Material strength determination in the shock compressed state using x-ray diffraction measurements

Analytic developments are presented to determine the strength of shock compressed single crystals from real-time x-ray diffraction (XRD) measurements. Both linear elastic and nonlinear elastic analysis methods are considered. Material strength in the shocked (constant) state may be determined using one of two approaches: from measurements of longitudinal and lateral lattice strains; or from measurements of longitudinal lattice strains and longitudinal wave profiles. The second approach is demonstrated for aluminum single crystals following shock compression along [100] to peak impact stresses of 5.5-12.7 GPa and partial release (reflection from the window material) to final stresses of 3.5-7.1 GPa. The material strength of the Al(100) in the final state was found to increase with peak stress or plastic strain. The material strength at the Hugoniot elastic limit was 0.025 GPa and the material strength in the final state was 0.52 GPa for the highest stress experiment. Because of the large final stresses, incorporating nonlinear elasticity into the analysis was necessary to obtain accurate values of the material strength; for the highest stress experiment, the material strength in the final state determined using the linear elastic analysis overestimated the strength by approximately 80%. The use of XRD measurements and the nonlinear elastic analysis method for strength determination in the shocked state is expected to be particularly useful for extreme pressures and temperatures where continuum methods for strength determination may face experimental limitations. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3597817]