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.     

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.     

Elasto-plastic fracture properties of an all-aluminium gas cylinder with different cracks

All-aluminium cylinders are used for on-board storage of compressed natural gas in vehicles. Besides being subjected to the maximum fill pressure, these cylinders are subjected to fluctuating pressures, due to refuelling operations. In order to establish a relevant test method to ensure leak before break failure performance, elasto-plastic finite element stress analysis of the design containing various defects was carried out to obtain a theoretical basis for the establishment of the test method. Axial semi-elliptical cracks in the central portion of the cylinder and circumferential cracks in the bottom of the cylinder are modelled using 20-node hexahedron elements. Not only the cylindrical body but also the neck and transition areas of the cylinder are considered in the modelling. Slender cracks with lengths approximately five times the wall thickness of the cylinder, which often appear in applied all-aluminium gas cylinders, are considered. Crack depths varied from 22.5% to 100% of the wall thickness. Through discussions about the calculated J-integral and crack mouth opening displacement (CMOD) of the axial and circumferential cracks, the effects of the different cracks on all-aluminium cylinders in the elasto-plastic deformation state are made clear. The analyses show that under the elasto-plastic deformation state, axial cracks in the centre of the cylinder are more dangerous for the cylinder than circumferential cracks in the bottom of the cylinder, if these are of the same size and under the same conditions. The axial external crack is found to be most severe among these different crack types. Finally, the CMOD of cylinders with an axial external crack have been measured by the experimental method and a good agreement between the calculated CMOD and the tested CMOD was reached.     

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.     

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 review of limit load solutions for cylinders with axial cracks and development of new solutions

Limit load solutions for axially cracked cylinders are reviewed and compared with available finite element (FE) results. New limit solutions for thick-walled cylinders with axial cracks under internal pressure are developed to overcome problems in the existing solutions. The newly developed limit load solutions are a global solution for through-wall cracks, global solutions for internal/external surface cracks and local solutions for internal/external surface cracks. The newly developed limit pressure solutions are compared with available FE data and the results show that the predictions agree well with the FE results and are generally conservative.     

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 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.     

Surface flaw in a pressurised and thermally-shocked hollow cylinder

The first part of this paper deals with stress intensity factors of a semi-elliptical crack, with a third order polynomial pressure distribution in a finite thickness flat plate. These solutions are determined by the alternating technique in three-dimensional fracture mechanics where both the front and back surface effects of the flat plate are accounted for. The second part is concerned with the applications of these solutions in deriving approximate solutions for a semi-elliptical crack in a pressurised cylinder and in a thermally-shocked cylinder. Curvature effects of the cylinder are estimated from two-dimensional finite element solutions of fix-gripped single-edge notched plates with prescribed crack pressure and single-edge notched cylinders with the same prescribed crack pressure. The stress intensity factors of a pressurised semi-elliptical crack in a flat plate are modified by this curvature correction factor to yield an estimate of the stress intensity factors of semi-elliptical cracks in a pressurised or thermally-shocked cylinder, with outer to inner diameter ratios ranging from 10:9 to 3:2 at crack depths of 0·4 to 0·8.     

Elastic analysis of semi-elliptical axial cracks in cylinders under thermal shock using the BS 7910 framework

One of the most common and important situations involving flaws in pressure vessels is the internal thermal shock of a hollow circular cylinder with an axial semi-elliptical internal surface crack. The current approaches available to analyse this specific problem are excessively conservative or cumbersome. This paper considers the internal thermal shock problem and determines the stress-intensity factors for shallowest and deepest points for cylinders with the ratio of thickness to inner radius 0.1 and 0.25. The results of calculations are presented in a similar form to the draft standard BS 7910:1997 and thus permit numerous practical applications. These results are in many cases much less conservative than the draft standard and also reveal some important cases.     

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.     

Remaining life assessment of welded pipes containing cracks

The presence of flaws, their size and location in the welded region affects the safe service life of pressure pipes operating at elevated temperature. A remaining life assessment was required to determine the probable remaining safe life of pressure pipes in a high-temperature steam distribution system in which crack-like defects had been identified in many welds. The crack-like defects indicated by NDE lacked the required information to fully identify their locations within the pipe wall. The effect of not knowing complete details of the location of the identified cracks was studied by considering a 360° circumferential crack with initial radial dimension a₀. The crack positions evaluated were: an internal surface crack, an external surface crack, and embedded cracks at various distances from the internal wall of the pipe. Crack growth was modeled using time-dependent fracture mechanics and a newly developed computer code.     

