Interaction Effects in Combined Arrays of Radial and Longitudinal Semi-Elliptical Surface Cracks in Pressurized Thick-Walled Cylinder

1997 ◽  
Vol 119 (2) ◽  
pp. 167-174 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
J. Wang
Keyword(s):  
Stress Intensity ◽  
Crack Depth ◽  
Crack Density ◽  
Longitudinal Crack ◽  
Interaction Effects ◽  
Surface Cracks ◽  
Fe Method ◽  
Relative Spacing ◽  
Wide Range ◽  
Radial Cracks

In two previous papers, the interaction effects for two separate cases of large arrays of semi-elliptical, internal, surface cracks in a thick-walled, cylindrical pressure vessel were studied. First, arrays of radial cracks were considered followed by the study of longitudinal-coplanar crack arrays. Circumferential crack density and longitudinal crack spacing were found to have opposing effects on the prevailing stress intensity factors (SIFs). Consequently, in the present paper, combined arrays of both radial and longitudinal cracks are considered, and their interaction effects are studied. The mode I stress intensity factor (SIF) distribution for numerous configurations of combined semi-circular and semi-elliptical crack arrays are evaluated. The 3-D analysis is performed by the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. The effects of crack density in the circumferential direction and of relative spacing in the longitudinal direction on the SIFs are studied for combined arrays of up to 32 circumferentially equispaced, radial cracks and having longitudinal relative spacing of 2c/d of 0.25 to 0.99; for a wide range of crack depth to wall thickness ratios, a/t, from 0.05 to 0.4; and for various ellipticities of the crack, i.e., the ratio of crack depth to semicrack length, a/c, from 0.2 to 1.5. The results clearly indicate that the SIFs are considerably affected by the interaction among the cracks, and that the SIF values depend upon the circumferential density and longitudinal spacing, the crack depth and ellipticity, as well as the three-dimensional nature of the problem.

Three-Dimensional Interaction Effects in an Internally Multicracked Pressurized Thick-Walled Cylinder—Part II: Longitudinal Coplanar Crack Arrays

1996 ◽  
Vol 118 (3) ◽  
pp. 364-368 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
N. Kokkavessis
Keyword(s):  
Radial Crack ◽  
Crack Depth ◽  
Crack Density ◽  
Three Dimensional ◽  
Longitudinal Crack ◽  
Interaction Effects ◽  
Fe Method ◽  
Wide Range ◽  
Coplanar Crack ◽  
Walled Cylinder

In the first part of this paper, the interaction effects among many radial, internal, semi-circular, and semi-elliptical cracks in a pressurized, thick-walled vessel were quantified. In the present paper, the mode I stress intensity factor (SIF) distribution for numerous longitudinal coplanar, internal, semi-circular, and semi-elliptical arrays of surface cracks in an infinite, pressurized, thick-walled cylinder are evaluated. The 3-D analysis is performed by the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. The effects of dense and sparse interacting longitudinal coplanar crack arrays on the SIFs are studied for a wide range of crack depth to wall thickness ratios, a/t, from 0.05 to 0.6; and, for various ellipticities of the crack, i.e., the ratio of the crack depth to semi-crack length, a/c, from 0.2 to 2.0. An analysis is performed to determine the influence of the three major parameters—crack density, crack ellipticity, and crack depth—on the interaction effects between adjacent cracks. The results clearly indicate that crack density, and, in some cases, ellipticity have opposing effects on the SIF of longitudinal crack arrays as compared to radial crack arrays. As a result of these contrasting behaviors, thick-walled cylinders having combined longitudinal and radial crack arrays would need further study.

