Stress intensity factors for thick-walled cylinders

Stress intensity factors for a single radial crack in a thick-walled cylinder, calculated using a finite element technique, are compared with those found using a ‘modified mapping—collocation’ technique. Values for two diametrically-opposed cracks in cylinders of several diameter ratios are also presented since they appear to represent the worst case of multiple cracking which can occur in vessels of large diameter ratio.     

Three-dimensional analyses of surface cracks in pressurised thick-walled cylinders

Stress intensity factors for semi-elliptical surface cracks in internally pressurised thick-walled cylinders of radius ratio 3 are presented for a wide range of crack sizes. These solutions were obtained using the boundary integral equation method for three-dimensional stress analysis. Only one crack shape is considered—a semi-ellipse with the length of its semi-minor axis equal to 0·6 times the length of its semi-major axis —but the ratio of crack depth to wall thickness ranged from 0·2 to 0·8. Hoop strain distributions at the outer circumference of the cylinder are also presented for the different crack sizes analysed; the results are useful for experimentally monitoring crack growth.     

Numerical analysis of fatigue growth of external surface cracks in pressurised cylinders

Fatigue crack growth is modelled by a novel numerical technique for various external surface cracks with initially either semi-elliptical or irregular crack fronts. The technique employs a three-dimensional finite element analysis to estimate the stress intensity factors at a set of points of the crack front, then calculates local crack advances by integrating a type of Paris fatigue crack growth law at this set of points, and finally establishes a new crack front and its corresponding finite element model. The multiple degrees-of-freedom model enables the crack shape to be predicted directly during crack growth without having to make the common semi-elliptical assumption, and therefore provides more accurate predictions. Fatigue analysis results are presented and discussed, including fatigue shape developments and deviations from the semi-elliptical shape, together with aspect ratio changes, stress intensity factor variations during crack growth and fatigue life predictions. Some of these results are also compared with those obtained by two simplified predictive methods based on one and two degrees-of-freedom models together with a stress linearisation.     

Evaluation of stress intensity factors for internally pressurised cylinders with surface flaws

The aim of this paper is to examine the different methods currently available for evaluating stress intensity factors in cylinders subjected to internal pressure and containing surface cracks. The techniques of analysis involve the use of both two- and three-dimensional models. For a given situation, the most pertinent choice of analysis is not yet clearly established because of the difficulty and uncertainty in interpreting the currently available experimental data. Consequently, it is of interest to review and compare the different analytical techniques now available, particularly with reference to their underlying assumptions.     

Stress intensity factors for circumferential cracks in pressure vessel door closures

Bandlock pressure vessel door closures and many other commonly used engineering geometries can be simplified to that of a tube with an axisymmetric internal projection. When the projection is axially loaded, the maximum stress is seen at the start of the fillet between the tube and the projection, and this is the site of potential fatigue crack growth. Stress intensity factors for circumferential cracks in tubes with axially loaded axisymmetric internal projections are presented for a wide range of geometries, governed by five parameters: tube diameter, projection depth and length, fillet radius and crack length. The dominant mode is shown to be mode I. Results are presented to allow the variation of Y_I, with fillet radius, tube diameter, projection depth, projection length and crack length, to be determined. Y_I is shown to vary widely, between 0.59 and 12.65, and is seen to be strongly dependent on projection depth. Y_I is dependent on fillet radius for short crack lengths, but for crack lengths approaching half the tube wall thickness, it becomes independent of fillet radius. Y_I results for the simplified loaded projection are compared with results from a finite element analysis of a typical pressure vessel door closure, and the results are seen to correlate to within 3.2%.     

A comparison of methods of calculating stress intensity factors for cracks in pipes and thin walled cylinders

This paper presents results of a study undertaken to compare stress intensity factor solutions for various crack geometries in pipes and thin walled cylinders against the equivalent flat plate K solutions. The exercise was restricted to cylinders and pipes with wall thickness to radius ratios (t/R) of 0·1.

