Modeling the magnetic field dependence of magnetoacoustic emission and its dependence on creep damage

Abstract

In the past, there has been little numerical modeling of magneto-acoustic emission (MAE). Only very simple models exist and there has been disagreement about the mechanism of MAE and about how to physically interpret the various peaks of MAE vs. magnetic field H. Furthermore, no one has provided a numerical model for the field dependence of the MAE. In addition, experimental research has found sometimes two peaks in MAE vs. H, sometimes three, and sometimes one. When two peaks are present, there is usually asymmetry in peak height. This diverse behavior will be accounted for in this paper in a single phenomenological model, which will also be utilized in predicting the effect of creep damage on MAE. The model represents an extension to field dependent behavior of an earlier model of Ng et al., who used the basic notion to explain frequency dependent behavior of the MAE. Its basic notion is that all of the MAE phenomena can be interpreted in terms of three peaks—a central peak associated with MAE generated by domain wall motion, primarily non-180 degree wall motion, peaking at H=Hc (the coercive field), and two side peaks, due to nucleation and annihilation of domain walls, peaking at fields corresponding to the knees of the magnetization curve, one knee at H<0 and the other at positive H>Hc, the positions of which are here determined by where the second derivative of the permeability if zero. The permeability is here computed from the Sablik-Jiles model. Also, in the present model, the MAE is proportional to the square root of the permeability and to the square root of the sum of the squares of the MAE peak amplitudes, which are assumed to have a Gaussian dependence on the field. The relative amplitudes and widths of the peak dependences on H account for whether one, two, or three peaks are observed. By including dependence on creep damage in the expression used for the permeability, one finds that creep damage causes a decrease in the MAE peaks and a greater separation between the peaks.