Parameter study of variable order fractional model for the strain hardening behavior of glassy polymers

In this work, a novel approach of variable order fractional derivative model of viscoelasticity is provided to describe the strain hardening behavior of amorphous glassy polymers, which has been considered as a combined viscoelastic phenomenon in recent studies. The proposed model contains only four parameters as the order function is assumed to linearly vary with time. To validate the model, experimental tests of constant true strain rate uniaxial compression are conducted on PC to get the stress–strain data at different temperatures and strain rates. Comparison between the model prediction and experimental data show that the model can well describe the strain hardening behavior. It is also indicated by the linearly decreasing order function that strain hardening is a continuous stiffening process of material property because the smaller fractional order means that the property of material is closer to solid. Furthermore, a study on parameter is performed to investigate the physical significance of model parameters. It is shown that the slope of order change determines the rate of strain hardening and the intercept of order function mainly affects the initial stress of strain hardening. Finally, the rule of order function under various temperatures and strain rates reveals that during strain hardening the mechanical property of amorphous glassy polymers is softer but stiffens faster at higher temperatures and smaller strain rates.