An estimation of maximum pressure for a thick-walled tube subjected to internal pressure

The plastic deformation of a thick-walled tube subjected to internal pressure is investigated by an incremental finite element method and the maximum bearing pressure is estimated. The results are compared with some approximate solutions proposed by MacGregor and others. A useful design formula is derived in order to estimate the maximum pressure and it is shown that better estimation can be made by this formula than by others proposed previously.     

Exact and numerical elastodynamic solutions for thick-walled functionally graded cylinders subjected to pressure shocks

In the present paper, analytical and numerical elastodynamic solutions are developed for long thick-walled functionally graded cylinders subjected to arbitrary dynamic and shock pressures. Both transient dynamic response and elastic wave propagation characteristics are studied in these non-homogeneous structures. Variations of the material properties across the thickness are described according to both polynomial and power law functions. A numerically consistent transfinite element formulation is presented for both functions whereas the exact solution is presented for the power law function. The FGM cylinder is not divided into isotropic sub-cylinders. An approach associated with dividing the dynamic radial displacement expression into quasi-static and dynamic parts and expansion of the transient wave functions in terms of a series of the eigenfunctions is employed to propose the exact solution. Results are obtained for various exponents of the functions of the material properties distributions, various radius ratios, and various dynamic and shock loads.     

On the use of elliptical side branches to thick-walled cylinders

The boundary integral equation (boundary element) method of numerical stress analysis is used to compute stress concentration factors at the intersections between side branches and thick-walled tubes or pressure vessels. Cases of both circular and elliptical side branch cross sections are considered, the effect of the latter being to significantly reduce the maximum stresses generated under internal pressure. For the typical geometries considered, reductions of more than 20% are obtained at optimum ellipse aspect ratios of about 0·8.     

The fatigue performance at room temperature and 550°C of relatively thin-walled cylinders subjected to repeated internal pressure

The work described was carried out to establish data for the design of mortar barrels, which can, under high rates of fire, reach an operating temperature of 550°C. This necessitated the construction of two repeated pressure machines, one to test closed and open-ended cylindrical specimens at room temperature at repeated pressures up to 200 MN/m² (13 tonf/in²), and the other for tests on closed-ended cylindrical specimens at 550°C. These machines are fully described.Test data on a 3% Cr-Mo-V steel (EN40C) are given for specimens with a diameter ratio of 1·1 and 1·2 under the conditions stated above.At room temperature the data appear to correlate reasonably well on the basis of the Mises-Hencky criterion. At 550°C the pressure in the short-termed fatigue region is reduced in proportion to yield stress, and in the longer life region lives approaching those at room temperature are obtained.     

A hybrid method of photoelastic and numerical analysis for nozzles subjected to internal pressure

In this paper, a method is presented that separates the stress components in the interior of spherical and cylindrical vessels with nozzles.

The natural variational principle of the Laplace equation is first set up. The finite element method is used to compute the values of the sum of principal stresses in the interior of a spherical nozzle. Thus, the stress components can be separated. Furthermore, by using equilibrium equations a difference equation of the sub-principal direction angle is set up to reduce the use of the isoclinics. Then the longitudinal symmetric plane section of a cylindrical nozzle is taken as that of the supposed flat plate nozzle. The half analysis method is used to compute the value of the sum of principal stresses in the interior of the supposed flat plate nozzle. Thus, the stress components in this section of the cylindrical nozzle can be separated. In conclusion, a number of computations have been made for several photoelastic models of flat plate nozzles and these results are compared with those of the finite element solutions.     

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.     

Residual stress analysis of autofrettaged thick-walled spherical pressure vessel

In this study, residual stress distributions in autofrettaged homogenous spherical pressure vessels subjected to different autofrettage pressures are evaluated. Results are obtained by developing an extension of variable material properties (VMP) method. The modification makes VMP method applicable for analyses of spherical vessels based on actual material behavior both in loading and unloading and considering variable Bauschinger effect. The residual stresses determined by employing finite element method are compared with VMP results and it is demonstrated that the using of simplified material models can cause significant error in estimation of hoop residual stress, especially near the inner surface of the vessel. By performing a parametric study, the optimum autofrettage pressure and corresponding autofrettage percent for creating desirable residual stress state are introduced and determined.     

In-plane instability tests of bellows subjected to internal pressure and deformation load

The in-plane instability of U-shaped bellows is analyzed. The in-plane instability critical pressure of bellows which are subjected to zero, tensile and compressive deformation are measured experimentally. The in-plane instability critical pressure of bellows under compressive deformation is apparently lower than that under zero deformation, and the in-plane instability critical pressure of bellows under tensile deformation is higher than that under zero deformation.     

Elastoplastic crack analysis of thick-walled cylinders using the symmetric-iterative scheme of coupled BE and FE discretizations

This paper uses the symmetric-iterative method of coupled FE and BE discretizations for the solution of elastoplastic thick-walled cylinders with symmetric cracks which are discretized partly by finite elements and partly by boundary elements. The calculations for J-integrals, by means of the present method and the finite element method, agree well.     

