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Research Papers

# Shock Waves in Dynamic Cavity Expansion

[+] Author and Article Information
Tal Cohen1

Faculty of Aerospace Engineering, Technion, Haifa 32000, Israelbtal@tx.technion.ac.il

Rami Masri, David Durban

Faculty of Aerospace Engineering, Technion, Haifa 32000, Israel

1

Corresponding author. This work is based on a part of a M.Sc thesis to be submitted to the Technion.

J. Appl. Mech 77(4), 041009 (Apr 09, 2010) (8 pages) doi:10.1115/1.4000914 History: Received April 12, 2009; Revised October 22, 2009; Published April 09, 2010; Online April 09, 2010

## Abstract

High velocity cavitation fields are investigated in the context of large strain $J2$ plasticity with strain hardening and elastic compressibility. The problem setting is that of an internally pressurized spherical cavity, embedded in an unbounded medium, which grows spontaneously with constant velocity and pressure. Expansion velocity is expected to be sufficiently high to induce a plastic shock wave, hardly considered in earlier dynamic cavitation studies. Jump conditions across singular spherical surfaces (shock waves) are fully accounted for and numerical illustrations are provided over a wide range of power hardening materials. Simple formulae are derived for shock wave characteristics and for the asymptotic behavior within near cavity wall boundary layer.

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## Figures

Figure 11

Variation in V along the radial coordinate ξ within the near cavity zone for material 1, as specified in Table 1, for m=0.2,0.6. Dashed line represents the asymptotic expansion 76.

Figure 12

Variation in Σr along the normalized radial coordinate ξ in the near cavity zone as specified in Table 1 with m=0.2,0.6. Dashed line represents the asymptotic approximation from relation 711.

Figure 13

Variation in ρ/ρo along the normalized radial coordinate ξ in the near cavity zone as specified in Table 1 with m=0.2,0.6. Dashed line represents the asymptotic approximation from relation 710.

Figure 1

Diagram of the field induced by self-similar expansion of a spherical cavity (with current radius A) in an unbounded Mises medium in the presence of an elastoplastic shock wave. p is the applied pressure and ξ=R/A is the nondimensional radial coordinate. ξE and ξP represent the rigid/elastic and the plastic wave fronts, respectively, while ξi denotes the elastoplastic interface where σe=σy.

Figure 2

Comparison of shock intermediate effective stress values from exact solution of Eq. 56 with approximate value from Eq. 58. Hardening relation 27 is used with varying values of hardening index n. Predictions of ΣP are practically identical.

Figure 3

Variation in effective stress along the radial coordinate ξ with different values of m, for material 1, as specified in Table 1. The dashed line shows the approximate value of ΣP calculated from relation 58.

Figure 4

Variation in V along the normalized radial coordinate ξ with different values of m for material 1, as specified in Table 1. The dashed lines represent the calculated values of ξP from relation 513, for m=0.6,0.7, respectively.

Figure 5

Variation in density ratio ρ/ρo along the normalized radial coordinate ξ with different values of m for material 1, as specified in Table 1. Sub figure is enlargement of curve for m=0.6, showing the sharp drop in density near the cavity wall, indicating the existence of a boundary layer.

Figure 6

Variation in radial stress along the normalized radial coordinate ξ with different values of m for material 1, as specified in Table 1

Figure 7

Variation in applied pressure P with cavity expansion velocity for (a) materials 1 and 2 as specified in Table 1 (different values of hardening index n) and (b) materials 1, 6, and 7, as specified in Table 1 (different values of Poisson ratio ν)

Figure 8

Variation in applied pressure P with cavity expansion velocity for materials 1, 4, and 5, as specified in Table 1 (different values of Σy). Dynamic branch 3m2/2 for incompressible solids (ν=0.5) is shown by circles.

Figure 9

Variation in C with cavity expansion velocity for materials specified in Table 1

Figure 10

Variation in Σ along the normalized radial coordinate ξ within the near cavity zone for material 1, as specified in Table 1, for m=0.2,0.6. The dashed line represents the asymptotic expansion 75.

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