An Adaptive Total Focusing Method for Ultrasonic Imaging ofArbitrarily Stacked Carbon Fiber-Reinforced Composites

The total focusing method (TFM) is increasingly recognized as a powerful ultrasonic imaging technique for the quality assessment and internal defect detection of carbon fiber-reinforced composites (CFRPs). Due to their unique structural and mechanical properties, CFRPs are widely used in aerospace, automotive, and energy industries, where stringent reliability and safety requirements demand advanced inspection techniques. However, the inherent characteristics of CFRPs, including high attenuation, high dissipation, and strong anisotropy, present significant challenges to ultrasonic imaging. These factors cause beam distortion, residual artifacts, false images, and low signal-to-noise ratios (SNR), making it difficult to achieve accurate imaging and detection of internal defects. To address these challenges, this study proposes an adaptive TFM method specifically designed for arbitrarily stacked CFRPs. The method begins by characterizing the anisotropic acoustic properties of CFRPs, which arise from their layered structure and the orientation-dependent stiffness of the carbon fiber plies. A stiffness matrix for CFRPs with arbitrary stacking angles is derived based on the mechanical constitutive relations of composite materials and a coordinate transformation matrix. The anisotropic acoustic velocity distributions are then computed using the Christoffel equation. These theoretical calculations are validated through experimental measurements of the actual anisotropic acoustic velocities in CFRP laminates. Comparisons between the theoretical and measured values demonstrate the accuracy and reliability of the proposed velocity modeling approach. The adaptive TFM method incorporates the obtained anisotropic velocity matrices and the stacking angles of the CFRP laminates to correct the time delay laws used in TFM imaging. To validate the effectiveness of the proposed method, experiments were conducted using CFRP laminate samples containing flat-bottom hole defects. The imaging results demonstrate that the adaptive TFM method achieves a substantial improvement in SNR and more precise delineations of defects compared to traditional TFM approaches. This work establishes a foundation for the development of high-precision ultrasonic inspection technologies tailored to the unique challenges posed by anisotropic composite materials, which have significant implications for quality assurance and reliability evaluation in industries that rely on CFRPs.