On the shakedown analysis of welded pipes

This paper presents the shakedown analysis of welded pipes subjected to a constant internal pressure and a varying thermal load. The Linear Matching Method (LMM) is applied to investigate the upper and lower bound shakedown limits of the pipes. Individual effects of i) geometry of weld metal, ii) ratio of inner radius to wall thickness and iii) all material properties of Weld Metal (WM), Heat Affected Zone (HAZ) and Parent Material (PM) on shakedown limits are investigated. The ranges of these variables are chosen to cover the majority of common pipe configurations. Corresponding individual influence functions on the shakedown limits are generated. These are then combined to allow the creation of a safety shakedown envelope, which can be used for the design of any welded pipes within the specified ranges. The effect of temperature-dependent yield stress (in PM, HAZ and WM) on these shakedown limits is also investigated.     

Shakedown analysis of thick-walled cylinders subjected to internal pressure with the unified strength criterion

Most previous studies on shakedown of thick-walled cylinders were based on the assumption that the compressive and tensile strengths of the materials were identical. In this paper the shakedown of an internally pressurized cylinder made of a material with a strength-difference and intermediate principal stress effects is dealt with by using a unified strength criterion which consists of a family of convex piecewise linear strength criteria. Through an elasto-plastic analysis the solutions for the loading stresses, residual stresses, elastic limit, plastic limit and shakedown limit of the cylinder are derived. It is shown that the present solutions include the classical plasticity solutions as special cases and have the ability to account for the strength-difference and intermediate principal stress effects. Finally, the influence of the two effects on the shakedown limit of the cylinder is investigated. The results show that the shakedown limit depends on the two effects and is underestimated if these effects are neglected as in the classical plasticity solution based on the Tresca criterion.     

Shakedown and limit analysis of 90° pipe bends under internal pressure,cyclic in-plane bending and cyclic thermal loading

The Linear Matching Method is used to create the shakedown limit and limit load interaction curves of 90° pipe bends for a range of bend factors. Two load cases are considered i) internal pressure and in-plane bending (which includes opening, closing and reversed bending) and ii) internal pressure and a cyclic through wall temperature difference giving rise to thermal stresses. The effects of the ratios of bend radius to pipe mean radius (R/r) and mean radius to wall thickness (r/t) on the limit load and shakedown behaviour are presented.     

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.     

Thermomechanical stability and inelastic energy dissipation as durability criteria for fuel cell gas diffusion media with pre-assembly effects

In this article, pre-assembly hot-press pressure and thermal expansion effects in gas-diffusion layers (GDLs) are addressed to explore the practicalities of the constitutive model reported in the companion article. A facile technique is proposed to include deformation history dependent residual strain effects. The model is implemented in the numerical environment and compared with widely followed conventional models such as isotropic and orthotropic material models. With the normal and accelerated thermal expansion effects no significant variation in stresses or strains is reported with the compressible GDL model in contrast to the conventional incompressible form of the GDL model. The present work identifies the critical differences with advanced and extended variants of the model along with conventional GDL material models in terms of planar stress/strain distribution and the membrane response. Finally, the model is simulated for micro-cyclic stress loads of varying amplitudes that imitate the real working conditions of fuel cell. The inelastic energy dissipation in GDLs is predicted using the proposed model, which is utilized further to distinguish the safe (elastic) and unsafe (inelastic shakedown) operating limits. The inelastic collapse of GDLs is shown to be a active function of high amplitude micro-cyclic load with high initial clamping load.     

The structural behaviour of a bolted,flanged connection subjected to a cyclic load

This paper presents the results of an elastic—plastic bi-dimensional finite element analysis for a bolted flange in a boiling water reactor vessel.The calculations were performed by the finite element program ADINA using the incremental-iteration technique. The aim was to follow the stress and the strain of a bolted flange subjected to a cyclic load, consisting of four steps: the bolt load; the pressure load with decreasing of bolt load; depressurisation with increasing bolt load; and, at the end, unbolting.The calculations were performed progressively varying the height of the flange so that the maximum stress intensity was $\text{3S}{}_{\mathrm{<mtext>m</mtext>}}$.The number of cycles was sufficient to verify the conditions of shakedown or ratcheting.Numerical analysis can clarify our knowledge in this field, where the ASME III Code NB-3228 rules are obtained from an analytical computation for simple structure, using over-simplified assumptions on material constitutive equations, such as perfect plasticity.     

