The increasing use of polyethylene in diverse applications motivates the need for understanding
how its molecular properties relate to the overall behaviour of the material.
Although microstructure and mechanical properties of polymers have been the subject of
several studies, the irreversible microstructural rearrangements occurring at large deformations
are not completely understood. The purpose of this thesis is to describe how the
concepts of Continuum Damage Mechanics can be applied to modelling of polyethylene
materials under different loading conditions.
The first part of the thesis consists of the theoretical formulation and numerical
implementation of a three-dimensional micromechanical model for crystalline polyethylene.
Based on the theory of shear slip on crystallographic planes, the proposed model is
expressed in the framework of viscoplasticity coupled with degradation at large deformations.
Earlier models aid in the interpretation of the mechanical behaviour of crystalline
polyethylene under different loading conditions; however, they cannot predict the microstructural
damage caused by deformation. The model, originally due to Parks and
Ahzi (1990), was further developed in the light of the concept of Continuum Damage
Mechanics to consider the original microstructure, the particular irreversible rearrangements,
and the deformation mechanisms. Damage mechanics has been a matter of intensive
research by many authors, yet it has not been introduced to the micromodelling
of semicrystalline polymeric materials such as polyethylene. Regarding the material representation,
the microstructure is simplified as an aggregate of randomly oriented and
perfectly bonded crystals. To simulate large deformations, the new constitutive model
attempts to take into account existence of intracrystalline microcracks.
The second part of the work presents the theoretical formulation and numerical
implementation of a three-dimensional constitutive model for the mechanical behaviour
of semicrystalline polyethylene. The model proposed herein attempts to describe the deformation and degradation process in semicrystalline polyethylene following the approach
of damage mechanics. Structural degradation, an important phenomenon at large
deformations, has not received sufficient attention in the literature. The modifications to
the constitutive equations consist essentially of introducing the concept of Continuum
Damage Mechanics to describe the rupture of the intermolecular (van der Waals) bonds
that hold crystals as coherent structures. In order to model the mechanical behaviour,
the material morphology is simplified as a collection of inclusions comprising the crystalline
and amorphous phases with their characteristic average volume fractions. In the
spatial arrangement, each inclusion consists of crystalline material lying in a thin lamella
attached to an amorphous layer. To consider microstructural damage, two different approaches
are analyzed. The first approach assumes damage occurs only in the crystalline
phase, i.e., degradation of the amorphous phase is ignored. The second approach considers
the effect of damage on the mechanical behaviour of both the amorphous and
crystalline phases.
To illustrate the proposed constitutive formulations, the models were used to predict
the responses of crystalline and semicrystalline polyethylene under uniaxial tension
and simple shear. The numerical simulations were compared with experimental data
previously obtained by Bartczak et al. (1994), G‘Sell and Jonas (1981), G‘Sell et al. (1983),
Hillmansen et al. (2000), and Li et al. (2001). Our model’s predictions show a consistently
good agreement with the experimental results and a significant improvement with
respect to the ones obtained by Parks and Ahzi (1990), Schoenfeld et al. (1995), Yang
and Chen (2001), Lee et al. (1993b), Lee et al. (1993a), and Nikolov et al. (2006). The
newly proposed formulations demonstrate that these types of constitutive models based
on Continuum Damage Mechanics are appropriate for predicting large deformations and
failure in polyethylene materials.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3427 |
| Date | 11 1900 |
| Creators | Alvarado Contreras, Jose Andres |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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