Mechanical Engineering Journal (Jun 2024)
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 (Tg) to the deformation point (At). However, the molding temperature is set above At 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 Tg. Nevertheless, the applicability of the time-temperature superposition principle to optical glasses within the temperature range below Tg and above At has not been thoroughly investigated. Therefore, in this study, uniaxial compression creep tests were conducted over a wide temperature range from approximately Tg - 20 °C to At + 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 Tg to At, in two types of glasses, they exhibited a curved change below Tg and above At. 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 Tg - 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 At.
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