Direct finite element route for design-by-analysis of pressure components

In the new European standard for unfired pressure vessels, EN 13445-3, there are two approaches for carrying out a Design-by-Analysis that cover both the stress categorization method (Annex C) and the direct route method (Annex B) for a check against global plastic deformation and against progressive plastic deformation. This paper presents the direct route in the language of limit and shakedown analysis. This approach leads to an optimization problem. Its solution with Finite Element Analysis is demonstrated for mechanical and thermal actions. One observation from the examples is that the so-called 3f (3Sm) criterion fails to be a reliable check against progressive plastic deformation. Precise conditions are given, which greatly restrict the applicability of the 3f criterion.     

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.     

Elastic stress and deformation analyses on an all-steel cylinder without defects and with axial cracks

Using the three-dimensional elastic finite element method, stress analyses and the deformation analyses on an all-steel cylinder without defects and with axial cracks were carried out. The severe effect of the defects on an all-steel cylinder was shown through comparisons of the stress analyses and the deformation analyses on the cylinder without defects and with an axial crack. The analyses show that there appear both the inhomogeneous deformation and the stress singularities around the defects. The influences of defect size, internal pressure and defect types (internal crack or external crack), on the stress distributions and on the deformation distributions were discussed. The crack mouth opening displacement and the stress intensity factor K_I for the cylinders containing the axial deep cracks, which was detected in a practical applied cylinder, were presented and discussed. The effects of the location of the cracks (whether external or internal) and the shape of the through-thickness crack front (whether elliptical or straight front) on the crack driving forces are quantified. All the results of the stress analysis, the deformation analyses and the fracture analyses are supported by each other very well.     

A simple procedure to evaluate the stress intensity factor in internally pressurized cylinders

The evaluation of stress intensity factors in internally pressurized cylinders, with both surface and sub-surface flaws, is examined. The method of analysis is based on the equivalent linear representation of the circumferential stress distribution in accordance with ASME rules, the non-linear hoop stress distribution then being conservatively approximated by the membrane and bending stresses. The stress intensity factor for an elliptical crack embedded in an elastic solid and subjected to internal pressure is considered for two conditions of load (tension and bending) and the effects are added.The results are presented in non-dimensional form to evaluate the effect on stress intensity factor of the various parameters (outside and inside radius, crack position, cylinder thickness, form of ellipse).     

Neural network applied to prediction of the failure stress for a pressurized cylinder containing defects

An application of the neural network to predict the failure stress of a cylinder with penetrating flaws under internal pressure is studied in this article. The results from the new method are compared with the experimental results. In addition, the neural network method is used to analyze the sensitivity of parameters of a pressurized cylinder with defects. Satisfactory results are obtained. It is shown that the neural network could be a potential tool in engineering practice.     

Shakedown and limit analyses for 3-D structures using the linear matching method

A recently developed method for 3-D shakedown and limit analyses is evaluated in the present paper. The shakedown and limit loads of a holed plate subjected to biaxial loading are calculated by implementing the upper bound linear matching method into the commercial FE code ABAQUS. A defective pipeline under the combined action of internal pressure and axial tension is also analysed for both shakedown and limit capacities and the results compared with a standard programming method. All the numerical examples confirm the applicability of this procedure to complex 3-D structures.     

Linear matching method for creep rupture assessment

The recently developed linear matching method (LMM), which is easily implemented within commercial FE codes, has been successfully used to evaluate elastic and plastic shakedown loads. In this paper, the method is extended to the prediction of the creep rupture life of a structure, based upon a bounding method currently used in the life assessment method R5. The method corresponds to the requirement that, for the operating load history, the structure should shakedown where the yield stress is given by the lesser of the plastic yield stress and a high temperature rupture stress corresponding to a rupture time. A holed plate subjected to cyclic thermal load and constant mechanical load is assessed in detail as a typical example to confirm the applicability of the above procedures. The examples show that the method remains numerically stable, even when the method is inverted.     

多工况下内燃机示功图的试验测试与分析

进行多工况下内燃机示功图的试验测试研究与分析可以对内燃机工作性能进行全面考察。阐述了多工况下示功图测试的基本方法,并结合某柴油机,通过试验对不同负荷、转速条件下的示功图测量结果进行了详细的对比分析。研究结果表明,转速条件一定时,在膨胀做功阶段,高负荷时的缸内压力明显要高于低负荷时的缸内压力,而在其它阶段,不同柴油机负荷条件下缸内压力大小差异不明显。在同种大小负荷程度下,随着转速的增加,缸内最大爆发压力的变化不是很明显。但在同一转速下,缸内最大爆发压力随着柴油机负荷的升高明显增加。     

Computing the SCF for a hollow cylinder with hoop groove under torsion by means of a spherical section assumption

In this paper, a new method for calculating the stress concentration factor (SCF) and the elastoplastic limit load of a hollow cylinder with hoop groove under torsion is proposed by means of spherical section assumption. The relations of SCF at notch root with the notch depth t, the radius of the notch root and the internal radius a₁ of the cylinder are discussed. The elastoplastic limit torsions are derived for a hollow cylinder for two cases. The results obtained show the effectiveness of this method.     

