A History of Research and a Review of Recent Developments

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