Loading and Unloading of Thick-Walled Cylindrical Pressure Vessels of Strain-Hardening Material

1994 ◽  
Vol 116 (2) ◽  
pp. 105-109 ◽  
Author(s):  
A. Loghman ◽  
M. A. Wahab
Keyword(s):  
Residual Stresses ◽  
Strain Hardening ◽  
Yield Criterion ◽  
Strain Curve ◽  
Pressure Vessels ◽  
Critical Conditions ◽  
Hardening Material ◽  
Wide Range ◽  
Reverse Yielding ◽  
Von Mises

A thick-walled closed-end cylinder of isotropic, homogeneous and strain-hardening material is considered in this study. Loading is assumed to consist of a temperature gradient as well as an internal pressure. Unloading is completely elastic without considering a Bauschinger effect. A generalized plane strain case in which the material obeys Von Mises yield criterion is studied. Using the yield criterion, critical conditions for a wide range of loading combinations and thickness ratios are investigated. After the critical condition is established, load is increased beyond the critical values and calculations are made for plastic stresses and strains and progress of plastic zone using an incremental theory of plasticity. Residual stresses are obtained as the cylinder is unloaded from a 25 and 50-percent overstrained condition. Reverse yielding is not considered while the residual stresses at the onset of reverse yielding are calculated. Loading function is assumed to follow the stress-strain curve of SUS 304 at a constant temperature of 400°C, which is selected from the experimental work of earlier researchers.

THE BAUSCHINGER AND HARDENING EFFECT ON RESIDUAL STRESSES IN THICK-WALLED CYLINDERS OF SUS 304

2003 ◽  
Vol 26 (4) ◽  
pp. 361-372
Author(s):  
A. Ghorbanpour ◽  
A. Loghman ◽  
H. Khademizadeh ◽  
M. Moradi
Keyword(s):  
Numerical Model ◽  
Residual Stresses ◽  
Yield Criterion ◽  
Material Model ◽  
304 Stainless Steel ◽  
Hardening Material ◽  
Effect Factor ◽  
Reverse Yielding ◽  
Von Mises Yield Criterion ◽  
Von Mises

A thick-walled cylinder of strain hardening material with closed ends, which is assumed to obey Von-Mises yield criterion is considered. An elastoplastic and residual stress analysis of thick-walled cylinders is performed with the incremental theory of plasticity. Critical pressures of direct and reverse yielding are investigated using the Von-Mises yield criterion as well as the Bauschinger effect factor (BEF). The material selected is SUS 304 stainless steel. The material's loading and unloading properties including the (BEF) are obtained experimentally and represented mathematically as a continuous function of effective plastic strain. The material model and the BEF have been incorporated in an analytical-numerical model so as to predict the cylinders plastic and residual stresses as well as the critical pressures of direct and reverse yielding. The analytical-numerical model for the prediction of critical inner pressure, plastic stress distributions and the subsequent residual stresses of thick-walled cylinders is validated by using experimental results. Residual stresses with and without the BEF are obtained and the corresponding results are compared. In the case study of a specific cylinder (Radii ratio of β=2), it has been concluded that residual stresses subsequent to a 45% overstrained condition are at the onset of reverse yielding when the BEF is considered.

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.

Investigation of Residual Stress Development During Swage Autofrettage, Using Finite Element Analysis

2009 ◽  
Author(s):  
Michael C. Gibson ◽  
Amer Hameed ◽  
John G. Hetherington
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Axial Stress ◽  
Slope Angle ◽  
Subsequent Development ◽  
Element Model ◽  
Pressure Vessels ◽  
Element Analysis ◽  
Reverse Yielding

Swaging is one method of autofrettage, a means of pre-stressing high-pressure vessels to increase their fatigue lives and load bearing capacity. Swaging achieves the required deformation through physical interference between an oversized mandrel and the bore diameter of the tube, as it is pushed through the tube. A Finite Element model of the swaging process was developed, in ANSYS, and systematically refined, to investigate the mechanism of deformation and subsequent development of residual stresses. A parametric study was undertaken, of various properties such as mandrel slope angle, parallel section length and friction coefficient. It is observed that the axial stress plays a crucial role in the determination of the residual hoop stress and reverse yielding. The model, and results obtained from it, provides a means of understanding the swaging process and how it responds to different parameters. This understanding, coupled with future improvements to the model, potentially allows the swaging process to be refined, in terms of residual stresses development and mandrel driving force.

scholarly journals A Finite Element Study of the Residual Stress and Deformation in Hemispherical Contacts

