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Research Papers

Plastic Collapse of a Thin Annular Disk Subject to Thermomechanical Loading

[+] Author and Article Information
Sergei Alexandrov

A.Yu. Ishlinskii Institute for
Problems in Mechanics,
Russian Academy of Sciences,
101-1 Prospect Vernadskogo,
119526 Moscow, Russia;
Department of Mechanical Engineering
and Advanced Institute for Manufacturing
with High-tech Innovations,
National Chung Cheng University,
62102 Chia-Yi, Taiwan

Elena Lyamina

A.Yu. Ishlinskii Institute for
Problems in Mechanics,
Russian Academy of Sciences,
101-1 Prospect Vernadskogo,
119526 Moscow, Russia

Yeau-Ren Jeng

Department of Mechanical Engineering
and Advanced Institute for Manufacturing
with High-tech Innovations,
National Chung Cheng University,
62102 Chia-Yi, Taiwan

1Corresponding author.

Manuscript received February 27, 2012; final manuscript received November 29, 2012; accepted manuscript posted January 22, 2013; published online July 12, 2013. Assoc. Editor: Nick Aravas.

J. Appl. Mech 80(5), 051006 (Jul 12, 2013) (6 pages) Paper No: JAM-12-1082; doi: 10.1115/1.4023478 History: Received February 27, 2012; Revised November 29, 2012; Accepted January 22, 2013

A semi-analytic solution for plastic collapse of a thin annular disk subject to thermomechanical loading is presented. It is assumed that the yield criterion depends on the hydrostatic stress. A distinguished feature of the boundary value problem considered is that there are two loading parameters. One of these parameters is temperature and the other is pressure over the inner radius of the disk. The general qualitative structure of the solution at plastic collapse is discussed in detail. It is shown that two different plastic collapse mechanisms are possible. One of these mechanisms is characterized by strain localization at the inner radius of the disk. The entire disk becomes plastic according to the other plastic collapse mechanism. In addition, two special regimes of plastic collapse are identified. According to one of these regimes, plastic collapse occurs when the entire disk is elastic, except its inner radius. According to the other regime, the entire disk becomes plastic at the same values of the loading parameters at which plastic yielding starts to develop.

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Figures

Grahic Jump Location
Fig. 1

Curve corresponding to the initiation of plastic yielding derived from Eq. (17). Special solutions when the conditions for the initiation of plastic yielding and plastic collapse coincide are denoted by k and s.

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Fig. 2

Illustration of the general structure of the solution. Curve 1 corresponds to the initiation of plastic yielding. Straight line 2 corresponds to the plastic collapse mechanism characterized by localization of deformation at the inner radius of the disk. Curve 3 corresponds to a fully plastic disk.

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Fig. 3

Illustration of the dependence of p on τ at plastic collapse at a = 0.5, ν = 0.3, and several α values. The broken lines track the positions of points k and s.

Grahic Jump Location
Fig. 4

Illustration of the dependence of p on τ at plastic collapse at a = 0.3, ν = 0.3, and several α values. The broken lines track the positions of points k and s.

Grahic Jump Location
Fig. 5

Illustration of the dependence of p on τ at plastic collapse at a = 0.7, ν = 0.3, and several α values. The broken lines track the positions of points k and s.

Grahic Jump Location
Fig. 6

Illustration of the dependence of the state of plastic collapse on Poisson's ratio at a = 1/2 and α = 0 (the solid line corresponds to ν = 0.3 and the broken line to ν = 0.2)

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