Dipole modelling of temperature-dependent magnetic flux leakage

Due to the nonlinear coupling, assessing the direct effect of temperature on magnetic flux leakage (MFL) signal is a complicated task. If temperature induces inner stress, it makes the problem doubly difficult, so few models are available for predicting the MFL signal under this condition. To model the effect of temperature on MFL signal, the temperature-dependent magnetic dipole models are proposed. In the first case, where the direct thermal effect is involved only, the dipole model is improved via the modified temperature-dependent Jiles-Atherton (J-A) model. While in the second case, where the combined effects of temperature and thermal stress are considered, the magnetomechanical J-A parameters are further introduced into the dipole model. The thermal stress distribution around a cylindrical through-hole defect is solved by thermoelastic and solid mechanics theories. The magnetomechanical theory is employed to analyse the stress-dependent magnetisation distribution, the key parameter in the magnetic dipole model. The verified experiments are conducted on an M250-50A non-oriented grain (NO) silicon steel specimen with a cylindrical through-hole defect. And the MFL signals predicted by both proposed models agree with the experimental results. When the direct effect of temperature is involved only, the peak-to-peak amplitude of the MFL signal (MFLpp) presents approximately linear dependence on temperature in the range from −40 to 60 . In addition, when both temperature and thermal stress are considered, the MFLpp changes as a parabolic function of temperature, this being much more significant than the direct effect. The proposed models can act as effective tools to understand the temperature and thermal stress influences on MFL signals. They are also appropriate to solve the inverse problem of sizing the defects accurately when the temperature is involved.