Post on 27-Feb-2021
transcript
RHEOLOGICAL CHARACTERISTICS OF PULP-
FIBRE–REINFORCED POLYAMIDE COMPOSITE
by
Robenson Cherizol
A thesis submitted in conformity with the requirements
for the degree of Doctor Philosophy
Department of Chemical Engineering & Applied Chemistry
University of Toronto
© Copyright by Robenson Cherizol 2016
ii
RHEOLOGICAL CHARACTERISTICS OF PULP-FIBRE–REINFORCED
POLYAMIDE COMPOSITE
Robenson Cherizol
Doctor of Philosophy
Department of Chemical Engineering & Applied Chemistry
University of Toronto
2016
iii
Abstract
Recently, there has been increasing interest in utilizing pulp-fibre–reinforced, higher-
melting–temperature engineering thermoplastics, such as polyamide 11 and polyamide 6
in the automotive, aerospace and construction industries. Moreover, the rheological
characteristics of those composites were not fully investigated in relation to processing
approaches and pulp-fibre aspect ratio. Two processing approaches were used in this
thesis: the extrusion compounding process and the Brabender mixer technique using
inorganic salt lithium chloride (LiCl). The fibre-length distribution and content, and the
densities of the PA11 and modified bio-based PA11 after compounding, were
investigated and found to coincide with the final properties of the resultant composites.
The effects of fibre content, fibre aspect ratio, and fibre length on rheological properties
were studied. The rheological properties of high-yield–pulp (HYP) –reinforced bio-based
Polyamide 11 (PA11) composite (HYP/PA11) were experimentally investigated using a
capillary rheometer. Experimental test results showed a steep decrease in shear viscosity
with increasing shear rate; this melt-flow characteristic corresponds to shear-thinning
behavior in HYP/PA11. The morphological properties of HYP/PA11 composite were
examined using SEM: no fibre pullout was observed. This was due to the presence of the
hydrogen bond, which created excellent compatibility between high-yield pulp fibre and
bio-based Nylon 11. The viscoelastic characteristics of biocomposites derived from
natural-fibre–reinforced thermoplastic polymers and of predictive models were reviewed
to understand their rheological behavior. Novel predicted multiphase rheological-model–
based polymer, fibre, and interphasial phases were developed. Rheological characteristics
iv
of the composite components influenced the development of resultant microstructures;
this in turn affected the mechanical characteristics of a multiphase composite.
Experimental and theoretical test results of HYP/PA11 showed a steep decrease in
apparent viscosity with increasing shear rate; this melt-flow characteristic corresponds to
shear-thinning behavior in HYP/PA11.The nonlinear mathematical model to predict the
rheological behavior of HYP/PA11was validated experimentally at 200˚C and 5000S-1
shear rate.
v
Acknowledgments
I would like to thank my advisors, Prof. Mohini Sain and Jimi Trong Ph.D., for their
supervision and support. They have inspired me with their valuable qualities as
professionals and scientists. I am also very grateful to my committee members, Profs.
Christopher Yip, Hani Naguib and Saed Sayad, for their scientific and constructive input,
criticisms, advice, and time.
I genuinely appreciate the financial support of MITAC, Automotive Partnership Canada
(APC), the University of Toronto, and Ford Motor Company that allowed me to pursue
my three-year internship at Ford facilities at Windsor.
I wish to express my warm and sincere thanks to my fellow students and other
department staff at the Faculty of Forestry, and Pauline Martini and Joan at the
Department of Chemical Engineering and Applied Chemistry. Special thanks to Mr. S.
Law, Mr. Lynn, MS. Birat KC, MSc. Ahmed Sobh, Dr. S. Kunar, and Dr. Suhara
Panthapulakkal, and the staff of “PERDC” of the Ford Essex engine plant at Windsor for
their help and support during this thesis work.
I am permanently indebted to my beloved friends and relatives for their love and support.
I would like to thank my parents, Applys and Lucilda Cherizol, for their constant
encouragement, inspiration, and valuable guidance throughout my life.
vi
Finally, words alone cannot express the thanks I owe to my wife Ernette, to my kids
Alyssa and Daniel. They not only gave me their unconditional love, but also supported
me unconditionally through the ups and downs of my doctoral studies.
vii
Table of Contents
Abstract .............................................................................................................................. iii
Acknowledgments............................................................................................................... v
Table of Contents .............................................................................................................. vii
List of Tables ................................................................................................................... xiv
List of Figures ................................................................................................................... xv
Chapter 1 Introduction ....................................................................................................... 1
1.1 Background and Motivation ..................................................................................... 1
1.2 Hypotheses ................................................................................................................ 3
1.3 Objectives ................................................................................................................. 4
1.4 Outline of the Thesis ................................................................................................. 4
Chapter 2 Literature Review ............................................................................................ 10
2.1 High-Yield Pulp fibre ............................................................................................. 10
2.2 Polymeric matrix ..................................................................................................... 10
2.2.1 Bio-based Nylon 11 (PA11)............................................................................. 11
2.2.2 Surface modification of natural fibres ............................................................. 13
2.3 Extrusion Process .................................................................................................... 15
2.3.1 Effects of processing parameters on properties of composites ........................ 16
viii
2.3.2 Low-temperature compounding ....................................................................... 19
2.4 Rheology ................................................................................................................. 20
2.5 Modeling of Fluid Flows ........................................................................................ 23
2.5.1 Classification of fluid flow modeling .............................................................. 23
2.5.1.1 Continuum hypothesis .............................................................................. 24
2.5.1.2 Molecular theory ....................................................................................... 25
2.5.2 Continuum models of fluid flows and constitutive equations ......................... 26
2.6 Viscoelasticity of composite materials ................................................................... 28
2.7 Problem Statement .................................................................................................. 30
Chapter 3 Evaluation of the Influence of Fibre Aspect Ratio and Fibre Content on the
Rheological Characteristic of High-Yield-Pulp Fibre–Reinforced Polyamide 11
(HYP/PA11) Green Composite......................................................................................... 33
3.1 Abstract ................................................................................................................... 33
3.2 Introduction ............................................................................................................. 34
3.3 Materials and Methods ............................................................................................ 36
3.3.1 Materials .......................................................................................................... 36
3.3.2 Methods............................................................................................................ 37
3.3.2.1 Composites preparation ............................................................................ 37
3.3.2.2 Effect of processing conditions ................................................................. 37
ix
3.3.2.3 Fibre content analysis and determination of fibre length distribution
(original fibre length) ............................................................................................ 38
3.3.2.4 Rheological properties measurement ........................................................ 39
3.3.2.5 Scanning electron microscopy .................................................................. 39
3.4 Results and Discussion ........................................................................................... 40
3.4.1 Effect of fibre content on the length and shape distribution on HYP-fibre–
reinforced bio-based nylon composite ...................................................................... 40
3.4.2 Rheological characteristics of HYP–reinforced bio-based polyamide ............ 41
3.4.3 Effect of the temperature on the shear viscosity versus shear rate of HYP-
reinforced PA11 ........................................................................................................ 43
3.4.4. Effect of HYP fibre content on the rheological behavior of HYP/PA11 ........ 45
3.4.5 Effect of high-yield–pulp fibre aspect ratio on rheological properties ............ 47
3.4.6 Scanning electron microscopy ......................................................................... 48
3.5 Conclusions ............................................................................................................. 49
CHAPTER 4 Effect of Lithium Chloride on the Fibre Length Distribution, Processing
Temperature and the Rheological Properties of High-Yield-Pulp-Fibre–Reinforced
Modified Bio-Based Polyamide 11 Composite ................................................................ 50
4.1 Abstract ................................................................................................................... 50
4.2 Introduction ............................................................................................................. 51
4.3 Material and Methods ............................................................................................. 53
x
4.3.1 Materials .......................................................................................................... 53
4.3.2 Methods............................................................................................................ 54
4.3.2.1 Composites preparation ............................................................................ 54
4.3.2.2. Effect of processing conditions ................................................................ 55
4.3.2.3 Fibre content and length distribution analysis after compounding ........... 56
4.3.2.4 Actual density measurement ..................................................................... 56
4.3.2.5 Differential scanning calorimetry (DSC) .................................................. 57
4.3.2.6 Rheological properties measurement ........................................................ 57
4.4 Results and Discussion ........................................................................................... 58
4.4.1 Effect of the lowering the processing temperature on the pulp fibre distribution
and the bio-based polyamide density after processing ............................................. 58
4.4.2 Densities and actual fibre contents .................................................................. 60
4.4.3 Effect of fibre content on the length and shape distribution on HYP-reinforced
bio-based modified PA11 composite ........................................................................ 62
4.4.4 Rheological characteristics of HYP–reinforced bio-based polyamide ............ 65
4.4.5 Effect of the processing parameters on the rheological property .................... 67
4.4.6 Effect of the inorganic salt lithium chloride on the rheological properties of
HYP fibre–reinforced bio-based polyamide composite ............................................ 68
4.4.7 Effect of HYP fibre content on the rheological characteristics of modified bio-
base (PA11 + 3%LiCl) composite ............................................................................ 70
xi
4.5 Conclusions ............................................................................................................. 72
CHAPTER 5 Review of Non-Newtonian Mathematical Models for Rheological
Characteristics of Viscoelastic Composites ...................................................................... 73
5.1 Abstract ................................................................................................................... 73
5.2 Introduction ............................................................................................................. 74
5.3 Viscoelastic characteristics of materials ................................................................. 75
5.4 Rheological modelling of viscoelastic composites ................................................. 78
5.5 Governing Equations .............................................................................................. 80
5.6 Constitutive equations ............................................................................................. 81
5.6.1 K-BKZ model .................................................................................................. 81
5.6.2 Upper-Convected Maxwell model (UCM) ...................................................... 83
5.6.3 White-Metzner Model ...................................................................................... 84
5.6.4 Phan-Thien-Tanner model (PTT) .................................................................... 85
5.6.5 Giesekus-Leonov model .................................................................................. 88
5.6.6 Oldroyd-B Model ............................................................................................. 89
5.7 Conclusion .............................................................................................................. 89
CHAPTER 6 Modeling the Rheological Characteristics of Flexible High Yield Pulp-
Fibre–Reinforced Bio-Based Nylon 11 Bio-Composite ................................................... 91
6.1 Abstract ................................................................................................................... 91
6.2 Introduction ............................................................................................................. 92
xii
6.3 Mathematical model................................................................................................ 94
6.3.1 Governing Equations ....................................................................................... 94
6.3.2 Assumptions and boundary conditions ............................................................ 95
6.3.3 Model development ......................................................................................... 96
6.4 Materials and Methods ............................................................................................ 99
6.4.1 Materials .......................................................................................................... 99
6.4.2 Experiment ....................................................................................................... 99
6.4.3 Rheological Measurements .............................................................................. 99
6.5 Results and discussion .......................................................................................... 100
6.5.1 Experimental Results ..................................................................................... 100
6.5.2 Variation of the viscosity with a function of shear rate of HYP reinforced
PA11 at various temperatures ................................................................................. 103
6.5.3 Effect of fibre content on the rheological behavior of HYP/PA11 ................ 104
6.5.4 Effect of the fibre aspect ratio on the rheological property ........................... 105
6.5.5 Predicted results ............................................................................................. 107
6.5.6 Modeling results versus experimental results ................................................ 109
6.6 Conclusions ........................................................................................................... 111
CHAPTER 7 Conclusions and Recommendations ......................................................... 112
7.1 Conclusions ........................................................................................................... 112
7.2 Scientific and engineering contribution of this thesis ........................................... 113
xiii
7.3 Study limitations ................................................................................................... 113
7.4 Recommendations ................................................................................................. 114
7.5 Publications and Conferences ............................................................................... 115
References ....................................................................................................................... 117
xiv
List of Tables
Table 3.1 ............................................................................................................. 39
Table 3.2. ............................................................................................................ 41
Table 4.1 ............................................................................................................. 56
Table 4.2 ............................................................................................................. 60
Table 4.3 ............................................................................................................. 61
Table 4.4 ............................................................................................................. 62
Table 4.5. ......................................................................................................................... 63
Table 4.6. ......................................................................................................................... 64
xv
List of Figures
Figure 2.1. Nylon 11
Figure 2.2. Structure of Nylon 11
Figure 2.3. Molecular and continuum flow models (Gad-el-Hak, 1999)
Figure 2.4. Process development and optimization
Figure 3.1. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Figure 3.2. Variation of the viscosity with a function of shear rate of HYP/PA11 at
various temperatures.
Figure 3.3. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Figure 3.4. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Figure 3.5. An SEM micrograph of pulp-fibre–reinforced polyamide composite fracture
surface showing partially melted nylon fibre.
