The Combined Stress Intensity Factors of Multiple Longitudinally Coplanar Cracks in Autofrettaged Pressurized Tubes Influenced by the Bauschinger Effect

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
S. Kotagiri
Keyword(s):  
Stress Intensity ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Crack Spacing ◽  
Pressure Effects ◽  
3D Analysis ◽  
Combined Stress ◽  
Spacing Ratio ◽  
Walled Cylinder

The influence of the Bauschinger effect (BE) on the three dimensional, Mode I, combined 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 combined SIFs, KIN, that depend on pressure effects and the “realistic”—Bauschinger effect dependent Autofrettage (BEDA), or, that depend on pressure effects and the “ideal”—Bauschinger effect independent autofrettage (BEIA), are obtained and compared for crack depth to wall thickness, a∕t=0.01–0.25; crack ellipticity, a∕c=0.5–1.5; crack spacing ratio, 2c∕d=0.25–0.75; and autofrettage level, e=30%, 60%, and 100%. The 3D analysis is performed via the finite element 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. The combined SIF, KIN, is found to vary along the crack front with the maximum determined by the crack ellipticity, crack depth, and crack spacing ratio. For a partially autofrettaged cylinder, the influence of the BE on the combined SIF, KIN, is substantially reduced as the level of overstrain becomes smaller. For some cases, when comparing like crack distributions, the KIN values obtained from the BEDA model are found to be as much as 100% higher than the KIN values that are computed using the BEIA model. A pressurized thick-walled cylinder with BEDA can be most critical when small cracks are farther apart. As crack depth increases, or when the spacing between cracks is smaller, the SIFs increase. Though the differences in the BEDA SIF, KIA, between e=100% and 60% are small (7–15%, in most cases), the increased level of autofrettage produces a 23–30% decrease in the combined SIF values, KIN. In certain cases, the BEIA model implies an infinite fatigue life, whereas the BEDA model for the same parameters implies a finite life. Therefore, it is important to perform a full 3D analysis to determine the real life cycle of the pressurized cylinder for materials that exhibit the BE.

The Influence of the Bauschinger Effect on the Combined Stress Intensity Factors of Multiple Longitudinally Coplanar Cracks in Autofrettaged Pressurized Cylinders

2006 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
S. Kotagiri
Keyword(s):  
Stress Intensity ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Real Life ◽  
Crack Spacing ◽  
Combined Stress ◽  
Fe Method ◽  
Spacing Ratio ◽  
Walled Cylinder

The influence of the Bauschinger Effect (BE) on the three dimensional, Mode I, Combined 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 combined SIFs, KIN, that depend on both the “realistic” - Bauschinger Effect Dependent Autofrettage (BEDA) and “ideal” - Bauschinger Effect Independent Autofrettage (BEIA) are obtained and compared for crack to wall thickness, a/t = 0.01–0.25; crack ellipticity, a/c = 0.5–1.5; crack spacing ratio, 2c/d = 0.25–0.75; and autofrettage level, e = 30, 60 and 100%. 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. The KIN is found to vary along the crack front with the maximum determined by the crack ellipticity, crack depth and crack spacing ratio. For a partially autofrettaged cylinder, the influence of the BE on the combined SIF, KIN, is considerably reduced as the level of overstrain becomes smaller. For some cases, when comparing like crack distributions, the KIN values obtained from the BEDA model are found to be as much as 100% higher than the KIN values that are computed using the BEIA model. A pressurized thick-walled cylinder with BEDA can be most dangerous when small cracks have small spacing ratio, i.e., when the cracks are farther apart. As crack length increases, or, for increased spacing ratio when the spacing between cracks is smaller, the SIFs increase. Though the differences in the BEDA SIF, KIA, between e = 100% and 60% are small (7–15%, in most cases), the increased level of autofrettage produces a 23–30% decrease in the combined SIF values, KIN. In certain cases, the BEIA model implies an infinite fatigue life, whereas the BEDA model for the same parameters implies a finite life. Therefore, it is important to perform a full 3-D analysis to determine the real life cycle of the pressurized cylinder for materials that exhibit the Bauschinger effect.

