Page 363 - Mechanics Analysis Composite Materials

348 Mechanics and analysis of composite materials

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Fig. 7.41. Fordeflection diagrams for square aramid fabric membranes -couple of layers with
orthogonal orientations,---- superposition of the diagrams for individually tested layers.

Let us change the model of the process and assume that the fabric layers fail one
after another rather than all of them at once, as it is presented in Eq. (7.63). The
result is expected to be different because the problem under study is not linear, and
the principle of superposition is not valid for it. Bearing this in mind, we write
Eq. (7.63) in the following incremental form:

(7.64)

Here, 6-1and F$ are the projectile velocities before and after the failure of the kth
couple of fabric layers, W is, as earlier, the fracture work consumed by the kth
couple of layers, G-1 = 0.0006 55, and the last term in the right-hand side of
Eq. (7.64) means that we account for the kinetic energy of only those fabric layers
that have been already penetrated by the projectile. Solving Eq. (7.64) for V, we
arrive at

I '1
L
V, = ,/[l -0.0048(k- l)]G%, -- W. (7.65)
mP
Fork = 1, we take V, = 320 m/s, in accordance with the experimental ballistic limit,
and have fi =318.5 m/s from Eq. (7.65). Taking k = 2 we repeat the calculation