Figure 4.1. Schematic figure of twin-screw extruder
Figure 4.2. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Figure 4.3 Variation of the viscosity with a function of shear rate of HYP/PA11 at
various temperatures.
Figure 4.4. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
xvi
Figure 4.5. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Figure 4.6. An SEM micrograph of pulp-fibre–reinforced polyamide composite fracture
surface showing partially melted nylon fibre.
Figure 6.1. High yield pulp fibre of length L before load is applied
Figure 6.2. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C
Figure 6.3. Variation of the viscosity with a function of shear rate of HYP/PA11 at
various temperatures.
Figure 6.4. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Figure 6.5. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Figure 6.6. Prediction of shear viscosity vs. shear rate of HYP/PA11at 200˚C
Figure 6.7. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
1
Chapter 1
Introduction
1.1 Background and Motivation
Pulp-fibre–reinforced thermoplastic composites are in high demand in the automotive,
aerospace, and construction industries. Pulp fibres are biodegradable and renewable, they
consume less energy than glass fibres, and consequently they generate less pollution
[Krigstin & Sain., 2006; Ananinedjiwala et al., 2011; Mohanty et al., 2002]. High-yield
pulps (HYP) are increasingly gaining importance as a partial replacement for hardwood
bleached Kraft pulp (HBKP) in uncoated and coated wood-free paper grades. Although
HYP was chiefly used as a cheaper alternative to HBKP throughout the 1990s, the pulp
and paper industry has come to value it for its ability to confer certain physical properties
on paper in order to meet customer or equipment demands. For example, replacing birch
or eucalyptus BKP with aspen-bleached chemithermomechanical pulp (BCTMP), a type
of HYP, has been found to be the most cost-effective method of increasing paper bulk
while maintaining tensile strength and brightness [Ananinedjiwala et al., 2011]. Other
reasons for the high demand for the utilization of green high-yield pulp fibres are their
low density and good thermal and acoustic properties. Pulp fibres, moreover, do not
abrade processing tools [Ananinedjiwala et al., 2011; Mohanty et al., 2002].
Materials from biological sources regroup natural polymers, so they can be expected to
exhibit viscoelastic behavior. Appropriate processing and production conditions of
2
polymer products are determined by their rheological characteristics. The high yield pulp
“HYP” fibres derived from hardwood that were used in this study are short crystalline
fibres [Saheb & Jog, 1999; Awal et al., 2010]. Short-fibre reinforced-polymer composites
are extensively used in manufacturing industries due to their light weight and improved
mechanical properties [Awal et al., 2010]. Hence, HYP has been used not only for its low
lignin content, but also for its potential thermal stability and its strong adhesion when it is
bonded with high-temperature–engineering thermoplastic polymers [Saheb & Jog, 1999;
Awal et al., 2010; Awal et al., 2009].
The study of the rheological behavior of viscoelastic polymer composites is mostly
limited to a two-phase fibre-polymer. The so-called interphase zone appears in the
viscoelastic damping of polymer composite processing [Van Rijswijk & Bersee, 2007].
This deformation significantly affects the predicted overall rheological characteristics of
natural-fibre–reinforced thermoplastic composites [Ho et al., 2012]. During processing,
fibre-reinforced polymers are subjected to rigorous deformations that cause fibres to
translate, agglomerate, bend, and rotate with the flow of the fibre matrix [Van Rijswijk &
Bersee, 2007; Ho et al., 2012; Huq et al., 2006]. This strongly influences the rheological
and mechanical properties in different parts of the final product because of the close
dependence of these properties on the orientation state of the fibres. Likewise, rheological
properties that are a function of the flow-induced fibre configuration in the matrix also
influence the physical properties of fibre-reinforced polymer composite [Ho et al., 2012;
Huq et al., 2006; Agarwal, 2009].
The rheological characteristics of natural-fibre–reinforced thermoplastic composites are
vital to their final mechanical properties. Although natural-fibre–reinforced polymer
3
composites and their processing have been partially addressed in several papers, models
of their rheological behavior and analysis of the rheology–processing parameter
relationships have been neither developed nor reported. This study reports on the state-of-
the-art technology in the rheology of lightweight composites from wood-fibre
thermoplastic composites, including their viscoelasticity and complex rheological
behaviors as influenced by different conditions. Hence, an overview of the viscoelastic
properties of biomaterials derived from natural-fibre–reinforced thermoplastic polymers
is presented in order to analyze their rheological behavior as part of predicting the
apparent shear viscosity of polymer melts.
Modeling the rheological properties of natural fibre reinforced bio-based thermoplastic
polymer composite is very challenging and poorly considered in the research. In addition,
study of the effect of the pulp aspect ratio and interphase element on the rheological
properties of green composite is absent from the literature. The purpose of this work is
therefore to present the experimental and predicted results of the rheological
characteristics of high-yield pulp-fibre–reinforced bio-based polyamide (HYPP/PA11)
composite as a function of fibre aspect ratio and their interphasial effect.
1.2 Hypotheses
The main hypotheses of this work are:
The apparent viscosity of bio-fibre–reinforced thermoplastic melt increases with
increase of the fibre aspect ratio.
4
The processing temperature of bio-based polyamide 11 decreases with the
addition of the inorganic salt lithium chloride (LiCl).
1.3 Objectives
The objectives of this work are:
To investigate the effect of the fibre content and aspect ratio on the rheological
behavior of high-yield pulp-fibre–reinforced bio-based polyamide composite.
To study the processability and the rheological characteristics of high-yield pulp-
fibre–reinforced bio-based polyamide composites for different compounding
process approaches.
To develop a mathematical model for prediction of the rheological characteristics
of bio-fibre–reinforced polyamide composite.
1.4 Outline of the Thesis
This thesis is divided into seven chapters: A general introduction, a general literature
review, four chapters that include the main findings of this thesis, and a final chapter
containing the main conclusions and recommendations.
Chapters 1 and 2 offer a general literature review and background on the scientific
concepts discussed in the context of this thesis. They review thermoplastic polymer, pulp
fibre, the extrusion process, and viscoelasticity. In more detail, they then survey the
rheological characteristics of polymeric material in order to identify the ones contributing
5
to the composite’s final properties. The modeling and rheology approaches are introduced
since they are the main scientific focus of this study.
Chapters 1 and 2 present the theoretical basis of this work as well as investigating the
potential of pulp fibre to be used as a reinforced in composite manufacturing. More in-
depth literature review is also provided in Chapters 3 to 6 as necessary.
Chapter 3 is based on a paper published in the Open Journal of Polymer Chemistry, 2015,
5, 1-8. It presents the results of the evaluation of the influence of fibre aspect ratio and
fibre content on the rheological characteristic of high-yield pulp-fibre–reinforced
polyamide 11 (HYP/PA11) Green Composite. Moreover, this chapter includes detailed
results of the effects of processing conditions, fibre breakage, and agglomeration, and
fibre orientation on the rheology of HYP-fibre–reinforced nylon composite. The results
of the investigation of the flow properties of composite materials made with bio-based
polyamide 11 (PA11) and HYP fibre is presented in this chapter. The apparent viscosity
of HYP/PA11 composite pellets was investigated at medium and elevated shear rate
using a capillary rheometer. The experimental results showed that identically for fibre
content and aspect ratio, the shearing effects decreased as the temperature increased: that
is, the HYP/PA11 became more non-Newtonian in the higher temperature region, which
corresponds to the high pseudoplasticity of the HYP/PA11. At low pulp-fibre content, the
apparent viscosity was expected to increase rapidly with increasing concentrations of the
fibres because of the swiftly increasing interactions between particles as they became
more closely packed. Nevertheless, at elevated and very high pulp-fibre content, random
anisotropic structures of fibres were created in polymer melts. The increase in the
6
apparent viscosity was greater at lower shear rates, where pulp fibre and polymer
molecules were not completely oriented.
Further characterizations of HYP/PA11 in terms of the effect of pulp-fibre content and
processing conditions on the rheological properties of HYP-fibre–reinforced bio-based
nylon composite are presented in Chapter 4. The results presented in this chapter are
submitted as a paper in the Journal of Composite Materials. The aim of this work was to
investigate the effect of the inorganic salt lithium chloride on the melting temperature and
rheological characteristics of viscoelastic natural-fibre–reinforced bio-based polyamide
composite materials. Different lithium chloride concentrations were used to lower the
melting temperature of bio-based polyamide 11. The concentration of lithium chloride
decreases the melting temperature of bio-based polyamide 11, and increases its degree of
crystallinity and consequently its density. The increase in the concentration of lithium
chloride in the HYP/PA11 composite is inversely proportional to the melting temperature
of PA11, and proportional to the fibre content after compounding. In addition, the
reduction of the high-yield pulp-fibre length distribution after compounding is less
pronounced for the modified polyamide 11 using the Brabender mixer technique
compared to the values obtained using the extrusion process method.
Rheological testing was performed and compared for both compounding process
methods. The rheological properties of HYP-reinforced bio-based polyamide 11
(HYP/PA11) composite were investigated using a capillary rheometer. Rheological
characteristics of the composite components influenced the development of resultant
microstructures; this development in turn affected the mechanical characteristics of a
multiphase composite. The rheological tests were performed at steady state in function of
7
the shear rate. The low-temperature process compounding had higher apparent viscosity;
this is because during the Brabender mixing technique process the temperature was low,
and the mixing and melting were induced by the high shear rate created during
compounding process.
The Effect of Lithium Chloride on the Fibre Length Distribution, Processing Temperature
and the Rheological Properties of High-Yield-Pulp-Fibre–Reinforced Modified Bio-
Based Polyamide 11 Composite was investigated by keeping the fibre content constant at
30% while varying the salt concentration from 1 to 5%. In addition, the effect of the pulp-
fibre content on the rheological characteristics of high-yield pulp-fibre–reinforced
modified polyamide 11 composite were performed for 10%, 20%, and 30% pulp content
while the salt concentration was kept at 3% LiCl. Rheological tests were performed for
all the formulations and both compounding techniques. Experimental test results show a
steep decrease in shear viscosity with increasing shear rate, and this melt-flow
characteristic corresponds to shear-thinning behavior in (HYP)-fibre–reinforced modified
bio-based polyamide composite (HYP/PA11) material. The rheological behavior of the
modified bio-based polyamide 11 “PA11 + LiCl" presented higher shear viscosity
corresponding to shear thinning behavior at intermediate and high shear rate.
Chapter 5 is based on a paper published in the Journal of Green and Sustainable
Chemistry (GSC). This chapter is a review of the mathematical models for the prediction
of the rheological characteristic of wood-fibre–reinforced thermoplastic nylon
composites. An overview of the viscoelastic characteristics of biocomposites derived
from natural-fibre–reinforced thermoplastic polymers and of predictive models is
presented in order to explicate the composites' rheological behavior. In addition,
8
significant reviews of constitutive equations were carried out so as to gain a better
understanding of their applicability to pulp-fibre–reinforced bio-based polymer
composite in determining the viscosity. The principal models investigated in this chapter
are the Giesekus-Leonov model, the Upper Convected Maxwell (UCM) model, the
White-Metzner model, K-BKZ model, the Oldroyd-B model, and the Phan-Thien-Tanner
models. The aforementioned models are the most powerful for predicting the rheological
behavior of hybrid and green viscoelastic materials in the presence of high shear rate and
in all dimensions. However, the Phan-Thien Tanner model, The Oldroyd- B model, and
the Giesekus model were found to be usable in various modes to fit the relaxation
modulus accurately and to predict both shear-thinning and shear-thickening
characteristics. Moreover, the Phan-Thien Tanner, K-BKZ, Upper Convected Maxwell,
Oldroyd-B, and Giesekus models can predict the steady shear viscosity and the transient
first normal stress coefficient better than the White-Metzner model for pulp fibre
reinforced bio-based thermoplastic composites.
Chapter 6 details the results gained from the mathematical model for the rheological
characteristics of HYP–reinforced bio-based polyamide 11 composite. The results in
Chapters 6 were first published in the Journal of Encapsulation and Adsorption Sciences.
The main purpose of this work was to develop a mathematical model to investigate the
rheological characteristics of viscoelastic pulp fibre composite materials. This chapter is
divided into two parts: In the first part, the apparent viscosity in function of high shear
rate and steady state of the extrudate (HYP)-fibre–reinforced bio-based Polyamide 11
(PA11) composite (HYP/PA11) were investigated using a capillary rheometer. In the
second part, novel predicted multiphase rheological-model–based polymer, fibre, and
9
interphasial phases were developed. The influence of the rheological characteristics of the
composite components on the development of resultant microstructures was broadly
investigated; the effects of these in turn on the mechanical characteristics of a multiphase
composite, are presented in this chapter. The rheological testing parameter conditions
were similar to those described in the previous chapters. Experimental and theoretical test
results of HYP/PA11 showed a steep decrease in apparent viscosity with increasing shear
rate, and this melt-flow characteristic corresponded to shear thinning behavior in
HYP/PA11 composite. The results of the nonlinear mathematical model for predicting the
rheological behavior of HYP/PA11 were compared to those obtained experimentally at
220˚C and 5000S-1 shear rate. Predicted and experimental apparent viscosity results were
found to be in strong agreement.
