Measurement of Higher-Order Elastic Constants, Using Finite Deformations

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 10¹² dyn/cm²) c₁₁₁T=-28, c₁₁₂T=-8.0, and c₁₂₃T=-6.1. For fused quartz, it is possible to make an estimate of a combination of the fourth-order elastic constants: c₁₁₁₁T-1.4c₁₁₁₂T+0.34c₁₁₂₂T+0.23c₁₁₂₃T=5.5±1.5×10¹⁴ dyn/cm².