Physicsof the high-speed impact of solid objects with ...

, ;Physics of the high-speed impact of solid objects with poreus media A. S. Balankin (Submitted September 2, 1987j Zh. Tekh. Fiz. 58, 2380-2382 (December 1988)

The befthvior of salid objects on impact is of significant interest in various areas of present-day physics and technology. Particular attention has been paid to the problem of high-speed impact in which the colliding bodies interact by a hydrodynamic

or explosive mechanism.

The main results

1-3

both experimental and theoretical, pertain penetration of strikers into salid materials.

the same time, the existing

~ata

6-8

here,

to the 1-5 At

indica te that

the destruction of porous media in high-speed impact can be of a substantiaIly different character from the destruction of salid materials. However, the theoretical investigation of the penetration and destruction of porous media in high-speed impact has been clearly inadequate. In the present paper a physical model is proposed which accounts for the known characteristics of the destruction of porous media in collisions with salid strikers and predicts some new features. We shaIl consider the impact of a salid striker against a porous target of the same material. The pares are assumed to be much smaIler than the characteristic geometric dimensions of the striker, and the pares are assumed closed, i. e., they are not filled with air. In addition, the linear dimension of the striker in the direction of impact wiIl be assumed smaIl enough that the conditions of its penetration into the target remain unchanged up until the end of the interaction. The porous medium is described by a model of spherical (or cylindrical) ceIls.9 The initial porosity wiIl be characterized by the ratio of the specific volume of the b~HbP-¿~n1, where !:io and b o are the initial radü of the pare and cell: n 2 for cylindrical and 3 for spherical ceIls. The rheological behavior of the porous medium at the impact velocities considered, vo > 2/ostl Po (ost and Po are the ultimate dyn~mic strength and density of the salid material; we are neglecting the difference of the physical properties of the materials of the striker and target), can be described in the general case in the framework of a model of a compressible vis coplas tic medium in which for ao ; 1.2 (0.0 is the ratio of the density of the material to the density of the porous medium) the compressibility

=

of the

porous

medium

is determined

solely

by

ao

.

shock wave front). Depending on the relative values of these parameters, various interaction regimes of the striker and porous medium are possible: a) For Ma < 1 but vo > 2/ostl Po the interaction wiIl occur by a modified hydrodynamic mechanism, interaction regime being determined by the param-

eters Re, Y, Ma' and Mo.

I. For Re < R[l + ao(2ao-1)-1/2], where R "8.5 at the shock wave front formed during impact, a smooth coIlapse (filling up) of the pares wiIl occur, and,depending on the values of Ma and M o, three different regimes of penetration of the striker into the target arepossible: 1) In the case of a sufficiently low porosity, a subsonic regime of pemitration, U < ca, is possible, whel'ein the coIlapse óf pares with a o < acr occur at the front of the shock wave propagating away from the contact surface (Fig. la), and in the steady stage the velocity and penetration depth are independent of the porosity (for porous copper with 1.05 this re gime exigís, for example, at vo = ao 3 km/s and ao ::; 20 ¡lID).

=

2) Since the speed of sound decreases rapidly with increasing porosity, 10 fol' fioufficiently large ao the penetration wiIl be supersonic with respect to the porous medium and subsonic with respect to the salid material, M o < 1 < M a' In this case in the steady 'stage of penetration the shock wave wiIl be stationary relative to the point of contact (Fig. lb), and the velocity u and the penetration depth L and time To are given by u=aovo!ao+ (2ao-1¡'lor\ '0=

ao. Mo=-,

CO

M.=.-,

u

c.

Re=-,

aou

.

~: [1+0;0(20;0-1(10];

=

a

b

z

ao.st Y=-;¡-,

pou

(2)

L=loo;o(Zao-I¡-'lo.

We see from this that the penetration depth into salid ~and porous targets (of different materials having the same density) wiIl be smaIler in the second case (e.g., for vo = 3 km/s the penetration depth of an aluminum striker ( 2-0 = 5 cm, da = 0.3 cm, Po = 2.7 g/cm3) into porous copper (ao = 1.94, Pp = 4.6 g/cm3, a o < 5 ].lm) is smaIler by a factor of 1.13 than the penetration depth into salid titanium 4.5 g/cm3). . with Pp

Analysis of the problem suggests the foIlowing dimensionless parameters governing the dynamics of the interaction of the striker with the target: u

the

c

J

J

J tu '=40'

j.(a),

Vo' C(T¡~(T)'

aou' 1!.H"ap'

(1)

where v is the viscosity, Hvap is the heat of vaporization, co and ca are the speed of sound in the salid material and porous medium, C(T) and J3(T) are the specific heat and coefficient of thermal expansion, )..(a) is the parameter of the shock adiabat, and D = c + Au, (D and u are the shock wave velocity and mass velocity of the material behind the 1451

SOy. Phys. Tech. Phys. 33(12).

December 1988

o o -" 00000'00 0000"00 ooooe,o ocoooe,o o o e

It

0038-5662/89/12

FIG.

1.

pare size 1) Striker front, y
M o> 1, Y < 1.