The Influence of Autofrettage With Bauschinger Effect on the SIFS of Multiple Longitudinal Coplanar Cracks in Pressurized Cylinders

2005 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
S. Kotagiri
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Crack Density ◽  
Crack Plane ◽  
Fe Method ◽  
Wide Range

The influence of the Bauschinger Effect (BE) on the three dimensional, Mode I, Stress Intensity Factor (SIF) distributions for arrays of longitudinal coplanar, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. The generation and comparison of the SIFs for a “realistic” - Bauschinger Effect Dependent Autofrettage (BEDA) and those for an “ideal” - Bauschinger Effect Independent Autofrettage (BEIA), which until now did not exist, is undertaken. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. More than 250 different crack configurations are analyzed. SIFs for various crack densities (2c/d = 0.25–0.75), a wide range of crack depth to wall thickness ratios (a/t = 0.01–0.25), various ellipticities (a/c = 0.5–1.5), and different levels of autofrettage (ε = 30%–100%) are evaluated. The Bauschinger Effect (BE) is found to significantly lower the beneficial stress intensity factor due to autofrettage, KIA, by up to 52%, as compared to the case of “ideal” autofrettage. The reduction in KIA varies along the crack front with the maximum determined by the crack ellipticity, crack depth and crack separation distance. In some cases the maximum occurs at the deepest point of the crack and in others the maximum is at the point of intersection between the crack plane and the inner surface of the cylinder. In certain situations, the maximum transitions from one to the other as crack density increases. The detrimental influence of the BE increases as the crack density decreases and as crack depth decreases. For a partially autofrettaged cylinder, as the level of overstrain becomes smaller the influence of the BE is considerably reduced. As a result, the SIFs due to 100% BEDA differ by less than 15–17% when compared to 60% BEDA, and on the average the difference is only about 6%. Furthermore, the results indicate that crack density, and, in some cases, crack depth and crack ellipticity have opposing effects on the SIF of longitudinally coplanar crack arrays.

Stress Intensity Factors for Closely and Densely Packed Cracks in Partially Autofrettaged Pressurized Thick-Walled Cylinders

2009 ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Radial Crack ◽  
Crack Depth ◽  
Crack Density ◽  
Longitudinal Crack ◽  
Internal Surface ◽  
Crack Spacing ◽  
Surface Cracks

Due to acute temperature gradients and repetitive high-pressure impulses, extremely dense internal surface cracks can be practically developed in highly pressurized thick-walled vessels, typically in gun barrels. In our previous studies, networks of typical radial and longitudinal-coplanar, semi-elliptical, internal surface cracks have been investigated with an ideal or realistic autofrettage level of 100 percent. We have shown that the combined SIFs are considerably influenced by the three-dimensionality of the problem and the Bauschinger effect (BE) along with dependence on other parameters, such as radial crack density, longitudinal crack spacing, crack depth, crack ellipticity, and the autofrettage level. When pressure is considered solely, radial crack density and longitudinal crack spacing were found to have opposing effects on the prevailing stress intensity factor, KIP. Furthermore, the addition of the negative stress intensity factor (SIF), KIA, resulting from the residual stress field due to autofrettage, whether ideal or realistic, tended to decrease the combined SIF KIN = KIP − |KIA|. Therefore, to assess the fracture endurance and the fatigue life of a cylindrical, autofrettaged, pressure vessel containing such a network of cracks, it is necessary to determine the KIA’s and the KIN’s. However, to assess the SIFs accurately, significant computational efforts and strategies are necessary, especially for networks with closely and packed cracks. In this study, our effort will focus on the KIA and the KIN distribution for numerous configurations of closely and densely packed semi-circular and semi-elliptical networked cracks affected by pressure and partial-to-full autofrettage levels of 30–100%, which is practically seen in autofrettaged thick-walled pressure vessels. The 3-D analysis will be performed via the finite element (FE) method and the submodeling technique employing singular elements along the crack front and the various symmetries of the problem. The network cracks will include up to 128 equally spaced cracks in the radial direction; with relative, longitudinal crack spacing, 2c/d, from 0.1 to 0.99; autofrettage level of 30–100 percent; crack depth to wall thickness ratios, a/t, from 0.01 to 0.4; and, cracks with various ellipticities of crack depth to semi-crack length, a/c, from 0.2 to 2.

