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Nt1310 Lab 3.3

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CHAPTER 3:
3.1: Formulation of Mathematical Model

Consider the impact of a bullet on a fabric of soft armor made up of interlinked and crisscrossed yarns. The fabric consists of n layers stacked above one another. The bullet carries a momentum which it transfers to the yarns in the fabric. These yarns, due to their capability to quickly dissipate the energy of the bullet by transferring it to neighboring yarns in all directions, prevent the bullet from passing through. The mechanism of the bullet impact and the subsequent stoppage can be modelled as given below.

Figure 3.1: schematic study of bullet hitting ballistic armor

Let the mass of the fired bullet be Mb. It is fired at an initial velocity of v. The momentum
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Energy absorbed= volumetric energy density* volume =1/2*Y*volume*(strain)^2 (4)

The volume is given by, volume= n m A c*dt (5)
Here, c= Velocity of the sound in the armor material
From equations (4) and (5), we get,

Energy absorbed=1/2*Y*n m A c∫_0^t▒〖∈^2 (t)dt〗 (6)

The strain is integrated with time from the time of impact to the time of failure as it keeps on changing during the impact of the bullet and is not constant.

The change in kinetic energy of the bullet is given by: Change in kinetic enregy= 1/2 M_b (V_f^2 - V_i^2 ) (7)

Where, Vf = Final velocity of the bullet Vi = Initial velocity of the bullet

The energy absorbed by the fabric in the armor is equal to the loss of kinetic energy carried by the bullet during impact.

Energy absorbed by armour =change in kinetic energy of
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