Autofrettage of a Spherical Pressure Vessel

2007 ◽  
Author(s):  
Anthony P. Parker ◽  
Xiaoping Huang
Keyword(s):  
Close Agreement ◽  
Bauschinger Effect ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Numerical Procedure ◽  
Analytic Solutions ◽  
Spherical Vessel ◽  
Steel Vessel ◽  
Von Mises ◽  
Spherical Pressure

There is a numerical procedure for modeling autofrettage of thick-walled cylinders that incorporates Bauschinger effect as a function of prior plastic strain and Von Mises’ yield criterion. In this paper the numerical procedure is extended to solve the analogous problem of a spherical, thick walled steel vessel. An equivalent new analytical solution for the case of a spherical vessel is also formulated. The analytical and numerical solutions are shown to be in close agreement. It is demonstrated numerically that a re-autofrettage procedure, previously proposed for cylindrical vessels, may be extremely beneficial for spherical vessels. Additional commentary is provided on the limitations of certain analytic solutions.

Autofrettage and Reautofrettage of a Spherical Pressure Vessel

2006 ◽  
Vol 129 (1) ◽  
pp. 83-88 ◽  
Author(s):  
A. P. Parker ◽  
X. Huang
Keyword(s):  
Close Agreement ◽  
Bauschinger Effect ◽  
Numerical Solutions ◽  
Yield Criterion ◽  
Numerical Procedure ◽  
Analytic Solutions ◽  
Spherical Vessel ◽  
Steel Vessel ◽  
Von Mises ◽  
Spherical Pressure

There is a numerical procedure for modeling autofrettage of thick-walled cylinders that incorporates the Bauschinger effect as a function of prior plastic strain and Von Mises’ yield criterion. In this paper the numerical procedure is extended to solve the analogous problem of a spherical, thick walled steel vessel. An equivalent new analytical solution for the case of a spherical vessel is also formulated. The analytical and numerical solutions are shown to be in close agreement. It is demonstrated numerically that a reautofrettage procedure, previously proposed for cylindrical vessels, may be extremely beneficial for spherical vessels. Additional commentary is provided on the limitations of certain analytic solutions.

Limit pressure for a spherical vessel with a circumferential slot at its junction with a radial cylindrical protruding branch

1987 ◽  
Vol 22 (4) ◽  
pp. 215-227 ◽  
Author(s):  
M Robinson ◽  
C S Lim ◽  
R Kitching
Keyword(s):  
Spherical Shell ◽  
Lower Bounds ◽  
Yield Criterion ◽  
Spherical Vessel ◽  
Non Linear Programming ◽  
Limit Pressure ◽  
Wide Range ◽  
Cylindrical Branch ◽  
Von Mises ◽  
Plastic Limit Pressure

One of the requirements of the two criteria method of safety assessment of a pressure vessel with a defect is an estimate of the plastic limit pressure. Here the defect is in a spherical shell close to its junction with a protruding radial cylindrical branch. The defect is assumed to be an axisymmetric circumferential slot of uniform depth on the outer surface of the shell. Lower bounds to the limit pressure are calculated for a wide range of geometries. The material is assumed to obey the von Mises yield criterion and a non-linear programming method is used to give optimum lower bounds. Data is supplied for spherical shell radius to thickness ratios from 25 to 100, nozzle radius to vessel radius ratios from 0 to 0.4, nozzle to vessel thickness ratios from 0.25 to 1.0 and ligament thickness to vessel thicknesses (ligament efficiencies) of 0 to 1. Slot widths vary from the significant to the infinitesimal, where it becomes a crack. Vessels of some proportions were shown to have their limit pressures reduced only a little by very low ligament efficiencies.

