A Unique Fractional Derivative Operator to Simulate All Dynamic Piezoceramic Dielectric Manifestations: From Aging to Frequency-Dependent Hysteresis

Ferroelectric materials are utilized in many applications ranging from capacitors to data storage. The hysteresis frequency dependence of ferroelectric materials has been well studied. However, the long-term dynamic behavior including aging has not been well documented due to the long time frame required to gather experimental data, but it is critical for understanding the lifespan of these materials in application. Previous work has shown that the hysteresis frequency dependence of dielectric properties can be accurately modeled in the time domain using fractional derivative operators applied on a large frequency bandwidth. Currently, the lowest frequencies tested have been restrained to the hysteresis cycle quasi-static threshold. Below this threshold, the hysteresis shape remains unchanged. This research expands the current knowledge by validating the use of fractional derivative operators in long-term aging models. The model data are experimentally validated using aged piezoelectric samples up to 107 s. These results confirm that the low and high dynamic dielectric material behaviors are linked and can be consequently modeled using fractional derivative operators.