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.

scholarly journals Stress-Intensity Factors for Internal Surface Cracks in Cylindrical Pressure Vessels

1980 ◽  
Vol 102 (4) ◽  
pp. 342-346 ◽  
Author(s):  
J. C. Newman ◽  
I. S. Raju
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Wall Thickness ◽  
Stress Intensity Factors ◽  
Crack Depth ◽  
Internal Surface ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Wide Range

The purpose of this paper is to present stress-intensity factors for a wide range of semi-elliptical surface cracks on the inside of pressurized cylinders. The ratio of crack depth to crack length ranged from 0.2 to 1; the ratio of crack depth to wall thickness ranged from 0.2 to 0.8; and the ratio of wall thickness to vessel radius was 0.1 to 0.25. The stress-intensity factors were calculated by a three-dimensional finite-element method. The finite-element models employ singularity elements along the crack front and linear-strain elements elsewhere. The models had about 6500 degrees of freedom. The stress-intensity factors were evaluated from a nodal-force method. An equation for the stress-intensity factors was obtained from the results of the present analysis. The equation applies over a wide range of configuration parameters and was within about 5 percent of the present results. A comparison was also made between the present results and other analyses of internal surface cracks in cylinders. The results from a boundary-integral equation method were in good agreement (± 2 percent) and those from another finite-element method were in fair agreement (± 8 percent) with the present results.

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.

Stress intensity factors for semi-elliptical surface cracks in semicircularly notched tension plates

1997 ◽  
Vol 32 (3) ◽  
pp. 229-236 ◽  
Author(s):  
X B Lin ◽  
R A Smith
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Depth ◽  
Finite Thickness ◽  
J Integral ◽  
Surface Cracks ◽  
Intensity Factors ◽  
Wide Range ◽  
Half Length ◽  
Half Thickness

Stress intensity factors for semi-elliptical surface cracks located at the centre of a semicircular edge notch in a finite thickness plate subjected to a remote tensile load are presented in a tabulated format. A wide range of geometry ratios are considered. They are all combinations of the following ratios: the ratio of crack surface half-length to plate half-thickness, c/t = 0.2, 0.4, 0.6, 0.8 and 0.95; the ratio of crack depth to surface half-length, a/c = 0.2, 0.4, 0.6, 0.8 and 1; and the ratio of notch radius to plate half-thickness, r/t = 0.5, 1, 2 and 3. Both the quarter-point displacement and J.-integral methods based on three-dimensional finite element analyses were employed for the calculation of stress intensity factors. The calculation accuracy was studied by analysing the J.-integral path independence and comparing stress intensity factor results with other solutions available in the literature.

3-D Stress Intensity Factors for Internal Cracks in an Overstrained Cylindrical Pressure Vessel—Part I: The Effect of Autofrettage Level

2000 ◽  
Vol 122 (4) ◽  
pp. 421-426 ◽  
Author(s):  
M. Perl ◽  
A. Nachum
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Three Dimensional ◽  
Internal Surface ◽  
Favorable Effect ◽  
Residual Stress Field ◽  
Fe Method ◽  
Wide Range

Three-dimensional, mode I, stress intensity factor (SIF) distributions for arrays of internal surface cracks emanating from the bore of an autofrettaged thick-walled cylinder are evaluated in Part I of this paper. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. The autofrettage residual stress field is simulated using an equivalent temperature field. More than 200 different crack configurations were analyzed. SIFs for numerous crack arrays (n=1–180 cracks), a wide range of crack-depth-to-wall-thickness ratios a/t=0.05-0.6, various ellipticities a/c=0.2-1.5, and different levels of autofrettage (e=10–100 percent) were evaluated. The results clearly indicate the importance of autofrettage in reducing the effective stress intensity factor, and thus, slowing the crack growth rate. The sensitivity of this favorable effect to the number of cracks in the array as well as to the level of autofrettage are also discussed. The combined effect of pressure and autofrettage is discussed in detail in Part II of this paper. [S0094-9930(00)00604-1]