Finally, Chapter 7 reviews the main conclusions of this thesis and offers
recommendations for further work on modeling the rheological properties of pulp fibre
reinforced bio-based polyamide composites.
10
Chapter 2
Literature Review
2.1 High-Yield Pulp fibre
Rising environmental awareness is driving companies' search for more environmentally
friendly materials for their products. Compared to synthetic fibres, natural fibres have a
strong set of advantages: they are lightweight, recyclable, biodegradable, and renewable
[Additives, 2009; Stewart, 2011; Bavan & Kumar, 2010; John & Thomas, 2008].
High-yield pulp is short fibre derived from a process that involves the chemical pre-
treatment of wood chips combined with mechanical fibre separation to enable production.
A recent survey reported that the integrated worldwide production of high-yield pulp is
approximately 4 million tonnes per year, of which 85% is obtained through the bleached
Chemithermomechanical pulp “BCTMP” process [Botha & Hunter, 2010]. The annual
production of BCTMP pulp in Canada is nearly 1.5 million tones of hardwood grades and
about 0.5 million tones per annum of softwood grades. Due to their higher content of
cellulose and hemicellulose and consequently lower percentage of lignin, hardwoods are
more desirable than softwoods.
2.2 Polymeric matrix
The matrix plays a critical role in the performance of composites. The polymeric matrix
transfers the load to the stiff fibres through shear stresses at the interface [Stamboulis et
11
al., n.d., Ho et al., 2012; Young & Montes-Moran, 2002]. Both thermoplastic and
thermoset polymers can be used as matrices in composites.
The thermoset composites are chemically reacted to a cross-linked three-dimensional
network component, which increases the composite performance [Talreja et al., 2001;
Adekunle et al., 2011; Aminabhavi et al., 1987; Van Rijswijk & Bersee, 2007].
Thermoplastics provide advantages such as low processing cost, design flexibility, ease
of molding complex structures, and recyclability. Thermoplastic polymers are a group of
polymeric materials with a wide range of flexibility, a medium range of elasticity, and a
wide range of upper temperature limits [Eder & Winkler, 2001; Bhatnagar et al., 2007;
Parlevliet et al., 2006; Ludvik et al., 2007]. For semicrystalline materials, maximum use
temperatures are limited by the melting point of the crystalline phase [Nahar et al., 2011;
Sahoo et al., 2011]. The properties of such materials are governed by the interplay of the
crystalline phase providing strength and temperature resistance and the amorphous phase
rendering the material tough and flexible [Nahar et al., 2011; Sahoo et al., 2011; Herrera-
Franco & Valadez-González, 2004]. Typical examples of semicrystalline polymers are
high-density polyethylene (HDPE), polyamide or nylon (PA) and polyvinylidene fluoride
(PVDF).
2.2.1 Bio-based Nylon 11 (PA11)
Polyamide 11 is a specialty nylon. It combines high ductility, excellent aging resistance,
and high barrier properties with mechanical strength and resistance to creep and fatigue
[Fornes & Paul, 2004; Xu et al., 2006]. It thus compares favorably to standard nylons
such as 6 and 66. Notably, its significantly lower water absorption results in better aging
12
resistance, higher chemical resistance, and less property fluctuation due to plasticization
by water [Fornes & Paul, 2004; Xu et al., 2006; Zhang et al., 2006; Liu et al., 2003].
Figure 2.1: Nylon 11
Although polyamide 11 is highly resistant to aging and chain breakdown, the reaction of
water with amide bonds creates a limit to the use of polyamide at higher temperatures and
in the presence of water [Xu et al., 2006]. The specific reaction induced by water, called
hydrolysis, can be accelerated in the presence of acids. At continuous service
temperatures of 65°C and below, however, the impact of hydrolysis on polyamide 11 in a
neutral medium such as water can be neglected. Under these conditions, the material can
have a service life of 20 years or more. Use at higher continuous service temperatures
depends on the performance requirements and more precise conditions.
Figure 2.2: Structure of Nylon 11
13
The excellent properties of polyamides and of polyamide 11 in particular are a result of
the amide linkages in the chain, which allow a strong interaction between the chains by
hydrogen bonds. Low creep, high abrasion resistance, good resistance to fatigue, and high
barrier properties are a direct result of these strong inter-chain links [Xu et al., 2006;
Zhang et al., 2006; Liu et al., 2003; Botelho, E. C., & Rezende, 2009; Barkoula et al.,
2008].
2.2.2 Surface modification of natural fibres
The final properties of composite materials depend on the properties of fibre and matrix,
fibre loading, and fibre-matrix adhesion. Compositing hydrophilic fibres with
hydrophobic polymer will negatively affect their mechanical properties due to poor
adhesion at interface [Herrera-Franco & Valadez-Gonzalez, 2004; Mohanty & Misra,
2008]. These properties may be improved by changing the fibre properties through
physical and chemical treatments.
There exist several techniques for modifying the surface energy of the fibres; these
include physical treatments (cold plasma treatment, corona treatment) and chemical
treatment (maleic anhydride, organosilanes, isocyanates, sodium hydroxide,
permanganate and peroxide) [Herrera-Franco & Valadez-Gonzalez, 2004; Mohanty &
Misra, 2008; Wang, B. & Sain, 2007; Dominkovics et al., 2007]. Physical treatments
such as electric discharge or calendaring modify the structural and surface properties of
fibres, and the mechanical bonding increases with the matrix [Mohanty & Misra, 2008].
However, these treatments do not modify the chemical composition of the fibres.
Chemical treatments, therefore, have been used extensively to change the surface
14
properties of natural fibres. Chemical modifications increase the compatibility of fibres
and dispersion in the matrix, which leads to better stress transfer at the fibre/matrix
interface [Dominkovics et al., 2007].
Various studies reported that the utilization of silanes-treated Jute-Epoxy composites
resulted in improved tensile and flexural strength and stiffness [Taylor, 2006; Severini et
al., 2002; Awal et al, 2012]. Similar studies reported that adhesion may be improved by
using coupling agents like maleic anhydride to incorporate hydroxyl groups on the matrix
through hydrophilization and consequently enhancing the wetting effect of the resin on
the fibres [Behzad, 2007; Brandl et al., 2004; Da Silva et al., 2012]. The hydroxyl groups
then interact with –OH molecules on the lignocellulosic fibres via hydrogen bonding,
thus producing a stronger bond [Severini et al., 2002; Awal et al, 2012; Brandl et al.,
2004]. The properties of fibre composite have also been found to improve after chemical
treatment of fibres with maleic anhydride, acetic anhydride, and silanes [Brandl et al.,
2004; Da Silva et al., 2012].
Acetylation is an important mechanism for improving the properties of natural fibres. The
reaction involves the generation of acetic acid as a by-product that must be removed from
the lignocellusic material before the fibre is used [Dittenber & GangaRao, 2012].
Chemical modification with acetic anhydride replaces the cell-wall polymer groups with
acetyl groups, modifying the properties of these polymers so that they become
hydrophobic [Dittenber & GangaRao, 2012; Sobczak et al., 2012]. Consequently, fibre-
matrix interfacial adhesion is improved. [Dittenber & GangaRao, 2012; Sobczak et al.,
2012].
15
Another important method for surface modification is graft copolymerization. For
instance, the treatment of cellulose fibres with hot polypropylene-maleic anhydride
copolymers provides covalent bonds across the interface [Tong et al., 2004]. The
mechanism of reaction can be divided into two steps: activation of the copolymer by
heating at 170˚C (before treating the fibre) and esterification of the fibres [Tong et al.,
2004; Ho et al., 2012]. The surface energy of the fibres becomes closer to the surface
energy of the matrix after the treatment. Accordingly, improved wettability and higher
interfacial adhesion can be expected [Ho et al., 2012].
2.3 Extrusion Process
There are two types of extruder: single-screw and twin-screw.
Twin-screw extruders are used as continuous mixers, devolatilizers, and reactors, with
pellets being the finished products. They perform the basic functions: feeding, melting,
mixing, venting, developing die pressure, and conveying [Conshohocken, 2012; Liu et
al., 2009; Ku & Lin, 2005]. A compounding extruder can either be co-rotating or counter-
rotating [Conshohocken, 2012; Liu et al., 2009; Ku & Lin, 2005]; however, the industry
prefers co-rotators. The motor inputs energy into the screw shafts, causing the rotating
screws to impart shear and energy into the process to melt the components, mix,
devolatilize, and pump as required [Liu et al., 2009].
Twin-screw extruders have modular barrels and screws [Ku & Lin, 2005]. Extruder
screws are assembled on high-torque splied shafts. The barrels can be configured as
feeding, plain, venting, side stuffing, and liquid addition. Each barrel section is
16
electrically heated, uses its own temperature controller, and is internally cored for high-
intensity cooling near the screw bores [Liu et al., 2009; Ku & Lin, 2005]. The modular
nature of screw extruders offers extreme process flexibility with respect to rearranging
barrels, making L/D longer or shorter, and for modifying screws.
The main functions of the various zones of the conical twin-screw extruder are as
follows:
(1) The feed section feeds the material through the hopper.
(2) The compression and melting zone: the polymer chips are compressed in this zone by
screw flights reducing their volume. The polymer starts melting in this zone, where the
first liquid film forms at the barrel wall, which is heated above melting temperature.
(3) The mixing zone: Here the feedstock is intensively mixed, becoming a homogenous
product.
(4) The metering zone: In this zone, the pressure builds up and the melt is transported to
the die head for exiting [Ku & Lin, 2005].
2.3.1 Effects of processing parameters on properties of composites
The final properties of fibre-reinforced polymer composites are strongly influenced by a
number of factors, including: interaction between the fibre and the polymer matrix, fibre
length, fibre dispersion, fibre degradation, and fibre orientation. The processing
parameters, such as screw speed, feeding rate, and temperature profiles, will also affect
17
the final properties of composites by influencing these factors. Various studies about the
effects of processing parameters on mechanical properties of fibre-reinforced
thermoplastics have been reported [Takase & Shiraishi, 1989; Lau et al., 2010].
Various authors have investigated the effects of processing conditions on the fibre length
distribution of fibre-reinforced Nylon 11. They found that fibre length was mainly
determined by shear rate and gave the major factors that affect the shear rate [Tadmor &
Gogos, 1979; Sperling, 2006; Selvakumar & Bhatnagar, 2009]. In the majority of cases,
the composites were extruded with a co-rotating conical twin-screw extruder. Effects of
different processing factors on fibre length distribution were reported [Tadmor & Gogos,
1979]. At high screw speed, temperature is increased because of the viscous heat
generation [Sperling, 2006]. Therefore, at higher screw speeds, higher temperature and
lower viscosity may result in lower shear stress acting between the glass fibre and the
polymer matrix at the interface; consequently, the fibre length may decrease less than
proportionally to the screw speed [Sperling, 2006; Selvakumar & Bhatnagar, 2009].
Similarly, the feed rate will also affect fibre length. Screw speed, feed rate, and feed ratio
will all affect fibre length [Selvakumar & Bhatnagar, 2009].
Natural fibre processing is a little different with glass fibre because natural fibre is more
flexible. Czarnecki et al. [Selvakumar & Bhatnagar, 2009] compared the rheological
behavior and fibre damage of glass and cellulose fibre reinforced polystyrene melts. They
found that glass fibres break down rapidly to very small aspect ratios while cellulose
fibres showed less damage [Mukhopadhyay et al., 2003]. They also mentioned that the
shear viscosity of the melt materials increases with fibre percentage increase [Taylor et
al., 2011; Deitzel et al., 2001; Barkoula et al., 2009].
18
The mixing time and temperature profiles are important factors for wood-fibre–reinforced
composites because of the thermal degradation of wood fibre. For pulp-fibre–reinforced
composites, sometimes these two factors are dominant and need to be considered first
during study [Mukhopadhyay et al., 2003; Taylor et al., 2011; Deitzel et al., 2001].
Recently, Stade investigated the temperature profile in an extruder [Segerholm et al.,
2007]. In his experiment, he inserted the kneading teeth with thermocouples arranged
around the screw to measure the actual temperature of the melting mixture. He observed
that inserting the fibres to the polymer melt initially decreases the melt temperature, but
then leads to a rapid rise in temperature due to the increased shear viscosity of the
compound [Segerholm et al., 2007].
