Inverse-Problem Approach for 3MA Electromagnetic NDT on Laser-Hardened Materials

This work presents a numerical framework for the electromagnetic modeling and inverse characterization of laser-hardened steels using 3MA (Micromagnetic Multiparameter Microstructure and Stress Analysis) non-destructive testing. The proposed methodology combines a simplified two-layer eddy current model, representing the hardened case and the softer core, with the Jiles–Atherton hysteresis model. The associated inverse problem is solved by means of a genetic algorithm, enabling the identification of depth-dependent local hysteresis parameters from measured 3MA incremental permeability signals. The Jiles–Atherton hysteresis parameters are first calibrated using bulk B-H loops. Subsequently, the coupled forward model is used to establish the relationship between these parameters and the measured incremental permeability response for different hardening depths. As a proof of concept, the framework is applied to laser-hardened specimens. The identified local hysteresis and permeability characteristics show clear correlations with both case depth and excitation conditions, demonstrating the potential of the proposed approach for physics-based, non-destructive characterization of laser-hardened layers.