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Research Papers

The Onset of Plastic Yielding in a Spherical Shell Compressed by a Rigid Flat

[+] Author and Article Information
Longqiu Li1

 Harbin Institute of Technology, Harbin 150001, China; University of California, San Diego, La Jolla, CA 92093-0401longqiuli@gmail.com

Izhak Etsion

 Technion-Israel Institute of Technology, Haifa 32000, Israel

Andrey Ovcharenko, Frank E. Talke

 University of California, San Diego, La Jolla, CA 92093-0401

1

Corresponding author.

J. Appl. Mech 78(1), 011016 (Oct 22, 2010) (7 pages) doi:10.1115/1.4001994 History: Received October 13, 2009; Revised May 22, 2010; Posted June 16, 2010; Published October 22, 2010; Online October 22, 2010

The onset of plastic yielding in a spherical shell loaded by a rigid flat is analyzed using finite element analysis. The effect of spherical shell geometry and material properties on the critical normal load, critical interference, and critical contact area, at the onset of plastic yielding, is investigated and the location where plastic yielding first occurs is determined. A universal dimensionless shell parameter, which controls the behavior of the spherical shell, is identified. An empirical relation is found for the load-interference behavior of the spherical shell prior to its plastic yielding. A limiting value of the dimensionless shell parameter is identified above which the shell behaves like a solid sphere.

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Figures

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Figure 1

Schematic sketch of a spherical shell compressed by a rigid flat (a), and direct stress resultants (Nrr,Nθθ), bending stress couples (Mrr,Mθθ) and shear stress resultants (Vθ,Vr) in meridian and circumferential direction for a typical shell segment (b)

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Figure 2

Mesh of the finite element model for a small thickness ratio t/R≤0.05 (a) and for a larger thickness ratio t/R>0.05 (b). Zones I, II, III, and IV represent different mesh densities.

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Figure 3

Schematic of the model of spherical shell contacting a rigid flat and its boundary conditions

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Figure 4

The critical load ratio, Pc_shell/Pc_solid, versus the thickness ratio, t/R, at different values of E/Y

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Figure 5

The critical load ratio, Pc_shell/Pc_solid, versus the shell parameter λ

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Figure 6

The critical interference ratio, ωc_shell/ωc_solid, versus the shell parameter λ at different E/Y values

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Figure 7

The dimensionless expression logα(ωc_shell/ωc_solid), versus the shell parameter λ

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Figure 8

A schematic description of the three typical locations of yield inception within the spherical shell, corresponding to the three regions, respectively, of the shell parameter λ values shown in Figs.  57

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Figure 9

Dimensionless stresses versus the dimensionless coordinate z/t along the axis of symmetry for the critical interference, ωc_shell, and three typical values of the shell parameter: (a) λ=0.2, (b) λ=0.7, and (c) λ=1.0

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Figure 10

Dimensionless stresses along the dimensionless radial coordinate x/a at z/t=0.05 for the critical interference, ωc_shell, and three typical values of the shell parameter: (a) λ=0.2, (b) λ=0.7, and (c) λ=1.0

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Figure 11

Contour plot of the through-thickness von Mises stresses for the critical interference, ωc_shell, and three typical values of the shell parameter: (a) λ=0.2, (b) λ=0.7, and (c) λ=1.0

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Figure 12

The power β used in Eq. 17 as a function of the shell parameter λ

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Figure 13

The dimensionless normal load P∗, as a function of the dimensionless interference ω∗, prior to yield inception

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