The results of the exercise indicate that structural integrity assessments of pipes and thin walled cylinders which contain flaws should ideally incorporate representative stress intensity factor solutions. Nevertheless there are a number of crack geometries for which flat plate K solutions can provide reasonable estimates of the stress intensity factor.     

Stress intensity factors for underclad and through clad defects in a reactor pressure vessel submitted to a pressurised thermal shock

CEA has launched important work on the development of a Stress Intensity Factors compendium for cracks in a Reactor Pressure Vessel (RPV) taking into account the cladding.The work is performed by Finite Element analysis with a parametric mesh for two types of defects (under clad defect and through clad defect) and a wide range of geometrical and material parameters.In addition, an analytical stress solution for Pressurised Thermal Shock (PTS) on the RPV is proposed to allow a complete analytical estimation of the stress intensity factor K_I for the PTS problem.The results are validated by comparison with a complete 3D finite element calculation performed on a complex and realistic case study.     

Stress intensity factors for an axially oriented internal crack embedded in a buried pipe

In this paper, the finite element method has been used to study the effect of soil weight on the stress intensity factors of an axially oriented semi-elliptical crack located on the inner surface of a buried pipe. The Burns and Richard model has been utilized to take into account the interaction between the soil and the pipe. The finite element results revealed that the cracks in a buried pipe are subjected to mixed mode loading. The mode I and mode II stress intensity factors depend on the circumferential location of internal crack. K_I is always significantly larger than K_II and is maximum when the internal crack is along the vertical direction. A comparison between the results of two-dimensional and three-dimensional cracks also signified that the two-dimensional analysis always represents more conservative results. Depending on the crack aspect ratio (a/c), the discrepancy between the results of two and three-dimensional analyses can be significant.     

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.     

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.     

Methods of calculating stress intensity factors for nozzle corner cracks

The various methods of determining stress intensity factors for transverse cracks in pressure vessel nozzles are reviewed. An estimate of the accuracy of experimental and finite element analyses is made by comparing the results of different studies. Methods are proposed for calculating approximate stress intensity factors for part-circular and straight fronted cracks using the weight function method. Approximate procedures are described for taking into account the two-dimensional nature of the nozzle corner stress distribution, and the curvature of the inner wall local to the nozzle corner. Where possible, stress intensity factors derived using these procedures are compared with published results. In general, agreement to within 20 per cent is obtained and, in most cases, the agreement is significantly better than this.     

Creep fracture mechanics parameters for internal axial surface cracks in pressurized cylinders and creep crack growth analysis

In the present study, a low alloy Cr–Mo steel cylinder subjected to internal pressure at high temperature with a semi-elliptical crack located at the inner surface is considered. The creep crack driving force parameter C1-integrals calculated by finite element (FE) method, are compared with results from previous studies, which indicates that empirical equations may be inaccurate under some conditions. A total of 96 cases for wide practical ranges of geometry and material parameters are performed to obtain systematic FE results of C1-integral, which are tabulated and formulated in this paper. It is observed that the maximum C1-integral may occur neither at the deepest point nor at the surface point when the aspect ratio is large enough and the value of C1-integral is significantly sensitive to the crack depth ratio. Furthermore, based on the proposed equations for estimating C1-integrals and a step-by-step analysis procedure, crack profile development, crack depth, crack length and remaining life prediction are obtained for surface cracks with various initial aspect ratios. It is found that when the crack depth ratio is increased, there is no obvious convergence of crack aspect ratio observed. The magnitude of half crack length increment is always minor compared with the crack depth increment. In addition, the remaining life is much more dependent on the surface crack depth than on the surface crack length.     

Calculation of stress intensity factors for semielliptical cracks in a thick-wall cylinder

Weight functions for the surface and the deepest point of an internal semielliptical crack in a thick-wall cylinder were derived from a general weight function and two reference stress intensity factors. For several linear and nonlinear crack face stress fields, the weight functions were validated against finite element data. Stress intensity factors were also calculated for the Lamé through the thickness stress distribution induced by internal pressure. The weight functions appear to be particularly suitable for fatigue and fracture analysis of surface semielliptical cracks in complex stress fields. All stress intensity factor expressions given in the paper are valid for cylinders with an inner radius to wall thickness ratio, R_i/t = 4.     

