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RESEARCH PAPERS

Analytical Approach in Autofrettaged Spherical Pressure Vessels Considering the Bauschinger Effect

[+] Author and Article Information
R. Adibi-Asl1

Department of Mechanical Engineering, University of Tehran, Tehran, Iranradibi@engr.mun.ca

P. Livieri2

Department of Engineering, University of Ferrara, Ferrara, Italyplivieri@ing.unife.it

1

Present address: Faculty of Engineering and Applied Science, Memorial University of Newfoundland, Canada

2

Corresponding author.

J. Pressure Vessel Technol 129(3), 411-419 (Nov 21, 2006) (9 pages) doi:10.1115/1.2748839 History: Received December 19, 2005; Revised November 21, 2006

This paper presents an analytical study of spherical autofrettage-treated pressure vessels, considering the Bauschinger effect. A general analytical solution for stress and strain distributions is proposed for both loading and unloading phases. Different material models incorporating the Bauschinger effect depending on the loading phase are considered in the present study. Some practical analytical expressions in explicit form are proposed for a bilinear material model and the modified Ramberg–Osgood model.

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Figures

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Figure 1

Spherical pressure vessels: (a) spherical coordinate system and (b) elastic-plastic region (loading and unloading)

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Figure 2

Bilinear material model

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Figure 3

Bilinear material under unloading: kinematic hardening

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Figure 4

Bilinear material under unloading: α constant (isotropic hardening with α=1)

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Figure 5

σ-ε curve for the Ramberg–Osgood law

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Figure 6

Three different cases in unloading phase in σ-ε curve of the Ramberg–Osgood law

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Figure 7

Typical finite element mesh

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Figure 8

The variation of residual stress components in the thick wall of a sphere for a=0.06m, b=0.240m, P=3σy, E=206GPa, and Et=Etu=10GPa with the BKH material model

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Figure 9

The variation of residual stress components in the thick wall of a sphere for a=0.06m, b=0.240m, P=3σy, E=206GPa, and Et=Etu=10GPa with the BIH material model

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Figure 10

The stress distribution along the wall thickness for BKH (a=0.06m, b=0.240m, P=3σy, σy=850MPa, E=206GPa, and Et=Etu=10GPa), (a) loading, (b) unloading, (c) residual

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Figure 11

The stress distribution along the wall thickness for BIH material model (a=0.06m, b=0.240m, P=3σy, σy=850MPa, E=206GPa, and Et=Etu=10GPa), (a) loading, (b) unloading, (c) residual

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Figure 12

The stress distribution along the wall thickness for the Ramberg–Osgood kinematic hardening material model (a=0.06m, b=0.240m, P=3σy, σy=850MPa, E=206GPa, and n=5), (a) loading, (b) unloading, (c) residual

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Figure 13

The stress distribution along the wall thickness for the Ramberg–Osgood isotropic hardening material model (a=0.06m, b=0.240m, P=3σy, σy=850MPa, E=206GPa, and n=5), (a) loading, (b) unloading, (c) residual

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