Since the permeability of ferromagnetic materials is sensitive to the stress changes, it is feasible to acquire the stress level through detecting the change in permeability. In this study, to explore the distribution of stress or residual stress along the depth direction, a multi-layer model was established and a new inversion algorithm was proposed; and the hypothesis of uniformity of the material's physical properties for each layer was introduced. Under laboratory conditions, the four-point bending experiment was then implemented with a sample of 45# steel. Global Fourier series fitting based on the least-squares method was used for signal process. The amplitude ratio of the induced voltage to the excitation current was extracted. The effective permeability and the associated hysteresis angle at the 0.25 mm deflection were calculated and presented good regular variations. Finally, under the 0.25 mm deflection, the effective permeability change along the depth was obtained, and the inversely fitted curve was consistent with the theoretical curve. It is verified that the sensor has good robustness by adding deviation of the detection depth. Thereby, it is feasible to test stress or residual stress as a function of depth by multi-frequency eddy current (EC) method.
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