Research Papers: Design and Analysis

Collapse of Thick Tubes Pressurized From Outside: An Accurate Predictive Formula

[+] Author and Article Information
Leone Corradi1

Department of Nuclear Engineering, Politecnico di Milano, via Ponzio 34/3, 20133 Milano, Italyleone.corradi@polimi.it

Christian Ghielmetti

Department of Mechanics, Politecnico di Milano, via La Masa 34, 20158 Milano, Italy

Lelio Luzzi

Department of Nuclear Engineering,  Politecnico di Milano, via Ponzio 34/3, 20133 Milano, Italy



Corresponding author.

J. Pressure Vessel Technol 130(2), 021204 (May 13, 2008) (9 pages) doi:10.1115/1.2894316 History: Received June 18, 2007; Revised October 30, 2007; Published May 13, 2008

Several engineering applications require cylindrical shells subjected to external pressure, and an increasing need for tubes of significant thickness has been experienced in recent years. So far, little study has been devoted to very stocky tubes, and a great amount of uncertainty exists on some important aspects, such as the consequences of imperfections on their failure pressure. This can only be computed by performing numerical analyses that consider both material (plasticity) and geometric (large displacement) nonlinearities. Such a procedure is feasible, but its use for design purposes is cumbersome, and handy alternatives are worth searching. In this paper, a comparatively simple formula is proposed, based on an interpretation of the relative role that plasticity and instability play in the thick tube range. The formula depends on a crucial coefficient, which can be defined so as to provide safe but reasonably accurate approximations to the collapse pressures computed numerically for tubes made of different metals. The proposal may be useful for preliminary design purposes and can be considered as a first contribution toward a precise assessment of the collapse behavior of tubes in a thickness range so far overlooked.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

ASME reference failure and allowable pressures compared to theoretical limits (dashed): pT=min{p0,pE}, qT=min{q0,qE}; (a) ASME Sec. 3, (b) Code Case 2286-1

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Figure 2

Margin with respect to theoretical failure pressure. Black: pT∕pa; gray: qT∕pa

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Figure 3

Computed results compared to ASME reference values and theoretical limits

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Figure 4

Interaction domain for the tube cross section: 1, elastic limit; 2, limit curve; and 3, approximation considered for lower bounds

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Figure 5

Limit curve for thick tubes: Eq. 9 and computed results

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Figure 6

Collapse pressure (black lines) and bounding values (gray)

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Figure 7

Coefficient μ for INCONEL 690 and different assumptions for material properties; black: material 1; gray: material 2; and white: material 3

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Figure 8

Values of μ for tubes made of the metals in Table 2; (a) black: steel, gray: copper; (b) black: aluminum, gray: titanium

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Figure 9

Predicted versus computed collapse pressures for two extreme cases; (a) INCONEL 690 (κ=832), (b) Titanium alloy (κ=150)

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Figure 10

Coefficient μ for the different materials considered

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Figure 11

Safety margin with respect to qT=min{q0,qE}; material properties 4,4



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