A Gaussian Beam Based Recursive Stiffness Matrix Model to Simulate Ultrasonic Array Signals from Multi-Layered Media

Abstract

Ultrasonic testing using arrays is becoming widely used to test composite structures in the Aerospace industry. In recent years, the Full Matrix Capture (FMC) technique has been implemented to extract the signals for post-processing to form an image. The inherent anisotropy and the layering of the structure pose challenges for the interpretation of this FMC data. To overcome this challenge, modeling techniques are required that take into account the diffraction caused by finite-size transducers and the response of the structure to these bounded beams. Existing models either homogenize the entire structure, use computationally expensive finite difference time domain (FDTD) methods, or do not consider the shape of the bounded beam, which is used to test such structures. This paper proposes a modeling technique based on combining the Multi-Gaussian beam model with the recursive stiffness matrix method to simulate the FMC signals for layered anisotropic media. The paper provides the steps required for the modeling technique, the extraction of the system efficiency factor, and validation of the model with experimentally determined signals for aluminum as an isotropic material such as aluminum and Carbon Fiber Reinforced Plastic (CFRP) laminate as a layered material. The proposed method is computationally inexpensive, shows good agreement with the experimentally determined FMC data, and enables us to understand the effects of various transducer and material parameters on the extracted FMC signals.

Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media

“…Figure 7 a shows the TFM image of the CFRP laminate without the SDH. The FMC signals were simulated using the model developed in a previous paper [ 16 ]. This image is the noise image as it shows the structural reverberations and internal reflections from the layers in the laminate, which contributed to the noise generated in the FMC signals.…”

“…T is the transmission coefficient of the plane waves traveling from layered media into homogeneous equivalent anisotropic media, β is the system function [ 16 , 21 ], v t is the acoustic wavefield at the face of the transmitting transducer, and v r is the acoustic wavefield at the face of the receiving transducer calculated from the previous section. A is the scattering magnitude of the SDH calculated using Equation (37).…”

“…These approaches are either computationally expensive when used for layered materials, singular when interacting with curved interfaces, or do not reflect the real-world situation of bounded beams. Anand et al [ 16 ] used Gaussian beams due to their computational efficiency and non-singularity when interacting with curved interfaces, combined with the recursive stiffness matrix method, which enables the response of the layered structure to be taken into account, when modeling the bounded beam interaction between phased arrays and multilayered media. One of the preliminary assumptions of the model was that the multilayered laminate is bounded by a semi-infinite water layer, allowing only longitudinal waves to impinge onto the composite laminate and thereby reducing the number of unknowns [ 17 ].…”

“…To the best of the authors’ knowledge, the use of Gaussian beams to simulate such an interaction with defects embedded in a multilayered material does not exist. The model developed by Anand et al [ 16 ] is based on the assumption of water bounding layers, which is invalid as the defect is surrounded by a homogeneous isotropic or anisotropic elastic medium. To address this limitation, in this paper, we provide a method to calculate the reflection and transmission coefficients for a multilayered laminate bounded by a semi-infinite anisotropic medium.…”

A Non-Destructive Imaging Method Based on Integral Signals of Ultrasonic Pulse

“…If each receiver receives time-domain signals excited by multiple excitation sources, the signals obtained by each receiver from those sources can be combined into a multistatic matrix. Anand et al [9] proposed a total focusing algorithm based on the full matrix capture model. The principle of the algorithm is as follows: The signals are excited separately by multiple sources, and each receiver in the array receives the excitation signals from each source; then, the multiple groups of received time-domain signals are processed by delay superposition to obtain the damage image.…”