Numerical Study of a Phased Array-Based Ultrasonic Polar Scan to Determine Plane-Wave Reflection Coefficients of Plates

Abstract

Numerical finite elements simulations and postprocessing analysis methods are presented for Ultrasonic Polar Scan (UPS) measurements involving a Circular Phased Array (C-PA) to determine the plane wave reflection coefficient of plates. Apodization weights for the C-PA elements are determined in order to assure the generation of a quasi-plane wave upon excitation at the plate surface and to mitigate bounded beam effects on the assessed reflection coefficient. In addition, postprocessing of the reflection signals is performed via the synthetic plane wave technique to further filter out any bounded beam effects. Reflection coefficients for three test cases are presented, namely for an aluminum, a unidirectional Carbon Epoxy and a cross-ply Carbon Epoxy plate. For all three cases, the comparison with analytical plane wave theory shows an excellent agreement with the reflection coefficients obtained by the C-PA and the additional post-processing steps for both pulsed and harmonic signals. It is also shown that the agreement becomes considerably worse if the non-specular reflection field is disregarded in the post-processing treatment, thus enforcing the need to capture the full reflected field via the Phased Array whenever plane wave reflection coefficients are needed.

Optimal Design Parameters for a Phased-Array-Based Ultrasonic Polar Scan

“…While the 2D simulations reported in previous work were conducted using FEM [12], full 3D FEM simulations of the proposed design proved to be too computationally expensive to perform. Therefore, it was opted to build an analytical model, also shown in Fig.…”

“…To understand this effect, one can consider the spatial extend of the reflected field, consisting of a direct, specular component and an indirect, non-specular component which is due to guided waves travelling through the plate and leaking into the surrounding water. Indeed, the leakage can be quite extensive such that part of this field may not be captured by the C-PA if its radius is too small [12]. This results in a loss of information, due to which the DFT-based post-processing procedure used to retrieve the reflection coefficients cannot be performed properly.…”

“…In previous work, it was already shown via 2D simulations that the concept of using a C-PA can work along the main axes of orthotropy of a material [12]. However, in order to determine the full viscoelastic C-tensor, measurement data related to different polar angles are also needed, and unfortunately these incident angles could not be investigated with the 2D model.…”