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.

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.

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 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.

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.

Overstraining of flush plain cross-bored cylinders

2004 ◽  
Vol 218 (2) ◽  
pp. 143-153 ◽  
Author(s):  
J M Kihiu ◽  
G O Rading ◽  
S M Mutuli
Keyword(s):  
Finite Element Method ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Yield Condition ◽  
Solution Technique ◽  
Stress Distributions ◽  
Dimensional Finite Element ◽  
Von Mises ◽  
Three Dimensional Finite Element ◽  
Incremental Theory Of Plasticity

A three-dimensional finite element method computer program was developed to establish the elastic-plastic, residual and service stress distributions in thick-walled cylinders with flush and non-protruding plain cross bores under internal pressure. The displacement formulation and eight-noded brick isoparametric elements were used. The incremental theory of plasticity with a 5 per cent yield condition (an element is assumed to have yielded when the effective stress is within 5 per cent of the material yield stress) and von Mises yield criterion were assumed. The frontal solution technique was used. The incipient yield pressure and the pressure resulting in a 0.3 per cent overstrain ratio were established for various cylinder thickness ratios and cross bore-main bore radius ratios. For a thickness ratio of 2.25 and a cross bore-main bore radius ratio of 0.1, the stresses were determined for varying overstrain and an optimum overstrain ratio of 37 per cent was established. To find the accuracy of the results, the more stringent yield condition of 0.5 per cent was also considered. The benefits of autofrettage were presented and alternative autofrettage and yield condition procedures proposed.

Complete Bandgap in Three-Dimensional Holey Phononic Crystals With Resonators

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Yan-Feng Wang ◽  
Yue-Sheng Wang
Keyword(s):  
Three Dimensional ◽  
Phononic Crystals ◽  
Vibration Modes ◽  
The Finite Element Method ◽  
Local Resonance ◽  
The Matrix ◽  
Order Of Magnitude ◽  
Complete Bandgap ◽  
Careful Design ◽  
Shape And Size

In this paper, the bandgap properties of three-dimensional holey phononic crystals with resonators are investigated by using the finite element method. The resonators are periodically arranged cubic lumps in the cubic holes connected to the matrix by narrow connectors. The influence of the geometry parameters of the resonators on the bandgap is discussed. In contrast to a system with cubic or spherical holes, which has no bandgaps, systems with resonators can exhibit complete bandgaps. The bandgaps are significantly dependent upon the geometry of the resonators. By the careful design of the shape and size of the resonator, a bandgap that is lower by an order of magnitude than the Bragg bandgap can be obtained. The vibration modes at the band edges of the lowest bandgaps are analyzed in order to understand the mechanism of the bandgap generation. It is found that the emergence of the bandgap is due to the local resonance of the resonators. Spring-mass models or spring-pendulum models are developed in order to evaluate the frequencies of the bandgap edges. The study in this paper is relevant to the optimal design of the bandgaps in light porous materials.

Cracks Emanating From an Erosion in a Pressurized Autofrettaged Thick-Walled Cylinder—Part II: Erosion Depth and Ellipticity Effects

1998 ◽  
Vol 120 (4) ◽  
pp. 354-358 ◽  
Author(s):  
M. Perl ◽  
C. Levy ◽  
H. Fang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Radius Of Curvature ◽  
Mode I ◽  
Constant Depth ◽  
Erosion Depth ◽  
Short Cracks ◽  
Order Of Magnitude ◽  
Two Parameters ◽  
Walled Cylinder

In Part I of this paper, the effects of constant depth erosion on the mode I stress intensity factor (SIF) were determined for a crack emanating from the erosion deepest point in a pressurized, autofrettaged, thick-walled cylinder. The erosion geometries investigated included semi-circular erosions and several arc erosions of various radii of curvature. Due to the trends found in that portion of the study, erosion depth and ellipticity are believed to have equally important impact on the SIFs. The present paper delves further into these two parameters using the following configurations: (a) semi-circular erosions of relative depths of 1–10 percent of the cylinder’s wall thickness, W; and (b) semi-elliptical erosions with ellipticities of d/h = 0.3 – 2.0. Deep cracks are found to be practically unaffected by the erosion, similar to the results presented in Part I of the paper. The effective SIF for relatively short cracks is found to be dramatically enhanced by the stress concentration factor (SCF), which encompasses the depth of the erosion as well as its radius of curvature at the tip. As a result of the increased effective SIF, a significant decrease in the vessel’s fatigue life of up to an order of magnitude may occur.

Crack Non-Circularity and Finite Erosion Effects on the 3D SIFs of a Bauschinger Modified Pressurized Thick-Walled Cylinder

2015 ◽  
Author(s):  
Qin Ma ◽  
Cesar Levy ◽  
Mordechai Perl
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Fatigue Life ◽  
Numerical Analysis ◽  
Material Properties ◽  
Thermal Loading ◽  
Circular Crack ◽  
Finite Element Package ◽  
Pressurized Cylinder ◽  
Walled Cylinder

Our previous studies have demonstrated that the 3D SIFs of a pressurized cylinder can be greatly affected by many factors. While an autofrettage process may introduce favorable residual stresses at the bore of the cylinder, other factors such as erosions and cracks, once introduced, may greatly reduce the effectiveness of the autofrettage results. In this study, we focus on how the non-circularity of cracks affects the 3D SIFs for a cylinder that contains finite erosions while keeping other conditions and material properties unchanged. Numerical analysis was performed using ANSYS, a standard commercially available finite element package. The residual stress due to any autofrettage process was simulated using the equivalent thermal loading. A closer look was given to problems with different crack configurations and how non-circularity of cracks affects the overall fatigue life of the cylinder when combined with other factors in comparison with circular crack only configurations.

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