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/${\mathrm{cm}}^2$) ${c_{111}}^T=-28\mathrm{}$, ${c_{112}}^T=-8.0\mathrm{}$, and ${c_{123}}^T=-6.1\mathrm{}$. For fused quartz, it is possible to make an estimate of a combination of the fourth-order elastic constants: ${c_{1111}}^T-1.4\mathrm{}{c_{1112}}^T+0.34\mathrm{}{c_{1122}}^T+0.23\mathrm{}{c_{1123}}^T=5.5\mathrm{}\pm 1.5\times {10}^{14}$ dyn/${\mathrm{cm}}^2$.