Cavity-Opening Tensor Method and its Applications to Reflection and Transmission of Ultrasonic Wave by Defects

Abstract

The reflection and transmission of ultrasonic waves by an array of planar defects are investigated using the cavity-opening tensor (COT) method, whereby each defect or flaw can be simulated as a three-dimensional tensor in terms of the displacement distribution over the surface of the defect. The closed-form expressions of reflection and transmission coefficients represented by one set of COTs are derived, and the interaction factors of COTs are computed using the boundary integral equation with the approximate integral only on the single defect surface. Moreover, the analytical expressions of scattered fields at a distance from the defects are given by the representation of COT. As compared with the conventional numerical method, the COT method greatly simplifies the calculations, and also makes it possible to more efficiently characterize defects with more complicated distributions.