Investigation of the applicable temperature range of time-temperature superposition principle for thermo-viscoelastic properties of optical glasses

Abstract

Many commercial optical glasses exhibit thermorheologically simple behavior, which allows the application of the time-temperature superposition principle within the temperature range from the glass transition temperature (T_g) to the deformation point (A_t). However, the molding temperature is set above A_t in cases involving significant deformation during glass molding press, such as with large-aperture concave meniscus lenses. Additionally, stress relaxation is observed in optical glasses even at temperatures below T_g. Nevertheless, the applicability of the time-temperature superposition principle to optical glasses within the temperature range below T_g and above A_t has not been thoroughly investigated. Therefore, in this study, uniaxial compression creep tests were conducted over a wide temperature range from approximately T_g - 20 °C to A_t + 50 °C using three types of commercial optical glasses to evaluate their thermo-viscoelastic properties. The results revealed that when the creep functions at each test temperature were shifted along a logarithmic time axis, they formed a smooth single curve (master curve), indicating the applicability of the time-temperature superposition principle. Moreover, while the shift factors for all glasses exhibited Arrhenius behavior within the temperature range of T_g to A_t, in two types of glasses, they exhibited a curved change below T_g and above A_t. Therefore, applying the Williams–Landel–Ferry (WLF) equation to approximate these shift factors revealed that they could be well approximated across the entire test temperature range. However, when applying the WLF equation to optical glass, limiting the temperature to a range higher than T_g - 30 °C was necessary. To express the shift factor over a wide temperature range of several hundred degree Celsius, from room temperature to molding temperature, it was practical to use the multi-linear Narayanaswamy equation, in which the apparent activation energies vary near A_t.