Inertia and strain-rate effects in a simple plate-structure under impact loading

Abstract

Previous studies have shown that the way in which metal structures absorb energy by gross distortion under impact conditions depends on the generic type of structure. In particular they have shown that structures which respond to quasi-static testing by means of an initial peak load followed by a falling load as deformation proceeds (‘type II’ response, corresponding broadly to plates loaded endwise) exhibit both inertia and strain-rate effects under impact loading from moving strikers. This paper describes a detailed study of these phenomena by means of experiment and theory. Experiments were conducted in a drop-hammer rig on a large number of specimens having the same general geometry, but made in two different sizes and of two different materials (mild steel, aluminium alloy) chosen for their different strain-rate characteristics in the plastic range. The experiments involved the overall measurement of final distortion of the specimens in relation to a wide range of testing conditions with moderate velocity; strain gauge studies, high-speed photography and other investigations of the detailed behaviour. The main emphasis of the various assays was to discover the way in which the initial kinetic energy of the striker was dissipated within the structure. During the course of the work, Zhang and Yu proposed a simple analysis of the same phenomena by means of a model based on the ideas of classical inelastic impact theory. According to their theory, a significant fraction of the incident kinetic energy of the striker is absorbed during the initial impact event; and this fraction depends only on the ratio of the mass of the striker to the mass of the spicimen and the initial crookedness, but not on the velocity of impact. Our experiments agreed with this analysis in some overall respects, but were irreconcilable with it in several others, for which we had amassed substantial data. We therefore produced a revised analysis, which was less austere than that of Zhang and Yu but which nevertheless remained essentially simple. We show in the paper that this new theory agrees satisfactorily with all aspects of the experimental observations. The analysis reveals clearly the roles of inertia and strain rate in impact conditions. It also produces two new dimensionless groups, which together provide a key to classification of the various patterns of behaviour which are possible in the impact response of ‘type II’ specimens.