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.

scholarly journals Airy-based equilibrium mesh-free method for static limit analysis of plane problems

2016 ◽  
Vol 38 (3) ◽  
pp. 167-179
Author(s):  
Canh V. Le ◽  
Phuc L. H. Ho ◽  
Hoa T. Nguyen
Keyword(s):  
Limit Analysis ◽  
Yield Criterion ◽  
A Priori ◽  
Numerical Procedure ◽  
Equilibrium Equations ◽  
Mesh Free ◽  
Arbitrary Geometries ◽  
Mesh Free Method ◽  
Von Mises ◽  
Lower Bound Limit Analysis

This paper presents a numerical procedure for lower bound limit analysis of plane problems governed by von Mises yield criterion. The stress fields are calculated based on the Airy function which is approximated using the moving least squares technique. With the use of the Airy-based equilibrium mesh-free method, equilibrium equations are ensured to be automatically satisfied a priori, and the size of the resulting optimization problem is reduced significantly. Various plane strain and plane stress with arbitrary geometries and boundary conditions are examined to illustrate the performance of the proposed procedure.

Limit pressures for spherical vessels with radial branches of differing protrusion lengths

1987 ◽  
Vol 22 (4) ◽  
pp. 209-214 ◽  
Author(s):  
M Robinson ◽  
R Kitching ◽  
C S Lim
Keyword(s):  
Yield Criterion ◽  
Branch Pipe ◽  
Plastic Limit ◽  
Linear Programming Method ◽  
Rigid Plastic ◽  
Design Rules ◽  
Non Linear Programming ◽  
Von Mises ◽  
Plastic Limit Pressure ◽  
Spherical Pressure

The effectiveness of the length by which a radial branch pipe extends within a spherical pressure vessel is discussed with reference to the plastic limit pressure of the vessel and the design rules of BS 5500. Lower bound limit pressures are calculated using a non-linear programming method, the stress resultants being expressed in polynomial form. The material was assumed to be rigid-plastic and to obey the von Mises yield criterion.

Analytical Solutions of Crack Tip Plasticity Zone Shape for a Semi-Infinite Crack

2003 ◽  
Author(s):  
Peihua Jing ◽  
Tariq Khraishi ◽  
Larissa Gorbatikh
Keyword(s):  
Plane Strain ◽  
Plane Stress ◽  
Analytical Solutions ◽  
Yield Criterion ◽  
Plasticity Zone ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Classical Plasticity ◽  
Elastic Perfectly Plastic ◽  
Von Mises

In this work, closed-form analytical solutions for the plasticity zone shape at the lip of a semi-infinite crack are developed. The material is assumed isotropic with a linear elastic-perfectly plastic constitution. The solutions have been developed for the cases of plane stress and plane strain. The three crack modes, mode I, II and III have been considered. Finally, prediction of the plasticity zone extent has been performed for both the Von Mises and Tresca yield criterion. Significant differences have been found between the plane stress and plane strain conditions, as well as between the three crack modes’ solutions. Also, significant differences have been found when compared to classical plasticity zone calculations using the Irwin approach.

scholarly journals Determination of Avalanche Dynamics Friction Coefficients from Measured Speeds

1983 ◽  
Vol 4 ◽  
pp. 170-173 ◽  
Author(s):  
D. M. McClung ◽  
P. A. Schaerer
Keyword(s):  
Complex Terrain ◽  
Sliding Friction ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Dynamics Model ◽  
Friction Coefficients ◽  
Turbulent Friction ◽  
Constant Friction ◽  
Avalanche Dynamics

An avalanche dynamics model, appropriate for complex terrain, for real avalanche paths was developed by Perla, Cheng and McClung in 1980. The model has two friction terms, one for sliding friction which is independent of speed, and one for turbulent friction which is proportional to V2, where V is the centre-of-mass speed along the incline. By introducing speed maxima for avalanches, along with start and stop reference positions, it is possible to determine the the two constant friction coefficients for the model. When this is done, it is found that speed data often exceed a model speed limit implied by the application of V = 0 at the start and stop positions. This effect is illustrated by analytic solutions of the relevant equations, as well as numerical solutions for actual avalanche paths. Some limitations and properties of the fundamental modelling are outlined and suggestions given for future use of such models.

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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