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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.

Application of Closed Magnetic Circuit Method for Evaluating the Stress Distribution along Depth Direction