Fracture behaviors of all-steel gas cylinder with different axial cracks

Using the three-dimensional finite element method, the researches on the linear elastic and the nonlinear elasto-plastic fracture behaviors of all-steel gas cylinders with different axially oriented cracks were carried out. The crack mouth opening displacement CMOD and the crack driving forces for the cylinders containing axial deep cracks, which have the crack depth of 25%–100% of the wall thickness, and the crack length of ten times the wall thickness, were obtained. 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 respectively quantified in the linear elastic deformation state and in the elasto-plastic deformation state.     

Different fracture performance of all-steel and all-aluminium cylinders with axial cracks

The linear elastic and the nonlinear elasto-plastic fracture mechanics analysis on all-metal (all-steel and all-aluminum) cylinder with different axially oriented cracks were carried out using the three-dimensional finite element method and the experimental method. The crack mouth opening displacement CMOD and the crack driving forces (K_I for elastic deformation state and J_I for elasto-plastic deformation state) of the all-steel cylinder and the all-aluminum cylinder containing axial deep cracks, were obtained. Through analysis of the calculated CMOD and crack driving forces for the all-steel cylinder and the all-aluminum cylinder with cracks, whose sizes are often met, respectively, in the engineering applications, the fracture behaviors of the two kinds of all-metal cylinders are compared. The CMOD for the two kinds of all-metal cylinders with external axial cracks were measured by an experimental method and good agreements between the calculated CMOD and tested CMOD were reached. Some CMOD and crack driving force expressions about the crack sizes, internal pressure and location along the crack front are obtained.     

Elastic fracture properties of all-steel gas cylinders with different axial crack types

All steel cylinders are being used for on-board storage of compressed natural gas in vehicles. Typical maximum fill pressure for these cylinder is 25.85 MPa (3750 psi). These cylinders are subjected to fluctuating pressures, due to the refueling operation. In order to establish a relevant test method to ensure leak before break failure performance in the event of a through-wall cracking, the finite element stress analysis of the design containing various defects has to be firstly carried out to get some theoretical basis for the establishment of the test method. External and internal axial semi-elliptical surface cracks are modeled. 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. Slender cracks with approximately 10 times the wall thickness of the cylinder, which often appear in the engineering application of all steel gas cylinders, are considered. The crack depths varied from 25% to 100% of the wall thickness. Analysis is also carried out for the cylinder with through-wall axial cracks, which have similar crack lengths with external and internal surface cracks. The cylinders are assumed to be in the elastic deformation state. Stress intensity factor, K_I, and crack mouth opening displacement, CMOD, as the functions of internal pressure, crack size, location (external verdus internal) and shape (elliptical versus straight-fronted), are established. Calculated results are compared with published results. Deep axial external cracks are found to be more severe than axial internal surface cracks having similar crack lengths. Crack driving force for a semi-elliptical through-wall crack is found to be significantly less than that of a straight-fronted through-wall cracks, which have the same crack length. So, the establishment of a relevant test method to ensure leak before break failure performance in the event of through-wall cracking is of high practical value for the engineering design and application of these cylinders.     

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.     

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.     

Effect of composite wrapping on the fracture behavior of the steel-lined hoop-wrapped cylinders

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

Deterministic assessment of reactor pressure vessel integrity under pressurised thermal shock

Numerical investigations were carried out to assess the integrity of reactor pressure vessels under pressurised thermal shock (PTS). The 4-loop reactor pressure vessel with cladding was subjected to thermo-mechanical loading owing to loss of coolant accident. The loss of coolant accident corresponding to small break as well as hot leg breaks were considered separately, which led to axisymmetric and asymmetric thermal loading conditions respectively. Three different crack configurations, 360° circumferential part through, circumferential semi-elliptical surface and circumferential semi-elliptical under-clad cracks, were postulated in the reactor pressure vessel. Finite element method was used as a tool for transient thermo-elastic analysis. The various fracture parameters such as crack mouth opening displacement (CMOD), stress intensity factor (SIF), nil ductility transition temperature (RT_NDT) etc. were computed for each crack configuration subjected to various type of loading conditions. Finally for each crack a fracture assessment was performed concerning crack initiation based on the fracture toughness curve. The required material RT_NDT was evaluated to avoid crack initiation.     

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.     

Limit loads of circumferentially flawed pipes and cylindrical vessels under internal pressure

Published limit load formulae for circumferential defects overestimate the burst pressure for penetrating defects in pipes by the factor two in the short crack limit, because they only consider axial stress. Therefore, a class of limit load solution is discussed which takes the triaxial state of stress into account. The solutions for pressure loaded crack faces are improved analytically. Primal–dual limit analysis with the finite element method is used to adjust all solutions to numerical results. Limit loads are obtained for circumferential cracks of all sizes in thick-walled cylinders.     

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.     

Stress intensity factors for internal and external cracks in pressurised thick-walled cylinders

Stress intensity factors for both internal and external semi-circular and semi-elliptical surface cracks in internally pressurised thick-walled cylinders of radius ratios between 2 and 3 are presented for a wide range of crack sizes. These solutions were obtained using the boundary integral equation (BIE) method for three-dimensional numerical stress analysis. Hoop strain distributions at the outer circumference of the cylinder are also presented for some external cracks, and shown to be useful for experimentally monitoring crack growth.     

