Analytical model of magnetic Barkhausen noise testing on surface-modified ferromagnetic plates with stress distributions

Surface treatment is a critical technology in engineering that enhances the mechanical properties of materials, in which the stress state within the material and the thickness of the surface modification layer are essential for optimizing performance. Magnetic Barkhausen Noise (MBN) serves as an effective nondestructive evaluation technique for ferromagnetic structures. In this work, we develop an analytical model that incorporates the attenuation mechanism of the MBN signal strength, and the strength of the stress-induced magnetic Barkhausen excitation (MBE) as determined by the magneto-mechanical constitutive law of the material. The proposed theoretical model can accurately characterize the MBN signal influenced by internal stresses and surface modification layers, as confirmed by comparison with existing experimental results. The theoretical analysis shows the influence of internal stress fields, layer dimensions, and electromagnetic properties on the MBN signal, revealing a positive relationship between signal intensity and the thickness of surface modification layer and the magnitude of internal stresses. This research provides a valuable reference for interpreting MBN signals and evaluating internal stress distributions for surface-modified ferromagnetic plates.