Measurement of Higher-Order Elastic Constants, Using Finite Deformations

Abstract

The deviations from Hooke's law of single-crystal "whiskers" of copper, silver, and iron and fibers of fused quartz have been measured. These deviations are related to the third-order elastic constants. The results are in agreement with third-order elastic constants measured by ultrasonic techniques for copper, silver, and fused quartz. Using the pressure derivatives of the second-order elastic constants of iron as measured by Rotter and Smith and the present results, three of the third-order elastic constants of iron have been determined. The values are (in units of ${10}^{12}$ dyn/${\mathrm{cm}}^{2}$) ${{c}_{111}}^{T}=\ensuremath{-}28$, ${{c}_{112}}^{T}=\ensuremath{-}8.0$, and ${{c}_{123}}^{T}=\ensuremath{-}6.1$. For fused quartz, it is possible to make an estimate of a combination of the fourth-order elastic constants: ${{c}_{1111}}^{T}\ensuremath{-}1.4{{c}_{1112}}^{T}+0.34{{c}_{1122}}^{T}+0.23{{c}_{1123}}^{T}=5.5\ifmmode\pm\else\textpm\fi{}1.5\ifmmode\times\else\texttimes\fi{}{10}^{14}$ dyn/${\mathrm{cm}}^{2}$.