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TECHNICAL PAPERS

Autofrettaged Cylindrical Vessels and Bauschinger Effect: An Analytical Frame for Evaluating Residual Stress Distributions

[+] Author and Article Information
Paolo Livieri

Department of Engineering, University of Ferrara, 44100 Ferrara, Italye-mail: plivieri@ing.unife.it

Paolo Lazzarin

Department of Management and Engineering, University of Padova, 36100 Vicenza, Italye-mail: plazzarin@gest.unipd.it

J. Pressure Vessel Technol 124(1), 38-46 (Jul 20, 2001) (9 pages) doi:10.1115/1.1425809 History: Received February 26, 2001; Revised July 20, 2001
Copyright © 2002 by ASME
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References

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Wang,  G. S., 1988, “An Elastic-plastic Solution for a Normally Loaded Center Hole in a Finite Circular Body,” Int. J. Pressure Vessels Piping, 33, pp. 269–284.
Bonn,  R., and Haupt,  P., 1995, “Exact Solution for Large Elastoplastic Deformations of a Thick-Walled Tube Under Internal Pressure,” Int. J. Plast., 11(1), pp. 99–118.
Rees,  D. W. A., 1987, “A Theory of Autofrettage With Applications to Creep and Fatigue,” Int. J. Pressure Vessels Piping, 30, pp. 57–76.
Loghman,  A., and Wahab,  M. A., 1994, “Loading and Unloading of Thick-Walled Cylindrical Pressure Vessels of Strain-Hardening Material,” ASME J. Pressure Vessel Technol., 116, pp. 105–109.
Lazzarin,  P., and Livieri,  P., 1997, “Different Solution for Stress and Strain Fields in Autofrettaged Thick-Walled Cylinders,” Int. J. Pressure Vessels Piping, 71, pp. 231–238.
Stacey,  A., and Webster,  G.A., 1988, “Determination of Residual Stress Distributions in Autofrettaged Tubing,” Int. J. Pressure Vessels Piping, 31, pp. 205–220.
Parker,  A. P., and Underwood,  J. H., 1999, “Influence of Bauschinger Effect on Residual Stress and Fatigue Lifetimes in Autofrettage Thick-Walled Cylinders,” Fatigue and Fracture Mechanics: 29th Vol, ASTM STP , 1332, pp. 565–583.
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.
Franklin,  G. J., and Morrison,  J. L. M., 1961, “Autofrettage of Cylinder: Prediction of Pressure/Expansion Curves and Calculation of Residual Stresses,” Proc. Inst. Mech. Eng., 174, pp. 947–65.
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Figures

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Loading and unloading σ−ε curves in the presence of the Bauschinger effect
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Bauschinger effect factor for a bilinear (a) and a power hardening σ−ε curve (b) for different hardening rules (σy=600 MPa,E=206 GPa)
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Power hardening σ−ε curve for the unloading phase plotted in the εeqpeq plane
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Errors in percentage associated to the use of the approximate Eqs. (38), (40) with respect to the exact Eqs. (45), (47). Bilinear material (a=60 mm,b=240 mm,σy=850 MPa, ν=0.3, E=206 GPa,Et=Etu=10000 MPa).
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Residual stress fields (a) and errors in percentage (b) with respect to the numerical solution. Material modeled with a power hardening σ−ε curve, kinematic hardening (a=60 mm,b=180 mm,σy=600 MPa,E=206 GPa,p=4σy/3).
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(a) Residual stress fields for a power hardening σ−ε curve as dependent on the hardening rule, n=6; (b) residual stress field as a function of hardening exponent n for a power hardening σ−ε curve and kinematic hardening. (In all cases: a=60 mm,b=240 mm,σy=900 MPa,E=206 GPa,p=3σy/2.)
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Residual stress fields for a bilinear material plotted for two hardening rules (a) and in the presence of a constant Bauschinger effect (b); (a=60 mm,b=240 mm,σy=850 MPa, ν=0.3, E=206 GPa,Et=Etu=10000 MPa,p=1.65σy)
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Schematic representation of the cross section

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