Elasto-Plastic Stresses in Thick Walled Cylinders

2003 ◽  
Vol 125 (3) ◽  
pp. 248-252 ◽  
Author(s):  
Joseph Perry ◽  
Jacob Aboudi
Keyword(s):  
Residual Stress ◽  
Yield Criterion ◽  
Plastic Region ◽  
Weight Ratio ◽  
Theoretical Development ◽  
Cylinder Wall ◽  
Residual Stress Field ◽  
Gun Barrel ◽  
Von Mises ◽  
Made In

In the optimal design of a modern gun barrel, there are two main objectives to be achieved: increasing its strength-weight ratio and extending its fatigue life. This can be carried out by generating a residual stress field in the barrel wall, a process known as autofrettage. It is often necessary to machine the autofrettaged cylinder to its final configuration, an operation that will remove some of the desired residual stresses. In order to achieve a residual stress distribution which is as close as possible to the practical one, the following assumptions have been made in the present research on barrel analysis: A von Mises yield criterion, isotropic strain hardening in the plastic region in conjunction with the Prandtl-Reuss theory, pressure release taking into consideration the Bauschinger effect and plane stress conditions. The stresses are calculated incrementally by using the finite difference method, whereby the cylinder wall is divided into N-rings at a distance Δr apart. Machining is simulated by removing rings from both sides of the cylindrical surfaces bringing the cylinder to its final shape. After a theoretical development of the procedure and writing a suitable computer program, calculations were performed and a good correlation with the experimental results was found. The numerical results were also compared with other analytical and experimental solutions and a very good correlation in shape and magnitude has been obtained.

A 3-D Model for Evaluating the Residual Stress Field Due to Swage Autofrettage

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
J. Perry ◽  
M. Perl
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Three Dimensional ◽  
Weight Ratio ◽  
Computer Code ◽  
Residual Stress Field ◽  
Three Dimensional Model ◽  
Equilibrium Equations ◽  
Von Mises ◽  
Experimental Findings

In order to maximize the performance of modern gun barrels in terms of strength-to-weight ratio and total fatigue life, favorable compressive residual stresses are introduced to the inner portion of the barrel, commonly by the autofrettage process. There are two major autofrettage processes for overstraining the tube: the hydrostatic and the swage. There are several theoretical solutions for hydrostatic autofrettage based on Lamé’s solution and the von Mises or Tresca yield criteria. The residual stress field due to hydraulic autofrettage is treated as an axisymmetric two-dimensional problem solved in terms of the radial displacement solely. Once the Bauschinger effect was included in these models they yield very realistic results. Unlike in the case of hydraulic autofrettage, swage autofrettage needs to be modeled by a three-dimensional model. The present analysis suggests a new 3-D axisymmetric model for solving the residual stress field due to swage autofrettage in terms of both the radial and the axial displacements. The axisymmetric equilibrium equations are approximated by finite differences and solved then by Gauss–Seidel method. Using the new computer code the stresses, the strains, the displacements, and the forces are determined. A full-scale instrumented swage autofrettage test was conducted and the numerical results were validated against the experimental findings. The calculated strains, the permanent bore enlargement, and the mandrel pushing force were found to be in very good agreement with the measured values.

A 3-D Model for Evaluating the Residual Stress Field Due to Swage Autofrettage

2006 ◽  
Author(s):  
J. Perry ◽  
M. Perl
Keyword(s):  
Residual Stress ◽  
Stress Field ◽  
Three Dimensional ◽  
Weight Ratio ◽  
Computer Code ◽  
Residual Stress Field ◽  
Three Dimensional Model ◽  
Equilibrium Equations ◽  
Von Mises ◽  
Experimental Findings

In order to maximize the performance of modern gun barrels in terms of strength-to-weight ratio and total fatigue life, favorable compressive residual stresses are introduced to the inner portion of the barrel, commonly by the autofrettage process. There are two major autofrettage processes for overstraining the tube: the hydrostatic, and the swage. There are several theoretical solutions for hydrostatic autofrettage, based on Lame´’s solution and the von Mises or Tresca yield criteria. The residual stress field due to hydraulic autofrettage is treated as an axisymetric, two-dimensional problem solved in terms of the radial displacement solely. Once the Bauschinger effect was included in these models they yield very realistic results. Unlike in the case of hydraulic autofrettage, swage autofrettage needs to be modeled by a three-dimensional model. The present analysis suggests a new 3-D axisymmetric model for solving the residual stress field due to swage autofrettage in terms of both the radial and the axial displacements. The axisymetric equilibrium equations are approximated by finite differences and solved then by Gauss-Seidel method. Using the new computer code the stresses, the strains, the displacements and the forces are determined. A full-scale instrumented swage autofrettage test was conducted and the numerical results were validated against the experimental findings. The calculated strains, the permanent bore enlargement, and the mandrel pushing force were found to be in very good agreement with the measured values.