Most recently, P.V. Joseph [Peltola et al., 2011] examined the effect of processing
variables on the mechanical properties of sisal-fibre reinforced polypropylene composites
using a Haake Rheocord mixer. He reported that mixing time is too short; the mechanical
properties are low because of the ineffective mixing and poor dispersion of the fibre in a
PP matrix [Peltola et al., 2011]. Consequently, the composite properties and the fibre
dispersion improve once the mixing time increases. However, as the mixing time
increases, fibre breakage becomes predominant so properties decrease. At low
temperature, the apparent viscosity of the mixture is very high, and this causes the
breakdown of the fibres during processing. The rotor speed, mixing time, and
temperature profiles affect the strength of the composite’s mechanical properties [Peltola
et al., 2011]. The decrease in strength at a mixing temperature above 170 ºC can be due to
the thermal degradation of the wood fibres. Moreover, the dispersion of fibre in PP will
be poor due to the decrease in viscosity at high temperature [Peltola et al., 2011; Ramani
19
et al., 1995]. At low rotor speed, the poor dispersion of fibre in PP causes low tensile
strength, and at too-high rotor speed, fibre breakage is dominant and also causes
reduction in strength [Ramani et al., 1995]. Other studies realized later on indicated that
numerous process parameters, such as screw speed, feeding rate, temperature profiles,
melting time, and so forth, will affect the mechanical properties of composites [Lodge,
1988; Le Moigne et al., 2011]. To optimize processing, accordingly, many parameters
and their interactions need to be considered and a mathematical model used to predict the
effects of those parameters on the final properties of the materials.
2.3.2 Low-temperature compounding
Even though the early research did not yield encouraging results, the automotive and
construction markets' needs for low-density reinforcement for engineering thermoplastics
inspired researchers to take a second look at wood-fibre–reinforced engineering
thermoplastics [Valenti et al., 1973].
Recently, USDA Forest Products Lab and Rayonier Inc. partnered to develop an
exceptional compounding method called low temperature compounding (LTC) to
produce pulp fibre reinforced nylon 6 composites [Ackley, D. E. & Rudder, 2014; Khor
et al., 2009]. In this new compounding approach, there are three phases: start-up
conditions, a transition phase, and steady-state conditions [Ackley, D. E. & Rudder,
2014; Khor et al., 2009]. During the start-up conditions, the process temperature is higher
and the temperature zones of the extruder are set at 232ºC, a little bit above the melt
temperature of nylon 6. The melt viscosity will increase in the presence of the natural
fibre. With the increase of melt viscosity from adding fibre, the melt temperature and
20
torque load on the extruder increase dramatically, which leads to the degradation of
natural fibre during the compounding process. Accordingly, the temperature of
intermediate zones is gradually reduced. This process is the ‘transition phase’. At steady-
state conditions, the twin-screw extruder is at equilibrium [Ackley, D. E. & Rudder,
2014; Khor et al., 2009].
2.4 Rheology
Rheology is the study of the mechanical principles of continuous mediums, whose
function is to determine the stresses and deformations at every point of these mediums
[Mason, 2006]. In general, polymers are viscoelastic liquids: that is, they exhibit both
viscous and elastic properties [Guo et al., 2005; Xie et al., 2012]. Viscoelastic materials
are most used in strategic industries because of their favourable mechanical properties
and typically high quality [Chopra & Larson, 2002; Rao, 2007; Wang et al., 2011;
Moutee et al., 2006]. These materials are rigid and have high resistance properties since
they consist of fibre levels and resin [Wang et al., 2011; Moutee et al., 2006].
The rheology of long-fibre polymers is quite complex because of various factors such as
fibre-matrix interaction, fibre-fibre interaction, fibre migration, and fibre breakage during
processing. Fibre flexibility is another factor that plays an important role in determining
the rheological behavior of long-fibre composites [Sin et al., 2010]. Because the fibre
length in these materials is greater than a critical value, they, unlike short fibres, do not
remain straight; they change their curvature under flow deformations. Typically, for glass
fibre, this critical value is assumed to be 1 mm. Fibre flexibility varies with the intrinsic
properties of the fibre, its aspect ratio, and strength of the flow field [Sin et al., 2010;
21
Eberle et al., 2009; Park et al., 2008]. If the fibres are flexible enough, bending forces
acting through the velocity field can influence their orientation state, which in turn can
influence the macroscopic properties of the fluid [Eberle et al., 2009]. As a result, fibre
flexibility has shown to be responsible for a considerable increase in polymer melt
viscosity [Eberle et al., 2009; Park et al., 2008].
Many experimental results have emphasized the role of flexibility on fluid viscosity.
Nawab and Mason, in their study of threadlike particles in castor oil, found that viscosity
becomes more and more shear-dependent with increasing fibre length [Eberle et al. 2008;
Sepehr et al., 2004c.]. They deduced that this behavior was due to elastic deformation of
the fibres. Blakeney showed that even a ‘slight curvature’ of fibres has a pronounced
effect on the viscosity [Sepehr et al., 2004a.]. Kitano et al. and Goto et.al. illustrated the
effect of fibre stiffness on suspension rheology [Ojo, A., & Akanbi, 2006; Qiao et al.,
2009]. They showed that fibres that are more flexible had a more pronounced effect on
the rheological properties [Eberle et al. 2008; Sepehr et al., 2004c.; Sepehr et al 2004a;
Ojo, A., & Akanbi, 2006; Qiao et al., 2009].
Recently, Keshtkar et al. performed a study on the effect of the fibre flexibility
parameters, stiffness, and aspect ratio, in semi-dilute and semi-concentrated regimes
[Kucharczyk et al., 2012]. They concluded that there exists a considerable increase in
steady-state shear viscosity in the semi-concentrated regime compared to the semi-dilute
regime. The viscosity of these suspensions also increased considerably with fibre
flexibility. They found that in both regimes, the addition of fibres results in significant
normal forces under shear flow, and as the fibre content increases, the first normal force
increases with it. Keshtkar and co-workers are also among the very few authors to
22
observe transient stress growth behavior for long-fibre composites [Kucharczyk et al.,
2012].
Physical properties such as elasticity modulus, strength, thermal expansion and thermal
conductivity, depend on the concentration, type, size, and orientation of reinforced fibres
in polymer composites. This greatly influences the mechanical properties in different
parts of the final product because of the close dependence of these properties on the
orientation state of the fibres. Similarly, rheological properties that are a function of the
flow-induced fibre configuration in the matrix also influence the physical properties of
the fibre composite [Müller et al., 2011].
Rheology of biomaterials is likewise very complex because various factors such as fibre-
matrix interaction, fibre-fibre interaction, moisture content, and fibre breakage and
migration affect flow-induced fibre orientation in these polymer melts [Ansari et al.,
2011; La Mantia & Morreale,2011; Abraham & George, 2007]. In high concentration
regimes, fibre-matrix and fibre-fibre interaction both become more important as the
conformation of the polymer chains is influenced by the orientation of neighbouring
fibres [La Mantia & Morreale, 2011; Abraham & George, 2007]. In addition, as fibres
flow in close proximity to each other, there is an increased possibility of encountering
enhanced hydrodynamic forces, friction and other mechanical interactions between fibres
[Sengupta et al., 2007]. For short-fibre composites (SFCs), flexibility is not important, as
their length is small enough to assume that the fibre remains straight and that their
curvature does not change during flow [Chen et al, 2007; Larson, 2005; Li & Renardy,
2000]. However, in the case of long fibres (average fibre length > 1mm), the curvature of
fibres cannot be neglected because it considerably affects the composite's properties and
23
has been shown to be responsible for large increases in melt viscosity [Larson, 2005; Li
& Renardy, 2000]. The flexibility of a fibre varies with the intrinsic properties of the
fibre, its aspect ratio, and the strength of the flow field. As a result, the rheological
properties of green-fibre composite are said to be affected by fibre properties, fibre
interactions, moisture content, melt fluid properties and the flow rate imposed [Soulages
et al., 2008; Switzer & Klingenberg, 2003; Keshtkar et al., 2009].
2.5 Modeling of Fluid Flows
2.5.1 Classification of fluid flow modeling
A fluid flow can be modeled based on two approaches: (i) continuum hypothesis and (ii)
molecular theory [Batchelor, 1967; Gad-el-Hak, 1999]. A classification of flow models is
displayed schematically in Figure 2.3 (Gadel-Hak, 1999).
24
Figure 2.3. Molecular and continuum flow models (Gad-el-Hak, 1999)
2.5.1.1 Continuum hypothesis
In the continuum hypothesis, a fluid is assumed to be a continuous medium describable in
terms of the spatial coordinate and time variations of macroscopic flow quantities such as
density, pressure, velocity, and temperature, and cannot be divisible; the molecular
structure and forces (e.g. intermolecular forces) of a fluid are ignored [Batchelor, 1967].
Principles of mass, momentum, and energy balance (also commonly called conservation
of mass, momentum, and energy) lead to a set of nonlinear partial differential equations
such as Navier-Stokes and Euler equations.
25
The continuum models are generally easier to solve mathematically at a relatively low
cost and short time and are more commonly used by engineers than the molecular models
[Gad-el-Hak, 1999]. Continuum models should therefore be used as long as they are
applicable. However, in cases where continuum models fail to accurately predict the fluid
flow at the microscale, high-cost molecular models are the only approach available to
determine the fluid flow in microchannels [Batchelor, 1967; Gad-el-Hak, 1999].
Conceptually, the continuum hypothesis is valid and leads to accurate predictions as long
as local properties of the fluid, such as density and velocity, can be defined as standards
over elements. These elements are large compared to the molecular structure, but small
enough compared to the macroscopic length scale that mathematical differentiation and
integration can be used to represent them. However, the flow condition must be near
thermodynamic equilibrium. The averaged-property condition is usually satisfied, but the
near-equilibrium condition mostly limits the validity of the continuum models [Gad-el-
Hak, 1999].
2.5.1.2 Molecular theory
The molecular theory characterizes fluid flow as a set of discrete particles to represent
molecules, atoms, ions, and electrons [Batchelor, 1967; Gad-el-Hak, 1999]. The
macroscopic state behaviors at any position in the flow are suitably averaged from a
sufficient number of the discrete particles within the smallest significant dimensions of a
flow [Gad-el-Hak, 1999]. The final objective is to determine the position, velocity, and
state of all particles at all times. Molecular-based flow models comprise molecular
dynamics (MD), direct simulation Monte Carlo (DSMC), and Boltzmann equations, as
26
shown in Figure 2.3. Molecular modeling of fluid flows, however, is not in the objective
of this thesis research.
2.5.2 Continuum models of fluid flows and constitutive equations
Continuum models are usually derived from the conservation of mass, momentum, and
energy, which as earlier noted are also called mass, momentum, and energy balances. The
conservation of mass, momentum, and energy can be expressed at every point in space (x,
y, z) and time (t) as a set of partial differential equations [Batchelor, 1967; Gad-el-Hak,
1999; Den, 1990; Landau & Lifshitz, 1987]. The general form of the momentum balance
equation is shown as follows:
g (2.1)
where ρ is the density of fluid, v is the velocity vector (vx, v
y, v
z), t is the time, p is the
pressure, and τ is the (extra) stress tensor.
In addition to the balance equations, which correspond to the governor equations,
constitutive equations that describe the response of the material to applied stress are also
required to solve problems of the rheological behavior of materials [Den, 1990].
Constitutive relations can be determined from numerous approaches, including
experimental observations and correlations, phenomenological theories, and molecular
theories [Landau & Lifshitz, 1987]. The mathematical description of a viscoelastic fluid
is much more complex than its Newtonian counterparts [Kundu, 1990; Panton, 1996]. In
addition to the conservation equations of mass and momentum an additional equation, the
constitutive equation or rheological equation of state, is required; this equation relates the
27
stress to the deformation [Sherman, 1990; Oliveira, 2009; Den, 1990; Argyris et al.,
1991; Gava , 2012; Likhtman & Graham, 2003]. For a viscoelastic liquid this relationship
is nonlinear and it has no standard form that is universally valid for each fluid in every
flow situation [Den, 1990; Argyris et al., 1991; Gava, 2012; Likhtman & Graham, 2003].
This situation is one of the reasons why the subject of viscoelasticity is so challenging.
The constitutive equation should not only describe the rheological characteristics of the
polymer melt, but also give the final fibre orientation of the composite [Banks et al.,
2006]. For this reason, it is fundamental to evaluate the role of the polymer rheology and
the fibre-polymer interaction. Enthusiasm for the utilization of a composite constitutive
equation arose due to the observation of the calculated experimental stresses of polymer
suspensions. It was reported that the total stress of the composite increases with the
addition of fibres [Kajiwara et al., 1995; Wang & Birgisson, 2007], and therefore a
satisfactory constitutive equation could be had by adding an extra stress term to an
already existing constitutive equation; this amended equation adequately describes the
polymer melt.
