Third-Order Elastic Moduli of Polycrystalline Metals from Ultrasonic Velocity Measurements

The third-order elastic moduli of several isotropic polycrystalline metals have been determined from measurements of the velocities of both longitudinal and shear ultrasonic waves in uniaxially stressed specimens. In each case, the wave-propagation direction was chosen normal to the applied stress, and the shear waves were polarized either normal or parallel to the stress direction. Hence, a unique evaluation of all three third-order moduli was possible using the recent theory of Thurston and Brugger, specialized for isotropic symmetry. The measuring equipment is based on a new variation of the pulse-echo interferometric technique and is capable of resolving velocity changes of a few parts in 106. Results are presented for several steels, aluminum alloys, magnesium, tungsten, and molybdenum, and are shown to be in good agreement with alternative nonlinear elasticity data, including static measurement of the pressure derivatives of the bulk and shear moduli.