A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
A History of Research and a Review of Recent Developments
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142<br />
Penetration <strong>and</strong> fragmentation<br />
research work <strong>of</strong> that era. One <strong>of</strong> the earliest penetration theories [7.1] was<br />
due to J.V. Poncelet (1788–1867), mentioned earlier in the Introduction, who<br />
was a French military engineer <strong>and</strong> pr<strong>of</strong>essor <strong>of</strong> engineering mechanics at the<br />
military school in Metz. He had a perceptive view <strong>of</strong> the physics <strong>of</strong> the<br />
penetrative process, in which he combined the resistance <strong>of</strong> a medium to the<br />
static penetration by a body with a resistance linked to the speed at which the<br />
body was moving. He considered that the dynamic resistance in a material<br />
such as soil or s<strong>and</strong> should be analogous to resistance to fluid dynamic flow.<br />
He therefore assumed that the force resisting penetration would be given<br />
by the equation<br />
F=–A(a+bV (7.1)<br />
where<br />
F = resisting force<br />
A = cross sectional area <strong>of</strong> the projectile<br />
V = impact velocity<br />
a, b were constants to be determined by experiment.<br />
If the mass <strong>of</strong> the projectile=m, the equation <strong>of</strong> motion is<br />
2 ),<br />
<strong>and</strong> by integration we get the relationship<br />
(7.2)<br />
(7.3)<br />
where p=vertical penetration.<br />
This assumes that the material has sufficient depth in the direction <strong>of</strong><br />
penetration to bring the projectile to rest before it ‘breaks out’ <strong>of</strong> the far side.<br />
If this is not so, adjustments have to be made to the analysis, as we shall see<br />
later. The difference between penetration into soil or concrete, or other frangible<br />
materials, <strong>and</strong> into strong, ductile materials is very great, <strong>and</strong> is influenced by<br />
the average pressures resisting penetration. These can be 15 times greater in<br />
steel armour, for example, than for concrete. For all materials it is the kinetic<br />
energy <strong>of</strong> an undeforming projectile that crushes <strong>and</strong> distorts the target.<br />
The contribution <strong>of</strong> Poncelet to many problems in materials science has<br />
been well documented in the book <strong>History</strong> <strong>of</strong> Strength <strong>of</strong> Materials (ref. [7.2]),<br />
<strong>and</strong> it is from this that we learn that he started from poor beginnings before<br />
winning scholarships that eventually took him to the Ecole Polytechnique.<br />
He joined Napoleon’s army in 1812 <strong>and</strong> was taken prisoner during the retreat<br />
from Moscow. His ideas about projective geometry were developed during<br />
his confinement for two years in Saratov. After his subsequent career at Metz<br />
he became comm<strong>and</strong>ant <strong>of</strong> the Ecole Polytechnique between 1848 <strong>and</strong> 1850.