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.

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).

A Study of the Residual Stress Distribution in an Autofrettaged, Thick-Walled Cylinder With Cross-Bore

2004 ◽  
Vol 126 (4) ◽  
pp. 497-503 ◽  
Author(s):  
Amer Hameed ◽  
R. D. Brown ◽  
John Hetherington
Keyword(s):  
Residual Stress ◽  
Circumferential Stress ◽  
Stress Profile ◽  
Outer Diameter ◽  
Residual Stress Field ◽  
Element Analysis ◽  
Residual Stress Profile ◽  
Gun Barrel ◽  
The Cross ◽  
Walled Cylinder

It may be necessary to provide a radial opening such as gas evacuator holes, or an opening to operate the unlocking of the bolt mechanism by means of exhaust gases, in a gun barrel, which is a thick walled cylinder. A three dimensional finite element analysis has been performed to evaluate the effect of introducing a radial cross-bore in an autofrettaged thick-walled cylinder. From the analysis of the cross-bored autofrettaged cylinder, it was observed that there is a severe localized change in the residual stress profile in the vicinity of the cross-bore. The residual circumferential stress increases in compression at the bore. Similarly it increases in tension at the outer diameter, thus making the outer diameter more vulnerable to fatigue failure or crack initiation under stresses arising as a result of firing. Analyses were also performed by varying the cross-bore diameter and it was observed that, by increasing the diameter of the radial hole, the residual circumferential stress at the bore reduces, while it increases at the outer diameter, with an increase in the cross bore diameter. The re-pressurization pressure of an autofrettaged cylinder with radial cross-bore was found to be approximately 65 percent less than the actual autofrettage pressure in a particular case discussed in this paper. A comparison is also made with the residual stress field which would result if the cross-bore was machined before autofrettage.

Effect of Yield Criterion on Stress Distribution and Maximum Safe Pressure for an Autofrettaged Gun Barrel

2017 ◽  
Vol 67 (5) ◽  
pp. 504
Author(s):  
Amit Bhetiwal ◽  
Sunil Kashikar ◽  
Haribhau Markale ◽  
Shailendra Gade
Keyword(s):  
Stress Distribution ◽  
Yield Criterion ◽  
The Other ◽  
Uniform Thickness ◽  
Theoretical Weight ◽  
Gun Barrel ◽  
Von Mises Criterion ◽  
Tresca Criterion ◽  
Von Mises

<p>World artillery in the present scenario is changing its role from defensive to aggressive nature and is attempting to achieve higher penetration into enemy targets. Even for an autofrettaged gun barrel, higher ranges requirement leads to higher barrel weight and its associated demerits. The design of gun barrel is based on the choice of yield criteria. Tresca yield criterion provides conservative design for a ductile barrel material. On the other hand, more accurate von Mises criterion presents complexity. The two criteria to evaluate various parameters required for design of an autofrettaged gun barrel are compared. The methodology for evaluation of maximum safe pressure, based on von Mises criterion, for an autofrettaged gun barrel is also included in the paper. Based on case study included in the article, for an autofrettaged gun barrel or pressure vessel with uniform thickness, a theoretical weight reduction of approximately 16 per cent is feasible with von Mises criterion as compared to Tresca criterion.</p>

Yield Pressure Measurements and Analysis for Autofrettaged Cannons

2002 ◽  
Author(s):  
John H. Underwood ◽  
David B. Moak ◽  
Michael A. Audino ◽  
Anthony P. Parker
Keyword(s):  
Residual Stress ◽  
Yield Strength ◽  
Yield Criterion ◽  
Axial Stress ◽  
Design Procedure ◽  
Pressure Vessels ◽  
Pressure Measurements ◽  
Strain Rate Effects ◽  
Axial Residual Stress ◽  
Von Mises

Yield pressure corresponding to a small permanent OD strain was measured in quasi-static laboratory tests of autofrettaged ASTM A723 steel cannon pressure vessels. Yield pressure was found to be a consistent ratio of the yield strength measured from specimens located in close proximity to the area of observed yielding. Yield pressure measurements for dynamic cannon firing with typically a 5 ms pressure pulse duration gave 14% higher yield pressures, attributed to strain rate effects on plastic deformation. Calculated Von Mises yield pressure for the laboratory test conditions, including the Bauschinger-modified ID residual stress and open-end vessel conditions, agreed with measured yield pressure within 3–5%. Calculated yield pressure was found to be insensitive to the value of axial residual stress, since axial stress is the intermediate value in the Von Mises yield criterion. A description of yield pressure normalized by yield strength was given for autofrettaged A723 open-end pressure vessels over a range of wall ratio and degree of autofrettage, including effects of Bauschinger-modified residual stress. This description of yield pressure is proposed as a design procedure for cannons and other pressure vessels.