Stress intensity factors for a pipe-plate welded joint

A major component of any linear elastic fracture mechanics model for fatigue crack growth is the calculation of the crack tip stress intensity factor. This is particularly difficult for welded joints due to the complex geometry. While some data are available for cracks in welded T-plate joints, there is relatively little data available for larger cracks in more complex tubular joints. Such cracks are of significant interest since the most practical application of fracture mechanics models is the prediction of remaining life for cracks discovered in service.

A pipe-plate joint has been developed as a simplified model of tubular joint geometries for fatigue studies. Two such specimens have been tested in air, with detailed monitoring of crack growth behaviour using potential drop techniques. These data were used to obtain crack growth rate data from which estimates of stress intensity factors were made. Separately, finite element analyses for various discrete crack configurations were performed. The results of these analyses are presented and discussed, with particular emphasis on the accuracy of the results and the implications for fracture mechanics modelling.     

The fracture behavior of the aluminum lined hoop-wrapped cylinders with internal axial cracks

Aluminum lined hoop-wrapped cylinders with internal axial semi-elliptical cracks in the cylindrical portion center of the aluminum-liner are modeled by 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 the transition areas of the cylinder are considered in the modeling. The stress intensity factor K_I and the crack mouth opening displacement (CMOD) are calculated. The influence of the hoop-wrapped materials, the internal pressure and the crack sizes on the fracture behavior of the cylinder are discussed.     

An internal reformer for a pressurised SOFC system

A novel reformer design has been demonstrated that converts the methane required for a multi kilowatt SOFC stack. Results show the influence of temperature and the benefits of operating at elevated pressure on the reforming-catalyst fundamental reaction kinetics. Due to the high heat demand of the steam reforming reaction, efficient heat transfer between the SOFC stack and the reforming catalyst is essential. Parameters such as the volume/surface area ratio, choice of catalyst, and catalyst metal loading are key to the design, and these have been determined through a combination of computer modelling and experimental measurements. The thermal properties of the unit have been evaluated over a range of temperatures and fuel compositions that simulate system operating-conditions in the final product.     

Theoretical and finite-element modeling of autofrettage process in strain-hardening thick-walled cylinders

The optimum autofrettage pressure and the optimum radius of the elastic–plastic boundary of strain-hardening cylinders in plane strain and plane stress have been studied theoretically and by finite-element modeling. Equivalent von-Mises stress is used as yield criterion. Comparison of the results of the two methods shows good agreement. Although there is no explicit expression for the optimum autofrettage pressure in plane stress, the equation for plane strain can be used with good accuracy. It has also been observed that the optimum autofrettage pressure is not a constant value but depends on working pressure.     

Stress intensity factors for a surface crack in a tubular T-joint

This paper describes a systematic modelling of a general cracked tubular Y-joint commonly found in offshore structures. The Y-joint under consideration may contain either a through-thickness or surface crack which can be of any length and located at any position along the brace–chord intersection. This is particularly significant, as it has always been found in practice that the initiation site of a surface crack does not always start from the saddle or crown position when tubular joints are subjected to a complex loading condition. The geometrical model developed in the work described in this paper includes the weld detail which is compatible with the American Welding Society (AWS) standard [1]. Based on this geometry, well-graded finite element (FE) meshes were generated for a T-joint, which is a specific type of Y-Joint, to obtain the stress intensity factors (SIFs) for a surface semi-elliptical crack along the crack tip using quarter-point elements. The numerical analysis indicated that the FE models generated are appropriate to the geometry of the joints since converging values of SIF were obtained as the meshes used were refined. The accuracy of the Mode I, Mode II and Mode III SIFs demonstrates that the proposed model is reliable.