Ultrasonic Attenuation Method for the Evaluation of Damage

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The results of the study are summarized in the following three stages.1. Formulation to calculate the elastodynamic scattering energyThe elastodynamic scattering cross sectin was introduced to evaluate the elastodynamic scattering energy from a compact scatterer. The approximate expression of the elastodynamic scattering cross section was formulated in the following three steps. (1) Expression of the scattered field by the scattering amplitude. (2) Relation between scattering amplitude and scattering cross section. (3) Approximate calculation of the scattering cross section by considering the interference effect of the incident wave and the scattered waves. From the numerical calculation, it was confirmed that the approximate expression (Elastodynamic optical theorem) has good accuracy to evaluate the elastodynamic scattering cross section.2. A relation for scattering cross section, attenuation, and damageThe damage was modeled by the dilute distribution of scatterers. From the consideration of attenuation induced by the scattering, the distribution of damage was connected to the scattering cross section and a relation among scattering cross section, attenuation, and damage was formulated.3. A method to evaluate the damageA method to evaluate the damage was proposed. In this method, the attenuation is measured from the experiment and the scattering cross section is calculated by the numerical procedure. Then the damage is evaluated from the relation derived in stage 2. For the practical use of the method, the following two points should be clarified. (1) The method to calculate the scattering cross section for arbitrary shape is available. (2) The negligible distance of the multi-scattering effect is known for the assumption of the dilute distribution of the damage. The first point was clarified numerically by using the boundary element method. The second point was clarified by solving the multiple scattering problem.