Determination of the higher-order elastic compliance constants of metals from measurements of the dependence of ultrasound velocity on stress

A new approach to describe the dependence of ultrasound velocity on stress in metals is presented to analyze the relation between acoustoelasticity which shows that the change of the ultrasound velocity depends on the stress in metals and the macroscopic characteristics of metals. It uses the effective higher-order elastic compliance constants which are determined from measurements of the ultrasound velocity in a metal. First, the nonlinear relation between stress and strain is described in terms of the second-, third-, and fourth-order elastic constants. Then, for the quasilongitudinal and quasitransverse waves which propagate in the symmetry planes of the metal, the ultrasound velocities in the statically stressed metals are presented by using these constants. They are explicitly derived as a function of the applied stress. The measurements of the dependence of ultrasound velocity on the applied stress due to the uniaxial compression in an aluminum alloy are performed and their results show the nonlinea...