The Influence of the Bauschinger Effect on 3D Stress Intensity Factors for Internal Radial Cracks in a Fully or Partially Autofrettaged Gun Barrel

2005 ◽  
Vol 128 (2) ◽  
pp. 233-239 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
V. Rallabhandy
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Three Dimensional ◽  
Crack Plane ◽  
3D Analysis ◽  
Wide Range

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 three-dimensional (3D) analysis is performed via the finite element 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 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 toward 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 <10% as compared to 60% BEDA, and on the average the difference is only about 2–4%.

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%.

The Influence of the Bauschinger Effect on the Combined Stress Intensity Factors for 3-D Internal Radial Cracks in a Fully or Partially Autofrettaged Gun Barrel

2005 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
V. Rallabhandy
Keyword(s):  
Fatigue Life ◽  
Stress Intensity ◽  
Crack Front ◽  
Bauschinger Effect ◽  
Pressure Ratio ◽  
Crack Depth ◽  
Internal Surface ◽  
Fe Method ◽  
Gun Barrel ◽  
Wide Range

The influence of the Bauschinger Effect (BE) on KIN — the combined, Mode I, 3-D Stress Intensity Factor (SIF) distributions for arrays of radial, internal, surface cracks emanating from the bore of a fully or partially autofrettaged gun barrel is investigated. A thorough comparison between the combined SIFs for a “realistic” - Bauschinger Effect Dependent Autofrettage (BEDA) and those for an “ideal” - Bauschinger Effect Independent Autofrettage (BEIA) is performed. 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 and more than 1200 different crack configurations are analyzed. SIFs for numerous crack arrays (n=1 to 64 cracks), a wide range of crack depth to wall thickness ratios (a/t=0.01 to 0.2), various ellipticities (a/c=0.5 to 1.5), several values of the yield-stress to pressure ratio (ψ=σyp/p=1.93 to 3.55) and different levels of autofrettage (ε=30% to 100%) are evaluated. The level of autofrettage efficiency for all BEDA cases is determined, and is thoroughly compared with that of BEIA. The largest combined SIF KNmax can be found at any angular location along the crack front and can reach its largest values for arrays of any number of cracks from 1 to 16, and therefore needs to be evaluated for each particular case. The Bauschinger Effect is found to have a dramatic detrimental impact on the fatigue life of the gun barrel. Even in the case were autofrettage has its minimal beneficial effect, (ψ=1.93), the BE can reduce the fatigue life of the barrel by a factor of 2 to 5. In other cases this factor can reach orders of magnitude, and in extreme cases, when autofrettage completely overcomes the pressure yielding a nil KNmax, this factor might become infinite, i.e., an infinite fatigue life for BEIA versus a finite fatigue life for BEDA. For a partially autofrettaged barrel, it is found that the lower the level of autofrettage, the smaller the Bauschinger Effect is. Increasing the level of autofrettage beyond ε=60% is found to be counterproductive, and therefore, it is not recommended.

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 Concentration and Stress Intensity for Pressurized Eroded Autofrettaged Thick Cylinders With Bauschinger Effect

2010 ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Stress Intensity ◽  
Stress Concentration ◽  
Bauschinger Effect ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Short Cracks ◽  
Finite Element Package ◽  
Von Mises ◽  
Walled Cylinder

