Uniform Arrays of Unequal-Depth Cracks in Thick-Walled Cylindrical Pressure Vessels—Part I: Stress Intensity Factors Evaluation

1990 ◽  
Vol 112 (4) ◽  
pp. 340-345 ◽  
Author(s):  
M. Perl ◽  
K. H. Wu ◽  
R. Arone´
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Initial Crack ◽  
Pressure Vessels ◽  
Intensity Factors ◽  
Interaction Range ◽  
Sequence Of Events ◽  
Wide Range ◽  
Final Failure ◽  
Level Model

The influence of the unevenness of crack lengths on the mode I stress intensity factors (SIF) for large uniform arrays of radial cracks of unequal depth in thick-walled pressurized cylinders is investigated applying the previously proposed “two-crack-length level model.” Using the finite element method, SIFs are evaluated for numerous configurations of crack arrays bearing a wide range of crack lengths. The interaction range for various combinations of crack arrays and crack lengths is then determined. The numerical results anticipate that any statistical unevenness of the initial crack lengths, prevailing in the pressurized cylinder, will be amplified during the process of fatigue crack growth. Thus, while the fatigue life of the vessel is determined by a large number of cracks, its final failure, which is governed by a small number of the largest cracks, is likely to be caused by one major crack, as is usually the case. This sequence of events results from the particular nature of the inter-crack stress field, which is analyzed and discussed in detail in Part II of the paper.

The Effect of Crack Length Unevenness on Stress Intensity Factors Due to Autofrettage in Thick-Walled Cylinders

1997 ◽  
Vol 119 (3) ◽  
pp. 274-278 ◽  
Author(s):  
M. Perl ◽  
D. Alperowitz
Keyword(s):  
Stress Intensity ◽  
Crack Length ◽  
Stress Intensity Factors ◽  
Relative Length ◽  
Intensity Factors ◽  
Residual Stress Field ◽  
Interaction Range ◽  
Wide Range ◽  
Level Model ◽  
Radial Cracks

The effect of crack length unevenness on the mode I stress intensity factors (SIFs) for large uniform arrays of radial cracks of unequal depth in fully or partially autofrettaged thick-walled cylinders is investigated. The analysis is based on the previously proposed “two-crack-length level model.” Values for KIA—the SIF due to the compressive residual stress field—for various crack arrays bearing n1 = n2 = 2−512 cracks, a wide range of nondimensional crack lengths l1/a=0.01−0.1, and numerous levels of autofrettage ε = 30−100 percent are evaluated by the finite element method for a cylinder of radii ratio of b/a = 2. The interaction range for different combinations of crack arrays and crack length is then determined. The obtained results show that the unevenness in the SIFs depends on all three parameters, i.e., the number of cracks in the array, the cracks’ lengths, and the level of autofrettage, while the interaction range between adjacent cracks is determined only by the relative length of the cracks and the density of the array.

3-D Stress Intensity Factors for Arrays of Inner Radial Lunular or Crescentic Cracks in Thin and Thick-Walled Spherical Pressure Vessels

2008 ◽  
Author(s):  
M. Perl ◽  
V. Bernstein
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Depth ◽  
Pressure Vessels ◽  
Life Assessment ◽  
Intensity Factors ◽  
Fe Method ◽  
Inner Radius ◽  
Wide Range ◽  
Spherical Pressure

Some spherical pressure vessels are manufactured by methods such as the Integrated Hydro-Bulge Forming (IHBF) method, where the sphere is composed of a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels one needs to evaluate the Stress Intensity Factors (SIF) distribution along the fronts of these cracks. However, to date, only one 3-D solution for the SIF for a circumferential crack in a thick sphere is available, as well as 2-D SIFs for one through the thickness crack in thin spherical shells. In the present paper, mode I SIF distributions for a wide range of lunular and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front, for five geometries representing thin, moderately thick, and thick spherical pressure vessels with outer to inner radius ratios of η = Ro/Ri = 1.01, 1.05, 1.1, 1.7, and 2.0. SIFs are evaluated for arrays containing n = 1–20 cracks; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.95; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem and by the following parameters: the geometry of the sphere-η, the number of cracks in the array-n, the depth of the cracks-a/t, and their ellipticity-a/c.

