Ultrasonic contact pulse transmission for elastic wave velocity and stiffness determination: Influence of specimen geometry and porosity

摘要

Elasticity determination by means of ultrasonic pulse transmission requires experimental realization of non-dispersive, i.e. frequency-independent, wave propagation, be it in form of bulk waves propagating in an (approximately) infinite medium, or of extensional waves propagating through a 1D bar system. While it is conceptually known that wavelengths need to tend towards zero (as compared to the specimen dimensions perpendicular to the pulse propagation direction) in the 3D case, and towards infinity in the 1D case, we here report on a new systematic experimental assessment of the influence of the sample geometry on wave type: tests on solid isotropic aluminum samples reveal that the extensional (or bar) wave propagation mode requires transmission of truly slender samples (required slendemess ratio of 20 or larger for wavelengths equal to the wave travel distance; this minimum slenderness ratio is increasing with increasing travel distance-over-wavelength ratio). After a transition zone with dispersive wave propagation, non-dispersive bulk waves are detected once the slenderness ratio is reduced to 5 or lower (at wavelengths equal to the wave travel distance; this maximum slenderness ratio is increasing with increasing travel distance-over-wavelength ratio). On the other hand, it is conceptually known from continuum mechanics that the wavelength needs to be larger than the investigated material volume or representative volume element (RVE), as to reveal the material's elastic properties, while corresponding quantitative data are rare. As a remedy, we here report on new experiments on transversely isotropic, porous aluminum samples, which reveal that minimum pore dimension-over-wavelength ratios of 1 and 10, respectively, relate to detection of normal and shear stiffnesses, respectively, of the solid material between the pores, while these ratios need to be smaller than 0.01 and 0.1, as to detect the normal and shear stiffnesses of the overall porous materials. The latter can be quantified through various homogeni-zation techniques.