Electromagnetic nondestructive evaluation method is feasible in assessing stress or residual stress levels in ferromagnetic structures, for there is a strong inherent correlation between the permeability and the stress. This study is based on the closed magnetic circuit method for testing stress distribution along depth. Firstly, a theory is proposed for describing the propagation of electromagnetic energy inside ferromagnetic materials. A layered model is established considering the electromagnetic field experienced different attenuation at different depths. And each layer is assumed to have the identical physical state. Then, multi-frequency eddy current method is proposed to testing the in-depth permeability variation and consequently the stress-depth profile. For simply using the convolution integral, a novel inversion algorithm is given to resolve the convolution integral. To apply the proposed method for testing the stress-depth profile, multi-frequency eddy current experiments are conducted through a four-point bending device; with the specimen material employed is 45# steel. Finally, map the experimental data fitting curve to the theoretical calculation curve, and hence can verify the proposed theory and the inversion algorithm.
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