Note that assumptions and boundary conditions are very important in the
phenomenological description provided by mathematical models. A perfect model in this
case must use constitutive relations that accurately describe the material behavior under
the shear.
28
2.6 Viscoelasticity of composite materials
Materials from biological sources are viscoelastic [Banks et al., 2006]. A material is said
to be viscoelastic if it manifests both viscous and elastic properties under the same
conditions when it undergoes deformation. Viscous materials present resistance to shear
flow and strain linearly with time when a stress is applied [Zhou, 2011; Snijkers et al.,
2011; Assie, 2011; Wang & Birgisson, 2007]. The shear stress of elastic materials
depends on strain: when strain is applied and then released, they return to their initial
configuration [Zhou, 2011; Snijkers et al., 2011; Assie, 2011; Wang & Birgisson, 2007;
Doraiswamy,1998; Mason, 2006].
A fluid that does not behave in a Newtonian trend between shear stress and shear rate
when it undergoes deformation is commonly termed non-Newtonian [Chhabra, 2010;
Malkin & Isayev, 2006]. This means that the relation between shear stress and shear is
not a straight line but is non-linear [Malkin & Isayev, 2006]. High-molecular-weight
liquids, which include polymer melts and solutions of polymers, as well as liquids in
which fine particles are suspended, are usually non-Newtonian. In this case, the slope of
the shear-stress–versus–shear-rate plot will not be constant as we change the shear rate
[Han, 2007]. When viscosity decreases with increasing shear rate, the fluid is described
as shear-thinning [Goodwin & Hughes, 2008; Chhabra & Richardson, 2008]. In the
opposite case, where the viscosity increases as the fluid is subjected to a higher shear
rate, the fluid is described as shear-thickening [Goodwin & Hughes, 2008; Chhabra &
Richardson, 2008]. Shear-thinning fluids also are called pseudoplastic fluids, and shear-
29
thickening fluids are also called dilatants. Shear-thinning behavior is more common than
shear-thickening [Han, 2007; Goodwin & Hughes, 2008; Chhabra & Richardson, 2008].
Another type of non-Newtonian fluid is viscoplastic or “yield stress” fluid [Goodwin &
Hughes, 2008; Chhabra & Richardson, 2008; Graessley, 2004]. This is a fluid that will
not flow when only a small shear stress is applied [Goodwin & Hughes, 2008; Chhabra &
Richardson, 2008; Graessley, 2004]. The shear stress must exceed a critical value known
as the yield stress for the fluid to start flowing [Chhabra & Richardson, 2008; Graessley,
2004]. Hence, viscoplastic fluids behave like solids when the applied shear stress is less
than the yield stress. Once it exceeds the yield stress, the viscoplastic fluid will flow just
like an ordinary fluid [Graessley, 2004].
On the other hand, some classes of fluids exhibit time-dependent behavior [Goodwin &
Hughes, 2008; Chhabra & Richardson, 2008; Graessley, 2004]. This means that even at a
given constant shear rate, the viscosity may vary with time. This category of material
comprises thixotropic and rheopectic fluids, whose behaviors in this respect are opposites
[Goodwin & Hughes, 2008; Chhabra & Richardson, 2008; Graessley, 2004]. The
viscosity of a thixotropic liquid will decrease with time under a constant applied shear
stress [Graessley, 2004]. However, when the stress is removed, the viscosity will
gradually recover with time as well [Chhabra & Richardson, 2008; Graessley, 2004]. By
contrast, rheopectic fluid behavior can be observed when the fluid increases in viscosity
with time when a constant shear stress is applied [Chhabra & Richardson, 2008;
Graessley, 2004].
30
2.7 Problem Statement
Recently, there has been a large demand for the utilization of carbon fibre in industries
such as automotive, aerospace, and construction. Consequently, carbon-fibre waste
products will become an important environmental issue because such products are not
biodegradable. In addition, the cost of virgin carbon fibre is high, which means recovery
could provide considerable economic and environmental advantages. Thus, there is
strong and widespread interest in the development of composite pulp-fibre–reinforced
thermoplastic polymer composite. Materials from biological sources regroup bio-based
polymers, so polymer composites that contain them can be expected to exhibit
viscoelastic behavior. The preferred processing conditions for partially bio-based
composite products are determined by their rheological characteristics. This is despite the
fact that natural-fibre–reinforced bio-based polymer composites and their processing
conditions have not yet been even partially reviewed.
Modeling of the rheological characteristics of pulp-fibre–reinforced bio-based
thermoplastic polymer and the analysis of their rheological processing parameter
relationships has not hither to been investigated. This study reports on the state-of-the-art
technology in the rheology of composites, including viscoelasticity and complex
rheological behaviors as influenced by differing conditions, the pulp fibre aspect ratio,
the fibre content, and processing temperature effects. The present research focuses on the
processing of wood-fibre–reinforced polyamide composites, their rheological properties,
and the development of mathematical model to predict these properties.
31
In order to achieve the primary goals of this project, the processing parameters during the
extrusion process and the flow properties were both investigated. Also, the effects of the
fibre content and aspect ratio of high-yield pulp (HYP) were studied. An extrusion
process was adopted in order to develop the pulp-fibre–reinforced bio-based polyamide
composite. The biocomposites were processed under three different processing conditions
in order to gain a better understanding of the HYP fibre in the composite system in
relation to fibre breakage, burning, and agglomeration. Rheological tests were performed
using a capillary rheometer at steady state and at elevated shear rate. Finally, the
mathematical model was developed in order to predict and validate the apparent shear
viscosity in function of the pulp aspect ratio, the pulp fibre diameter, and the interphase
effect of the composite from high-yield pulp-fibre–reinforced bio-based polyamide. The
proposed project plan of the process development and optimization is as follows (See
Figure 2.4):
32
Yes
No
Figure 2.4. Process development and optimization
Fibres Reinforced Bio-
Based Polyamide
Experimental approach:
PA11 and Pulp: Aspect ratio;
Fibre length and content
Theoretical approach:
Rheological Model: Viscosity;
Shear rate and Shear stress
Structure Thermal and
Mechanical
Properties
Pro
cess
Op
tim
izati
on
Processing Parameters:
Temperature profiles; Screw
Speed; Feeding rate; Mixing
time
Natural Fibres
Renewable and biodegradable
Low energy consumption; less
pollution; low density and lightweight;
good thermal and acoustic properties
Validation
End
33
Chapter 3
Evaluation of the Influence of Fibre Aspect Ratio
and Fibre Content on the Rheological
Characteristic of High-Yield-Pulp Fibre–
Reinforced Polyamide 11 (HYP/PA11) Green
Composite
3.1 Abstract
The rheological behavior of composites made with low-density polyamide 11 (PA11) and
high yield pulp fibre (HYP) were evaluated. The rheological properties of high- yield
pulp-reinforced bio-based Nylon 11 HYP/PA11 composite were investigated using a
capillary rheometer. The rheological tests were performed in function of the shear rate for
different temperature conditions. The experimental results showed that identically for
fibre content and aspect ratio, the shearing effects decreased as the temperature increased;
that is, the HYP/PA11 became more non-Newtonian in the higher temperature region,
which corresponds to the high pseudoplasticity of the HYP/PA11. At low HYP content,
the shear viscosity was expected to increase rapidly with increasing concentrations of the
fibres because of the rapidly increasing interactions between particles as they become
more closely packed. However, at very high fibre content, random anisotropic structure
34
of the fibres in polymer melts was created. The increase in shear viscosity was greater at
lower shear rates, where fibre and polymer molecules are not completely oriented.
3.2 Introduction
Green-fibre–reinforced thermoplastic composites are in high demand in the automotive,
aerospace, and construction industries. Vegetable fibres are biodegradable and renewable,
they consume less energy than glass fibres, and consequently they generate less pollution
[Pervaiz & Sain, 2003; Bourmaud & Baley, 2009; Duc, 2011]. Other reasons for the high
demand for the utilization of green fibres are their low density and good thermal and
acoustic properties [Bourmaud & Baley, 2009]. Pulp fibres, moreover, do not abrade
processing tools [Bourmaud & Baley, 2009; Duc, 2011]. As noted in Chapter 2, materials
from biological sources regroup natural polymers, so they can be expected to exhibit
viscoelastic behavior [Bourmaud & Baley, 2009; Duc, 2011; Ayroud, 1983]. Appropriate
processing and production conditions for polymer products are determined by their
rheological characteristics [Ayroud, 1983; Thumm & Dickson, 2013]. Short-fibre
reinforced polymer composites are extensively used in manufacturing industries due to
their light weight and superior mechanical properties [Sadeghian & Golzar, 2008;
Thomen, 2001]. Hence, pulp fibre has been used not only for its low lignin content but
also for its potential thermal stability and for its strong adhesion when bonded with high-
temperature engineering thermoplastic polymers [Gu & Kokta, 2010; TAAPI, 2006;
Rijswijk & Bersee. H. E. N., 2007]. The high-yield pulp “HYP” fibres derived from
hardwood that were used in this study are short semicrystalline fibres.
35
Various experimental studies have emphasized the investigation of the role of flexibility
on fluid viscosity [Plackett et al., 2010; Kaw & Besterfield, 1998; Yeh, 1992]. These
studies concluded that the more flexible the fibres, the more pronounced their effect on
the rheological characteristics [Yeh, 1992; Gohil & Shaikh, 2010].
A novel study on the effect of fibre-length distribution on the rheological behavior of
castor oil composite showed that at high fibre length the shear viscosity becomes more
dependent on shear rate [Yeh, 1992; Kari et al., 2005]. This behavior is due to elastic
deformation of the fibres [Gohil & Shaikh, 2010].
Recently, several researchers have investigated the effect of fibre content on polymer
melt rheology [Lamnawar & Maazouz, 2008; Larache et al., 1994; George et al., 2001; -
Liu et al., 2000]. One such study showed an important increase in shear viscosity with
increased fibre loading at low shear rates, but only a small increase in viscosity at high
shear rates [Uhlherr et al., 2005]. Another similar study on polypropylene-based long
fibre observed an increase in shear viscosity with increased fibre content and fibre length;
however, this viscosity increase was very small, which the authors attributed to high
shear rates and fibre breakage during processing [Huq.& Azaiez, 2005; Sepehr et al.,
2004]. Non-Newtonian fluid characteristics such as shear thinning were also observed in
these studies.
That said, the literature devoted to experimental studies of the rheology of pulp fibres in
reinforced polymer composites is very restricted. This is likely due to the complex nature
of these materials, the difficulties encountered during their processing, and also the
36
difficulty of characterizing them rheologically [Eberle et al., 2009; Larson, 1999; Eberle,
2008].
Processing technique and conditions have a significant influence on the rheological and
overall properties of pulp-fibre–reinforced polymer composites because they dictate the
degree of dispersion and distribution of the fibre in the polymer matrix [Le Moine et al.,
2013; Guo et al., 2005; Le Moine et al., 2011]. Compared to other natural fibres, HYP is
more thermally stable in the presence of high-melting–temperature engineering
thermoplastics (under 180˚C) such as PA11, PA6, and PA66 [Guo et al., 2005; Le Moine
et al., 2011].
The aim of the study described in this chapter was to investigate the rheological
characteristics of high-yield-pulp–reinforced bio-based polyamide 11 composite.
Experiments were mainly carried out by varying the rheological testing temperatures, the
fibre content, and the aspect ratio.
3.3 Materials and Methods
3.3.1 Materials
The matrix biopolymer, bio-based Nylon 11, density 1.03, MFI 11, was supplied by
Arkema, France. Aspen HYP fibres were supplied by Tembec (Montreal, QC). The HYP
is the type used in wood-free printing and in writing-paper grades and multiple-coated
folding-board grades; pulp fibre length is 0.230 to 0.85mm. Finally, the pulp-fibre length
37
was reduced by using a mechanical crib in order to investigate the aspect ratio effect on
the rheological behavior of the HYP/PA11 composite.
3.3.2 Methods
3.3.2.1 Composites preparation
The experiment was processed using a conical twin-screw extruder. In the mixing
method, the HYP fibre was dried at 80˚C for 6 hours and then added to the corresponding
PA11 and well mixed before it was introduced to the extruder. The average temperature
of the barrel was 200˚C.
3.3.2.2 Effect of processing conditions
Many processing parameters affect the properties of final products. For extrusion,
temperature profiles affect the fibre degradation. In addition, screw speed and feeding
rate change fibre length, distribution, and orientation. The mechanical properties are the
combined result of all these changes. The processing parameters are optimized to obtain
the best properties. Table 3.1 represents the processing parameters for HYP/PA11 used in
this study.
38
Table 3.1. Extrusion temperature profile for 10%, 20%, and
30% HYP/PA11, 120 RPM (10 and 20%), 130 RPM (30%)
and 10 RPM feed rates.
