on the characteristic behavior of the system is discussed. The Finite Element (FE) software package ABAQUS is used to construct more than 3000 FE models of the sandwich pipes with practical configurations. Four design configurations are considered for the sandwich pipes with respect to the adhesion among the interfaces. The post-buckling behavior of each of these configurations is determined, with emphasis on a wide practical range of parameters. The behavior of these configurations is examined and the efficiency of each system is discussed. Finally, a simplified and fairly accurate equation is developed and recommended for calculating the pressure capacity of sandwich pipes. The parameters of the proposed equation are also fully defined.