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TECHNICAL PAPERS

Dynamic Spherical Cavity Expansion in an Elastoplastic Compressible Mises Solid

[+] Author and Article Information
Rami Masri1

 Faculty of Aerospace Engineering, Technion, Haifa 32000, Israelmasri@aerodyne.technion.ac.il

David Durban

 Faculty of Aerospace Engineering, Technion, Haifa 32000, Israel

1

Author to whom correspondence should be addressed. This work is based on part of a Ph.D. thesis to be submitted to Technion.

J. Appl. Mech 72(6), 887-898 (Dec 13, 2004) (12 pages) doi:10.1115/1.1985428 History: Received July 20, 2004; Revised December 13, 2004

The elastoplastic field induced by a self-similar dynamic expansion of a pressurized spherical cavity is investigated for the compressible Mises solid. The governing system consists of two ordinary differential equations for two stress components where radial velocity and density are known functions of these stresses. Numerical illustrations of radial profiles of field variables are presented for several metals. We introduce a new solution based on expansion in powers of the nondimensionalized cavity expansion velocity, for both elastic/perfectly plastic response and strain-hardening behavior. A Bernoulli-type solution for the dynamic cavitation pressure is obtained from the second-order expansion along with a more accurate third-order solution. These solutions are mathematically closed and do not need any best fit procedure to numerical data, like previous solutions widely used in the literature. The simple solution for elastic/perfectly plastic materials reveals the effects of elastic-compressibility and yield stress on dynamic response. Also, an elegant procedure is suggested to include strain-hardening in the simple elastic/perfectly plastic solution. Numerical examples are presented to demonstrate the validity of the approximate solutions. Applying the present cavitation model to penetration problems reveals good agreement between analytical predictions and penetration depth tests.

Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Scheme of self-similar field in dynamic expansion of a spherical cavity. Cavitation pressure is pc. The radial coordinate ξ is nondimensionalized with respect to the current radius of the cavity. The rigid-elastic wave front is at ξ=ξw. Plastic yielding occurs at the elastic-plastic interface ξ=ξi. The remote boundary at infinity is stress free.

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Figure 2

Radial profiles of essential field variables for a compressible strain-hardening Mises solid. Results are for AL 7075-T6.

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Figure 3

Radial profiles of essential field variables for a compressible strain-hardening Mises solid. Results are for ST D6AC.

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Figure 4

Radial profiles of essential field variables for a compressible strain-hardening Mises solid. Results are for Stainless steel.

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Figure 5

Radial profiles of essential field variables for a compressible strain-hardening Mises solid. Results are for TI B120VCA.

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Figure 6

Variation of cavitation pressure Pc with expansion velocity m for four metals. The different markers represent the second order approximation 46.

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Figure 7

Variation of cavitation pressure Pc with expansion velocity m for elastic/perfectly plastic compressible Mises solids (Σy=0.01) with several values of Poisson’s ratio. The different markers represent the second-order approximation 72.

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Figure 8

Variation of cavitation pressure Pc with expansion velocity m for elastic/perfectly plastic compressible Mises solids (Σy=0.01). The different markers represent the third-order approximation 79.

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Figure 9

Variation of cavitation pressure Pc with expansion velocity m for four metals. The different markers represent the modified solution 80.

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Figure 10

Variation of cavitation pressure Pc with expansion velocity m for four metals. The different markers represent the equivalent solution 82.

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Figure 11

Variation of cavitation pressure Pc with expansion velocity m for aluminum 6061-T651. The circle markers represent the equivalent solution 82 with Σyc=0.00466.

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Figure 12

Comparison between cavitation model and penetration depth tests for conical-nose projectiles (Forrestal (11)). Differences between relation 83 and the logarithmic expression 86 are hardly noticeable.

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Figure 13

Comparison between cavitation model and penetration depth tests for ogival-nose projectiles (Forrestal (11)). Differences between relation 83 and the logarithmic expression 86 are hardly noticeable.

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Figure 14

Comparison between cavitation model and penetration depth tests for spherical-nose projectiles (Forrestal (11))

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Figure 15

Comparison between cavitation model and penetration depth tests for spherical-nose projectiles (Forrestal [(12)-Table 1])

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Figure 16

Comparison between cavitation model and penetration depth tests for spherical-nose projectiles (Forrestal [(12)-Table 2])

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Figure 17

Comparison between cavitation model and penetration depth tests for spherical-nose projectiles (Forrestal [(12)-Table 3])

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Figure 18

Comparison between cavitation and Rankine ovoid models. The different markers represent penetration test results obtained by Forrestal (11) and here Yc represents Y¯.

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