Temperature (˚C)
Zone 1 Zone 2 Zone 3 Zone 4 Zone 5 Zone 6 Zone 7 Zone 8 Zone 9 Zone 10
200 200 200 200 200 205 205 205 205 205
3.3.2.3 Fibre content analysis and determination of fibre length distribution
(original fibre length)
The samples of the fibre received from the provider were cut into small pieces and
immersed in formic acid for three days. The Nylon 11 was dissolved by the formic acid
and HYP was left. The wood fibre was filtered and washed with formic acid, then dried
in a vacuum oven for four hours. By measuring the weight of composite and fibre, we
could calculate the actual fibre content.
HYP fibre length was measured with the Fiber Quality Analyzer (FQA). The fibre was
diluted with D.I. water, and the diluted fibre entered a thin-planar channel. This channel
helped to gently orient the fibre 2-dimensionally, so that the fibre could be fully viewed
by the camera. The picture taken by the camera was then analyzed by the software to give
the fibre length distribution.
39
3.3.2.4 Rheological properties measurement
The rheological measurements of the composites’ melt-flow properties were carried out
in a twin-bore Rosand Capillary Rheometer model RH2000. (The standard RH2000 range
supports temperatures from -40˚C to 500˚C. The standard maximum force applied is
12kN.) The composite samples for testing were cut into very small pieces, then placed
inside the barrel and forced down into the capillary with the plunger attached to the
moving cross-head. Representative steady-shear viscosity versus high shear rate is
presented in the figures below for HYP/PA11, which was processed at an average
extrusion temperature of 200˚C. The viscosity of the sample was obtained from steady-
shear measurements for different temperature profiles, with the rate ranging from 50 to
5000 S-1. The rheological viscosity data presented in this paper thus represents an average
value of three measurements.
3.3.2.5 Scanning electron microscopy
Studies on the morphology of the composites were carried out using a scanning electron
microscope (SEM). The rheological test samples were ruptured by the rheometer and the
fracture surfaces were examined. A Hitachi S-800 Scanning Electron Microscope (SEM)
was used to study the fracture surface and dissolved HYP-reinforced PA11 composites.
The observation conditions were the following: pressure 0.3 mbar, acceleration voltage
15 keV.
40
3.4 Results and Discussion
3.4.1 Effect of fibre content on the length and shape distribution on
HYP-fibre–reinforced bio-based nylon composite
During the extrusion process, the shear stress applied by the screw broke the fibres. The
resulting fibre lengths affect the ultimate mechanical properties. In spite of the influence
of fibre damage and breakage during processing, the initial fibre length in the feedstock
determined the fibres’ final lengths. It was therefore important to analyze the initial fibre-
length distribution. Table 3.2 represents the effect of fibre content on the length and
shape distribution on HYP-fibre–reinforced bio-based polyamide composite.
Table 3.2. Fibre length distribution of pulp fibre (original fibre
length).
Fibre
Mean Length (measured)
Arithmetic (mm)
Length weight
(mm)
Weight weighted
(mm)
Only HYP 0.38 0.57 0.73
HYP (10%) 0.20 0.29 0.43
HYP (20%) 0.20 0.29 0.44
HYP (30%) 0.18 0.28 0.51
41
The arithmetical length-weighted and weight-weighted values of fibre length were found
to be 0.18 mm, 0.28 mm and 0.51 respectively for the fibres from 30% HYP/PA11. Most
of the fibre lengths lie within the range of 0.2–0.52 mm, since crushed pulp was used in
this study. To obtain these average fibre lengths, 1500 single fibres were examined. The
measured initial fibre length is shorter than the original length of the fibres the company
provided.
3.4.2 Rheological characteristics of HYP–reinforced bio-based
polyamide
Rheological characteristics of the polymer, fibre, and interphasial phases influenced the
final characteristics of the resultant microstructure of the composite materials; these
characteristics in turn affected the mechanical properties of a multiphase polymer-
composite system. As obtained from experiment, the shear viscosity as a function of the
steady-shear rate of HYP/PA11 at 200˚C is shown in Figure 3.1 (As noted, these results
are the average of three different experimental tests.)
Figure. 3.1. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
0
100
200
300
400
500
600
700
800
0 1000 2000 3000 4000 5000Sh
ea
r vis
co
sit
y (
Pa
.S)
Shear rate (s-1)
42
As also noted, the composite material used in the experimental study had an average fibre
length of 0.73 mm, and the experiment was conducted at 200˚C. The experimental results
showed that the viscosity of HYP/PA11 composite decreases with increasing shear rate.
This decrease in the shear viscosity with the increase of the shear rate corresponds to the
pseudoplastic fluid characteristic of the composites. This pseudoplastic behavior (also
referred to as shear-thinning behavior) as plotted in Figure 3.1 is mainly influenced by
the orientation of the polymer molecules, the agglomeration of the flexible pulp fibre, and
the entanglements within the polymer chains in the capillary rheometer. On the other
hand, the chain agglomerations are produced simultaneously as one chain is collapsed
into another chain. The entanglements that lead to agglomerations of the chains, as well
as the entanglements within the chains, are caused by the Brownian motions and low
relaxation of HYP fibre. The high shear-thinning behavior obtained for HYP/PA11 can
be also associated to the thermal degradation of HYP during the rheological testing and
the compounding process. The molten polymers tend to arrange themselves with their
major axes in the direction of shear, whereby points of entanglement are reduced. As a
result, the viscosity decreases. In other words, in this instance of non-Newtonian flow
behavior in polymer melts, the decrease in viscosity when the shear rate is increased by
applying load is associated with high shear-thinning behavior and with viscoelastic
characteristics of biocomposite materials. However, at very high shear rates (from 3,000
to 5,000 S-1); the molten HYP/PA11 showed a less restrained decrease in viscosity. This
non-Newtonian behavior is associated with the alignment and orientation of the fibre in
the polymer chains and the effect of the fibre aspect ratio. At both low and high shear
rates, the formation of agglomerates is evident; therefore the pulp molecules are
43
completely oriented due to the good dispersion in the bio-based PA11 matrix. This means
that the breakage of the fibre length allows the maintenance of an accurate fibre-aspect
ratio when the diameter of flexible HYP is kept unchangeable during the process. The
shorter length of the fibres also supports their alignment in the direction of the flow, thus
reducing fibre-fibre collisions and leading to a greater decrease in viscosity.
3.4.3 Effect of the temperature on the shear viscosity versus shear
rate of HYP-reinforced PA11
The variation in shear viscosity as a function of the shear rate of HYP/PA11 at various
temperatures was investigated; the rheological test results are presented in figure 3.2. The
rheological conditions were kept constant. The results are presented in the figure below.
44
Fig. 3.2. Variation of viscosity as a function of shear rate of HYP/PA11 at various temperatures.
The shear viscosity of the HYP/PA11 depended on the rate of shear at which it was
measured and presented. The shearing effects decreased as the temperature increased:
that is, the HYP/PA11 became more non-Newtonian in the higher-temperature region. At
higher temperatures the reduction of shear viscosity was more pronounced at
intermediate shear rate, while for 190˚C, this reduction was maximized at higher shear
rates (from 3000 to 5000 S-1). At low testing temperature (190˚C) and for low and
intermediate shear rate, the flow deformation was challenging. This was due to the fact
that the HYP-reinforced PA11 fibres were entangled and agglomerated. At this point,
such rheological behavior is called Near-Newtonian. At high shear rate, the shearing
effects increased while the effect of temperature was less pronounced, and flow
0
200
400
600
800
1000
0 1000 2000 3000 4000 5000
Sh
ear
vis
co
sit
y (
Pa.s
)
Shear rate (s-1)
190 degree
200 degree
210 degree
45
deformation was mostly dominated by the shearing effect. However, from 3000 to 5000
S-1 all the shear-viscosity variations in function shear rates followed the same rate of
deformation for different temperature profiles, which corresponds to shear-thinning
behavior.
3.4.4. Effect of HYP fibre content on the rheological behavior of
HYP/PA11
The effect of fibre content on the rheological characteristics of the composite was
investigated. Figure 3.3 shows the experimental results for 10%, 20%, and 30% HYP-
reinforced polyamide 11. These curves are typical of pseudoplastic materials, which
show a decrease in viscosity with increasing shear rate. At high fibre content, the material
offers higher shear viscosity even for high shear rate. In general, the incorporation of
fibres in polymer systems increases the viscosity, which rises further as fibre content is
increased.
46
Figure 3.3. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
The difference between 10% and 20% fibre content at intermediate and high shear rate is
not very significant. At low HYP content, shear viscosity was expected to rise rapidly
with increasing concentrations of fibre because of the rapidly increasing interactions
between particles as they became more closely packed. Nevertheless, at very high fibre
content, random anisotropic structures of the fibres in polymer melts were created. The
increase in shear viscosity was found to be more predominant at lower shear rates, where
fibre and polymer molecules were not completely oriented. In addition, higher pulp
content at high temperature, the effect of the pulp moisture content is more pronounced
by producing the hydrolysis reaction of polyamide 11 and consequently tends to decrease
the melt viscosity [Giles et al., 2005].
0
200
400
600
800
1000
0 1000 2000 3000 4000 5000
Sh
ea
r vis
co
sit
y (
Pa
.s)
Shear rate (s-1)
10%HYP/PA11
20%HYP/PA11
30%HYP/PA11
47
3.4.5 Effect of high-yield–pulp fibre aspect ratio on rheological
properties
The results from the study of the effect of the aspect ratio of flexible-pulp–fibre-
reinforced bio-based Nylon 11 are presented below in figure 3.4.
At low fibre aspect ratio, the decrease in viscosity as a function of the shear rate was
greater for both low and high shear rate. Contrarily, at higher fibre-aspect ratio the shear
viscosity showed a moderate decrease for low and intermediate shear rate.
Figure 3.5. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
At low and intermediate shear rate, the viscosity curves are slightly decreased and the
distance between each viscosity curve remains large. However, at high shear rate the
viscosity plots are tightly close. This is because fibre agglomeration and entanglement
0
200
400
600
800
1000
1200
1400
0 1000 2000 3000 4000 5000
Shear Rate (s-1)
Ar1 Ar3 Ar2
48
were not pronounced at high shear rate or frequency, due to the complete orientation of
the fibre and polymer molecules. Much as with high fibre content, the increase in shear
viscosity was found to be greater at lower shear rates, where fibre and polymer molecules
are not completely oriented.
3.4.6 Scanning electron microscopy
Fracture surfaces of the extrudate of HYP/PA11 composite were examined using SEM.
No fibre pullout was observed. The chemical structures of polyamide and wood fibre
both include a hydrogen bond, which makes for better compatibility between high-yield
pulp and polyamide. Figure 3.5 represents the SEM micrograph of HYP/PA11 composite.
Figure 3.6. An SEM micrograph of pulp-fibre–reinforced polyamide composite fracture surface showing
partially melted nylon fibre.
49
This micrograph indicated efficient bonding between the high-yield fibre and bio-based
nylon. The experimental and predicted data fit very well, which meant that there was
strong adhesion at their interface due to the presence of the third phase.
3.5 Conclusions
This study demonstrates that it is possible to extrude natural fibre with high-
thermoplastic-engineering bio-based nylon. Fibre distribution after processing has been
characterized by FQA for high-yield fibre in composites containing 10, 20 and 30%
fibres. The low-temperature–process compounding presents higher shear viscosity than
the high-temperature processing of HYP/PA11 for the same rheological parameters. This
is because during the compounding process the temperature was low, and the mixing and
melting processes were generated by the high shear rate created during extrusion.
Experimental test results of HYP/PA11 for both processing parameters show a steep
decrease in shear viscosity with increasing shear rate, and this melt-flow characteristic
corresponds to shear thinning behavior in HYP/PA11. Experimental results showed high
shear-thinning behavior in HYP/PA11 associated with a high degree of pseudoplasticity;
this was due to the good dispersion of high-yield pulp fibre into Nylon11 and the
orientation of the flexible pulp fibre in the direction of the molten PA11. Finally, the
morphological properties of HYP/PA11 composite were examined using scanning
electron microscopy (SEM). Due to the presence of the hydrogen bond, no fibre pullout
was observed and there was good adhesion between high-yield pulp fibre and polyamide.
50
CHAPTER 4
Effect of Lithium Chloride on the Fibre Length
Distribution, Processing Temperature and the
Rheological Properties of High-Yield-Pulp-Fibre–
Reinforced Modified Bio-Based Polyamide 11
Composite
4.1 Abstract
The aim of this work was to investigate the effect of lithium chloride (LiCl) on the fibre
length distribution, melting temperature and the rheological characteristics of high yield
pulp fibre reinforced polyamide biocomposite. The inorganic salt lithium chloride (LiCl)
was used to decrease the melting and processing temperature of bio-based polyamide 11.
