Reexamination of the Kolsky Technique for Measuring Dynamic Material Behavior

Abstract

A one-dimensional wave propagation analysis is carried out to assess the validity of the Kolsky formulas [1] for average stress and strain in a specimen exhibiting bilinear elastic-plastic behavior when subjected to trapezoidal and triangular incident pulses. For this piecewise linear model, the method of characteristics relating stress and particle velocity rates coupled with loading-unloading boundary conditions connecting discontinuities in these same rates proves to be particularly convenient. For a specimen length which allows four complete reflections of the leading edge of the stress pulse before plastic deformation begins, a comparison is made between “reconstituted” stress-strain curves predicted by the Kolsky formulas and the reference bilinear curve. The reconstituted curves exhibit the following features: an underestimate of the initial elastic (primary) modulus; satisfactory agreement with the secondary modulus, particularly for the curve associated with the gentler trapezoidal stress pulse; and realistic “elastic” unloading again associated with the trapezoidal stress pulse. The analysis predicts some separation of the specimen from the bars near the end of the unloading process where influence on the reconstituted curve is small. It is concluded that when one-dimensional effects dominate, by careful selection of design parameters such as specimen length and pulse shape, one may use the Kolsky formulas with confidence in establishing the presence (or absence) of a strain-rate effect in elastic-plastic materials during plastic deformation.