A Thermo-Mechanically Coupled Large-Deformation Theory for Amorphous Polymers Across the Glass Transition Temperature

Abstract

Amorphous thermoplastic polymers are important engineering materials; however, their nonlinear, strongly temperature- and rate-dependent elastic-viscoplastic behavior is still not very well understood, and is modeled by existing constitutive theories with varying degrees of success. There is no generally agreed upon theory to model the large-deformation, thermo-mechanically-coupled, elastic-viscoplastic response of these materials in a temperature range which spans their glass transition temperature. Such a theory is crucial for the development of a numerical capability for the simulation and design of important polymer processing operations, and also for predicting the relationship between processing methods and the subsequent me- chanical properties of polymeric products. In this manuscript we briefly summarize a few results from our own recent research [1–4] which is intended to fill this need. We have conducted large strain compression experiments on three representative amorphous polymeric materials a cyclo-olefin polymer (Zeonex-690R), polycarbonate (PC), and poly(methyl methacrylate) (PMMA) in a temperature range from room temperature to approximately 50C above the glass transi- tion temperature, θ g, of each material, in a strain-rate range of roughly 0.0001 s⁻¹ to 0.1 s⁻¹, and compressive true strains exceeding 100%. We have specialized our constitutive theory to capture the major features of the thermo-mechanical response of the three materials studied experimentally. We have numerically implemented our thermo- mechanically-coupled constitutive theory by writing a user material subroutine for a widely used finite element program Abaqus/Standard. In order to validate the predictive capabilities of our theory and its numerical implementation, we present the following validation experiments: (i) a plane-strain forging of PC at a temperature below θg, and another at a temperature above Tg; (ii) blow-forming of thin-walled semi-spherical shapes of PC above θg; and (iii) microscale hot-embossing of channels in PMMA above θ g. By comparing the results from this suite of validation experiments of some key features, such as the experimentally-measured deformed shapes and the load-displacement curves, against corresponding results from numerical simulations, we show that our theory is capable of reasonably accurately reproducing the experimental results obtained in the validation experiments.