Hardened-layer depth measurement without prior velocity knowledge: An experimental study using FMC phased-array...

Hardened-layer depth is a critical parameter for assessing the surface strength, hardness, and wear resistance of steels. A quantitative ultrasonic approach for hardened-layer depth measurement is presented based on phased-array full matrix capture (FMC), removing the reliance of conventional backscattering methods on prior knowledge of sound velocity in the hardened region. Transmit-receive pairs sharing a common midpoint are selected to form a common-midpoint (CMP) gather, in which the interface reflection exhibits characteristic hyperbolic moveout. An energy-stacking velocity inversion scheme is introduced: velocity scanning is performed and received signals are coherently stacked along theoretical hyperbolic trajectories, with the velocity maximizing stacked energy taken as the optimal estimate. Experiments yield a base-material velocity of 5960 ± 10 m/s, consistent with the nominal value (5850-5950 m/s), and an increased velocity of 6020 ± 10 m/s in the hardened region, consistent with the expected post-quench velocity rise. The inverted velocity differs by less than 1% from the average value obtained by metallography. Using the inverted velocities, Kirchhoff integral migration is applied to image the hardened-layer interface, achieving an average depth error of 2.3%. Compared with B-scan and total focusing method (TFM) results, the proposed workflow provides improved interface resolution and more reliable depth estimation, offering a practical solution for hardened-layer quality evaluation in engineering applications.