Plate Resonances on Polycrystalline Samples

Sound waves are mechanical vibrations propagating in elastic media such as solids. In contrast to light waves, most solids are transparent to sound waves, a property exploited in many ultrasound-based measurement and imaging techniques in the medical field and materials testing. Typically, when analyzing elastic waves, it is assumed that the media are homogeneous and that the waves propagate with a constant, direction-independent velocity. However, most solids have an internal structure or irregularities at a microscopic level. Metals are usually polycrystalline, i.e., an accumulation of densely packed microscopic grains with a perfect crystal structure. In each single grain, sound waves propagate uniformly but with a direction-dependent propagation speed. At the boundaries between neighboring grains, they are partially reflected and refracted. From an external perspective at a macroscopic level, this grain boundary scattering changes the average speed of sound, and the wave is attenuated. That means that the material becomes increasingly opaque to the elastic wave. This effect strongly depends on the ratio between wavelength and average grain size and increases with decreasing wavelength or increasing grain diameter. On the one hand, attenuation impedes obtaining information from deeper material regions (e.g., internal defects) via the measurement of sound waves. On the other hand, how the waves are scattered also contains information about the origin of the scattering and the internal microstructure and can be used to retrieve information about it. A deep understanding of the behavior of sound waves in polycrystalline materials is, therefore, not only of academic interest but also highly relevant for applications in material characterization. This project will research the influence of a polycrystalline material microstructure on the behavior of guided plate waves. Like light in an optical fiber, sound waves are similarly guided in a plate or plate- like structure. However, the behavior of such plate waves differs significantly from that of bulk acoustic waves. For example, at specific frequencies, resonances with large vibration amplitudes may occur, and some of these resonances have the peculiar property that they do not propagate, which contradicts the intuitive picture of waves as propagating entities. If they are generated, for instance, by a short laser pulse that rapidly heats the sample surface, they remain localized at that generation spot. Thus, they can provide insights into local material properties like stiffness and plate thickness. The influence of a polycrystalline microstructure on plate resonances has not yet been studied in detail, a gap that this project intends to close. This shall be achieved through laser-ultrasonic experiments, numerical simulations, and the development of mathematical models for plate waves in polycrystals.