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.

1.
Bishop
,
R. F.
,
Hill
,
R.
, and
Mott
,
N. F.
, 1945, “
The Theory of Indentation and Hardness
,”
Proc. Phys. Soc. London
0370-1328
57
, pp.
147
159
.
2.
Nelson
,
R. W.
, 2003, “
Nuclear Bunker Busters, Mini-Nukes, and the US Nuclear Stockpile
,”
Phys. Today
0031-9228
56
, pp.
32
37
.
3.
Levi
,
M.
, 2004, “
Nuclear Bunker Buster Bombs
,”
Sci. Am.
0036-8733
291
, pp.
50
57
.
4.
Hopkins
,
H. G.
, 1960, “
Dynamic Expansion of Spherical Cavities in Metal
,” in
Progress in Solid Mechanics
, Vol.
1
, edited by
I. N.
Sneddon
,
R.
Hill
North-Holland
, Amsterdam.
5.
Goodier
,
J. N.
, 1965, “
On the Mechanics of Indentation and Cratering in the Solid Targets of Strain-Hardening Metal by Impact of Hard and Soft Spheres
,”
Proceedings of the 7th Symposium on Hypervelocity Impact. III
,
215
259
.
6.
Hill
,
R.
, 1948, “
A Theory of Earth Movement Near a Deep Underground Explosion
,” Memo No. 21-48,
Armament Research Establishment, Fort Halstead
, Kent, England.
7.
Hunter
,
S. C.
, and
Crozier
,
R. J. M
, 1968, “
Similarity Solution for the Rapid Uniform Expansion of a Spherical Cavity in a Compressible Elastic-Plastic Solid
,”
Q. J. Mech. Appl. Math.
0033-5614
21
, pp.
467
486
.
8.
Forrestal
,
M. J.
, and
Luk
,
V. K.
, 1988, “
Dynamic Spherical Cavity-Expansion in a Compressible Elastic-Plastic Solid
,”
J. Appl. Mech.
0021-8936
55
, pp.
275
279
.
9.
Forrestal
,
M. J.
,
Tzou
,
D. Y.
,
Askari
E.
, and
Longcope
,
D. B.
, 1995, “
Penetration Into Ductile Metal Targets With Rigid Spherical-Nose Rods
,”
Int. J. Impact Eng.
0734-743X
16
, pp.
699
710
.
10.
Luk
,
V. K.
,
Forrestal
,
M. J.
, and
Amos
,
D. E.
, 1991, “
Dynamic Spherical Cavity Expansion of Strain-Hardening Materials
,”
J. Appl. Mech.
0021-8936
58
, pp.
1
6
.
11.
Forrestal
,
M. J.
,
Okajima
K.
, and
Luk
,
V. K.
, 1988, “
Penetration of 6061-T651 Aluminum Targets With Rigid Long Rods
,”
J. Appl. Mech.
0021-8936
55
, pp.
755
760
.
12.
Forrestal
,
M. J.
,
Brar
,
N. S.
, and
Luk
V. K.
, 1991, “
Penetration of Strain-Hardening Targets With Rigid Spherical-Nose Rods
,”
J. Appl. Mech.
0021-8936
58
, pp.
7
10
.
13.
Jones
,
S. E
, and
Rule
,
W. K.
, 2000, “
On the Optimal Nose Geometry for a Rigid Penetrator, Including the Effects of Pressure-Dependent Friction
,”
Int. J. Impact Eng.
0734-743X
24
, pp.
403
415
.
14.
Durban
,
D.
, and
Masri
,
R.
, 2004, “
Dynamic Spherical Cavity Expansion in a Pressure Sensitive Elastoplastic Medium
,”
Int. J. Solids Struct.
0020-7683
41
, pp.
5697
5716
.
15.
Hill
,
R.
, 1950,
The Mathematical Theory of Plasticity
,
Oxford University Press
, London.
16.
Yarin
,
A. L.
,
Rubin
,
M. B.
, and
Roisman
I. V.
, 1995, “
Penetration of a Rigid Projectile Into an Elastic-Plastic Target of Finite Thickness
,”
Int. J. Impact Eng.
0734-743X
16
, pp.
801
831
.
17.
Durban
,
D.
, and
Fleck
,
N. A.
, 1997, “
Spherical Cavity Expansion in a Drucker-Prager Solid
,”
J. Appl. Mech.
0021-8936
64
, pp.
743
750
.
18.
Durban
,
D.
, and
Baruch
,
M.
, 1976, “
On the Problem of a Spherical Cavity in an Infinite Elasto-Plastic Medium
,”
J. Appl. Mech.
0021-8936
43
, pp.
633
638
.
You do not currently have access to this content.