Research Papers: Design and Analysis

Plastic Instability Pressure of Toroidal Shells

[+] Author and Article Information
Vu Truong Vu

Department of Mechanical Engineering, University of Liverpool, Liverpool L69 3GH, UKvutruongvu@gmail.com

J. Blachut

Department of Mechanical Engineering, University of Liverpool, Liverpool L69 3GH, UKem20@liverpool.ac.uk

J. Pressure Vessel Technol 131(5), 051203 (Jul 28, 2009) (10 pages) doi:10.1115/1.3148824 History: Received February 07, 2009; Revised May 08, 2009; Published July 28, 2009

This paper considers the determination of plastic instability pressure in toroidal shells under internal uniform pressure. Analytical and numerical approaches, as well as verification by experiments, are presented. This work is inspired by Mellor’s treatment (1983, Engineering Plasticity, Ellis Horwood Ltd., Chichester; 1960, “The Ultimate Strength of Thin-Walled Shells and Circular Diaphragms Subjected to Hydrostatic Pressure,” Int. J. Mech. Sci., 1, pp. 216–228; 1962, “Tensile Instability in Thin-Walled Tubes,” J. Mech. Eng. Sci., 4(3), pp. 251–256), which assumed that plastic instability occurs at the maximum load. A closed-form formula of plastic instability condition is derived analytically. This expression for toroidal shells turns out to be the general case of spherical and cylindrical shells given by Mellor. Then the corresponding pressure is obtained by semi-analytical analysis for a material with the strain hardening characteristic, σ=A(B+ε)n. For the numerical approach, plastic instability pressure is the maximum pressure at which a small pressure increment causes a very large deformation. This is identified by the slope of pressure—change of volume curve approaching zero. Both approaches predict the onset of instability at the inner equator point. Experimental results of two nominally identical stainless steel toroidal shells correlated well to both approaches in terms of the magnitude of pressure and failure location.

Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 2

Detail of a 90 deg elbow

Grahic Jump Location
Figure 3

Shapes of untested, tested virgin coupon (above) and tested coupon with a seam

Grahic Jump Location
Figure 7

Point marking on an elbow for wall-thickness measurement

Grahic Jump Location
Figure 9

(a) Shape of toroid T1 after burst, (b) burst position of toroid T1, (c) shape of toroid T2 after burst, and (d) burst position of toroid T2

Grahic Jump Location
Figure 16

Geometry of toroid T1 cross section before and after loading

Grahic Jump Location
Figure 1

Shape of untested toroid T1

Grahic Jump Location
Figure 6

Geometry of toroidal shell

Grahic Jump Location
Figure 8

Experimental and numerical pressure versus change of volume curves of toroids T1 and T2

Grahic Jump Location
Figure 10

Toroid shapes before (T2, right-hand side) and after test (T1)

Grahic Jump Location
Figure 11

View of both toroids T2 (left) and T1 after test. (a) Side view and (b) plan view.

Grahic Jump Location
Figure 12

Critical subtangent z to the generalized instability strain hardening curve (adapted from Swift (4))

Grahic Jump Location
Figure 13

Distribution of meridional stress σ1 along the meridian for various ratios of R/r

Grahic Jump Location
Figure 14

Value of critical subtangent z versus ratio R/r of toroid. Value z=0.557 is for cylindrical shells.

Grahic Jump Location
Figure 15

Analytical and experimental true stress-true strain curves

Grahic Jump Location
Figure 4

Normal stress-normal strain curves of tensile coupons

Grahic Jump Location
Figure 5

True stress-true strain curve of the virgin coupon



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In