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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170<br />
Penetration <strong>and</strong> fragmentation<br />
linear relationship between t/D <strong>and</strong> 2V 2 W p/D 3 , at the upper limit <strong>of</strong> scatter,<br />
<strong>and</strong> a power relationship at the lower limit. For the perforation <strong>of</strong> metal<br />
plates with a Brinell Hardness Number between 250 <strong>and</strong> 300, <strong>and</strong> a projectile<br />
striking with zero obliquity with t/D in the range 0 to 2.0, the lower scatter<br />
b<strong>and</strong> relationship was found to be W pV 2 /D 3 =(t/D) 3/2 .<br />
Early publications on metal penetration, taking account <strong>of</strong> the plastic<br />
deformation <strong>of</strong> the projectile were due to G.I.Taylor [7.42, 7.43]. An<br />
approximate theory <strong>of</strong> armour penetration, taking account <strong>of</strong> energy dissipation<br />
as the result <strong>of</strong> plastic deformation, <strong>and</strong> also considering the heating <strong>of</strong> the<br />
interface between the projectile <strong>and</strong> the plate, was established by Thomson<br />
[7.44] in 1955. During the 1960s <strong>and</strong> 1970s there was considerable analytical<br />
activity, <strong>and</strong> during this period ballistic perforation dynamics was examined<br />
by Recht <strong>and</strong> Ipson [7.45]. They analysed the relationship between the energy<br />
lost to deformation <strong>and</strong> heating <strong>and</strong> the change in kinetic energy <strong>of</strong> the projectile.<br />
Their equations gave good agreement with post-perforation velocities when<br />
thin plates were perforated by blunt cylindrical fragments. Perhaps the best<br />
documented work during this period was the extensive research carried out in<br />
the USA under the guidance <strong>of</strong> Goldsmith [7.46], whose work has been<br />
summarized in a number <strong>of</strong> fundamental papers. A typical review is contained<br />
in reference [7.47], written in the late 1970s.<br />
Much <strong>of</strong> the fragmentation that causes penetrative damage comes from the<br />
explosion <strong>of</strong> tubular bombs, <strong>and</strong> it was during the Second World War that the<br />
physics <strong>of</strong> the fragmentation process was first investigated, again by G.I.Taylor<br />
[7.48]. He showed analytically that the distribution <strong>of</strong> stress within the wall <strong>of</strong><br />
a tube containing detonating explosive was such that longitudinal cracks were<br />
likely to form at the outer surface. These cracks penetrate through to the inner<br />
wall <strong>and</strong> cause fragmentation when the internal pressure becomes equal to the<br />
tensile strength <strong>of</strong> the material. The longitudinal cracks in the steel casing <strong>of</strong> a<br />
bomb start close to the detonation wave point, <strong>and</strong> open out rapidly as the tube<br />
exp<strong>and</strong>s. Although the cracks are wide, they do not allow the pressurised content<br />
to escape until the tube has exp<strong>and</strong>ed to double its initial diameter.<br />
The maximum distances that fragments can be driven outwards from<br />
explosives depend, <strong>of</strong> course, on their initial velocities, <strong>and</strong> these are a function<br />
<strong>of</strong> the size <strong>of</strong> the explosion. The maximum radial horizontal distance in metres<br />
(V) is <strong>of</strong>ten given as 45W 1/3 , where W is the equivalent weight <strong>of</strong> TNT charge<br />
in kilograms. This was discussed by Kinney <strong>and</strong> Graham [7.49]. For an ejection<br />
angle <strong>of</strong> a with the horizontal, r=V 2 sin 2 a/g, so that the maximum range occurs<br />
when a=45°, <strong>and</strong> at this range the maximum fragment velocity=(rg) 1/2 .<br />
Observations <strong>of</strong> large explosions show that the number <strong>and</strong> mass <strong>of</strong> fragments<br />
are related exponentially.<br />
During the 1980s much <strong>of</strong> the analytical work was directed to providing<br />
finite element solutions for the action <strong>of</strong> penetrators on metal targets, <strong>and</strong> using<br />
computer initiated display techniques to plot the successive deformation patterns.<br />
The fundamental science was unchanged but the pictorial demonstration was