A scaling law for predicting the ballistic limit of aluminium alloy targets perforated in ductile hole formation

Abstract

The ballistic performance of monolithic targets perforated in ductile formation by rigid projectiles can be reasonably approximated by an energy balance based on the work done in expanding a hole from zero initial radius to that of the penetrating projectile. For a specific projectile, these energy balance laws can be expressed in terms of a simple scaling law which requires an empirical fit to ballistic data. However, once this fit has been performed for a specific projectile against a specific target material, predicting the performance of other materials against this projectile can be done from a simple quasi-static compression stress–strain curve, provided the target is perforated in ductile hole formation. Four variations of ductile hole formation analytical and semi-empirical models have been reformulated as scaling laws and evaluated for their ability to characterise the performance of monolithic aluminium plates impacted by 7.62 mm APM2 projectiles at normal incidence. The database used to fit and evaluate the performance of the scaling laws incorporates more than 1600 V50 measurements against 24 different alloys and tempering/strain-hardening combinations with thicknesses ranging from 16.2 to 63.5 mm. The highest performing scaling law formulation was found to characterize the measured V50 to within 5% of the experimental value for over 97% of the database entries. Further improvements in accuracy are likely impossible when representative stress–strain curves are used for performance characterization rather than tests of each individual plate used in the ballistic tests. The scaling law can be applied to predict the performance of targets perforated in ductile hole formation with a high level of confidence, an example of which is provided for the 12.7 mm APM2 projectile against a range of aluminium alloys.