A model for the Barkhausen frequency spectrum as a function of applied stress

We derive a two parameter multi-exponential model to describe the frequency spectrum of Barkhausen noise in bulk steel under high excitation rates and applied tensile stress. We show how the amplitude and shape of the frequency spectrum depend on two directly measurable quantities, Barkhausen voltage and effective magnetic permeability, respectively, and how these change with stress. By incorporating frequency and depth dependence components into our model, we provide a framework for identifying stress variations along depth, which can be used for the purposes of non-destructive characterization.