2005 ◽  
Vol 127 (3) ◽  
pp. 484-493 ◽  
Author(s):  
Robert Jackson ◽  
Itti Chusoipin ◽  
Itzhak Green
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Residual Stresses ◽  
Yield Criterion ◽  
Contact Region ◽  
Element Model ◽  
Von Mises Stress ◽  
Contact Radius ◽  
Perfectly Plastic ◽  
Von Mises

This work presents a finite element model (FEM) of the residual stresses and strains that are formed after an elastoplastic hemispherical contact is unloaded. The material is modeled as elastic perfectly plastic and follows the von Mises yield criterion. The FEM produces contours for the normalized axial and radial displacements as functions of the removed interference depth and location on the surface of the hemisphere. Contour plots of the von Mises stress and other stress components are also presented to show the formation of the residual stress distribution with increasing plastic deformation. This work shows that high residual von Mises stresses appear in the material pileup near the edge of the contact area after complete unloading. Values are defined for the minimum normalized interference, that when removed, results in plastic residual stresses. This work also defines an interference at which the maximum residual stress transitions from a location below the contact region and along the axis of symmetry to one near to the surface at the edge of the contact radius (within the pileup).

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.

scholarly journals Finite Difference Solution of Elastic-Plastic Thin Rotating Annular Disk with Exponentially Variable Thickness and Exponentially Variable Density

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Sanjeev Sharma ◽  
Yadav Sanehlata
Keyword(s):  
Finite Difference ◽  
Variable Thickness ◽  
Yield Criterion ◽  
Variable Density ◽  
Hardening Material ◽  
Annular Disk ◽  
Elastic Plastic ◽  
Flat Disk ◽  
Finite Difference Solution ◽  
Von Mises

Elastic-plastic stresses, strains, and displacements have been obtained for a thin rotating annular disk with exponentially variable thickness and exponentially variable density with nonlinear strain hardening material by finite difference method using Von-Mises' yield criterion. Results have been computed numerically and depicted graphically. From the numerical results, it can be concluded that disk whose thickness decreases radially and density increases radially is on the safer side of design as compared to the disk with exponentially varying thickness and exponentially varying density as well as to flat disk.

A Simple Technique for Calculating Shakedown Loads in Pressure Vessels

1972 ◽  
Vol 186 (1) ◽  
pp. 45-52 ◽  
Author(s):  
W. A. Macfarlane ◽  
G. E. Findlay
Keyword(s):  
Internal Pressure ◽  
Simple Technique ◽  
Yield Criterion ◽  
Pressure Vessels ◽  
Elastic Stresses ◽  
Graphical Construction ◽  
Wide Range ◽  
Current Design ◽  
Yield Behaviour ◽  
Line Construction

A fundamental examination has been made of the post-yield behaviour at discontinuities in pressure vessels with a view to determining shakedown loads. The results of this indicate that a simple graphical construction can be devised whereby such loads are easily determined with only a knowledge of the elastic stresses and a yield criterion; in particular, a ‘five line construction’ method is suggested which can be applied to a wide range of engineering stress problems. The method is exemplified by a study of shakedown loads for both flush cylinder-sphere and cylinder-cylinder intersections under internal pressure, and the implications of the results in terms of current design philosophies are discussed.

Analytical and Numerical Modelling of Sheet Plate Cold Expanded Hole Subjected to Reverse Yielding

2019 ◽  
Author(s):  
Abdel-Hakim Bouzid ◽  
Hacène Touahri
Keyword(s):  
Aluminum Alloy ◽  
Residual Stresses ◽  
Strain Hardening ◽  
Analytical Model ◽  
Life Assessment ◽  
Thick Wall ◽  
Plastic Behavior ◽  
Alloy Plate ◽  
Proposed Model ◽  
Reverse Yielding

Abstract Predicting and mitigating the effect of expansion induced by cold working on damage fatigue accumulation and life assessment of aluminum alloy is a common process in the aeronautics industry, especially to extend the fatigue lifetime of their structures. This process aims at generating residual stresses and increases thereby the strength of hollow parts including aluminum alloy plate holes that are employed in manufacturing the airplane fuselage. An analytical model to predict the residual stresses induced during the expansion process due to the cold strain hardening is developed. The proposed model is based on an elasto-plastic behavior, with a power law material behaviour and relies on the theory of autofrettaged thick wall cylinders in plane strain state to which reverse yielding is incorporated. The application of Hencky theory of plastic deformation is used in the analytical calculations of the stresses and strains. Finite-element numerical simulation is used to validate the developed analytical model by comparison of the radial, Hoop, longitudinal and equivalent stresses for both the loading and unloading phases. The obtained results show clearly that the level of residual stresses depends mainly on the interference and strain hardening while reverse yielding reduce the stresses near the hole.

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