Thermal–viscoelastic analysis of polymethyl methacrylate using a fractional differential viscoelastic model

Abstract

Vacuum forming is used to manufacture large molded parts. As forming conditions have a significant effect on the dimensional accuracy, these should be determined accordingly. In this study, a geometric nonlinear creep analysis of polymethyl methacrylate (PMMA), which is a common thermoplastic resin, was carried out at the target temperature of 393.15[Formula: see text]K and target strain of approximately 50% for vacuum forming. The proposed fractional differential viscoelastic model was extended to a three-element model, consisting of a single hyperelastic spring and two fractional differential (FD) models. It was further extended by time–temperature superposition (TTS) for thermo-viscoelastic analysis. The model determined all material constants by measuring the temperature/frequency sweeps at small strain amplitudes of 0.01% using dynamic mechanical analysis (DMA). Numerical analysis confirmed the validity of the proposed method through creep and stress-relaxation tests by DMA at the target temperature/strain. The results demonstrated that the finite element analysis constructed using the proposed method could predict the mechanical properties during vacuum-forming-oriented creep tests. These results are expected to provide important insights into the complex mechanical behavior of PMMA, which varies with the temperature and strain rate.