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.

The Impact of the Bauschinger Effect on Stress Concentrations and Stress Intensity Factors for Eroded Autofrettaged Thick Cylindrical Pressure Vessels

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Bauschinger Effect ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Intensity Factors ◽  
Stress Concentrations ◽  
Von Mises ◽  
The Impact

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) semicircular erosions of relative depths of 1%–10% 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.

Cracks Emanating From an Erosion in a Pressurized Autofrettaged Thick-Walled Cylinder—Part I: Semi-Circular and Arc Erosions

1998 ◽  
Vol 120 (4) ◽  
pp. 349-353 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
H. Fang
Keyword(s):  
Stress Intensity Factor ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Mode I ◽  
Displacement Method ◽  
Nodal Displacement ◽  
Short Cracks ◽  
Fem Method ◽  
Von Mises ◽  
Walled Cylinder

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from the erosion’s deepest point in an autofrettaged, pressurized, thick-walled cylinder are investigated. The problem is solved via the FEM method and knowledge of the asymptotic behavior of short cracks. Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs are evaluated for a variety of relative crack lengths, a0/W = 0.01 – 0.45, emanating from the tip of erosions of different geometries. In Part I of this paper, two configurations are considered: (a) semi-circular erosions of relative depths of 5 percent of the cylinder’s wall thickness, W; and (b) arc erosions for several dimensionless radii of curvature, r′/W = 0.05 – 0.4. While deep cracks are almost unaffected by the erosion, the effective SIF for relatively short cracks is found to be significantly enhanced by the presence and geometry of the erosion and might reduce the vessel’s fatigue life.

The Influence of Multiple Axial Erosions on a Three-Dimensional Crack in Determining the Fatigue Life of Autofrettaged Pressurized Cylinders

2001 ◽  
Vol 124 (1) ◽  
pp. 1-6 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
Q. Ma
Keyword(s):  
Fatigue Life ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Separation Distance ◽  
The Finite Element Method ◽  
Short Cracks ◽  
Order Of Magnitude ◽  
Von Mises ◽  
Walled Cylinder

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from an erosion’s deepest point in a multiply eroded, autofrettaged, pressurized, thick-walled cylinder are investigated. The problem is solved via the finite element method (FEM). Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs are evaluated for a variety of relative crack depths, a0/t=0.01-0.40, and crack ellipticities, a0/c=0.5-1.5, emanating from the tip of erosions of different geometry, namely: (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=0.3-2.0. The erosion separation angle, α, is taken from 7 to 360 deg. Deep cracks are found to be almost unaffected by the erosion. The effective SIF for relatively short cracks is enhanced by the presence, separation distance and geometry of the erosion, as well as the crack geometry, and may result in a significant decrease in the vessel’s fatigue life of up to an order of magnitude.

The Influence of Multiple Axial Erosions on the Fatigue Life of Autofrettaged Pressurized Cylinders

2001 ◽  
Vol 123 (3) ◽  
pp. 293-297 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
Q. Ma
Keyword(s):  
Fatigue Life ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Dimensional Problem ◽  
The Finite Element Method ◽  
Displacement Method ◽  
Short Cracks ◽  
Order Of Magnitude ◽  
Von Mises ◽  
Walled Cylinder

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from an erosion’s deepest point in a multiply eroded, autofrettaged, pressurized, thick-walled cylinder are investigated. The problem is simulated as a two-dimensional problem and is solved via the finite element method. Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs are evaluated for a variety of relative crack lengths, a0/t=0.01-0.45 emanating from the tip of erosions of different geometries, namely, (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 SIF for relatively short cracks is found to be increased by the presence of the erosion, which in turn may result in a significant decrease in the vessel’s fatigue life of up to an order of magnitude. Deep cracks are found to be almost unaffected by the erosion.

