Quantitative Prediction of Residual Stress, Surface Hardness, and Case Depth in Medium Carbon Steel Plate Based on Multifunctional Magnetic Testing Techniques

In this study, the methods of tangential magnetic field (TMF), magnetic Barkhausen noise (MBN), and incremental permeability (IP) were employed for in the simultaneous, quantitative prediction of target properties (bidirectional residual stress, surface hardness, and case depth) in the 45 steel plate. The bidirectional magnetic signals and target properties were measured experimentally. The results of Pearson correlation analyses revealed that most parameters of the MBN and IP signals are strongly correlated with both residual stress and surface hardness under the influence of multiple target properties. The multiple linear regression (MLR) model demonstrated highly accurate quantitative prediction of residual stress and hardness in the y-direction. However, the simultaneous prediction of residual stress and case depth in the x-direction proved less effective than expected. To address this limitation, an inversion method was developed based on the regression model with the single parameter as the dependent variable and the target properties as the independent variable. By incorporating known magnetic parameters and target properties, the model effectively determined the unknown target properties. After applying the method, the coefficient of determination (R²) for x-direction residual stress increased from 0.89 to 0.96 and the absolute error (AE) of case depth decreased from 0.10 mm to 0.04 mm for case depths below 0.15.