Voigt, Reuss, Hill, and Self-Consistent Techniques for Modeling Ultrasonic Scattering

Authors

Christopher M. Kube, University of Nebraska-LincolnFollow
Joseph A. Turner, University of Nebraska-LincolnFollow

Document Type

Article

Date of this Version

2015

Citation

AIP Conf. Proc. 1650, 926-934 (2015)

Abstract

An elastic wave propagating in a metal loses a portion of its energy from scattering caused by acoustic impedance differences existing at the boundaries of anisotropic grains. Theoretical scattering models capture this phenomena by assuming the incoming wave is described by an average elastic moduli tensorC_0ijkl (x) that is perturbed by a grain with elasticityC_ijkl (x ') where the scattering event occurs when x = x’. Previous models have assumed that C_0ijkl (x) is the Voigt average of the singlecrystal elastic moduli tensor. However, this assumption may be incorrect because the Voigt average overestimates the wave’s phase velocity. Thus, the use of alternate definitions of C_0ijkl (x) to describe the incoming wave is posed. Voigt, Reuss, Hill, and self-consistent definitions of C_0ijkl (x) are derived in the context of ultrasonic scattering models. The scattering-based models describing ultrasonic backscatter, attenuation, and diffusion are shown to be highly dependent on the definition of C_0ijkl (x)