Shock properties of homogeneous anisotropic dielectrics

Abstract

Anisotropy, the directional dependence of a physical quantity, is present in numerous physical processes involved in the shock compression of solid materials. The effect that a particular property’s anisotropy has on the propagation of a shock wave is obscured by other effects such as those from strain rate and material heterogeneity. Recent studies have focussed on single- and bi-crystal metals to understand the effect of crystal anisotropy on the mechanics of shock wave propagation. This thesis extends this work to optically transparent non-metallic dielectric single crystals by developing an optical model for anisotropic dielectrics and performing experimental measurements to test the validity of that optical model. Current optical models for shock compressed materials use an isotropic Gladstone- Dale model or isotropic modifications of the Gladstone-Dale model. This thesis extends the isotropic Gladstone-Dale model to an anisotropic photoelastic model for the optical behaviour of linear anisotropic materials under shock compression in the elastic regime. The model uses static photoelastic tensor values available in the literature to predict material response under uniaxial strain in an arbitrary crystal orientation. The effect of varying photoelastic tensor values is studied using Monte Carlo techniques, and confidence intervals on dynamic predictions are presented. Polarimetry is applied to experimentally measure birefringence under shock compression delivered using plate impact on a single stage light gas gun. This method is used to validate the linear photoelastic model developed in this thesis. Experiments were performed on <10-10> (a-cut) sapphire up to 15 GPa longitudinal stress and <10-10> (a-cut) calcite up to 2 GPa longitudinal stress. It was found that the birefringence of a-cut sapphire under shock compression behaved in agreement with the model in the elastic regime for a 5% error on the photoelastic tensor. Furthermore it was found that birefringence predictions for a-cut calcite as given by the same model did not agree with experimentally measured results. The discrepancy was 0.3% at 1.2 GPa, in excess of 5 standard deviations. Possible reasons for the discrepancy are put forward. Current optical models for shock compressed materials use an isotropic Gladstone-Dale model or isotropic modifications of the Gladstone-Dale model. This thesis extends the isotropic Gladstone-Dale model to an anisotropic photoelastic model for the optical behaviour of linear anisotropic materials under shock compression. The model uses static photoelastic tensor values available in the literature to predict material response under uniaxial strain in an arbitrary crystal orientation. The effect of varying photoelastic tensor values is studied using Monte Carlo techniques, and confidence intervals on dynamic predictions are presented. Polarimetry is applied to experimentally measure birefringence under shock compression. This method is used to validate the linear photoelastic model developed in this thesis. Experiments were performed on ⟨1 0 1 0⟩ (a-cut) sapphire and ⟨1 0 1 0⟩ (a-cut) calcite. It was found that the birefringence of a-cut sapphire under shock compression behaved in agreement with the model. Furthermore it was found that birefringence predictions for a-cut calcite as given by the same model did not agree with experimentally measured results. Possible reasons for the discrepancy are put forward.