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.

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.

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.

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.

Determination of C2 Stress Index of Back-to-Back Welded Piping Bends Using Finite Element Method

In current ASME Boiler and Pressure Vessel Code, the C2 stress index for back-to-back elbows welded together is taken as the product of the C2 index of the elbow and the C2 index of the girth butt weld. In recent years, many finite element analyses studies have been conducted on the elbow C2 index itself which have found that the code C2 value is conservative. The girth butt weld C2 given in the code resulted from analytical studies on transition joint between two straight pipes. While the code considers that the secondary stress due to the weld reinforcement including the effect from the mismatch to be small and practically negligible for a thick pipe, it recommends a formula to calculate C2 for weld in a thin pipe of thickness less than 0.237”. The purpose of this paper is to present an approach that C2 caused by weld mismatch can be determined by finite element analysis. Back-to-back bends are modeled with 2 typical configurations: in-plane and out-of-plane. Parametric studies of linear elastic secondary stresses are carried out to determine the “worst possible” two bend central line mismatch. The stress indices at elbows and weld location are established. It is found that the C2 index based on the code formula is overly conservative for back-to-back welded pipe bends and the multiplication by the C2 index of the weld is not needed.

Fatigue Growth Behaviour for Surface Crack in Welded Joints Under Combined Tension and Bending Stresses

The fatigue growth behaviour for surface crack in welded joints under combined tension and bending stresses is studied by fatigue crack growth tests of 16MnR steel in bow specimens. In this present paper the Newman-Raju empirical equation was used for the stress intensity factor of a surface crack. The experimental results show that the Paris’ relationship between crack growth rate and stress intensity factor range under tension and bending fatigue stresses is still valid, and the relationship between the Paris’ coefficients Ca and Cc can be represented as Cc = (0.89)mCa.

Failure of Locally Buckled Pipelines

Mechanical damage in steel pipelines in the form of local buckles due to excessive bending deformation, may severely threaten their structural integrity. The present paper describes experimental and numerical research conducted to assess the structural condition of buckled pipes, subjected to both bending and internal pressure. Fatigue failure under repeated loading is mainly investigated, whereas pipe burst due to internal pressure is also examined. Three full-scale buckled pipe specimens are tested under pressure and bending loads to determine their structural capacity. In addition, using nonlinear finite element tools, an extensive parametric study is conducted, to determine the critical locations at the buckled area, at which maximum strain variation occurs, as well as to investigate the influence of several geometrical and mechanical parameters. Using the maximum strain range from the finite element computations, and a simple S-N approach, reasonable predictions are obtained for the number of cycles to failure observed in the tests. The results of the present study demonstrate that under repeated loading, fatigue failure occurs in the buckled area at the location of maximum strain range. It is also found that the burst pressure may not be affected by the presence of buckles.

Performance of High-Pressure Fibre-Reinforced Polymer Composite Pipe Structures

Advanced fiber-reinforced polymer composite pipes offer high strength and superior corrosion resistance properties compared to conventional metallic pipeline materials. However, damage mechanisms in composite pipes are not fully understood and failure prediction methodologies are currently inadequate. Research is required to resolve these deficiencies which are an encumbrance to the certification of high-pressure composite pipe and its introduction into service. This is underlined by the findings reviewed in the present paper which derive from a comprehensive study on the performance and damage mechanisms in composite pipes and joint modules.