Critical angle measurement of elastic constants in composite material

Application of critical angle measurement for determination of elastic constants of composite materials is described. For general orientation of the composite material relative to the plane of incidence, three critical angles exist, for quasilongitudinal and fast and slow quasitransverse waves. It is shown that, for any two-dimensional composite material, the critical angles are directly related to the phase velocities of bulk waves in the sample plane. A simple and novel type of goniometer is developed for these measurements which utilize a cylindrical reflector for measurement of the double reflection coefficient. The values of the elastic constants are reconstructed from the measured velocity surfaces by using nonlinear least-squares optimization fitting. Analytical relations between ultrasonic velocity and elastic constants valid for arbitrary anisotropy are implemented in the fitting optimization.