# Nonlinearly viscoelastic response of glassy polymers

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## Abstract

This thesis consists of three chapters. After a brief introduction on the general aspects of polymer characterization and viscoelasticity in the first chapter, all major features of this research project are described in the following two chapters. The second chapter deals exclusively with the nonlinearly thermo-mechanical creep behavior of (bisphenol A) polycarbonate under pure shear loading at different temperatures (0 °C to 140 °C). The shear creep in the linearly viscoelastic range was measured with a torsiometer for reference purposes and a master curve, along with a shift factor curve, were deduced. While the master curve is well defined with no detectable deviation, the shift factor can be represented by two straight line segments interrupted at the β transition temperature of polycarbonate. The shear creep tests in the nonlinearly viscoelastic range were conducted on an Arcan specimen geometry at different temperatures and under different stress levels, utilizing digital image correlation for the recording of the creep strains. The difference between the nominal stress and the actual stress distribution in the Arcan specimen was explored via numerical simulations (ABAQUS) by assuming linear quasi-elastic and quasi-plastic analysis in place of the as yet uncertain material characterization. Isochronal plots were created from the creep data. Nonlinearly viscoelastic behavior starts to take effect near 1% strain at the temperatures considered. The applicability of the stress-clock representation for material characterization has been explored and is found to be dubious, at best, for this material. The "yield-like" behavior of polycarbonate has been examined in terms of the isochronal stress-strain response and a corresponding "yield-like shear stress" has been determined to be a monotonically decreasing function of the temperature, but again with an interruption at the β transition temperature. Time-temperature trade-off as practiced for "time-temperature shifting" at small strains does not apply in the nonlinear domain. The results are generally in agreement with those found for Poly(Methyl Methacrylate), thus fostering the idea that the present results can be generalized -with additional work- to other amorphous polymers. The third chapter focuses on the role of volumetric strain in nonlinearly viscoelastic behavior of polycarbonate. The creep responses of (bisphenol A) polycarbonate at 80 °C under combined two-dimensional shear and tensile/compressive stress states were measured on Arcan specimens in the nonlinearly viscoelastic regime. Of particular interest is the influence of the dilatational deformation component on the nonlinearly viscoelastic creep behavior. Because the nonlinear material response determines the stress distribution under fixed deformation or load, but is not known a priori, a re-estimation of the latter is essential to verify or adjust the stress state(s). This is accomplished by approximating isochronal stress-strain relations derived from shear creep behavior, encompassing the nonlinear domain, by a classical incremental elastoplastic material description at appropriate times. Inasmuch as the two-dimensional character of the test configuration places limits on accessing three-dimensional information, a coherent representation of the results in terms of maximum shear and/or octahedral representation is examined. It is found that the creep behavior under shear and normal stress or deformation imposition differ significantly: when viewed as a response in terms of a maximum shear description, there are material responses under combined loading when either one or the other dominates. Once the response is formulated in terms of an octahedral description the representation becomes less sensitive to normal vs. shear behavior. Within the precision underlying the measurements it is found that the shear and normal strain components accumulate under creep in nearly constant ratios. However, under this scenario it is demonstrated quite clearly that the addition of negative dilatational stress (or deformation) to pure shear leads to distinctly lower creep rates. The converse is true, if positive dilatational stresses are added, though not monotonically so.

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