Linear elastic analysis of semi-elliptical axial surface cracks in a hollow cylinder

The variation of the stress intensity factor along the front of two semi-elliptical axial surface cracks in a hollow cylinder subject to temperature and pressure loading is analysed. A three-dimensional elastic finite element analysis is performed using twenty noded isoparametric elements employing the quarter point singularities at the crack front and calculating the energy release rate. The solution is compared with analytical results as well as with results from other authors.     

Thermal stress intensity factors for a cracked cylinder under transient thermal loading

Transient thermal stress intensity factors are calculated at the deepest and the surface points of an internal axial semi-elliptical surface crack in a thick-walled cylinder under thermal shock. The method of calculation is based on the weight function and an effective procedure of integrating of the weight integrals. Time-dependent thermal boundary conditions are assumed to act on the inner surface of the pressurized cylinder. Exact analytical solutions are derived for the weight function, and then integrated to compute transient thermal stress intensity factors. In the special case of a steady state problem and also the pressurized cylinder, the results show to be in accordance with those cited in the literature.     

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.     

Fracture analyses on the all-metal cylinders and the metal-lined hoop-wrapped cylinders with axial cracks

The objective of this paper is to report on the research about the effects of the cylinder materials, the hoop-wrap materials and the crack size on all-metal cylinders and metal-lined cylinders with axially oriented internal cracks through comparisons of the fracture behaviors between the all-metal cylinders and the metal-lined hoop-wrapped cylinders. The three-dimensional finite element methods were used to model these different cylinders. The different fracture behaviors of these cylinders are presented by comparing the calculated normalized stress intensity factors and the crack-tip opening displacements of these cylinders. The effects of the crack sizes, the cylinder materials and the hoop-wrap materials on the crack driving forces are studied and discussed.     

Computational simulation of fatigue crack growth and demonstration of leak before break criterion

A thick plate with a semi-elliptical surface crack subjected to remote tension and tension fatigue loading is considered for the analysis. In the present study the material is assumed to have variable fracture toughness in the surface and thickness directions. Material with isotropic fracture toughness is also considered. The developed three dimensional finite element code which has the capability to handle singularity and evaluate fracture parameter based on force method is used to characterise the fatigue crack growth. Parametric study involving various initial crack sizes is carried out and Foreman’s equation is used to predict the crack growth. Various regions viz. break, leak before break are obtained.     

Hydrogen enhanced fatigue in full scale metallic vessel tests – Results from the MATHRYCE project

This study investigates the fatigue life of CrMo pressure vessels for hydrogen storage by hydraulic and hydrogen pressure cycle tests. Two different sized cylinders have been tested; 35 L inner volume and 28 MPa working pressure (WP) and 198 L volume and 41 MPa WP. On the inner surface of the cylinders U-shaped notches of different depths were machined by electro discharge machining technique. The initial notch sizes were designed based on a two stage fatigue predictive model based on fracture mechanics to develop through wall cracks in the deepest notches after about 50,000 hydraulic cycles together with crack propagation of the intermediate notches and crack initiation in the smallest. The cylinders were cycled between the nominal pressure of 2 MPa and the WP until leak before break (LBB). Strain gauges were placed at the external surface of the cylinders in correspondence of the internally machined notches. On the notches which developed through wall, the strain showed a progressive decrease followed by an increase of the hoop strain during the final stage of crack propagation until LBB failure. Hydrogen effect was clearly identified by the reduction in the number of cycles to failure comparing tests in hydrogen and in oil. Subsequent failure analysis at the end of each test revealed a typical trans-granular fatigue crack surface morphology (with fatigue striations) for tests in oil, while quasi cleavage and intergranular fracture appearance were found for hydrogen tests.     

Plastic collapse moment of 90° long radius elbows with internal circumferential surface crack at intrados under in-plane bending

Piping elbows under in-plane bending moment are vulnerable to cracking. The crack initiates at the surface and eventually reaches through the thickness and may lead to failure. The structural integrity assessment requires knowledge of the limit load. Limit load solutions for elbows with through-wall crack configurations are available in the open literature. But solutions for surface crack are not available. This paper presents a closed form expression for the plastic collapse moment (PCM) of 90°, long radius elbows with circumferential surface cracks at the intrados, under in-plane bending moment. The expression is derived, based on the results of non-linear (geometric and material) FE analyses covering a wide range of geometries and crack sizes. These plastic collapse moments evaluated herein will help in structural integrity assessment.