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

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.