Page 362 - Mechanics Analysis Composite Materials

Chapter 7. En~ironmental, special loading. and manufacturing effects 347

Fig. 7.40. Back view of plate No. 3 (see Table 7.2) after the impact test

Table 7.2
Ballistic test of plates made of aramid fabric.
Plate no. Projectile velocity (m/s) Test results

1 315 No penetration
2 320 The projectile is "caught"
by the containment
3 325 Penetration

further referred to as 0"/90" layers. All the plates listed in Table 7.2 have n = 32 of
such couples.
To calculate the projectile velocity below which it fails to perforate the plate (the
so-called ballistic limit) we use the energy conservation law according to which

imp( q - yz) = n( w + T) , (7.63)

where K is the projectile striking velocity, V, is its residual velocity, mp = 0.25 kg is
the projectile mass, n = 32 is the number of the 0"/90" layers, Wis the fracture work
for the 0"/90" layers, and Tis the kinetic energy of the layer. All the other factors
and the fiberglass cover of the plate are neglected.
Fracture work can be evaluated using the quasi-static test shown in Fig. 7.41. A
couple of mutually orthogonal fabric layers is fixed along the plate contour and
loaded with the projectile. The area under the force-deflection curve (solid line in
Fig. 7.41) can be treated as the work of fracture which for the fabric under study has
been found to be W = 120 Nm.
To calculate T, the deformed shape of the fabric membrane has been measured.
Assuming that the velocities of the membrane points are proportional to deflections
.f and that df,/dt = K kinetic energy of the fabric under study (density of the layer
unit surface is 0.2 kg/m') turn out to be T = 0.0006 v,'.
To find the ballistic limit, we should take V, = 0 in Eq. (7.63). Substituting the
foregoing results in this equation we get & = 190.5 m/s which is much lower than
the experimental result (& = 320 m/s) following from Table 7.2.