Exact formula for the effective yield stress of metals with arbitrary stress–strain curves

Abstract

Sufficiently thick ductile protective targets are perforated by rigid, pointed-nose projectiles in a hole enlargement process. Several recent studies have shown that the (spherical cavitation) effective yield stress YcS is an essential effective material parameter for analytical predictions of ballistic limit velocities. This effective yield stress is also found to be essential in determining ballistic equivalence between two different alloys of the same metal and between two different metals like aluminium and steel. First, the concept of the (spherical cavitation) effective yield stress is presented with comprehensive reference to previous studies, to emphasize the practical importance of this effective material parameter. Thereafter, an exact formula for YcS, which is based on the W−1(x) branch of the Lambert function, is derived and eliminates the need for solving the exact value of YcS by a numerical procedure. Moreover, while approximate expressions of YcS are exist for several stress–strain curves with definite yield stress, the new exact formula is applicable for any stress–strain relation, including stress–strain curves without a definite yield point and curves which take into account thermal softening effect.