8 / 17
Empirical coefficients in the compressibility equations of tungsten – nickel – iron
heavy alloy components
Material
A
, GPa
n
Tungsten
94.6
3.42
Nickel
45.3
4.507
Iron
19.5
5.642
elongated projectile. The density
ρ
0
of this alloy was
ρ
0
= 17170
kg/m
3
at
normal conditions. It was calculated by the formula
1
ρ
0
=
μ
1
ρ
10
+
μ
2
ρ
20
+
μ
3
ρ
30
.
Volume densities
ρ
i
in VNZh-90 alloy which are needed for drawing
a curve of the alloy dynamic compression (2) were calculated by the
equations
α
i
=
μ
i
ρ
0
/ρ
i
0
. They had the following values:
α
1
= 79
.
9
%
(for tungsten);
α
2
= 13
.
5
% (for nickel); and
α
3
= 6
.
6
% (for iron).
The obtained equation of the dynamic compressibility for VNZh-90
alloy in the form of equation (2) doesn’t allow developing an explicit
equation of the pressure
p
inside the material as a function of its density.
It makes this equation impossible to use for a numerical simulation (as
it is necessary to construct a special procedure for calculating pressure
based on this relationship; it results in increasing the computational time
significantly).
To solve this problem, equation (2) was approximated by the compressi-
bility equation (1); the coefficients
A
and
n
were selected respectively. In
order to determine these coefficients, the speed of sound in the alloy at
normal conditions was calculated.
c
0
=
s
dp
dρ
p
=0
.
When the function
p
(
ρ
)
is used in the form of equation (2),
c
0
is calculated
using the following equation:
1
ρ
0
c
2
0
=
3
X
i
=1
α
i
ρ
i
0
c
2
i
0
,
here
c
i
0
— are the speeds of sound in the alloy components at normal
conditions which are calculated on the basis of (1) as
c
i
0
=
p
n
i
A
i
/ρ
i
0
.
Calculation of the speed of sound inside VNZh-90 alloy at normal
conditions resulted in a value
c
0
= 3950
m/s. On the other hand, the
expression of
c
0
which uses the approximating compressibility equation
72 ISSN 0236-3941. HERALD of the BMSTU Series “Mechanical Engineering”. 2015. No. 1