A Finite Element Study of the Effect of Partial Autofrettage on the Fatigue Life of Thick-Walled Cylinders Containing Erosions and Cracks

2011 ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Stress Intensity ◽  
Life Stress ◽  
Bauschinger Effect ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Practical Importance ◽  
External Loading ◽  
Residual Stress Field

For the investigation of cracked problems in thick-walled pressurized cylindrical vessels, the displacement-based finite element method has become one of the main computational tools to extract stress intensity results for their fatigue life predictions. The process of autofrettage, practically from partial autofrettage level of 30% to full autofrettage level of 100%, is known to introduce favorable compressive residual hoop stresses at the cylinder bore in order to increase its service life. In order to extract the fatigue life, stress intensity factors (SIFs) need to be obtained a priori. The necessity for determining SIFs and their practical importance are well understood. However, it is usually not a trivial task to obtain the SIFs required since the SIFs largely depend on not only the external loading scenarios, but also the geometrical configurations of the cylinder. Our recent work has shown that the Bauschinger Effect (BE) may come into play and affect the effective SIFs significantly for an eroded fully autofrettaged thick-walled cylinder. In this study, we further investigate the SIFs for the Bauschinger effect dependent autofrettage (BEDA) and the Bauschinger effect independent autofrettage (BEIA) at various autofrettage levels. The crack is considered to emanate from the erosion’s deepest point in a multiply eroded cylinder. The commercial finite element package, ANSYS v12, was employed to perform the necessary analysis. A two-dimensional model, analogous to the authors’ previous studies, has been adopted for this investigation. The residual stress field of autofrettage process, based on von Mises yield criterion, is simulated by thermal loading. The combined SIFs are evaluated for a variety of relative crack lengths with cracks emanating from the tip of erosions with various geometrical configurations and span angles. 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 at the same autofrettage level, 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 may be considerably affected by BE as well as by the level of partial autofrettage.

A Study of the Combined Effects of Erosions, Cracks and Partial Autofrettage on the Stress Intensity Factors of a Thick Walled Pressurized Cylinder

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Q. Ma ◽  
C. Levy ◽  
M. Perl
Keyword(s):  
Finite Element ◽  
Fatigue Life ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Bauschinger Effect ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Practical Importance ◽  
External Loading ◽  
Intensity Factors

For the investigation of cracked problems in thick-walled pressurized cylindrical vessels, the displacement-based finite element method has become one of the main computational tools to extract stress intensity results for their fatigue life predictions. The process of autofrettage, practically from the partial autofrettage level of 30% to full autofrettage level of 100%, is known to introduce favorable compressive residual hoop stresses at the cylinder bore in order to increase its service life. In order to extract the fatigue life, stress intensity factors (SIFs) need to be obtained a priori. The necessity for determining SIFs and their practical importance are well understood. However, it is usually not a trivial task to obtain the SIFs required since the SIFs largely depend on not only the external loading scenarios, but also the geometrical configurations of the cylinder. Our recent work has shown that the Bauschinger effect (BE) may come into play and affect the effective SIFs significantly for an eroded fully autofrettaged thick-walled cylinder. In this study, we further investigate the SIFs for the Bauschinger effect dependent autofrettage (BEDA) and the Bauschinger effect independent autofrettage (BEIA) at various autofrettage levels. The crack is considered to emanate from the erosion's deepest point in a multiply eroded cylinder. The commercial finite element package, ANSYS v12, was employed to perform the necessary analysis. A two-dimensional model, analogous to the authors' previous studies, has been adopted for this investigation. The residual stress field of autofrettage process, based on von Mises yield criterion, is simulated by thermal loading. The combined SIFs are evaluated for a variety of relative crack lengths with cracks emanating from the tip of erosions with various geometrical configurations and span angles. 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 at the same autofrettage level, 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 may be considerably affected by BE as well as by the level of partial autofrettage.

The Influence of Finite Three Dimensional Multiple Axial Erosions on the Fatigue Life of Partially Autofrettaged Pressurized Cylinders

2002 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
Q. Ma
Keyword(s):  
Thermal Loading ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Rapid Decrease ◽  
Mode I ◽  
Displacement Method ◽  
Nodal Displacement ◽  
Fem Method ◽  
Von Mises ◽  
Walled Cylinder

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from the farthest erosion’s deepest point in a finitely or fully multiply eroded, partially autofrettaged, pressurized, thick-walled cylinder is investigated. The problem is solved via the FEM method. Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs were evaluated for a variety of relative crack depths, a/t = 0.01 – 0.30 and crack ellipticities, a/c = 0.5 – 1.5 emanating from the tip of the erosion of various geometries, namely, a) semi-circular erosions of relative depths of 1–10% of the cylinder’s wall thickness, t; b) arc erosions for several dimensionless radii of curvature, r′/t = 0.05 – 0.3; and C) semi-elliptical erosions with ellipticities of d/h = 0.5 – 1.5. In the cases of finite erosions, the semi-erosion length to the semicrack length, Le/c, was between 2 and 10, erosion angular spacing, α, was between 7 and 120 degrees, whereas autofrettage effects investigated were for 30%, 60% and 100% autofrettage. The normalized SIFs and the normalized effective SIFs of a crack emanating from the farthest finite erosion are found to rise sharply for values of Le/c < 3. Both the normalized SIF and normalized effective SIF values are mitigated as the amount of partial autofrettage increases with the most rapid decrease occurring between 0–60% autofrettage. The purpose of this study is to detail these findings.

