Shakedown of a Thick Cylinder With a Radial Crosshole

The shakedown behaviour of a thin cylinder subject to constant pressure and cyclic thermal loading is described by the well known Bree diagram. In this paper, the shakedown and ratchetting behaviour of a thin cylinder, a thick cylinder and a thick cylinder with a radial crosshole is investigated by inelastic finite element analysis. Load interaction diagrams identifying regions of elastic shakedown, plastic shakedown and ratchetting are presented. The interaction diagrams for the plain cylinders are shown to be similar to the Bree Diagram. Incorporating the radial crossbore in the thick cylinder significantly reduces the plastic shakedown boundary on the interaction diagram but does not significantly affect the ratchet boundary. The radial crosshole can therefore be regarded as a local structural discontinuity and neglected when determining the maximum shakedown or (primary plus secondary stress) load in Design by Analysis.

The Effect of Temperature Dependent Yield Strength on Upper Bounds for Creep Ratcheting

The Bree model and the elastic core concept have been used as the foundation for the simplified inelastic design analysis methods in the ASME Code for the design of components at elevated temperature for nearly three decades. The methodology provides upper bounds for creep strain accumulation and a physical basis for ascertaining if a structure under primary and secondary loading will behave elastically, plastically, shakedown, or ratchet. Comparisons of the method with inelastic analysis results have demonstrated its conservatism in stainless steel at temperatures representative of those in LMBR applications. The upper bounds on creep accumulation are revisited for very high temperatures representative of VHTR applications, where the yield strength of the material is strongly dependent upon temperature. The effect of the variation in yield strength on the evolution of the core stress is illustrated, and is shown to extend the shakedown regions, and affects the location of the boundaries between shakedown, ratcheting, and plasticity.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

Prediction of the Flow and Force Characteristics of Safety Relief Valves

The design of safety relief valves depends on knowledge of the expected force-lift and flow-lift characteristics at the desired operating conditions of the valve. During valve opening the flow conditions change from seal-leakage type flows to combinations of sub-sonic and supersonic flows It is these highly compressible flow conditions that control the force and flow lift characteristics. This paper reports the use of computational fluid dynamics techniques to investigate the valve characteristics for a conventional spring operated 1/4” safety relief valve designed for gases operating between 10 and 30 bar. The force and flow magnitudes are highly dependent on the lift and geometry of the valve and these characteristics are explained with the aid of the detailed information available from the CFD analysis. Experimental determination of the force and flow lift conditions has also been carried out and a comparison indicates good correspondence between the predictions and the experiment. However, attention requires to be paid to specific aspects of the geometry modeling including corner radii and edge chamfers to ensure satisfactory prediction.

Plastic Limit Pressure of Pressurized Cylinders With Hillside Nozzle

Cylinder-nozzle intersections are widely used in pressure vessel and piping industries. In order to get better mixing and energy exchange of the reactants, pipe-nozzle intersection with hillside nozzle is applied more and more widely. The purpose of this work is to investigate the plastic limit load of cylinders with hillside nozzle subjected to internal pressure. Three full-scale test models with different angles of the hillside nozzle were designed and fabricated specially for the test using strain gagues. 3-D finite element numerical simulations on the experimental models were performed. Based on both results, a group of basic data on plastic limit pressure defined by double elastic-slope method for cylinders with hillside nozzle is approximately obtained according to load-strain responses, and the plastic limit pressures determined by test and finite element analysis are in good agreement. The results indicate that the limit pressure increases with the increment of the angle of the hillside nozzle, and compared with radial nozzles in cylinders, the hillside nozzles have higher limit pressure, which can be served as the basis for developing a design guideline for pressurized cylinders with various angles of hillside nozzle.

Analysis of Pressure Vessel Sloshing

ASME BPVC Section VIII Division 1 Paragraph UG-22 (f) requires consideration of the loadings from seismic conditions. For a vessel containing a fluid, the loading due to sloshing must be considered. ASCE Standard 7-02 (Section 9.14.7.3) states that a damping value of 0.5% can be used to account for the fluid sloshing. This can lead to an overly conservative design by over-estimating the loads on the tank structure. A time-history analysis was performed on a horizontally mounted pressure vessel experiencing 3-axis time history loads in order to determine if this method is more accurate in determining the loads. The analysis employed a 3-dimensional computational fluid dynamics (CFD) model, using transient time-history techniques. The reactions at the mounting locations were compared to the reactions computed using closed form solutions, demonstrating good correlation. The results show that CFD is an excellent tool for investigating seismic sloshing loads in vessels.

