Quantitative characterization of tensile stress in electroplated nickel coatings with a magnetic incremental permeability sensor

Abstract

Quantitative characterization of tensile stress in electroplated nickel coatings on the copper substrate with the thickness range of 2.809 µm to 35.654 µm in the elastic stage was experimentally performed with a magnetic incremental permeability (MIP) sensor in the study. Firstly, a differential mutual-inductance sensor based on the parallel excitation of bifilar co-directional coil was proposed. With the proposed sensor, multiple signals including high-frequency eddy current (HFEC), tangential magnetic field strength, and magnetic incremental permeability butterfly curve (MIPBC) could be measured synchronously and eight typical magnetic parameters were obtained from experimental signals. Then, four parameters including the peak height of MIPBC, amplitude at cross point of MIPBC, difference frequency of HFEC, and sum frequency component of HFEC were selected to quantitatively characterize tensile stress. Experimental results showed that the four parameters depended on tensile stress and showed a parabolic trend. The parameters of the parabolic equation varied with nickel coating thickness. Finally, a polynomial surface fitting method based on the combination of the factors of thickness and tensile stress were derived with the selected four parameters and the coefficient of determination R2 was higher than 0.9. The further comparison between theoretical results and predicted stress confirmed that the proposed MIP sensor could realize the quantitative detection of tensile stress in different nickel coatings.