The Influence of Finite Three-Dimensional Multiple Axial Erosions on the Fatigue Life of Partially Autofrettaged Pressurized Cylinders

2003 ◽  
Vol 125 (4) ◽  
pp. 379-384 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
Q. Ma
Keyword(s):  
Thermal Loading ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Rapid Decrease ◽  
Mode I ◽  
Displacement Method ◽  
Nodal Displacement ◽  
Fem Method ◽  
Von Mises ◽  
Walled Cylinder

Erosion geometry effects on the mode I stress intensity factor (SIF) for a crack emanating from the farthest erosion’s deepest point in a multiply, finite-length or full-length eroded, partially autofrettaged, pressurized, thick-walled cylinder is investigated. The problem is solved via the FEM method. Autofrettage, based on von Mises’ yield criterion, is simulated by thermal loading and SIFs are determined by the nodal displacement method. SIFs were evaluated for a variety of relative crack depths, a/t=0.01-0.30 and crack ellipticities, a/c=0.5-1.5 emanating from the tip of the erosion of various geometries, namely, (a) semi-circular erosions of relative depths of 1–10% of the cylinder’s wall thickness, t; (b) arc erosions for several dimensionless radii of curvature, r′/t=0.05-0.3; and (c) semi-elliptical erosions with ellipticities of d/h=0.5-1.5. In the cases of finite erosions, the semi-erosion length to the semi-crack length, Le/c, was between two and ten, erosion angular spacing, α, was between 7 and 120 degrees, whereas percent autofrettage investigated included 30%, 60%, and 100%. The normalized SIFs and the normalized effective SIFs of a crack emanating from the farthest finite erosion are found to rise sharply for values of Le/c<3. Both the normalized SIF and normalized effective SIF values are mitigated as the amount of partial autofrettage increases with the most rapid decrease occurring between 0–60% autofrettage. The purpose of this study is to detail these findings.

Erosions and Their Effect on the Fatigue Life of Thick Walled, Autofrettaged, Pressurized Vessels

2003 ◽  
Vol 125 (3) ◽  
pp. 242-247 ◽  
Author(s):  
C. Levy ◽  
M. Perl ◽  
Q. Ma
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Thermal Loading ◽  
Yield Criterion ◽  
Intensity Factors ◽  
Displacement Method ◽  
Cylinder Length ◽  
Fem Method ◽  
Von Mises

This paper summarizes the results that have been found in evaluating the effect of erosions on thick walled, autofrettaged, pressurized, cracked vessels. The problem is solved numerically via the FEM method. Autofrettage, based on von Mises yield criterion, is simulated by thermal loading and stress intensity factors (SIF’s) are determined by the nodal displacement method. SIF’s were evaluated for a variety of relative crack depths a/t and crack ellipticities a/c emanating from the tip of the erosion of various geometries, namely, (a) semi-circular erosions of small relative depths of the cylinder’s wall thickness t; (b) arc erosions for several dimensionless radii of curvature r′/t; and (c) semi-elliptical erosions with ellipticities of d/h. Other parameters evaluated were, in the cases of finite erosions, the semi-erosion length to the semicrack length Le/c, the erosion angular spacing α, and the autofrettage level. First, we summarize the differences found between a vessel with one erosion and one with multiple erosions. We show that for full cylinder length erosions, the erosions tend to make smaller cracks more dangerous than larger cracks in fully autofrettaged vessels and that as the crack grows the stress intensity factor initially decreases. We then show that as the crack grows further, the effect is to increase the effective stress intensity factor (SIF) but also to practically void the existence of the erosion. We show further that lower levels of autofrettage will lead to higher effective SIF’s but that partially eroded cylinders (cylinders where erosions are a fraction of the cylinder length) lead to lower SIF’s. Affecting these values in all cases, of course, are the erosion geometry and depth as well as the crack geometry and depth.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

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