A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition

Abstract

Amorphous thermoplastic polymers are important engineering materials; however, their non-linear, 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 mechanical properties of polymeric products. In this paper we extend our recently published theory [Anand, L., Ames, N. M., Srivastava, V., Chester, S. A., 2009. A thermo-mechanically-coupled theory for large deformations of amorphous polymers. Part I: formulation. International Journal Plasticity 25, 1474–1494; Ames, N. M., Srivastava, V., Chester, S. A., Anand, L., 2009. A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part II: applications. International Journal of Plasticity 25, 1495–1539] 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 50 °C above the glass transition temperature, ϑg [theta subscript g], of each material, in a strain-rate range of ≈10-4 [10 superscript -4]to 10-1 s-1 [10 superscript -1 s superscript -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. In order to validate the predictive capabilities of our theory and its numerical implementation, we have performed the following validation experiments: (i) a plane-strain forging of PC at a temperature below ϑg [theta subscript g], and another at a temperature above ϑg [theta subscript g]; (ii) blow-forming of thin-walled semi-spherical shapes of PC above ϑg [theta subscript g]; and (iii) microscale hot-embossing of channels in Zeonex and PMMA above ϑg [theta subscript 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.