Attenuation models for material characterization

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Maess, Johannes Thomas
Jacobs, Laurence J.
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Ultrasonic attenuation is a useful tool in characterizing the damage state of different materials. The attenuation coefficients for the incident longitudinal and transverse waves are both derived from the scattering cross section of the material. Scattering cross section is defined as the ratio of the scattered energy to the incident energy. The incident wave field can be scattered at inclusions, voids and material defects; there is also grain boundary scattering in polycrystalline materials. For accurate material characterization, it is important to distinguish between the different types of scattering and to relate the attenuation to its appropriate source. This study first solves the single scatterer problem using either the Born approximation (for difficult scatterer shapes and for anisotropic scatterers), or the exact solution (in cases where it is necessary to provide an accurate description of the viscoelastic behavior of the surrounding effective medium). Multiple scattering effects are investigated by a differential self-consistent scheme and a self-consistent scheme. Both multiple scattering approaches are applicable for each single scatterer solution. The differential self-consistent scheme describes the scattering cross section dependent on the volume fraction of the scatterers, and is restricted to low volume fractions and materials, where the surrounding material is clearly distinguished from the inclusions. The self-consistent scheme is applicable to high volume fractions of inclusions as well as to polycrystalline materials, where the distinction between surrounding material and inclusions is not possible.
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