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TECHNICAL PAPERS

Autofrettage of Open-End Tubes—Pressures, Stresses, Strains, and Code Comparisons

[+] Author and Article Information
Anthony P. Parker

Engineering Systems Department, Royal Military College of Science, Cranfield University, Swindon, Englande-mail: tony_parker@tesco.net

J. Pressure Vessel Technol 123(3), 271-281 (Nov 24, 2000) (11 pages) doi:10.1115/1.1359209 History: Received April 15, 2000; Revised November 24, 2000
Copyright © 2001 by ASME
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References

Bauschinger,  J., 1881, “Ueber die Veranderung der Elasticitatagrenze und dea Elasticitatamoduls verschiadener Metalle,” Zivilingenieur, 27, pp. 289–348.
Chakrabarty, J., 1987, Theory of Plasticity, McGraw-Hill, New York, NY.
Jahed,  H., and Dubey,  R. N., 1997, “An Axisymmetric Method of Elastic-Plastic Analysis Capable of Predicting Residual Stress Field,” ASME J. Pressure Vessel Technol., 119, pp. 264–273.
Parker,  A. P., Underwood,  J. H., and Kendall,  D. P., 1999, “Bauschinger Effect Design Procedures for Autofrettaged Tubes Including Material Removal and Sachs’ Method,” ASME J. Pressure Vessel Technol., 121, pp. 430–437.
Milligan,  R. V., Koo,  W. H., and Davidson,  T. E., 1966, “The Bauschinger Effect in a High Strength Steel,” ASME J. Basic Eng., 88, pp. 480–488.
Troiano, E., 1998, private communication.
Davidson, T. E., and Kendall, D. P., 1970, “Design of High Pressure Containers,” Mechanical Behavior of Metals Under Pressure, Elsevier, H. Pugh, ed., pp. 54–77.
Marcal,  P. V., 1965, “A Note on the Elastic-Plastic Thick Cylinder with Internal Pressure in the Open and Closed-End Condition,” Int. J. Mech. Sci., 7, pp. 841–845.
ASME Pressure Vessel and Piping Design Code, 1997, “Design Using Autofrettage,” Division 3, Section 8, Article KD-5, pp. 71–73.
Hill, R., 1967, The Mathematical Theory of Plasticity, Oxford University Press, Oxford, UK.
Davidson, T. E., Barton, C. S., Reiner, A. N. and Kendall, D. P., 1963, “Overstrain of High Strength Open-End Cylinders of Intermediate Diameter Ratio,” Proc., First International Congress on Experimental Mechanics, Pergamon Press, Oxford, UK.
Weigle, R. E., 1960, “Elastic-Plastic Analysis of a Cylindrical Tube,” Watervliet Arsenal Technical Report WVTRR-6007.
Parker, A. P. and Underwood, J. H., 1998, “The Bauschinger Effect in Autofrettaged Tubes—A Comparison of Models Including the ASME Code,” Proc. ASME Pressure Vessels & Piping Conference, San Diego, CA.
Prager, W., and Hodge, P. G., 1951, Theory of Perfectly Plastic Solids, J. Wiley & Sons, New York, NY.
Sutherland, C. D., 1962, “Elastic-Plastic Analysis of a Cylindrical Tube, Part II,” Watervliet Arsenal Technical Report No. WVT-RR-6205.

Figures

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Bore pressure for given percentage overstrain, von Mises and plane stress conditions assumed
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Bore pressure for given percentage overstrain, von Mises and engineering plane strain (open-end) conditions assumed
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Bore pressure for 100 percent overstrain—comparison with other work, von Mises and engineering plane strain conditions
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Pressures at autofrettage peak for plane strain, open-end, and closed-end conditions, b/a=2. Results normalized using Eq. (1).
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Average axial stress/autofrettage pressure for plane strain and quasi-plane strain (b/a=2)
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Percentage error in bore hoop stress and in percentage overstrain resulting from use of Hill’s approximation 10
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Hoop residual stress profile for b/a=2 with various percentage overstrains; von Mises and engineering plane strain (EPS) conditions assumed
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Axial residual stress profile for b/a=2 with various percentage overstrains; von Mises and engineering plane strain (EPS) conditions assumed
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Bore hoop stress values as a function of c/a for a range of autofrettaged tube geometries. (I) indicates ideal solution, (B) indicates results incorporating Bauschinger effect.
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Ratio of bore hoop stresses, von Mises EPS/ideal Tresca plane stress. Broken lines indicate linear fit to Bauschinger-affected results.
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Bore hoop stresses, von Mises EPS, Tresca EPS, and von Mises TPS, each normalized with Tresca plane stress
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Percentage difference between ASME Code and von Mises EPS numerical model; negative values indicate code conservatism. Note: code validity limited to 40 percent overstrain.
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Bore hoop strain values at autofrettage peak for plane strain, open-end, and closed-end conditions
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Bore hoop strain values at autofrettage peak for plane strain, open-end, and closed-end conditions. Results normalized using Eq. (19).
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Bore hoop strain versus OD hoop strain at autofrettage peak for plane strain, open-end, and closed-end conditions. Results for open and closed-end conditions coincide with 8.
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OD hoop strain values at autofrettage peak for plane strain, open-end, and closed-end conditions
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OD hoop strain values at autofrettage peak for plane strain, open-end, and closed-end conditions. Results normalized using Eq. (20).
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ID and OD hoop strain values during unloading from autofrettage peak for plane, strain, open-end, and closed-end conditions. Results normalized using Eq. (21).
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Percentage difference between code predictions and numerical predictions of c/a and of residual bore hoop stress using OD strain at autofrettage peak
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Percentage difference between code predictions and numerical predictions of c/a and of residual bore hoop stress using permanent strain at ID after autofrettage

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