Our previous studies have shown that stress intensity factors (SIFs) are influenced considerably from the presence of the Bauschinger Effect (BE) in thick-walled pressurized cracked cylinders. For some types of pressure vessels, such as gun barrels, working in corrosive environment, in addition to acute temperature gradients and repetitive high-pressure impulses, erosions can be practically induced. Those erosions cause stress concentration at the bore, where cracks can readily initiate and propagate. In this study, The BE on the SIFs will be investigated for a crack emanating from an erosion’s deepest point in a multiply eroded autofrettaged, pressurized thick-walled cylinder. A commercial finite element package, ANSYS, was employed to perform this type of analysis. A two-dimensional model, analogous to the authors’ previous studies, has been adopted for this new investigation. Autofrettage with and without BE, based on von Mises yield criterion, is simulated by thermal loading and the SIFs are determined by the nodal displacement method. The SIFs are evaluated for a variety of relative crack lengths, a0/t = 0.01–0.45 emanating from the tip of the erosion of different geometries including (a) semi-circular erosions of relative depths of 1–10 percent of the cylinder’s wall thickness, t; (b) arc erosions for several dimensionless radii of curvature, r′/t = 0.05–0.4; and (c) semi-elliptical erosions with ellipticities of d/h = 0.5–1.5, and erosion span angle, α, from 6 deg to 360 deg. The effective SIFs for relatively short cracks are found to be increased by the presence of the erosion and further increased due to the BE, which may result in a significant decrease in the vessel’s fatigue life. Deep cracks are found to be almost unaffected by the erosion, but are considerably affected by BE.

Mode Mixity for Circular Hollow Section X Joints With Weld Toe Cracks

2005 ◽  
Vol 127 (3) ◽  
pp. 269-279 ◽  
Author(s):  
X. Qian ◽  
Robert H. Dodds ◽  
Y. S. Choo
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Front ◽  
Mixed Mode ◽  
Crack Depth ◽  
Intensity Factors ◽  
Mode Mixity ◽  
Hollow Section ◽  
Mode Stress ◽  
Circular Hollow Section

This paper describes the mode mixity of stress-intensity factors for surface cracks at weld toes located at the saddle point in circular hollow section X joints. The remote loading applies a uniform tensile stress at the end of the brace along its axis. The three-dimensional finite element models employ mesh tieing between a topologically continuous, global mesh and a separate, local crack-front mesh. Analyses of a simple plate model that approximates key features of toe cracks at the brace-chord intersection verify the negligible effects of the recommended mesh-tieing scheme on stress intensity factors. The linear-elastic analyses compute the mixed-mode stress intensity factors along the crack front using an interaction-integral approach. The mixed-mode stress intensity factors indicate that the crack front experiences predominantly mode I loading, with KIII→0 near the deepest point on the front (ϕ=π∕2). The total crack driving force, described by the J integral, reaches a maximum value at the deepest point of the crack for the crack aspect ratio a∕c=0.25 considered here. The mode-mixity angle, ψ=tan−1(KII∕KI), at ϕ=π∕2 is compared for a range of practical X-joint configurations and crack-depth ratios. The present study demonstrates that the mode-mixity angle ψ increases with increasing brace-to-chord diameter ratio (β) and decreasing chord radius to wall thickness ratio (γ). Values of the nondimensional stress intensity factors (FI=KI∕σ¯brπa and FII=KII∕σ¯brπa), however, show an opposite trend, with higher crack driving forces for small β and large γ ratios. The variations in the brace-to-chord wall thickness ratio (τ) and the crack depth ratio (a∕t0) do not generate significant effects on the mode mixity.

Stress Intensity Factor of a Circumferential Crack in a Thick-Walled Cylinder Under Thermal Striping

2004 ◽  
Vol 126 (2) ◽  
pp. 157-162 ◽  
Author(s):  
Toshiyuki Meshii ◽  
Katsuhiko Watanabe
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Depth ◽  
Crack Arrest ◽  
Characteristic Change ◽  
Fluid Temperature ◽  
Circumferential Crack ◽  
Thermal Striping ◽  
Walled Cylinder

This paper tries to explain the interesting field data that indicate a surface axisymmetric circumferential crack inside a hollow cylinder (circumferential crack) shows tendency toward crack arrest, when the temperature of the fluid inside the cylinder experiences sinusoidal fluctuation (thermal striping). For this purpose, transient stress intensity factor (SIF) range of a circumferential crack in a finite-length thick-walled cylinder with rotation-restrained edges, under thermal striping, was analyzed. It was assumed that the fluid temperature changes sinusoidally and that heat transfer coefficient is constant. First an analytical temperature solution for the problem was obtained and it was combined with our SIF evaluation method derived based on superposition principle and Duhamel’s analogy. Then we defined the maximum SIF range as the maximum value of the SIF range during thermal striping and studied the characteristic change of this maximum SIF range with the variation of crack depth to explain the crack arrest tendency. Results showed that the maximum SIF range under thermal striping decreases monotonously when crack depth is varied to become deeper than a specific value, which corresponds to the crack arrest tendency.

