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р
(
ρ
)
(1) can be written as
c
0
=
p
nA/ρ
0
which allows linking the
coefficients
A
and
n
:
A
=
ρ
0
c
2
0
/n
. So the equation (1) can be rewritten as:
p
=
ρ
0
c
2
0
n
ρ
ρ
0
n
−
1
,
where there is the only unknown coefficient
n
. This coefficient was selected
in case if a deviation of equation (1) from compressibility equation (2) of
the multicomponent material containing tungsten, nickel, and iron in the
given ratio is minimal. A pressure range was considered from 0 to 40 GPa
which overlapped the domain of pressures occurring during the material
interactions at velocities of 1000. . .2000 m/s.
In the end, to perform these numerical computations the dynamic
compressibility equation (1) with coefficients
A
= 57
.
1
GPa;
n
= 4
.
7
was
used. The contrastive analysis of the different dynamic compressibility
curves of the observed material showed that equation (1) with the given
values of the coefficients resulted in the similar way as the ones obtained
by equation (2) for a multicomponent medium.
The numerical computations were performed for a cylinder shaped
projectile made of VNZh-90 alloy with the length of
l
0
= 500
mm and
a diameter of
d
0
= 24
mm (elongation of
l
0
/d
0
≈
21
). The target was
assumed to be made of steel with the strength corresponding to the steel
Рис. 2. Steel target cavity shape during
the penetration of VNZh-90 alloy
elongated projectiles with different yield
strengths at initial interaction velocity of
1600m/s:
a
—
d
—
σ
Y
= 50
; 500; 1000; 1500MPa,
respectively
targets of a medium hardness (a
yield strength was set 1000MPa).
Dynamic compressibility of the steel
target was defined by equation (1)
with the coefficients
A
= 19
.
5
GPa;
n
= 5
.
642
[18]. Target thickness was
800 mm and its lateral size (diameter)
was 320 mm.
While analyzing the impact of
the projectile material strenght on the
target penetration, its yield strength
σ
Y
was taken to be equal to 50; 500;
1000, and 1500MPa.
Fig. 2 shows the final shapes
of the cavities in the steel targets
obtained during the penetration
of the elongated rods made of
VNZh-90 alloy with different yield
strengths and the initial interaction
velocity
v
0
= 1600
m/s. The results
ISSN 0236-3941. HERALD of the BMSTU Series “Mechanical Engineering”. 2015. No. 1 73