STRESS-STRAIN CHARACTERISTICS OF MATERIALS AT HIGH STRAIN RATES. PART IV. EXPERIMENTAL AND THEORETICAL ANALYSIS OF PLASTIC IMPACTS ON SHORT CYLINDERS

The effects of strain rate on the stress-strain characteristics of copper and lead were studied by measuring both stress and strain as functions of time using short cylindrical specimens supported at one end on a modified Hopkinson pressure bar and impacted at the other end by a steel projectile. Corresponding stresses and strains were computed according to an elementary nonstrain-rate theory (sometimes referred to as the von Karman theory) in which the dynamic stress-strain curve is assumed to be the same as the static stress- strain curve. Stresses and strains were also computed according to an elementary strain-rate theory (sometimes referred to as the Malvern theory) in which the dynamic stress may exceed the static stress for a given strain by an amount which depends upon the strain rate. It was found that the predictions of the nonstrain- rate theory agreed with measured values only for low impact velocities and for points at least two diameters from the impact end of the specimen. By proper choice of the flow or relaxation constant in the elementary strain-rate theory, measured and computed values of strain, or of stress, but not both simultaneously, could be brought into agreement. In the more general exponentialtype, strain-rate law, two independent parameters appear. Presumably with two constants to adjust, this theory could be made to correctly predict both stresses and strains for the conditions under which the tests were performed. If this procedure forces the theory to account for variations which are actually caused by lateral inertia and shear, erroneous conclusions regarding the properties of the material will be drawn. Further study of the effects of shear and lateral inentia is indicated. (auth