Ultrasonic Phased Array-Based Wave Velocity Inversion and Migration Imaging Method for Hardened Layers

Hardened layer depth detection is a key technical indicator for evaluating the comprehensive performance of steel parts such as surface hardness and fatigue strength. Through establishing a numerical model of alloy steel heat treatment, this study innovatively proposes an ultrasonic phased-array based method for hardened layer velocity inversion and interface detection imaging. The research reveals that the time-distance curves of reflected waves received by multiple array elements exhibit characteristic hyperbolic features in the common midpoint gather domain. Velocity inversion was achieved by extracting the maximum energy of hyperbolic wavefield coherence in corresponding common midpoint gathers through velocity scanning. Building upon these findings, $$f{\kern 1pt} - {\kern 1pt} k$$ wave equation offset technology is used to effectively solve the problem of uneven distribution or inclined interface imaging of the hardened layer caused by different heat treatment processes such as laser quenching. As a result, the relative error (RE) and root mean square error (RMSE) obtained by the hardened layer horizontal interface imaging obtained by this method are controlled at 1% and 0.03 mm and inclined interface are controlled at 1.5% and 0.04 mm respectively, with high detection accuracy and imaging resolution. This study provides a new technical approach for the nondestructive detection and characterization of complex surface modified layers (such as gradient coatings, nonuniform quenching layers, etc.).