An Ultrasonic Angle Beam Method for Determining Third Order Elastic Constants via Acoustoelasticity Measurements

Ultrasonic measurements of acoustoelastic constants, which relate wave speed changes to applied loads, are one of the few methods for experimentally determining third order elastic constants (TOECs). A typical set of measurements consists of multiple experimental setups using both longitudinal and shear transducers with directions of propagation both parallel and perpendicular to the direction of applied uniaxial stress. Experiments are generally tedious, time-consuming, and require access to both sides of a specimen, and can be problematic when the direction of propagation is parallel to the loading direction. Here we consider an angle beam technique where two transducers are mounted on the same side of a specimen with parallel sides. The general theory of acoustoelasticity is specifically considered for longitudinal and shear wave propagation at an angle to the principal stress directions for homogeneous and isotropic materials. The forward problem of calculating the acoustoelastic constants from the TOECs is considered as well as the inverse problem of determining the TOECs from measured acoustoelastic constants. Numerical results are given which show the sensitivity of the inverse calculations to small variations in the experimental measurements. Experimental data are shown for one measurement configuration and are compared to theoretical calculations using previously determined TOECs for 7075 aluminum.