Effect of Hard Particles on Magnetic Barkhausen Noise in Metal Matrix Composite Coatings: Modeling and Application in Hardness Evaluation

The hard particles in metal matrix composite (MMC) coatings can greatly improve the hardness of materials and further affect the mechanical properties. How to accurately evaluate the hardness of MMC coatings using a nondestructive method is always a challenge. The magnetic Barkhausen noise (MBN) has been proven to be very sensitive to the variations of microstructure. Thus, a theoretical model is established in this article to describe the effect of hard particle content on the magnetic Barkhausen activity, based on which the hardness can be evaluated by the MBN method. In this model, the key magnetic parameters of Jiles–Atherton (J-A) theory, the pinning parameter $k$ and reversibility factor $c$ , are dependent on the number and the interparticle distance of hard particles. A stochastic process of Barkhausen activity combined with J-A theory is then described to deduce the variations of hysteresis loop and MBN signals with hard particle contents in MMC coatings. The results show that the peak value of root mean square (rms) of MBN signals decreases, while the full-width at half-maximum (FWHM) increases with the increase in weight percentage of hard particles. Based on the leave-one-out cross-validation (LOO-CV) method, the variation trends of MBN characteristics can be described well by the second-order polynomial fitting. Also, the prediction error between experiment and theory is 15.28% and 17.40% for normalized rms peak value and FWHM, respectively. The variation mechanism of MBN signals is attributed to the anisotropic hypereutectic structure with flower stripe consisting of solid solution and secondary strengthening phase near hard particles, which promotes the pinning sites and hinders the domain wall movement. When the hard particle content is high, especially above 30%, the double peak distortion characteristics of MBN signals are easily induced by the different response of matrix alloy to the applied magnetic field in comparison to the magnetically hard phases in a hypereutectic structure. Finally, the complicated relationship between MBN characteristic values and hardness is deduced by using the hard particle content as an intermediate variable. The results show that our proposed theoretical model and evaluation method in this article can characterize the hardness of MMC coatings well.