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 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.     

A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending

This paper presents a comparison of the plastic collapse loads from experimental in-plane bending tests on three 90° single un-reinforced mitred pipe bends, with the results from various 3D solid finite element models. The bending load applied reduced the bend angle and in turn, the resulting cross-sectional ovalisation led to a recognised weakening mechanism. In addition, at maximum load there was a reversal in stiffness, characteristic of buckling. This reversal in stiffness was accompanied by significant ovalisation and plasticity at the mitre intersection. Both the weakening mechanism and the post-buckling behaviour are only observable by testing or by including large displacement effects in the plastic finite element solution. A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour.     

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.     

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 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.     

Characterizing the crack initiation load in circumferentially through-wall cracked elbows under bending load

Ductile fracture assessments of circumferentially through-wall cracked elbows, based on the elastic–plastic J-integral concept, are discussed with particular interest in its ability and accuracy to predict experimental results corresponding to the initiation of stable crack growth. 3D non-linear finite element analysis is backed up with experimental results to determine the crack initiation load. Non-linear finite element analyses were performed considering both material and geometrical non-linearity using the advanced fracture analysis code WARP3D. Numerical analyses have been carried out to understand the role of crack tip constraint in standard specimens and the elbow component. An attempt has been made to obtain a unique multiaxiality quotient (q) for evaluation of the level of constraint. The work provides benchmark data to assist in the engineering treatment of cracked piping elbows.     

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.     

Use of local and global limit load solutions for plates with surface cracks under tension

Some available experimental results for the ductile failure of plates with surface cracks under tension are reviewed. The response of crack driving force, J, and the ligament strain near the local and global limit loads are investigated by performing elastic-perfectly plastic finite element (FE) analysis of a plate with a semi-elliptical crack under tension. The results show that a ligament may survive until the global collapse load is reached when the average ligament strain at the global collapse load, which depends on the uniaxial strain corresponding to the flow stress of the material and the crack geometry, is less than the true fracture strain of the material obtained from uniaxial tension tests. The FE analysis shows that ligament yielding corresponding to the local limit load has little effect on J and the average ligament strain, whereas approach to global collapse corresponds to a sharp increase in both J and the average ligament strain. The prediction of the FE value of J using the reference stress method shows that the global limit load is more relevant to J-estimation than the local one.     

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.     

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.     

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.     

Limit and shakedown analysis of nozzle/cylinder intersections under internal pressure and in-plane moment loading

A simple technique called the elastic compensation method developed previously by Mackenzie & Boyle is used in combination with full three-dimensional finite-element analysis to obtain limit and shakedown interaction diagrams for nozzle/cylinder intersections subject to combined internal pressure and in-plane nozzle moment loading. The results are compared with solutions from the literature and also with detailed elasto-plastic thin shell finite-element analysis. It is found that the simple elastic compensation procedure can provide good estimates of plastic failure mechanisms for complex three-dimensional structures. A detailed discussion of various issues which arose relates to finite-element modelling and the measures taken to improve the results are also documented.     

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.     

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.     

Linear and non-linear analyses for semi-elliptical surface cracks in pipes under bending

In this paper, the J integral was calculated for semi-elliptical surface cracks in pipes under bending using three-dimensional finite element analysis. The computations were performed for elastic and elastic-plastic behaviours. For the elastic case, the numerical results allowed the extrapolation of shape functions for analytical determination of the J integral. The results are in a good agreement with those in the literature if the ratio between the radius and the thickness of the pipe (R/t) is from 1 to 10. The analysis was extended to values of the ratio R/t higher than 10. For the elastic-plastic, the numerical results are in good agreement with the analytical solution found in the literature for thick pipes (R/t ≥ 10). The effect of the ratio R/t becomes sensible when the ratio of the applied moment to the moment of reference (M/Mor) exceeds 0.9.     

Transient hydrogen diffusion analyses coupled with crack-tip plasticity under cyclic loading

The effect of hydrogen on the material strengths of metals is known as the hydrogen embrittlement, which affects the structural integrity of a hydrogen energy system. In the present paper, we developed a computer program for a transient hydrogen diffusion–elastoplastic coupling analysis by combining an in-house finite element program with a general purpose finite element computer program to analyze hydrogen diffusion. In this program, we use a hypothesis that the hydrogen absorbed in the metal affects the yield stress of the metal.     

Studies of poisson''s ratio variation for solid propellant grains under ignition pressure loading

For structural integrity evaluation of solid propellant grains, an accurate estimation of the stress and strain response is essential, because of the viscoelastic nature of the polymer material. The results of an investigation on solid propellant grains considering the effect of Poisson's ratio υ variation under ignition pressurization are presented. Traditionally the υ value of solid propellant grains is assumed to be a constant (e.g. 0.4999) to simplify the experimental task, but the real υ value is from 0.47 to 0.4999 depending on the chemical design of the solid propellant grains. In order to simulate the time–temperature-dependent behaviour of viscoelastic polymer materials for a range of Poisson's ratio values, the concepts of a time–temperature shift principle and reduced integration were used. In addition, eight different Poisson's ratio values from 0.47 to 0.4999 were assumed and compared using the finite element method. Results show that the Poisson's ratio variation effect is very important for structural integrity of solid propellant grains, and the stress and strain responses versus Poisson's ratio variation are nonlinear because the type of polymer material is changed from incompressible to compressible. Under ignition pressure loading, the stress and strain responses in the compressible case (υ≠0.5) are much higher than those of the incompressible case (υ0.5). Therefore unlike metallic structures, an exact value of Poisson's ratio for polymer materials is very important, and an improper assumption (υ0.5) may cause the structural integrity of a missile system subjected to pressure loading to be wrongly evaluated.     

Analysis of stresses in pipes indented by long external indentations and subsequent stress variations due to pressure fluctuations

The residual hoop stresses in pressurised pipes caused by long external indentations and the subsequent stress variations caused by internal pressure fluctuations are investigated for a range of residual indentation depths, support positions, pressure magnitudes and indenter radii, 7using the Finite Element (FE) method, including initial stress and geometrical non-linearity effects. Three materials are used in the investigation to assess the effects of material properties on the stress variations. A semi-empirical formulation is developed, based on an imperfect, indented pipe model and the results of the FE analyses, to predict the variations of the residual stresses in the pipes.