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 mechanical properties of polymeric products. In this paper we present a theory which aims 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 transition temperature, Tg, of each material, in a strain-rate range of 0.0001 to 0.1 /sec, and compressive true strains exceeding 100%. We have specialized our constitutive theory to capture the major features of the thermomechanical 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 Tg, and another at a temperature above Tg; (ii) blow-forming of thin-walled semi-spherical shapes of PC above Tg; and (iii) microscale, hot-embossing of channels in Zeonex above Tg. 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.

Details:

1. 1)Vikas Srivastava, Shawn A. Chester, Nicoli M. Ames, and Lallit Anand, 2010. A thermo-mechanically-coupled large-deformation theory for amorphous polymers in a temperature range which spans their glass transition. International Journal of Plasticity, 26 1138-1182.
   

Plane Strain Forging

In this example we consider the plane strain forging of PC.  Both the experiment and the simulation are at 25C or 160C and quasi-static rates.

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Below Tg (25C)                                                   Above Tg (160C)

Top: Blelow Tg (25C).  Bottom: Above Tg (160C).

Blow Forming

In this example we consider the axisymmetric blow forming of PC.  This is an example of a load-controlled situation where we have applied the pressure and measure the shape.

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The conditons for the above experiments and simulations are (top) 160C and 35psi, and (bottom) 150C and 20psi.