The linear matching method applied to the high temperature life integrity of structures. Part 1. Assessments involving constant residual stress fields

Design and life assessment procedures for high temperatures are based on ‘expert knowledge’ in structural mechanics and materials science, combined with simplified methods of structural analysis. Of these, R5 is one of the most widely used life assessment methods internationally with procedures based on reference stress techniques and shakedown calculations using linear elastic solutions. These have been augmented by full finite element analysis and, recently, the development of a new programming method, the linear matching method (LMM), that allows a range of direct solutions that include shakedown methods and simplified analysis in excess of shakedown. In this paper, LMM procedures are compared with calculations typical of those employed in R5 for cyclic loading problems when the assumption of a constant residual stress field is appropriate including shakedown and limit analyses, creep rupture analysis and the evaluation of accumulated creep deformation. A typical example of a 3D holed plate subjected to a cyclic thermal load and a constant mechanical load is assessed in detail. These comparisons demonstrate the significant advantages of linear matching methods for a typical case. For a range of cyclic problems when the residual stress field varies during the cycle, which include the evaluation of plastic strain amplitude, ratchet limit and accumulated creep strains during a high temperature dwell periods, the corresponding LMM and R5 procedures are discussed in an accompanying paper.     

The flat end to cylindrical shell connection—limit load and creep design

The influence of the shear force, acting at the cylinder–plate intersection, on the limit load pressure is shown, and graphs for the determination of the limit load pressure as well as the required plate thickness for a limit load design are given. The (ideal) plastic nonlinear viscoelastic analogue in generalized stresses for the determination of (highly nonlinear) creep results from given limit load results is described, and its usefulness and (technically satisfying) accuracy shown by means of two examples.     

Analysis of Al A359/SiCp Functionally Graded Cylinder Subjected to Internal Pressure and Temperature Gradient with Elastic-Plastic Deformation

In this article, an analytical elastic-plastic solution for thick-walled cylinders made of Functionally Graded Materials (FGMs) subjected to internal pressure and thermal loading is presented. Based on the experimental results, a mathematical model to predict the yielding through the thickness of FG AlA359/SiCp cylinder is developed. It is shown that under the temperature gradient loading, there is a point in the cylinder where the circumferential stress changes from compressive to tensile. The position of this point depends on the geometry and material properties of the FG cylinder and is independent of the temperature gradient.     

Cyclic loading of thick vessels based on the Prager and Armstrong–Frederick kinematic hardening models

The aim of this paper is to relate the type of stress category in cyclic loading to ratcheting or shakedown behaviour of the structure. The kinematic hardening theory of plasticity based on the Prager and Armstrong–Frederick models is used to evaluate the cyclic loading behaviour of thick spherical and cylindrical vessels under load and deformation controlled stresses. It is concluded that kinematic hardening based on the Prager model under load and deformation controlled conditions, excluding creep, results in shakedown or reversed plasticity for spherical and cylindrical vessels with the isotropy assumption of the tension/compression curve. Under an anisotropy assumption of the tension/compression curve, this model predicts ratcheting. On the other hand, the Armstrong–Frederick model predicts ratcheting under load controlled cyclic loading and reversed plasticity for deformation controlled stress. The interesting conclusion is that the Armstrong–Frederick model is well capable to predict the experimental data under the assumed type of stresses, wherever experimental data are available.     

Fracture analysis on the metal-lined hoop-wrapped cylinders with internal axial cracks

The metal-lined (steel-lined and aluminum-lined) hoop-wrapped cylinders with internal axial semi-elliptical cracks in the cylindrical portion center of the metal-liner are modeled by a three-dimensional finite element method. Crack front regions are modeled using singular elements, whereas the rest of the cylinder is modeled using twenty-node hexahedron elements. Not only the cylindrical body, but also the neck and transition areas of the cylinder, are considered in the modeling. The stress intensity factor K_I and crack mouth opening displacement (C ) for the metal-lined hoop-wrapped cylinders are calculated. The influence of the hoop-wrapped materials, the internal pressure and the crack sizes on the fracture behavior of these cylinders are discussed and the different fracture behaviors of the steel-lined hoop-wrapped cylinder and the aluminum-lined hoop-wrapped cylinder are discussed.