Dipole modeling of stress-dependent magnetic flux leakage

Existing magnetic dipole models cannot provide the accurate prediction result of the effect of the stress on the magnetic flux leakage (MFL) induced by defects in ferromagnetic materials. To solve this problem, an improved dipole model is proposed to investigate the stress-dependent MFL in tensioned specimens of Q235 steel. The stress concentration around the defect of a cylindrical through-hole leads to heterogeneous distribution of magnetization along the defect surface. Classic Timoshenko's theory is used to solve the localized compressive stress and tensile stress around the defect. The J-A model is employed to determine the stress-dependent magnetization distribution, which is the key parameter in the magnetic dipole model. The stress-dependent MFL signals predicted by the improved model are well consistent with the results of verification experiments and the peak-to-peak amplitude of the normalized MFL signal demonstrates the parabolic dependency on the applied tensile stress. A stress increment of 100 MPa can increase the amplitude of the MFL signal by 24%, which may cause a significant error in defect sizing. The proposed improved magnetic dipole model can reveal the effect of the stress concentration on the induced MFL signals and it is also applicable to solve the inverse problem for estimating the shapes and sizes of the defects even though the stress is involved.