Dijkstra’s algorithm-based ray tracing method for total focusing method imaging of CFRP laminates

Abstract

Accurate determination of ultrasonic travel time from a start point to an end point with known positions is fundamental to the application of total focusing method (TFM) to ultrasonic array imaging. However, this is particularly challenging for CFRP laminates whose wave propagation is complex due to material anisotropy and refractive ply interfaces. In this paper, a ray tracing method using Dijkstra’s path-finding algorithm is presented and used to calculate time delays of TFM. This modified TFM, termed ray tracing TFM, was demonstrated by post-processing full matrix capture (FMC) data from a 5.79-mm-thick multidirectional CFRP laminate containing three 1.5 mm diameter side-drilled holes (SDHs) at 3 mm depth. It shows that the ray tracing TFM enables the FMC signals to be accurately delayed and coherently summed to synthesize a focus at every image point. Consequently, peak amplitudes of the SDHs were increased by up to 49.74 dB and 2.69 dB with respect to those from paintbrush acquisition and the isotropic TFM with a constant velocity, respectively. Ray tracing results have also confirmed that use of a coupling layer is a simple way to minimize the anisotropic effect of CFRP and to reduce the structural noise from reflections at ply interfaces.