The Influence of the Bauschinger Effect on the Stress Intensity Factors for a Radially Cracked Autofrettaged Thick-Walled Cylinder

2005 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
V. Rallabhandy
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Crack Plane ◽  
Fe Method ◽  
Wide Range ◽  
Walled Cylinder

The influence of the Bauschinger Effect (BE) on the three dimensional, Mode I, Stress Intensity Factor (SIF) distributions for arrays of radial, internal, surface cracks emanating from the bore of a fully or partially autofrettaged thick-walled cylinder is investigated. A thorough comparison between the prevailing SIFs for a “realistic” - Bauschinger Effect Dependent Autofrettage (BEDA) and those for an “ideal” - Bauschinger Effect Independent Autofrettage (BEIA) is done. The 3-D analysis is performed via the finite element (FE) method and the submodeling technique, employing singular elements along the crack front. Both autofrettage residual stress fields, BEDA and BEIA, are simulated using an equivalent temperature field. More than 300 different crack configurations are analyzed. SIFs for numerous crack arrays (n = 1–64 cracks), a wide range of crack depth to wall thickness ratios (a/t = 0.01–0.2), various ellipticities (a/c = 0.5–1.5), and different levels of autofrettage (ε = 30%–100%) are evaluated. The Bauschinger Effect (BE) is found to considerably lower the beneficial stress intensity factor due to autofrettage, KIA, by up to 56%, as compared to the case of “ideal” autofrettage. The reduction in KIA varies along the crack front with a maximum at the point of intersection between the crack plane and the inner surface of the cylinder, decreasing monotonically towards the deepest point of the crack. The detrimental influence of the BE increases as the number of cracks in the array increases and as crack depth decreases. For a partially autofrettaged cylinder, as the level of overstrain becomes smaller the influence of the BE is considerably reduced. As a result, the SIFs due to 100% BEDA differ by less than 10% as compared to 60% BEDA, and on the average the difference is only about 2–4%.

Analysis of Uniform Arrays of Three-Dimensional Unequal-Depth Cracks in a Thick-Walled Cylindrical Pressure Vessel

2003 ◽  
Vol 125 (4) ◽  
pp. 425-431 ◽  
Author(s):  
M. Perl ◽  
B. Ostraich
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Three Dimensional ◽  
Fe Method ◽  
Depth Level ◽  
Interaction Range ◽  
Wide Range ◽  
Displacement Extrapolation Method

The effect of crack depth unevenness on the mode I stress intensity factor (SIF) distributions along the fronts of semi-elliptical surface cracks is studied. These three-dimensional radial cracks pertain to large uniform arrays of unequal-depth cracks emanating from the bore of a pressurized thick-walled cylinder. The analysis is based on the “two crack depth level model,” previously proposed, and is performed via the finite element (FE) method employing singular elements along the crack front. The distribution of KIP-the stress intensity factor due to pressurization, for numerous uneven array configurations bearing n=n1+n2=8 to 128 cracks, a wide range of crack depth to wall thickness ratios, a1/t=0.01 to 0.4, and various crack ellipticities, a1/c1=0.3 to 1.5, are evaluated for a cylinder of radii ratio Ro/Ri=2. To increase the accuracy of the evaluated SIFs an existing improved version of the displacement extrapolation method is used. The results clearly indicate that unevenness, as reflected in KIP distributions, depends on both the number of cracks in the array as well as on the cracks’ depths and ellipticities. The “interaction range” for the various configurations of uneven crack arrays is evaluated. The range of influence between adjacent cracks on the maximal SIF, KPmax, is found to be dependent on the density of the array, as reflected in the inter-crack aspect-ratio, as well as on the cracks’ elipticity.

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