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Design and Analysis

Experimental Demonstration of Shakedown in a Vessel Submitted to Impulsive Loading

[+] Author and Article Information
B. Simoens

e-mail: bart.simoens@rma.ac.be

M. H. Lefebvre

Royal Military Academy,
1000 Brussels, Belgium

R. E. Nickell

Applied Science and Technology,
San Diego, CA 92064 USA

F. Minami

University of Osaka,
Osaka 565-0871, Japan

Shakedown occurs when, after some plastic deformation in the first load cycles, the behavior becomes eventually elastic [3].

This is assumed to be far enough to avoid influence of the welding, and close enough to the center to represent the central response adequately.

TNT (chemical name trinitrotoluene) is a high explosive, in use since World War I and commonly used as reference explosive for comparison of other explosives.

The TNT-equivalent value on the centerline of the cylindrical charge of emulsion will depend on the length-to-diameter ratio of the cylinder, the value of 1.35 has been found for the 3 kg charges with L/D = 2.

The 2 kg and 2.5 kg charges showed very small amounts of localized plastic deformation, with almost imperceptible residual deformation.

The value of 0.73% can be found on the Fig. 4(a) as the experimental residual strain after the first 3 kg shot.

The value of 0.55% can be found on the Fig. 4(a) as the experimental residual strain after the second 3 kg shot.

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received November 19, 2010; final manuscript received February 17, 2011; published online October 17, 2012. Assoc. Editor: Edward A. Rodriguez.

J. Pressure Vessel Technol 134(6), 061201 (Oct 17, 2012) (6 pages) doi:10.1115/1.4003824 History: Received November 19, 2010; Revised February 17, 2011

Vessels subjected to internal impulsive loadings, such as those used for controlled-detonation chambers, can be designed for a single impulsive load application or for multiple impulsive loads. Design of a single-use vessel may take advantage of the capability of the vessel material to absorb energy through elastic-plastic behavior, provided that the public health and safety is protected, even though the owner’s investment in the vessel may be compromised because of severe distortion and potential loss of containment functionality. However, when the vessel is designed to contain multiple internal impulse loads, the usual design practice is to require completely elastic response or, at most, very localized elastic-plastic behavior. A recently approved ASME Boiler & Pressure Vessel Code, Section VIII, Division 3 action (Code Case 2564-2) provides limits for the accumulated plastic strains in such vessels, including a limit on the accumulated plastic strain averaged across the wall thickness of the vessel, that are sufficiently conservative to permit the design of vessels for both single-impulse and for multiple-impulse applications. Analytical or experimental demonstration to meet the Code Case 2564-2 strain limits is straightforward for the single-impulse vessel design and is relatively straightforward for multiple-impulse vessel designs when the vessel response to any of the individual impulsive loads is nearly elastic. However, when the design-basis impulsive loading for a multiple-impulse vessel design leads to significant plastic straining, the demonstration of design adequacy becomes extremely complex, raising issues of impulsive loading sequences (since elastic-plastic response is load-path dependent, what is the temporal order of the impulse loadings?) and demonstration of shakedown to elastic or near-elastic behavior. In such cases, an analytical demonstration of design adequacy may be impractical, while an experimental demonstration may be both practical and illuminating, especially if the demonstration is carried out at a scale that is both economical and convincing. Here, a one-seventh-scale model of a controlled-detonation vessel is used as the basis for demonstrating the effect of shakedown to essentially elastic behavior, with no further accumulation of plastic straining, along with the satisfaction of ASME Code Section VIII, Division 3, local ductility exhaustion requirements. The experiments on a scale model vessel have proved that the phenomenon of shakedown can be demonstrated experimentally, for internal detonation loadings that initially led to plastic strains up to 0.7%.

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References

Figures

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Fig. 2

Examples of measured circumferential strains on the beltline for two shots with 3 kg. (a) Shot 18, note strain gauge failure (monobloc 2) after first response cycle, (b) Shot 30, note strain gauge consistency.

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Fig. 1

Technical drawing of the 1/7-scale-model vessel with position of the explosive charges inside the vessel

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Fig. 3

Measurement over long time for monobloc 3, showing decreasing residual strains after each shot

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Fig. 4

(a) Residual and (b) peak strain for the different shots with 3 kg

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Fig. 5

Illustration of shakedown with stress-strain curves. (a) Ideal hysteresis loop becoming narrower and more elongated (from [3]), (b) Plastic work and elastic strain energy on a stress-strain curve (from [8]), (c) Hysteresis loop stable in time: shakedown, (d) Hysteresis loop moving in time: plastic ratcheting.

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