Elastic moduli as determined by shock-release experiments

Abstract

The relationship between release-wave velocity and longitudinal elastic modulus in the state following shock compression is examined. The shocked state is characterized by the density of pinned dislocation segments, their pinning separation, and the viscous drag coefficient, in addition to lattice strains representing volumetric and deviatoric stress components. Release from the shock-compressed state is similar to ultrasonic-wave propagation in metals containing pinned dislocation segments. The exceptions are that release-wave amplitudes are greater, dislocation displacement is larger (the restoring force is nonlinear), and frequency content of the release waves is broader. For FCC metals, in which the Peierls stress is low and provides little lattice resistance to dislocation motion, dislocation segments can undergo motion at low applied stress and thus contribute to anelastic deformation unless the driving frequency is very high or special precautions are taken to pin them by various point defects. It is well known that, without such precautions, the ultrasonically determined modulus can be much lower than the true elastic modulus of the crystal lattice. Shock compression can create dislocation segments of density ~10 9−10 10 cm −2 and pinning separation of 500 b. For materials with viscous drag coefficients on the order of 1–100 × 10 −3 dynes cm −2 in the shock-compressed state, the influence of shock-wave-generated dislocation segments is to reduce the effective elastic modulus and thus reduce the observable releasewave speed. This is due to the very short time scale for reverse dislocation motion making ideally elastic deformation unobservable in any practical sense. As a consequence, the modulus based on the release-wave speed in an FCC metal serves only as a lower limit to the fully elastic modulus in the shock-compressed state.