Detonation induced strain in tubes

Abstract

When a detonation wave propagates through a piping system, it acts as a traveling pressure load to the pipe wall. The detonation wave must be followed by an expansion wave in order to bring the combustion products to zero velocity at the ignition end. When it reaches a closed end-wall, a reflected shock is formed which propagates back into the tube with a decaying pressure. The present study aims to develop predictive models for the stresses and strains produced in such a situation. To this end, two series of experiments are discussed. The first series used strain gauges and a laser vibrometer to measure the elastic response of the tube to the incident detonation in thin aluminum tubes. The second series used strain gauges and high speed video to measure the plastic response of steel tubes to incident detonations and reflected shocks. In these experiments a novel mode of plastic deformation was discovered in which the residual plastic deformation in the tube wall had a periodic sinusoidal pattern. A semi-empirical model of the pressure history was developed for use as a boundary condition in models of the mechanical response of the tube. This model was tested against experiment, and it was found that the pressure and arrival time could not be simultaneously predicted from the simple model. This and the general form of the pressure traces in the experiment seem to suggest an interaction between the reflected shock and the boundary layer behind the detonation resulting in a possible bifurcation in the reflected shock wave. With these considerations in mind, the model was applied to single degree of freedom and finite element models of the tube wall. The ripples observed in the experiment were present in the 1-D single degree of freedom models, indicating that they are a result of the interaction of the reflected shock wave with the elastic oscillations set in motion by the detonation wave. Strain-rate hardening was found to be an important consideration under detonation loading conditions. With proper consideration of rate hardening, a single material model may be used to arrive at reasonable predictions the plastic strains resulting from detonations and reflections at initial pressures of 2 and 3 bar initial pressures.