Stress Intensity Factor of a Circumferential Crack in a Thick-Walled Cylinder Under Thermal Striping

2002 ◽  
Author(s):  
Toshiyuki Meshii ◽  
Katsuhiko Watanabe
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Temperature Change ◽  
Crack Depth ◽  
Crack Arrest ◽  
Fluid Temperature ◽  
Circumferential Crack ◽  
Thermal Striping ◽  
Walled Cylinder

This paper tries to explain the interesting field data that indicate a surface axisymmetric circumferential crack inside a hollow cylinder (circumferential crack) shows tendency toward crack arrest, when the temperature of the fluid inside the cylinder experiences sinusoidal fluctuation (thermal striping). Maximum stress intensity factor (SIF) range of a circumferential crack in a finite-length thick-walled cylinder with rotation-restrained edges, under thermal striping, was studied for this attempt. It was assumed that the fluid temperature changes sinusoidally and that heat transfer coefficient is constant. Results showed that the maximum SIF range under thermal striping decreases monotonously when crack depth is varied to become longer than a specific value, which corresponds to the crack arrest tendency. These results are similar to those obtained for the step temperature change. Thus, characteristics obtained for the step temperature change, such as the existence of an upper limit for the normalized crack arrest depth independent of the cylinder material and fluid temperature, are valid also for thermal striping (163 words).

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

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Residual Stress ◽  
Stress Intensity Factor ◽  
Fatigue Life ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Bauschinger Effect ◽  
Crack Depth ◽  
Internal Surface ◽  
Surface Cracks ◽  
Intensity Factors

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 the authors’ previous studies, networks of typical radial and longitudinal-coplanar, semi-elliptical, internal surface cracks have been investigated assuming both ideal and realistic full autofrettage residual stress fields (ε=100%). The aim of the present work is to extend the analysis twofold: to include various levels of partially autofrettaged cylinders and to consider configurations of closely and densely packed radial crack arrays. To accurately assess the stress intensity factors (SIFs), significant computational efforts and strategies are necessary, especially for networks with closely and densely packed cracks. This study focuses on the determination of the distributions along the crack fronts of KIP, the stress intensity factor due to internal pressure KIA, the negative stress intensity factor resulting from the residual stress field due to ideal or realistic autofrettage, and KIN, the combined SIF KIN=KIP−|KIA|. The analysis is performed for over 1000 configurations of closely and densely packed semicircular and semi-elliptical networked cracks affected by pressure and partial-to-full autofrettage levels of ε=30–100%, which is of practical benefit in autofrettaged thick-walled pressure vessels. The 3-D analysis is performed via the finite element 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%; crack depth to wall thickness ratios, a/t, from 0.01 to 0.4; and, cracks with various ellipticities of crack depth to semicrack length, a/c, from 0.2 to 2. The results clearly indicate that the combined SIFs are considerably influenced by the three dimensionality of the problem and the Bauschinger effect (BE). The Bauschinger effect is found to have a dramatic effect on the prevailing combined stress intensity factors, resulting in a considerable reduction of the fatigue life of the pressure vessel. While the fatigue life can be finite for ideal autofrettage, it is normally finite for realistic autofrettage for the same crack network. Furthermore, it has been found that there are differences in the character of the SIFs between closely packed and densely packed crack networks, namely, more dramatic drop-offs in KIA and KIN at the crack-inner bore interface for densely packed cracks further influenced by crack depth.

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