CIRCUMFERENTIAL CRACK PROBLEM FOR AN FGM CYLINDER UNDER THERMAL STRESSES

The main objective of this study is to determine the stress intensity factors associated with a circumferential crack in a thin-walled cylinder subjected to quasi-static thermal loading. The cylinder is assumed to be a functionally graded material. In order to make the problem analytically tractable, the thin-walled cylinder is modeled as a layer on an elastic foundation whose thermal and mechanical properties are exponential functions of the thickness coordinate. Hence a plane strain crack problem is obtained. First temperature and thermal stress distributions for a crack-free layer are determined. Then using these solutions, the crack problem is reduced to a local perturbation problem where the only nonzero loads are the crack surface tractions. Both internal and edge cracks are considered. Stress intensity factors are computed as functions of crack geometry, material properties, and time.     

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).     

Novel multi-center concave bottom for hydrogen storage cylinder

Hydrogen storage steel cylinders are the earliest and widely used hydrogen storage vessels. Fatigue cracks are easy to initiate and grow under hydrogen pressure, which threatens the safety of users. Although hydrogen has an effect on the initiation and growth of fatigue cracks, a reasonable structure of cylinder will make the stress distribution more reasonable and reduce the probability of crack initiation from the source. This paper researched the multi-center concave bottom for hydrogen storage cylinder. The geometric design parameters of the new base end are determined by the orthogonal design method. We analyze the effects of various parameters on the multi-center concave base end by using the finite element method. Based on the finite element analysis (FEA) of different structure, the results show that the stress concentration of new base end can be greatly reduced, and the minimum stress concentration factor is close to 1.1. The results provide valuable insights for designing and manufacturing the new type of seamless gas cylinder. The corresponding gas cylinder that we processed according to the simulation had successfully passed a series of tests.     

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.     

Application of approximate weight functions in fracture analyses of thermally stressed structures

The approximate weight function method is applied to two types of crack problems involving thermal stresses. An analytical stress intensity factor expression (approximate) is derived for the case of a centre crack in a finite plate subjected to a quadratic thermal gradient. The analytical solution agrees very well with the finite element results in the literature. Another problem studied is that of internal axial crack(s) in a long cylinder with steady state thermal gradient across the wall thickness; results for this case are also satisfactory. The success of the approximate weight function method suggests that it may sometimes be preferred to the finite element method, which is extensively used today when treating crack problems of thermally stressed structures.     

Plastic limit pressures for cracked pipes using finite element limit analyses

Based on detailed finite element (FE) limit analyses, the present paper provides approximations for plastic limit pressure solutions for plane strain pipes with extended inner axial cracks; axi-symmetric (inner) circumferential cracks; axial through-wall cracks; axial (inner) surface cracks; circumferential through-wall cracks; and circumferential (inner) surface cracks. In particular, for surface crack problems, the effect of the crack shape, semi-elliptical or rectangular, on the limit pressure is quantified. Comparisons with existing analytical and empirical solutions show a large discrepancy for short circumferential through-wall cracks and for surface cracks (both axial and circumferential). Being based on detailed 3D FE limit analysis, the present solutions are believed to be accurate, and thus to be valuable information not only for plastic collapse analysis of pressurised piping but also for estimating non-linear fracture mechanics parameters based on the reference stress approach.     

A note on cylinder stress-intensity factors

A comparison is made between Shannon's finite element $\text{K}$ results for internally pressurised thick-walled cylinders with one and two radial cracks and Bowie and Freese's mapping-collocation results for the same geometries. The comparison is good except for shallow cracks relative to the cylinder wall thickness. Based on the nature of the two calculation techniques and on the comparison of the results for shallow cracks with the known result in the limit of very shallow cracks, the collocation results appear to be the better representation of $\text{K}$. The difference becomes particularly important when the $\text{K}$ results are to be used for predictions of cylinder fatigue lives, since shallow crack growth rates dominate fatigue life.     

Transient Thermoelastic Analysis of a Solid Cylinder Containing a Circumferential Crack Using the C–V Heat Conduction Model

This article presents the transient thermoelastic analysis in a long solid cylinder with a circumferential crack using the C–V heat conduction theory. The outer surface of the cylinder is subjected to a sudden temperature change. The Laplace transform technique is adopted to solve the one-dimensional hyperbolic heat conduction equation, and the axial thermal stress is obtained for the un-cracked cylinder in the Laplace domain. Then this axial thermal stress with a minus sign is applied to the crack surface to form a mixed boundary value problem in the cylindrical coordinate system. A singular integral equation is derived by applying the Fourier and Hankel transforms to solve the mode I crack problem. The transient thermal stress intensity factors are obtained by solving the singular integral equation numerically. The influences of thermal relaxation time, crack geometry, and Biot's number upon transient temperature distributions, axial stress fields, and stress intensity factors are analyzed.     

Numerical study of elliptical cracks in cylinders with a thickness transition

The paper deals with elliptical cracks in a cylinder with a thickness transition. This structure is an assembly of two cylinders of thickness t and t₂ (t<t₂). In the transition zone, the thickness varies linearly. The purpose is to check whether tabulated data used for SIF calculations in a cylinder of uniform thickness t can be used for the cylinder with a thickness transition. A comparative study is made on the effect of a crack in a cylinder with a thickness transition and in a uniform thickness cylinder. Loads considered are pure tensile stress and bending moment. A numerical analysis was performed considering elastic behaviour at the crack tip. A crack mesh was designed and validated for 3D models. The results show that SIF calculations in the transition assuming a uniform thickness cylinder are conservative but not precise. The comparative study shows that the cylinder with a thickness transition is more vulnerable to a defect.