Strain hardening and anisotropy in solid polymers

Abstract

Mechanical properties of polymers strongly depend on the underlying microstructure. For instance, processing-induced molecular orientation may, in semi-crystalline polymers, lead to differences in lifetime up to a factor of 500 within a single injection molded product. Furthermore, enormous differences between the mechanical performance in tension and compression may arise as a result of an anisotropic distribution of the molecular orientation in a product. Considering that, due to their processing history, polymer products are rarely free of orientation, the importance of understanding the relation between molecular orientation and mechanical properties is evident. This thesis mainly focuses on the development of modeling concepts that capture the effects of molecular orientation on the deformation kinetics of solid polymers. For amorphous polymers, rubber-elastic theories are traditionally used to model the orienting network of entangled polymer chains, leading to reasonable descriptions of the experimentally observed strain hardening response. However, there are a number of issues regarding such entropic strain hardening models that still need to be solved. For instance, experiments show that the strain hardening response changes with strain rate and has a negative temperature dependence, both of which cannot be explained from an entropic origin. Another example is the large asymmetry between the yield stress in tension and compression that is observed experimentally in oriented amorphous polymers. Recently, it has been suggested that strain hardening in amorphous polymers primarily has an intermolecular origin, which would imply a viscous stress contribution on the macroscopic scale. The physical origin is that deformation leads to locally anisotropic chain conformations, which result in an intensification of activation barriers that is accompanied by an increase in segmental relaxation times. It is shown that the issues mentioned are indeed solved by employing a combined elastic-viscous strain hardening description. The model proposed for the viscous strain hardening contribution consists of an Eyring viscosity with parameters that evolve as a function of deformation. Incorporation of this modeling concept in the Eindhoven Glassy Polymer model and characterization using a set of uniaxial compression experiments on polycarbonate leads to accurate, quantitative descriptions of the material’s strain hardening response for a wide range of temperatures and strain rates. Additional support for the model proposed is found in the observation that it also quantitatively captures the mechanical response of polycarbonate in cyclic loading conditions, involving tension and compression on oriented samples, without any additional parameter fitting. In semi-crystalline polymers, frozen-in orientation in the amorphous domains is not the only possible source of anisotropy; the presence of possibly oriented and intrinsically anisotropic crystalline domains can have a significant contribution as well. In the macroscopic mechanical response of oriented semi-crystalline polymers, the influence of orientation is, therefore, twofold. On one hand, the frozen-in orientation in the amorphous phase leads to a large asymmetry between the mechanical response in tension and compression and introduces a dependence on loading direction in the material’s response, albeit relatively weak. On the other hand, the preferred orientation of the crystalline lamella gives rise to a strong direction dependence in the mechanical response, but does not enhance the differences between tension and compression. These aspects of the anisotropic deformation of oriented semi-crystalline polymers are assessed experimentally by measuring the tensile and compressive deformation kinetics of injection molded polyethylene at different loading angles with respect to the injection direction. For the first time, it is shown that a significant asymmetry between tension and compression exists in a melt-oriented (semi-crystalline) polymer. Also from a modeling perspective, the different origins of anisotropy in oriented semi-crystalline polymers are discussed; a model is formulated that combines the modeling concepts developed for oriented amorphous polymers with a model for anisotropic viscoplasticity. The model proposed accurately describes the tensile and compressive yield kinetics of injection molded polyethylene, for loading both parallel and perpendicular to the main orientation direction. Additionally, it captures the experimentally observed failure kinetics of these oriented polyethylene samples when subjected to a constant tensile load in these loading directions. The modeling concepts developed in this study provide a solid basis for future efforts to model failure of semi-crystalline polymers. An important open end is that the models proposed are essentially phenomenological, that is, the parameters only have a meaning on a macroscopic level and are not linked to a specific morphology. The next big challenge is to connect the macroscopic model parameters to microstructural parameters, such as crystallinity, lamellar thickness and orientation distributions. Ultimately, these parameters can, in turn, be related to processing history in terms of temperature, pressure and flow history, given the details of the molecular weight distribution.