A material-parameter-driven velocity-corrected phase-coherence fusion algorithm for total focusing imaging of CFRP defects
Abstract
Conventional ultrasonic total focusing method (TFM) imaging of carbon fiber reinforced polymer (CFRP) laminates is limited by anisotropic propagation-time mismatch and structural noise, which impair the detection and localization of small, deeply buried defects. Existing velocity-corrected phase-coherence methods often rely on experimentally obtained or pre-fitted group-velocity profiles. To reduce this dependence, a material-parameter-driven velocity-corrected phase-coherence fusion method is proposed. An angle-dependent effective group-velocity model is first established from CFRP material parameters through elastic-stiffness-matrix construction, Christoffel-equation-based wave-velocity calculation, and reverse ray tracing. The resulting model is used to calculate anisotropic propagation delays for velocity-corrected total focusing method (VC-TFM) reconstruction. The Hilbert transform is then applied to extract the instantaneous phase of full matrix capture signals, and a circular coherence factor (CCF) is used to weight the VC-TFM image, yielding a phase-coherence-enhanced total focusing method (PCE-TFM) image for structural-noise suppression. Experiments were performed on a CFRP laminate containing 18 flat-bottom holes with diameters of 2, 3, and 4 mm and buried depths of 7–17.5 mm. VC-TFM reduced the average depth error from 2.51% to 0.52%, corresponding to a 79.4% relative reduction, and reduced the maximum absolute localization error from 0.50 mm to 0.15 mm. After CCF weighting, the average signal-to-noise ratios of the 2, 3, and 4 mm defects reached 14.17, 20.02, and 28.62 dB in PCE-TFM, respectively, compared with 3.04, 4.67, and 8.92 dB in conventional TFM. These results indicate that velocity correction mainly improves propagation-delay matching and defect localization, while phase-coherence weighting mainly suppresses structural noise and enhances defect contrast. The proposed method improves the quantitative accuracy and detectability of small, deeply buried CFRP defects while reducing dependence on prior ultrasonic characterization of the group-velocity profile.