Creep test of type 304 stainless steel tube containing a notch subjected to internal pressure

This paper summarises the results of experimental creep tests of type 304 stainless steel tube subjected to internal pressure at 650°C. The equipment used was especially developed for these tests.

The tubes without notches were tested at pressures of 9·32 and 7·36 MPa. Test results indicate that the rupture time of the tubes without notches is in good agreement with that of uniaxial specimens when the maximum stress is taken as the rupture criterion. The tubes containing axial and circumferential surface notches were tested at a pressure of 7·36 MPa. Test results indicate that the ductile fracture theory is applicable to the life prediction in the case of axial notches.

An electric potential method was very useful for monitoring the creep crack growth from the notch root. The relationship between the creep crack growth rate and the fracture mechanics parameter, σ_net or K₁, was investigated.     

Analysis of composite hydrogen storage cylinders subjected to localized flame impingements

A comprehensive non-linear finite element model is developed for predicting the behavior of composite hydrogen storage cylinders subjected to high pressure and localized flame impingements. The model is formulated in an axi-symmetric coordinate system and incorporates with various sub-models to describe the behavior of the composite cylinder under extreme thermo-mechanical loadings. A heat transfer sub-model is employed to predict the temperature evolution of the composite cylinder wall and accounts for heat transport due to decomposition and mass loss. A composite decomposition sub-model described by Arrhenius's law is implemented to predict the residual resin content of thermal damaged area. A sub-model for material degradation is implemented to account for the loss of mechanical properties. A progressive failure model is adopted to detect various types of mechanical failure. These sub-models are implemented in ABAQUS commercial finite element code using user subroutines. Numerical results are presented for thermal damage, residual properties and profile of resin content in the cylinder. The developed model provides a useful tool for safe design and structural assessment of high pressure composite hydrogen storage cylinders.     

Yielding condition of a long,pressurised thick-walled cylinder subjected to a torsional moment

Stress equations are developed for a long, thick-walled cylinder loaded by both an internal pressure and an external torsional moment. The equations are applied to determine the yielding pressure of a thick-walled cylinder. A closed form equation is obtained which can be used to calculate the yielding pressure for design purposes.     

Stress concentration factors of flat end to cylindrical shell connection with a fillet or stress relief groove subjected to internal pressure

For fatigue assessment of pressure vessels (parts), as proposed by the CEN Technical Committee 54, the knowledge of some stress quantities in the structure is necessary, e.g. equivalent stresses according to Tresca's yield criterion and principal stresses at welds. In this article, these quantities are given in the form of stress concentration factors for the flat end to cylindrical shell connection with a fillet or stress relief groove subjected to internal pressure. In this context, a stress concentration factor is defined as the ratio of the ‘true’ stress (obtained by FE analysis) to the analytically determined stress corresponding to the linear elastic idealized shell plate model. For different values of the ratio of fillet/groove-radius to plate thickness, approximation functions for those stress concentration factors are obtained, covering the range of conventional flat end to cylindrical shell connection geometries.     

Elastic buckling of,and first yielding in,thin torispherical shells subjected to internal pressure

With the aid of the non-linear shell buckling computer program BOSOR 4, the internal pressures at which elastic circumferential buckling (or wrinkling) take place in thin torispherical shells have been calculated. The maximum equivalent (or effective) stresses in the shells in the axisymmetric pre-buckled state were also obtained; from these, the pressures at which first yielding in the shells commences were determined for $\text{1 <}\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{× 10}{}^3\text{< 4}$The calculations were performed for shells with $\text{diameter}\text{thickness}$ ratios of 500, 1000 and 2000; other geometric ratios, as detailed in the paper, were also varied. The computations were carried out for steel shells but the results have been presented in dimensionless form.Utilising the above results it is possible to determine whether a given torispherical end closure will buckle elastically or whether an elastic-plastic analysis of the shell is desirable. Factors which are conducive to elastic buckling are a high yield point, a low modulus of elasticity or a large value of the shell diameter-thickness ($\text{D}\text{t}$) ratio. For steel shells, elastic internal pressure buckling will occur (for some combinations of $\text{r}\text{D}$ and $\text{R}{}_{\mathrm{<mtext>S</mtext>}}\text{D}$) for $\text{D}\text{t}\text{= 2000}$ and $\text{σ}{}_{\mathrm{<mtext>yp</mtext>}}\text{E}\text{= 3 × 10}{}^{\mathrm{?3}}$. For $\text{D}\text{t}\text{= 1000}\text{and}\text{500}$, first yield always precedes elastic buckling for the parameters investigated. The failure mode for these cases is either elastic-plastic buckling or plastic collapse (an axisymmetric mode with large deformations).A comparison of the results of linear and non-linear elastic axisymmetric stress analyses of the shells shows that the linear theory sometimes underestimates the first yield pressure by considerable amounts. Limit pressures obtained from small-deflection shell theories can be too low in such cases.Also given in the paper are approximate simple expressions whereby the elastic internal buckling pressures of torispherical shells may be calculated. These expressions should be useful to designers.     

Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials

In this paper, we present an accurate method to carry out elastic analysis of thick-walled spherical pressure vessels subjected to internal pressure. Two kinds of pressure vessel are considered: one consists of two homogeneous layers near the inner and outer surfaces of the vessel and one functionally graded layer in the middle; the other consists of the functionally graded material only. The effects of Young's modulus of the outer layer, and Young's modulus and geometric size of the middle layer on the deformations and stresses in the vessels consisting of the three different layers are examined. A method to obtain an almost constant circumferential stress in the vessels consisting of the functionally graded material only is investigated.     

Modeling thermal response of polymer composite hydrogen cylinders subjected to external fires

With the anticipated introduction of hydrogen fuel cell vehicles to the market, there is an increasing need to address the fire resistance of hydrogen cylinders for onboard storage. Sufficient fire resistance is essential to ensure safe evacuation in the event of car fire accidents. The authors have developed a Finite Element (FE) model for predicting the thermal response of composite hydrogen cylinders within the frame of the open source FE code Elmer. The model accounts for the decomposition of the polymer matrix and effects of volatile gas transport in the composite. Model comparison with experimental data has been conducted using a classical one-dimensional test case of polymer composite subjected to fire. The validated model was then used to analyze a type-4 hydrogen cylinder subjected to an engulfing external propane fire, mimicking a published cylinder fire experiment. The external flame is modelled and simulated using the open source code FireFOAM. A simplified failure criteria based on internal pressure increase is subsequently used to determine the cylinder fire resistance.     

The residual strength of automotive hydrogen cylinders after exposure to flames

Fuel cell vehicles and some compressed natural gas vehicles are equipped with carbon fiber reinforced plastic (CFRP) composite cylinders. Each of the cylinders has a pressure relief device designed to detect heat and release the internal gas to prevent the cylinder from bursting in a vehicle fire accident. Yet in some accident situations, the fire may be extinguished before the pressure relief device is activated, leaving the high-pressure fuel gas inside the fire-damaged cylinder. To handle such a cylinder safely after an accident it is necessary that the cylinder keeps a sufficient post-fire strength against its internal gas pressure, but in most cases it is difficult to accurately determine cylinder strength at the accident site. One way of solving this problem is to predetermine the post-fire burst strengths of cylinders by experiments. In this study, automotive CFRP cylinders having no pressure relief device were exposed to a fire to the verge of bursting; then after the fire was extinguished the residual burst strengths and the overall physical state of the test cylinders were examined. The results indicated that the test cylinders all recorded a residual burst strength at least twice greater than their internal gas pressure for tested cylinders with new cylinder burst to nominal working pressure in the range 2.67–4.92 above the regulated ratio of 2.25.     

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.     

Numerical modelling of transient heat transfer of hydrogen composite cylinders subjected to fire impingement

To improve the current design standards of the hydrogen composite cylinders, it is essential to understand the thermal response of the hydrogen composite cylinders subjected to fire impingement. In the present study, a fully coupled conjugate heat transfer model based on a multi-region and multi-physics approach is proposed for modelling the transient heat transfer behaviour of composite cylinders subjected to fire impingement. The fire scenario is modelled using the in-house version of FireFOAM, the large eddy simulation (LES) based fire solver within the frame of OpenFOAM. Three dimensional governing equations based on the finite volume method are written to model the heat transfer through the regions of composite laminate, liner and pressurized hydrogen, respectively. The governing equations are solved sequentially with temperature-dependent material properties and coupled interface boundary conditions. The proposed conjugate heat transfer model is validated against a bonfire test of a commercial Type-4 cylinder and its transient heat transfer behaviour is also studied.     

Alleviation of quenching residual stresses by cold working the necks of seamless 6351 aluminium alloy thick-walled gas cylinders

The application of a compressive axial load to the apex of a gas cylinder neck results in the generation of Poisson-induced tensile circumferential stresses at the bore. As the compressive axial load is increased in magnitude, the stress distribution in the gas cylinder neck increases until finally yielding occurs at a specific location on the bore. Provided that the maximum compressive axial load is of sufficient magnitude, significant compressive residual circumferential stresses are generated at the bore. The purpose of this remedial action is to alleviate residual stresses that are introduced into the gas cylinder neck during the quenching stage of the manufacturing process. A destructive technique has been employed to determine quenching residual stresses in the neck of one production gas cylinder neck. This residual stress distribution is compared with one obtained by employing the destructive technique on a gas cylinder that has been cold worked by axial loading. Results indicate that tensile quenching residual circumferential stresses at the bore can be favourably modified resulting in compressive circumferential residual circumferential stresses at the bore.