Three-Dimensional Stress Intensity Factors for Arrays of Radial Cracks Emanating From the Inner Surface of a Thick-Walled Spherical Pressure Vessel

2008 ◽  
Author(s):  
M. Perl ◽  
V. Bernstein
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Depth ◽  
Pressure Vessels ◽  
Life Assessment ◽  
Geometrical Parameters ◽  
Intensity Factors ◽  
Fe Method ◽  
Wide Range ◽  
Spherical Pressure

Some spherical pressure vessels are manufactured by methods such as the Integrated Hydro-Bulge Forming (IHBF) method, where the sphere is composed of a series of double curved petals welded along their meridional lines. Such vessels are susceptible to multiple radial cracking along the welds. For fatigue life assessment and fracture endurance of such vessels one needs to evaluate the Stress Intensity Factors SIF distribution along the fronts of these cracks. However, to date, only two-dimensional SIFs for one through the thickness crack in a thin spherical shells is available. In the present paper, mode I SIF distributions for a wide range of lunular and crescentic cracks are evaluated. The 3-D analysis is performed, via the FE method employing singular elements along the crack front, for three sphere geometries with outer to inner radius ratios of η = Ro/Ri = 1.1, 1.7, and 2.0. SIFs are evaluated for arrays containing n = 1–20 cracks,; for a wide range of crack depth to wall thickness ratio, a/t, from 0.025 to 0.8; and for various ellipticities of the crack, i.e., the ratio of crack depth to semi crack length, a/c, from 0.2 to 1.5. The obtained results clearly indicate that the SIFs are considerably affected by the three-dimensionality of the problem and by the geometrical parameters: the geometry of the sphere – η, the number of cracks in the array – n, the depth of the crack – a/t, and its ellipticity – a/c.

Analysis of Surface Flaw in Pressure Vessels by a New 3-Dimensional Alternating Method

1982 ◽  
Vol 104 (4) ◽  
pp. 299-307 ◽  
Author(s):  
T. Nishioka ◽  
S. N. Atluri
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Surface Crack ◽  
Crack Surface ◽  
Pressure Vessels ◽  
Pressure Loading ◽  
Intensity Factors ◽  
Alternating Method ◽  
Magnification Factors

An alternating method, in conjunction with the finite element method and a newly developed analytical solution for an elliptical crack in an infinite solid, is used to determine stress intensity factors for semi-elliptical surface flaws in cylindrical pressure vessels. The present finite element alternating method leads to a very inexpensive procedure for routine evaluation of accurate stress intensity factors for flawed pressure vessels. The problems considered in the present paper are: (i) an outer semi-elliptical surface crack in a thick cylinder, and (ii) inner semi-elliptical surface cracks in a thin cylinder which were recommended for analysis by the ASME Boiler and Pressure Vessel Code (Section III, App. G, 1977). For each crack geometry of an inner surface crack, seven independent loadings, such as internal pressure loading on the cylinder surface and polynomial pressure loadings from constant to fifth order on the crack surface, are considered. From the analyses of these loadings, the magnification factors for the internal pressure loading and the polynomial influence functions for the polynomial crack surface loadings are determined. By the method of superposition, the magnification factors for internally pressurized cylinders are rederived by using the polynomial influence functions to check the internal consistency of the present analysis. These values agree excellently with the magnification factors obtained directly. The present results are also compared with the results available in literature.

scholarly journals Compression and Shear Fracture Analysis of Boundary Cracks Containing Water in Rock

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhensheng Yang ◽  
Fulin Li ◽  
Tianran Ma
Keyword(s):  
Stress Intensity ◽  
Friction Coefficient ◽  
Stress Intensity Factors ◽  
Underground Mining ◽  
Shear Fracture ◽  
Water Environment ◽  
Initial Crack ◽  
Open Boundary ◽  
Shear Stresses ◽  
Intensity Factors

In order to conserve the water resource during underground mining, the fracture and mechanical properties of rock are important for the stability of water-resisting layers, especially for the fracture behavior of boundary cracks containing water in rock. Considering the swelling of rock under water environment and the influence of water on rock, the stress intensity factors of modes I and II are derived for boundary cracks in rock under compressive and shear stresses. The cracks are divided into the closed and open states. The effects of the crack inclination angle, friction coefficient between crack surfaces, and initial crack length on stress intensity factors are also taken into account. The stress intensity factors for closed and open boundary cracks are verified by numerical and physical experiments, respectively, and the deviation of the results is within 5%. It is shown that pore pressure has different effects on the relationship between stress intensity factor and friction coefficient under different lateral pressures. The effect of water on crack propagation is mainly due to the deterioration of the fracture toughness of the rock. It is found that the critical coefficient λc is a key parameter to determine whether the boundary crack propagates in rock under compression-shear stress. Further studies should be performed to apply the present fracture theory to rock mass or water-resisting layers.

scholarly journals Influence Coefficients to Calculate Stress Intensity Factors for an Elliptical Crack in a Plate

2002 ◽  
Author(s):  
Patrick Le Delliou ◽  
Bruno Barthelet
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Atomic Energy Commission ◽  
Finite Thickness ◽  
Elliptical Crack ◽  
Intensity Factors ◽  
Normal Loading ◽  
Influence Coefficients ◽  
Wide Range

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work has been conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes) which is also of practical importance has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and crack eccentricity (2e/t ratio where e is the distance from the center of the ellipse to the plate mid plane). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18000 to 26000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions will be introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.

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