Variable-order fractional constitutive model for the time-dependent mechanical behavior of polymers across the glass transition

. In this paper, the variable-order fractional constitutive model is adopted to study the time-dependent mechanical behavior of polymers across the glass transition. The fractional order is assumed to vary with time to describe the evolution of the mechanical properties. In order to examine the proposed method, the stress responses of two representative polymers, PETG and PC, across the glass transition are experimentally obtained and compared with the model predictions. It is shown that, by adopting the parameter of critical strain, the variable-order fractional model is able to well fit the data at all temperatures, from below, through, to above the glass transition. Furthermore, the order functions are graphically plotted and analyzed to show the ability of the variable-order to capture the mechanical property evolution of polymers in all phases. It is observed that the features of the order curves at the glass transition temperature are a combination of those of the glassy phase and the rubbery phase. As a result, we demonstrate that the variable-order fractional model is efficient in describing the time-dependent behavior of polymers across the glass transition and the rule of order functions with temperature can intuitively predict the change of the mechanical properties.