@ 1989 American Institute of Physics '

1451

penetration in Ref. 7.

has been

investigated

experimentaIly

For y. < 1 and Mo < 1 < M a the interaction wiIl have a time-dependent character during the ~ntire penetration time, and the penetration depth of the striker into the target will be l/ao-1 (3) L=lo

3) For M o > 1 a compression of the pares with ao > acr óccurs, with cumulation of energy at the ao The rapid release of energy causes point a a sharp rige in the temperature and a transition of the material at the shock front to the plasma siRte For Cu with 0.0 25 and a o 2 mm this re gime

= .

b

a

FIG. 2. Collapse of pares witheo = 20 vvo-l (1 + 0.0 (20.01r 1 I 2 ] for Ha « 1, 1\:1= 3. e) Spherical pare, b) cylindrical pore; O = '[ 1 < '[ 2 < '[ 3 < '[ ~.

3) For 1 < M.o < M a' Re < 8.5[1 1)-1/2], and 0.0 > 1.2 we have

+ 0.0(20.0-

=

perimental data. 8 b) At ultrahigh impact velocities Vo » Co the kinetic energy of the striker is released by an explosive mechanism. The characteristic time '[o and intensity I of the energy release are given by lo (1/;;-'-1)(v';;-'

= l,aJ~' 2aJ-1 .

- Po/Plt behind the

where I3c= 1 the striker

"0= 1'0

and

shock

is the density wave.

Pl

of

n. For Re > 8.5[1 + 0.0(20.0 - 1)- 1/2] the interaction of the striker with the porous medium will be complicated by cumulation effects upon collapse of the pores. In this case also there are three possible interaction mechanisms:

1) For Ma. < 1, the coIlapse of the pares at the shock front propagating away from the point of contact (and having a width much greater than a o) is accompanied by a cumulation of energy at the point a = O, analogous to the cumulation that occurs during dynamic pressing of powders. 11 This cumulation leads to a rapid growth of the pressure and to the formation of strong shock waves which enhance the destructive effect of the impact. 2) For Cn < u < co the cumulation process wiIl differ substantia1ly from that discussed above. We see from the calculated results on the dynamics of pare coIlapse for Mo < 1 < M a. (Fig. 2) that a cumulative jet forros during the deformation of thepore; this jet has a high velocity Vjet determined by the values of u and Re and the po~ geometry: for spherical pares u < Vjet < co, while for cylindrical pares Vjet > co' The cumulative jet mechanism of shock front formation has been observed experimentaIly 8 during the loading of porous samples of copper

wave.

and lead

(a o > 5, ao

- 2 mm) by

a detonation

At high porosities, when Y » 1, the penetration for Mo < 1 < M a. is similar to the flow of a supersonic gas around the striker. Such a regime of

=

exigís for va> 6.8 km/s, as is confirmed by ex-

/~

L

.

v-¡;

from which

+ 1)3

110 Vao

Po~ v-¡; I'B

' I

we see that

2 (v-¡; -1)(Vao

the intensity

(4)

+ 1)5 ,

of the energy

release faUs off with increasing 0.0' The author expresses ros deep gratitude to A. A. Kozhushko and G. S. Pugachev for helpful discussion of the results.

lN. A. Zlatin, A. I. Krasil 'shchikov, G. I. Mishin, and N. N. Popov, Ballistic Devices and Their Application in Experimental Research (in Russian], Nauka, Moscow(1974). 2N. A. Zlatin, Zh. Tekh. Fiz. 31,982 (1961) (Sov. Phys. Tech. Phys. .2, 714 (1962)]. 3S. I. Anisimov, A. V. Bushman, G. I. !Canel', et al., Pis 'ma Zh. Eltsp. Teor. riz. 12, 9 (1984) [JErP Lett. 12, 8 (1984)]. ~N. A. Zlatin and A. A. Kozhushko, Zh. Tekh. Fiz. 52, 330 (1982) (Sov. Phys. Tech. Phys. 27, 212 (1982)]. sA. Ya. Sagomonyan, Penetration [in Russian] , Moscow (1974). 6Ya. B. Ze1'dovich and Yu. P. Raizer, Physics of Shock Waves and High Temperature Hydrodynamic Phenomena, 2 vo1s., Academic Pre.ss, NewYork (1966, 1967). 'G. V. Pryakhin and V. M. Titov, Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 110 (1969). 8yu. B. Khvostov, Dokl. Akad. NaukSSSR 294, 302 (1987) [SOY. Phys. Dok1. 14, 378 (1987)]. 9S. Z. Dunin and V. V. Surkov, 10

Prikl.

A. S. Ba1ankin, Author's Abstract (in

Russian]

Engineering

Physics

Mat. Mekh. 43,

of Candidate's Institute,

511 (1979).

Dissertation

Moscow (1986).

11 A. S. Balankin, L. P. Gorbachev, E. G. Grigor'ev, and D. H. Skorov,

Zh. Prikl.

Translated

Mekh. Tekh.

by Steve

Fiz.,

No. lo, 132 (1980).

Torstveit

,. ...-

1452

SOy.Phys. Tech. Phys. 33(12). December 1988

A. S. Balankin

1452