Yield Pressure Measurements and Analysis for Autofrettaged Cannons

2003 ◽  
Vol 125 (1) ◽  
pp. 7-10 ◽  
Author(s):  
John H. Underwood ◽  
David B. Moak ◽  
Michael J. Audino ◽  
Anthony P. Parker
Keyword(s):  
Residual Stress ◽  
Yield Strength ◽  
Yield Criterion ◽  
Axial Stress ◽  
Design Procedure ◽  
Pressure Vessels ◽  
Pressure Measurements ◽  
Strain Rate Effects ◽  
Axial Residual Stress ◽  
Von Mises

Yield pressure corresponding to a small permanent OD strain was measured in quasi-static laboratory tests of autofrettaged ASTM A723 steel cannon pressure vessels. Yield pressure was found to be a consistent ratio of the yield strength measured from specimens located in close proximity to the area of observed yielding. Yield pressure measurements for dynamic cannon firing with typically a 5-ms pressure pulse duration gave 14% higher yield pressures, attributed to strain rate effects on plastic deformation. Calculated Von Mises yield pressure for the laboratory test conditions, including the Bauschinger-modified ID residual stress and open-end vessel conditions, agreed with measured yield pressure within 3–5%. Calculated yield pressure was found to be insensitive to the value of axial residual stress, since axial stress is the intermediate value in the Von Mises yield criterion. A description of yield pressure normalized by yield strength was given for autofrettaged A723 open-end pressure vessels over a range of wall ratio and degree of autofrettage, including effects of Bauschinger-modified residual stress. This description of yield pressure is proposed as a design procedure for cannons and other pressure vessels.

A Numerical Model for Evaluating the Residual Stress Field in an Autofrettaged Spherical Pressure Vessel Incorporating the Bauschinger Effect

2007 ◽  
Author(s):  
M. Perl ◽  
J. Perry
Keyword(s):  
Differential Equation ◽  
Residual Stress ◽  
Stress Field ◽  
Pressure Vessel ◽  
Weight Ratio ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Plastic Strains ◽  
Residual Stress Field ◽  
Spherical Pressure

Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel’s wall, by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only few such studies exist for spherical ones. There are two principal autofrettage processes for pressure vessels: hydrostatic and swage autofrettage, but spherical vessels can only undergo the hydrostatic one. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a two-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elasto-plastic autofrettage problem using the form of the elastic solution. Substituting Hooke’s equations into the equilibrium equation and using the strain-displacement relations, yields a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl-Reuss flow rule and the differential equation is solved by the explicit finite difference method. The previously developed 2-D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The appropriate residual stresses are then evaluated using the new code. The presently obtained residual stress field is then compared to three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field.

The Beneficial Contribution of Realistic Autofrettage to the Load-Carrying Capacity of Thick-Walled Spherical Pressure Vessels

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
M. Perl ◽  
J. Perry
Keyword(s):  
Differential Equation ◽  
Residual Stress ◽  
Stress Field ◽  
Weight Ratio ◽  
Pressure Vessels ◽  
Flow Rule ◽  
Plastic Strains ◽  
Residual Stress Field ◽  
Explicit Finite Difference ◽  
Spherical Pressure

Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel’s wall by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only a few of such studies exist for spherical ones. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a one-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elastoplastic autofrettage problem using the form of the elastic solution. Substituting Hooke’s equations into the equilibrium equation and using the strain-displacement relations yield a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl–Reuss flow rule and the differential equation is solved by the explicit finite difference method. The existing 2D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The presently obtained residual stress field is then validated against three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field. The new code is applied to a series of spherical pressure vessels yielding two major conclusions. First, the process of autofrettage increases considerably the maximum safe pressure that can be applied to the vessel. This beneficial effect can also be used to reduce the vessel’s weight rather than to increase the allowable internal pressure. Second, the specific maximum safe pressure increases as the vessel becomes thinner. The present results clearly indicate that autofrettaging of spherical pressure vessels can be very advantageous in various applications.

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