The extrusion method and Brabender mixer approaches were used to carry out the
compounding process.
The densities and fibre content were found to be increased after processing using both
compounding methods. The HYP fibre length distribution analysis realized using the
FQA equipment showed an important fibre-length reduction after processing by both
techniques.
51
The rheological properties of HYP-reinforced net and modified bio-based polyamide 11
“PA11” (HYP/PA11) composite were investigated using a capillary rheometer. The
rheological tests were performed in function of the shear rate for different temperature
conditions. The low-temperature process compounding had higher shear viscosity; this
was because during the process the temperature was low and the mixing and melting
were induced by the high shear rate created during compounding process. Experimental
test results using the extrusion process showed a steep decrease in shear viscosity with
increasing shear rate, and this melt-flow characteristic corresponds to shear-thinning
behavior in HYP/PA11, this steep decrease in the melt viscosity can be associated to the
hydrolyse reaction of nylon for high pulp fibre moisture content at high temperature. In
addition to the low processing temperature, the melt viscosity of the biocomposite using
the Brabender mixer approach increases with increasing shear rate, and this stability in
the increase even at high shear rate for high pulp moisture content is associate to the
presence of inorganic salt lithium chloride which created the hydrogen bonds with pulp
during the compounding process.
4.2 Introduction
Short-fibre reinforced polymer composites are extensively used in manufacturing
industries due to their light weight and improved mechanical properties [Pervaiz & Sain,
2003; Bourmaud & Baley, 2009]. Hence, HYP has been used not only for its low lignin
content, but also for its potential thermal stability and its strong adhesion when it is
bonded with high-temperature engineering thermoplastic polymers [Sadeghian & Golzar,
2008; Thomen, 2001; Gu & Kokta, 2010; Bajpai, 2012].
52
Various experimental studies have investigated the effect of flexibility on fluid viscosity.
They concurred that the more flexible the fibres are, the more pronounced is their effect
on the rheological characteristics [Plackett et al., 2010; Kaw & Besterfield, 1998; Yeh,
1992]. A recent study on the effect of fibre-length distribution on the rheological
behavior of castor-oil composite showed that at high fibre length, the shear viscosity
becomes more dependent on shear rate [Gohil & Shaikh, 2010]. This behavior is due to
elastic deformation of the fibres [Gohil & Shaikh, 2010].
Recently, various authors have investigated the effect of fibre content on polymer melt
rheology [Kari et al., 2005; Lamnawar & Maazouz, 2008; Larache et al., 1994]. Their
study showed an important increase in shear viscosity with increased fibre loading at low
shear rates, but only a small increase in viscosity at high shear rates [Lamnawar &
Maazouz, 2008; Larache et al., 1994]. Another similar study on polypropylene-based
long fibre observed an increase in shear viscosity with increased fibre content and fibre
length [Larache et al., 1994]. However, this viscosity rise was very small, which the
authors attributed to high shear rates and fibre breakage during the processing [Larache et
al., 1994; George et al., 2001]. Non-Newtonian fluid characteristics such as shear
thinning were also observed in all the studies mentioned above.
There is only a very limited literature devoted to experimental studies of the rheology of
pulp-fibre–reinforced polymer composites due to the complex nature of these materials
and the difficulties encountered during their processing and their rheological
characterization [Larache et al., 1994; George et al., 2001; Liu et al., 2000; Uhlherr et al.,
2005; Huq & Azaiez, 2005].
53
The processing technique and conditions have a significant influence on the rheological
and overall properties of pulp-fibre–reinforced polymer composites because they dictate
the degree of dispersion and distribution of the fibre in the polymer matrix and the low
processing temperature required in order to avoid thermal degradation [Larson, 1999; -
Eberle, 2008; Le Moine et al., 2013; Guo et al., 2005]. Compared to other natural fibres,
HYP is more thermally stable in the presence of high- melting-temperature engineering
thermoplastics (under 180˚C) such as PA11, PA6, and PA66.
The principal objectives of the study described in this chapter were to determine the
effect of the addition of the inorganic salt lithium chloride (LiCl) to the bio-based
polyamide 11, and the characteristic of the modified bio-based polyamide 11 in the
presence of high yield pulp (HYP) fibre. The HYP fibre content, the length distribution,
and the density of the composites were measured and analyzed for both processing
techniques in order to investigate the effect of LiCl on the composite components.
Finally, the rheological results using the Brabender mixer technique and the conical twin
extruder respectively were determined and compared.
4.3 Material and Methods
4.3.1 Materials
The matrix biopolymer bio-based polyamide 11, density 1.03, MFI 11, was supplied by
Arkema (France). Aspen high yield pulp (HYP) fibres were supplied by Tembec
(Montreal, QC). The HYP is the type used in wood-free printing, in writing-paper grades
and in multiple-coated folding-board grades; fibre length is 0.230 to 0.85 mm.
54
4.3.2 Methods
4.3.2.1 Composites preparation
The experiment was processed using a conical twin screw extruder and a Brabender
mixer technique. In both mixing processes, the high yield pulp “HYP” fibre was dried at
80˚C for 6 hours and then added to the corresponding bio-based polyamide PA11 and
well mixed before the combination was introduced to the extruder. The average
temperature of the barrel was 200˚C. Figure 4.1 represents the different zones of the
conical twin-screw extruder. In addition, in the Brabender mixer technique process,
different lithium chloride content “LiCl” was added to the bio-based polyamide 11 at
corresponding process temperature prior to adding the pulp fibre.
Figure 4.1. Schematic figure of twin-screw extruder
55
4.3.2.2. Effect of processing conditions
Many processing parameters affect the properties of final products. For extrusion,
temperature profiles affect the fibre degradation. In addition, screw speed and feeding
rate change fibre length, distribution, and orientation. The mechanical properties reflect
all these changes, and the processing parameters are optimized to obtain the best
properties. Table 4.1 represents the processing parameters for HYP/PA11 used in this
study.
Table 4.1. Extrusion temperature profile for 10%, 20% and
30% HYP/PA11, 120 rpm (10% and 20%), 130 rpm (30%)
and 10 rpm feed rate.
Temperature (˚C)
Zone
1
Zone
2
Zone
3
Zone
4
Zone
5
Zone
6
Zone
7
Zone
8
Zone
9
Zone
10
200 200 200 200 200 205 205 205 205 205
However, the Brabender mixer technique was used as the principal compounding process
in this study. Inorganic salt lithium chloride (LiCl) was added to bio-based polyamide 11
in order to decrease it melting temperature, and consequently avoid fibre degradation and
burning. Different lithium chloride content was used to reduce the melting temperature of
polyamide 11 using the Brabender mixer technique.
56
4.3.2.3 Fibre content and length distribution analysis after compounding
The composite samples were cut into small pieces and immersed in formic acid for three
days. The bio-based PA11 was dissolved by the formic acid and HYP was left. The HYP
was filtered and washed with formic acid, then dried in a vacuum oven for four hours. By
measuring the weight of composite and pulp fibre, we could calculate the actual fibre
content.
HYP fibre length was measured with the Fiber Quality Analyzer (FQA). The HYP was
diluted with D.I. water. The diluted HYP fibre entered a thin-planar channel. This
channel helped to gently orient the fibre 2-dimensionally, so that the fibre could be fully
viewed by the camera. The picture taken by the camera was then analyzed by the
software to give the HYP fibre length distribution.
4.3.2.4 Actual density measurement
The density of polyamide 11 reinforced HYP fibre composites was determined by using
the ASTM D792 technique. The samples were first weighed both in water and air, and
then the density was calculated by:
ρ = a/[(a – w)ρwater] (4.1)
where ρ is the sample density in g/cm3, a is the sample weight in air in g, w is the sample
weight in water in g, and ρwater is the density of the water in g/cm3.
57
4.3.2.5 Differential scanning calorimetry (DSC)
The melting temperature and crystallization behavior of the yield pulp fibre reinforced
bio-based polyamide 11 composites were investigated using a TA instrument Q1000
differential scanning calorimeter (DSC) attached to a cooling system under a nitrogen
atmosphere. The DSC instrument was run from 45 °C to 250 °C with a heating rate of
10 °C /min. The sample weight was about 5 mg. The specimens were sealed in aluminum
pans by pressing and the prepared samples were placed in the furnace of DSC with an
empty reference pan. The heat flow rate as function of temperature was recorded
automatically. Melting temperature was identified on the peak point of the DSC curves.
The melting of polymer within a composite system would assist to select a suitable
temperature profile for the compounding process technique when the fibres and matrix
were compounded to produce green composite.
4.3.2.6 Rheological properties measurement
The rheological measurements of the composites’ melt-flow properties of were carried
out in a twin-bore Rosand Capillary Rheometer model RH2000. (The standard RH2000
range supports temperatures from -40˚C to 500˚C. The standard maximum force applied
is 12kN.) The composite samples for testing were cut into very small pieces, then placed
inside the barrel and forced down into the capillary with the plunger attached to the
moving cross-head. Representative steady-shear viscosity versus high shear rate is
presented in the figures below for HYP/PA11, which was processed at the average
extrusion temperature of 200˚C. The viscosity of the sample was obtained from steady-
shear measurements for different temperature profiles, with the rate ranging from 50 to
58
5000 S-1. The rheological viscosity data presented in this chapter thus represents an
average value of three measurements.
4.4 Results and Discussion
4.4.1 Effect of the lowering the processing temperature on the pulp
fibre distribution and the bio-based polyamide density after
processing
To avoid the degradation of the HYP fibre during the processing of the composite,
decreasing the melting temperature was attempted. The reduction of the melting point of
high-temperature–engineering polyamide was realizing by the utilization of inorganic salt
during the melt compounding processing in order to lower the melting temperature of
polyamide 11 (PA11). Lithium chloride (LiCl) was added to the polyamide 11 during the
extrusion process using the Brabender mixer technique. Next, the PA 11 and salt mixture
was used as a matrix and HYP fibre was incorporated into the matrix using a Brabender
mixer for the compounding.
59
Table 4.2. Melting temperatures of neat PA11 and modified
PA11 with varying LiCl content.
Composition Melting temperature (˚C)
Neat Polyamide (PA11) 188
PA11 + 1%LiCl 186
PA11 + 2%LiCl 182
PA11 + 3%LiCl 175
PA11 + 4%LiCl 172
PA11 + 5%LiCl 170
The melting temperatures of the PA 11/LiCl mixture are shown in Table 4.2. Table 4.3
shows the heat deflection temperatures of the PA11 polymer-reinforced HYP fibre
composites. 3% LiCl in PA11 was chosen in order to keep the concentration of LiCl low.
Figure 4.6 shows the rheological characteristics of Nylon 11 plastic-reinforced HYP
composites. From 3% to 5% LiCl in the PA11, the change in melting temperature is
insignificant. The stability of the melting point at high LiCl concentration is due to the
lowering of the crystallization temperature and the saturation of the degree of crystallinity
of the molecular chains.
60
Table 4.3. Heat deflection temperatures of polyamide 11
and HYP-fibre–reinforced bio-based PA11 composites.
Composition Heat deflection temperature (˚C)
Neat PA11 135
PA11 + 3%LiCl 52
PA11 + 3%LiCl + 10% HYP fibre 118
PA11 + 3%LiCl + 20% HYP fibre 126
PA11 + 3%LiCl + 30% HYP fibre 138
The heat deflection temperature was investigated for only 3% LiCl content. The addition
of LiCl to PA11 decreases the crystallization temperature and degree of crystallinity.
Consequently, the heat deflection temperature of PA11 decreased from 135ºC to 52ºC of
neat PA 11. However, with the addition of 10% HYP fibre, the heat deflection
temperature (HDT) increased to as high as 118ºC. For 30% HYP added to the modified
PA11, the heat deflection temperature rises up to 138 ºC. The higher is the content of the
pulp fibre, the higher is the heat deflection temperature of the composite. The increase in
the heat deflection temperature (HDT) of the resultant composite is proportional to the
concentration of high yield pulp fibre to the modified PA11 and LiCl.
4.4.2 Densities and actual fibre contents
The fibre contents of composites were controlled by the feeding rate of matrix and fibre.
However, the feeding rate cannot be calibrated precisely, especially the feeding rate of
61
HYP fibre. Table 4.4 shows the densities and actual fibre contents of composites
processed by the extrusion compounding method and the Brabender mixer technique.
Comparing the densities of bio-based polyamide 11 reinforced HYP composites made by
the two procedures, we can see that the composites made by the Brabender mixer
technique have higher density than composites made by the extrusion process at the same
fibre content. The 30% HYP/PA11 made via the Brabender mixer has a higher density
because its actual fibre content is 5% higher than the composite made by the extrusion
process. The different densities show that Brabender mixer technique gives samples with
fewer voids than the extrusion process.
