Analyzing the Tensile Creep Behavior of Different Types of Polypropylenes Using a Simple Fractional Differential Viscoelastic Model
Yasuhiko Otsuki, Kou Hashimoto, Yutaka Kobayashi, Shotaro Nishitsuji, Hisao Matsuno, Hiroshi Itô
Abstract
Fractional differential viscoelastic calculus was used to develop a model for predicting the primary to tertiary creep in the tensile creep deformation of various polypropylenes (PPs). The primary and secondary creep were described via simple fractional differential viscoelasticity with an empirical formula for the stress and temperature dependence of the fractional differential order. Tertiary creep was treated as a pure viscous body with damage. The temperature dependence is treated simply, and Arrhenius's law is applied. As for stress dependence, the Eyring law of the sinh function was applied to the primary and secondary creep processes, while the WLF-type shift function was adopted for tertiary creep. The primary and secondary creep behaviors of each model material showed creep growth rates according to the rigidity of each material. As for the tertiary creep, the homo PP showed a little damage progression with a damage index of 0.17, while the impact-resistant PP showed faster damage progression with a damage index of around 0.5. The three types of post-consumer recycled PPs showed intermediate properties between these virgin PPs, and no peculiarities were confirmed in the static creep behaviors. It was confirmed that the creep experimental results for all model materials fell on the same Monkman-Grant law. The presented creep model can predict the creep strain transition and minimum strain rate well and is effective in predicting the creep characteristics of PPs.