This thesis describes procedures and theory for a family of one-sided ultrasonic methods for determining third order elastic constants (TOEC) using sets of angle-beam wedges mounted on one side of a specimen. The methods are based on the well-known acoustoelastic effect, which is the change of wave speed with applied loads and is a consequence of the mechanical nonlinearity of a material. Increases in material nonlinearity have been correlated to the progression of damage, indicating that tracking changes in TOECs may provide a practical means of monitoring damage accumulation at the microstructural level prior to formation of macroscopic defects. Ultrasonic methods are one of the only ways to measure TOECs, and most prior techniques have utilized wave propagation paths parallel and perpendicular to the loading directions. A few additional ultrasonic techniques reported in the literature have employed oblique paths but with immersion coupling. These reported techniques are generally unsuitable for field implementation. The one-sided contact approach described here is applicable for in situ measurements of TOECs and thus lays the foundation for tracking of TOECs with damage. Theory is reviewed and further developed for calculating predicted velocity changes, and thus time shifts, as a function of uniaxial tensile loading for longitudinal, shear vertical, and shear horizontal waves in the context of angle-beam transducers mounted on the surface of the specimen. A comparison is made to published results where possible. The inverse problem of determining the three TOECs of an isotropic material from three measurements employing three different angle beam configurations is comprehensively analyzed. Four configurations providing well-posed solutions are identified and examined. A detailed sensitivity analysis is carried out to identify the best mounting configuration, wave mode combinations, refracted angles and geometry requirements for recovering the three TOECs. Two transducer mounting configurations are considered: (1) attached (glued-on) transducers potentially suitable for in situ monitoring, and (2) floating (oil-coupled) transducers potentially suitable for single measurements. Limited experimental results are presented for the attached case using two longitudinal measurements and one shear vertical measurement. The floating case experiments utilized three of the four well-posed solutions, and measurements were made on several aluminum alloys and low carbon steel. Key experimental issues are identified and discussed for both transducer mounting configurations.

Interrogating metals with ultrasonic waves can be used to evaluate their microstructural and mechanical properties. These techniques analyze ultrasonic wave features in order to make inferences on the medium of interest. Current research is being conducted to determine higher order elastic properties and characterize material degradation of 7075-T651 aluminum with ultrasonics. This thesis topic will use acoustoelasticity, the stress dependency of acoustic velocity, to accomplish these goals. Acoustoelasticity is a manifestation of the inherent nonlinearity in the interatomic binding energy, which appears mathematically as higher order elastic terms in the stress strain constitutive relation. The acoustoelasticity will be determined for longitudinal and shear waves propagating through a sample under uni-axial stress. Experimentally, specific techniques and tooling will be designed to insure accurate measurements of acoustic wave velocity as a function of stress. Using acoustoelasticity the third order elastic constants of 7075-T651 aluminum will be determined. Further, Al samples will be fatigue damaged and acoustoelasticity and third order elastic constants will be mapped versus damage. Literature will be used to verify measured values of acoustoelasticity as well as provide theoretical models for acoustoelastic dependence on damage.

This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formulated as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. The accuracy of the numerical method is first studied by comparing the numerical solution with the analytical solution for a half-space with linear response (the original Lamb's problem). The numerical results for the half-space with quadratic nonlinearity are than studied using signal-processing tools such as the fast Fourier transform (FFT) in order to analyze and interpret any nonlinear effects. This in particular gives the possibility to evaluate the excitation of higher order harmonics whose amplitude is used to infer material properties. To quantify and compare the nonlinearity of different materials, two parameters are introduced; these parameters are similar to the acoustical nonlinearity parameter for plane waves.