A method for scaling ballistic penetration phenomena

There are several established formulae for projectile penetration into semi-infinite concrete targets. Most of them include a term which indicates that regular scaling does not hold in this situation. Most of these formulae were derived using curve-fitting procedures, so that these terms do not represent any physical meaning. Non-scaling is also found in long rod penetrations, which cannot be attributed to strain rate effects. It is suggested here to differentiate the energy spent by the projectile during the penetration process into two parts, one - the energy expended for surface effects and the other - the energy expended for volume effects. By doing so, it is possible to derive expressions which account for the irregularity in scaling. These expressions are derived from the global, energy balance point of view, so they do not require the detailed characterization of the materials involved. They only require strict adherence to replica scaling procedures. A similar approach is used to account for strain rate effects, but in that case, the results are not as general and can be applied only to a narrow span of configurations. Examples are cited from tests with concrete penetration and long rod penetration into different targets.