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heavy alloys based on tungsten, nickel, and iron [13, 14]. Apart from
possessing a high density (from 16.9 to 18.7 g/sm
3
) these alloys feature
a complex of other essential physical and mechanical properties which
put them among major materials used for high penetrability projectiles
production. These properties comprise a high plasticity (elongation up to
20%), a high ultimate strength (above 1000MPa), and a high yield strength
(up to 900. . .1000MPa).
All the above considered, a numerical analysis of penetration of the
elongated projectiles made of tungsten-nickel-iron alloys proves important
to conduct. It is necessary to have a dynamic compression curve of
the alloy, which describes pressure inside the alloy as a function of its
density. Compressibility of materials has certain effect on the penetration of
elongated projectiles in a hydrodynamic mode [15, 16]. Therefore, a correct
choice of
р
(
ρ
)
for the materials of both the target and projectile determines
validity of the numerical simulation results and their correspondence to the
real physical process.
An equation of dynamic compressibility for such multicomponent
composition as a tungsten – nickel – iron alloy can be developed by
applying the equations of compressibility for individual components [17].
Both assuming that total volumetric deformation of a multicomponent
material is a sum of volumetric deformations of individual components
and assuming equality of pressures in all components, interconnection
between density and pressure in the tungsten – nickel – iron composition
can be defined as follows:
ρ
0
ρ
=
3
X
i
=1
α
i
1 +
p
A
i
−
1
/n
i
,
(2)
here values
α
i
describe phase composition of the heavy alloy and
correspond to the volume density of tungsten, nickel, and iron (it is
evident that the following relationship must be true:
α
1
+
α
2
+
α
3
= 1
);
A
i
and
n
i
are parameters in the compressibility equations (1) for each
individual component. When the phase composition is known, a standard
density
ρ
0
of a heavy alloy is defined as
ρ
0
=
α
1
ρ
10
+
α
2
ρ
20
+
α
3
ρ
30
, here
ρ
10
= 19350
kg/m
3
,
ρ
20
= 8870
kg/m
3
,
ρ
30
= 7850
kg/m
3
are individual
standard densities of tungsten, nickel, and iron respectively. Values of the
empirical coefficients in the compressibility equations of these materials,
which are used for obtaining the compressibility equation for the tungsten
– nickel – iron high-density composition, are shown in the table [18].
When calculating we considered VNZh-90 alloy (Russian abbrevation
for a W-Ni-Fe alloy) [14] with respective mass contents of tungsten, nickel,
and iron
μ
1
= 90
%,
μ
2
= 7
%,
μ
3
= 3
% as the main material of the
ISSN 0236-3941. HERALD of the BMSTU Series “Mechanical Engineering”. 2015. No. 1 71