The continuous development of constitutive equations for the finite strain deformation of glassy polymers has resulted in a number of sophisticated models that can accurately capture the materials' intrinsic behavior. Numerical simulations using these models revealed that the thermal history plays a crucial role in the macroscopic deformation. Generally, macroscopic behavior is assumed not to change during a test, however, for certain test conditions this does not hold and a relevant change in mechanical properties, known as physical aging, can be observed. To investigate the consequences of this change in material structure, the existing models are modified and enhanced by incorporating an aging term, and its parameters are determined. The result is a validated constitutive relation that is able to describe the deformation behavior of, in our case, polycarbonate over a large range of molecular weights and thermal histories, with one parameter set only.

Time-to-failure of polymers, and the actual failure mode, are influenced by stress, temperature, processing history, and molecular weight. We show that long-term ductile failure under constant load is governed by the same process as short term ductile failure at constant rate of deformation. Failure proves to originate from the polymer's intrinsic deformation behavior, more particularly the true strain softening after yield, which inherently leads to the initiation of localized deformation zones. In a previous study, we developed a constitutive model that includes physical aging and is capable of numerically predicting plastic instabilities. Using this model the ductile failure of polycarbonates with different thermal histories, subjected to constant loads, is accurately predicted also for different loading geometries. Even the endurance limit, observed for quenched materials, is predicted and it is shown that it originates from the structural evolution due to physical aging that occurs during loading. For low molecular weight materials this same process causes a ductile-to-brittle transition. A quantitative prediction thereof is, however, outside the scope of this paper and requires a more detailed study.

SynopsisIn this study a phenomenological constitutive model is proposed to describe the finite, nonlinear, viscoelastic behavior of glassy polymers up to the yield point. It is assumed that the deformation behavior of a glassy polymer up to the yield point is completely determined by the linear relaxation time spectrum and that the nonlinear effect of stress is to alter the intrinsic time scale of the material. A quantitative three-dimensional constitutive equation for polycarbonate as a model polymer was obtained by approximating the linear relaxation time spectrum by eighteen Leonov modes, all exhibiting the same stress dependence. A single Leonov mode is a Maxwell model employing a relaxation time that is dependent on an equivalent stress proportional to the Von Mises stress. Furthermore, a Leonov mode separates the ͑elastic͒ hydrostatic and ͑viscoelastic͒ deviatoric stress response and accounts for the geometrical complexities associated with simultaneous elastic and plastic deformation. Using a single set of parameters, the multi-mode Leonov model is capable of describing realistic constant strain rate experiments, including the strain rate dependent yield behavior. It is also capable of giving a quantitative description of nonlinear stress-relaxation experiments.

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