Unified Basis-Free Relation Between Two Stress Tensors Conjugate to Arbitrary Hill’s Strain Measures

The concept of energy conjugacy for stress and strain measures states that a stress tensor T is conjugate to a strain measure E if T: E˙ provides the rate of change of the internal energy per unit reference volume of the body in an adiabatic process. The applications of the conjugate stress and strain measures are in the development of the basic relations in nonlinear analysis of solids. In this paper using eigenprojection method, unified explicit basis-free relation between two arbitrary stress tensors T(f) and T(g), respectively conjugate to two measures of Hill’s strains is determined. The result is valid for arbitrary dimension of the Euclidean inner product space and for all cases of distinct and repeated eigenvalues of the right stretch tensor U.

Micro Mechanical Model of Filament Wound Composite Pipe With Damage Analysis

Filament winding (FW) is one of the most common techniques for manufacturing composite pipes. The material properties and failure mechanism of composite pipes depend largely on winding pattern. In this study a micro mechanical approach for filament wound composites (FWCs) is pursued. A diamond-shaped repeated unit cell (RUC) is first constructed which characterizes the micro architecture of FWC pipe, such as winding angel, shift between successive circuits and the area of local undulation region. The micro mechanical model is embedded into commercial FEM code of ABAQUS as user-defined subroutine thus the link between the analyses in macro engineering structural scale and in micro material structural scale is established. By averaging micro stiffness constants over the cell macro ones needed for engineering structural analysis can be obtained. On the other hand, the macro structural analysis provides average stresses/strains of the cell locating at any concerned region of the macro structure for local stress and damage analysis. Effects of tow undulation caused by tow crossover on micro stresses are taken into accounted. The model is applied to glass/epoxy wound pipes with various winding angles and winding shifts. Mechanical properties are predicted and damage evolutions are simulated. The effects of delamination damage, usually introduced by lateral low velocity impact, on stiffness and ultimate strength of FWC pipe are also investigated.

Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations

In this paper the shakedown limit load is determined for a long radius 90-degree pipe bend using two different techniques. The first technique is a simplified technique which utilizes small displacement formulation and elastic-perfectly-plastic material model. The second technique is an iterative based technique which uses the same elastic-perfectly-plastic material model, but incorporates large displacement effects accounting for geometric non-linearity. Both techniques use the finite element method for analysis. The pipe bend is subjected to constant internal pressure magnitudes and cyclic bending moments. The cyclic bending loading includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending. The simplified technique determines the shakedown limit load (moment) without the need to perform full cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit moment is determined by performing two analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit moment is determined through the calculation of the residual stresses developed in the pipe bend. The iterative large displacement technique determines the shakedown limit moment in an iterative manner by performing a series of full elastic-plastic cyclic loading simulations. The shakedown limit moment output by the simplified technique (small displacement) is used by the iterative large displacement technique as an initial iterative value. The iterations proceed until an applied moment guarantees a structure developed residual stress, at load removal, equals or slightly less than the material yield strength. The shakedown limit moments output by both techniques are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes for the three loading patterns stated earlier. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. Comparison between the shakedown diagrams generated by the two techniques, for the three loading patterns, is presented.

Fracture Failure Risk Analysis of Pressure Pipeline Containing Defects on Pile Foundation Settlement

Pile foundation settlement might cause a disastrous consequence to an in-service pressure pipeline. Flaws, which are unavoidable in the pipeline, lead to reduction of load-supporting capability and service life of the pipeline. So fracture failure risk analysis of in-service pressure pipeline is important in engineering. Failure probability of pipeline due to pile foundation settlement is computed by using the well-known safety assessment procedure R6. Three-moment equation is adopted to compute bending moment in the condition of n piles, where n is the number of piles. A numerical example was presented to illustrate the application of fracture failure risk analysis to determine the failure probability of the pressure pipeline, considering the uncertainties in various internal operating loadings and external forces, flaw sizes, material fracture toughness and flow stress. Furthermore, the failure probabilities of each defect and the whole pipeline were obtained.