Table 4.4. Densities and actual high-yield fibre contents.
Densities (g/cm3) Actual pulp fibre content
Polyamide 11 (PA11) reinforced HYP fibre composite : Extrusion compounding technique
PA11 1.03 0
PA11 + 10% HYP 1.05 12,5%
PA11 + 20% HYP 1.07 25%
PA11 + 30% HYP 1.12 33.2%
Modified Polyamide 11 (PA11) reinforced HYP fibre composite: Brabender mixer technique
PA11 + 3%LiCl + 10% HYP 1.07 14%
PA11 + 3%LiCl + 20% HYP 1.11 26%
PA11 + 3%LiCl + 30% HYP 1.21 38.3%
62
The modified bio-based PA11 reinforced HYP fibre composites have higher densities
than the regular bio-based PA11-reinforced HYP fibre composites at the same fibre
content even though the modified PA11 has a slightly higher density than regular PA11.
The reduction of the melting point, thus viscosity, could lead to a better fibre-matrix
wetting to eliminate free volume, holes/voids in the biocomposite with LiCl.
To minimize fibre thermal degradation, the processing temperature was set just below the
commercial melting temperature of polyamide. Table 4.4 shows that the densities and
actual fibre contents were proportional to the fibre content for both processing methods.
However, with the addition of LiCl to the Brabender mixer, the differences became more
pronounced.
4.4.3 Effect of fibre content on the length and shape distribution on
HYP-reinforced bio-based modified PA11 composite
During the extrusion process, the shear stress applied by the screw breaks the fibres. The
resulting fibre lengths affect the ultimate mechanical properties. In spite of the influence
of fibre damage and breakage during processing, the initial fibre length in the feedstock
determined the final fibre lengths. It was therefore important to analyze the initial fibre-
length distribution, which is one of the most significant parameters for natural fibre
reinforced polymer composites. After the polymer and fibre for the composite are
decided on, fibre length is the adjustable feature used to manage the ultimate properties
of bio-composite materials. Table 4.5 shows the results of HYP fibre length distribution
determined using a Fibre Quality Analyzer (FQA).
63
Table 4.5. Fibre length distribution of pulp fibre (extrusion
compounding process).
The arithmetical length and the length-weighted values of HYP fibre length were found
to be 0.20 mm, 0.27 mm, and 0.49 respectively for the pulp fibres from 30% HYP/PA11.
The arithmetic and length-weight measured values for 20% of pulp fibre were 0.24mm
and 0.36mm, and for 10% pulp fibre they were 0.29mm and 0.41 mm. Most of the fibre
lengths lie within the range of 0.20 mm to 0.57 mm, since HYP fibre was used in this
study. To obtain these average fibre lengths, 1,500 single fibres were examined. The
measured initial fibre length is greater than the actual length of the fibres in the
composites. The HYP fibre length decreases inversely with the increase of pulp fibre
content in the composite. This decrease of fibre length with the pulp fibre content in the
polymer melt concentration is due to fibre entanglement and agglomeration within the
polymer.
Fibre
Mean Length (measured)
Arithmetic (mm) Length weight
(mm)
Weight weighted
(mm)
Only HYP 0.38 0.57 0.73
HYP (10%) 0.29 0.41 0.63
HYP (20%) 0.24 0.36 0.54
HYP (30%) 0.20 0.27 0.49
64
Table 4.6. Fibre length distribution of pulp fibre (Brabender
mixer approach).
Table 4.6 shows that the HYP fibre length from the green composite produced using the
Brabender mixer technique did not decrease very much compared with the HYP fibre
length of the composite made using the conical twin extruder method. For modified bio-
based PA11-reinforced pulp fibre bio-composites processed using the Brabender mixer
technique, the mean fibre length did not decrease a great deal. In the normal bio-based
PA11 reinforced HYP fibre composites, the HYP fibre length is shorter than that of the
bio-based modified polyamide reinforced pulp fibre after extrusion, probably because the
higher temperature caused more thermal degradation of fibres, making them easier to
break. In addition, the use of LiCl to decrease the melting temperature of the bio-based
Fibre
Mean Length (measured)
Arithmetic (mm) Length weight
(mm)
Weight weighted
(mm)
Modified Bio-based PA11- reinforced HYP fibre composite: Brabender mixer
technique
Only HYP 0.38 0.57 0.73
HYP (10%) 0.33 0.46 0.68
HYP (20%) 0.28 0.38 0.60
HYP (30%) 0.26 0.35 0.56
65
PA11 may also have protected the pulp fibre from degradation and entanglement during
the slow and controlled process using the Brabender mixer technique, and consequently
kept the pulp fibre length constant after the compounding process.
4.4.4 Rheological characteristics of HYP–reinforced bio-based
polyamide
As already noted, rheological characteristics of the polymer, fibre, and interphasial
phases influence the final characteristics of the resultant microstructure of the composite
materials; these characteristics in turn affect the mechanical properties of a multiphase
polymer-composite system. As obtained from experiment, the shear viscosity as a
function of the steady-shear rate of HYP/PA11 at 200˚C is shown in Figure 4.2 (As
noted, these results are the average of three different experimental tests.)
Figure 4.2. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
0
100
200
300
400
500
600
700
800
0 1000 2000 3000 4000 5000
Sh
ea
r vis
co
sit
y (
Pa
.S)
Shear rate (s-1)
66
As noted, the composite material used in the experimental study had an average fibre
length of 0.73 mm, and the experiment was conducted at 200˚C. The experimental results
showed that the viscosity of HYP/PA11 composite decreases with increasing shear rate.
This decrease in the shear viscosity with the increase of the shear rate corresponds to the
pseudoplastic fluid characteristic of the composites. This pseudoplastic behavior (also
referred to as shear-thinning behavior) as plotted in Figure 4.2 is mainly influenced by
the orientation of the polymer molecules, the agglomeration of the flexible pulp fibre, and
the entanglements within the polymer chains in the capillary rheometer. The chain
agglomerations are produced simultaneously, as one chain is collapsed into another
chain. The entanglements that lead to agglomerations of the chains, as well as the
entanglements within the chains, are caused by the Brownian motions and low relaxation
of HYP fibre. The high shear-thinning behavior obtained for HYP/PA11 can be also
associated to the thermal degradation of HYP during the rheological testing and the
compounding process. The molten polymers tend to arrange themselves with their major
axes in the direction of shear, whereby points of entanglement are reduced. As a result,
the viscosity decreases. In other words, in this instance of non-Newtonian flow behavior
in polymer melts, the decrease in viscosity when the shear rate is increased by applying
load is associated with high shear-thinning behavior and with viscoelastic characteristics
of biocomposite materials. However, at very high shear rates (from 3000 to 5000 S-1) the
molten HYP/PA11 showed a less restrained decrease in viscosity. This non-Newtonian
behavior is associated with the alignment and orientation of the fibre in the polymer
chains and the effect of the fibre aspect ratio. Both at low and high shear rates the
formation of agglomerates is evident; therefore, the pulp molecules are completely
67
oriented due to the good dispersion in the bio-based PA11 matrix. This means that the
breakage of the fibre length allows the maintenance of an accurate fibre-aspect ratio
when the diameter of flexible HYP is kept unchangeable during the process. The shorter
length of the fibres also supports their alignment in the direction of the flow, thus
reducing the fibre-fibre collisions and leading to a greater decrease in apparent viscosity.
4.4.5 Effect of the processing parameters on the rheological
property
The rheological testing results for the different processing techniques (the extrusion
process for the high temperature process, and the Brabender mixer method for the low
temperature process) are presented below in Figure 4.3. The goal of decreasing the
process temperature was only realized for 30% HYP/PA11. The Brabender mixer
approach was used for the low-temperature compounding, and the process temperature
was below the melting point. The rheological properties of the high- and low-temperature
compounding are presented in Figure 4.3.
68
Figure 4.3. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
The low-temperature process compounding has higher shear viscosity compared to the
high temperature process; this is because a) during the low-temperature process the
polymer melting was generated by the high shear rate created during compounding and
also because the mixing process was incomplete.
4.4.6 Effect of the inorganic salt lithium chloride on the
rheological properties of HYP fibre–reinforced bio-based
polyamide composite
Variations in shear viscosity as a function of the shear rate of HYP/PA11 at various
processing temperatures using inorganic salt (LiCl) was realized in order to investigate
their effect on the melting point and the rheological properties HYP-fibre–reinforced bio-
based PA11 composite. The addition of inorganic salt lithium chloride to PA11 modified
it melting point and consequently modified the processing temperature. The rheological
0
200
400
600
800
1000
1200
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Sh
ea
r vis
co
sit
y (
Pa
.s)
Shear rate (S-1)
low temperature process
High temperature process
69
test results are presented in Figure 4.4 and were achieved using the Brabender mixing
technique. The processing conditions were 200˚C for the net polyamide without LiCl,
186˚C for 1% LiCl, 182˚C for 2% LiCl, 175˚C for 3%LiCl, 172˚C for 4%LiCl, and
170˚C for 5%LiCl content. In this chapter, LiCl + bio-based PA11 “LiCl + PA11” is
referred to as 'modified' polyamide 11 for brevity. The rheological test results presented
in the figure below are for constant fibre content (30%) and for various process
temperature and lithium chloride concentrations.
Figure 4.4 Variation of the viscosity with a function of shear rate of HYP/PA11 at various temperatures.
The variation in the shear viscosity of the HYP/PA11 in function of the rate of shear and
lithium chloride concentration was measured and presented. The shearing effects
decreased as the salt concentration increased: that is, the modified HYP/PA11 became
more non-Newtonian in the higher temperature region for low LiCl concentration. At
higher salt concentration the reduction of shear viscosity was more pronounced at
intermediate shear rate, while for 175˚C, this reduction is maximized at higher shear rates
(from 3000 to 5000 S-1). At low salt concentration and net processing temperature
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Shear rate (s-1
)
Sh
ea
r v
isc
os
ity
(P
a.s
)
5%LiCl(170˚C)
4%LiCl(172˚C)
3%LiCl (175˚C)
2%LiCl (182˚C)
1%LiCl (186˚C)
Net (200˚C)
70
(200˚C) and for low and intermediate shear rate, the flow deformation is challenging.
This is due to the fact that the HYP-reinforced PA11 fibres are entangled and
agglomerated. At this point, such rheological behavior is called Near-Newtonian. At high
shear rate, the shearing effects increased while the effect of temperature and the salt
concentration were less pronounced, and flow deformation was mostly dominated by the
shearing effect. However, from 3000 to 5000 S-1 all the shear-viscosity variations in
function of shear rates followed the same rate of deformation for different salt content
and temperature profiles, which corresponds to shear-thinning behavior.
4.4.7 Effect of HYP fibre content on the rheological characteristics
of modified bio-base (PA11 + 3%LiCl) composite
The effect of fibre content on the rheological characteristics of the HYP-fibre–reinforced
modified bio-based polyamide composite was investigated. Figure 4.5 shows the
experimental results for 10%, 20%, and 30% HYPP reinforced modified PA11 “PA11 +
LiCl”. These curves are typical of pseudoplastic materials, which show a decrease in
viscosity with increasing shear rate. At high fibre content, the material offers higher shear
viscosity even for high shear rate. In general, the incorporation of fibres in polymer
systems increases the viscosity, which rises further as fibre content is increased.
71
Figure 4.5. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
The difference between 10% and 20% fibre at intermediate and high shear rate is not very
significant. At low HYP content, shear viscosity is expected to rise rapidly with
increasing concentrations of fibre because of the rapidly increasing interactions between
particles as they become more closely packed and entangled. Nevertheless, at very high
pulp fibre concentration, random anisotropic structures of the fibres in polymer melts
were created, and they increased the shear viscosity. The increase in shear viscosity is
found to be more predominant at lower shear rates, where fibre and polymer molecules
are not completely oriented.
0
200
400
600
800
1000
1200
1400
1600
1800
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Shear rate (s-1)
Sh
ea
r V
isc
os
ity
(P
a.s
) 30%HYP/PA11+3%LiCl
20%HYPPA11+3%LiCl
10%HYP/PA11+3%LiCl
72
4.5 Conclusions
This study demonstrates that it is possible to process HYP fibre with high-thermoplastic-
engineering bio-based polyamide. For both processing methods and all formulations,
fibres showed a length reduction after compounding process. The observed fibre length
reduction using the extrusion process method was lower compared to the fibre length
reduction using the Brabender mixer technique. However, the highest fibre reduction was
observed for 30% pulp fibre in composite. The low-temperature compounding of
HYP/PA11 presents higher shear viscosity compared to the high-temperature
compounding for the same rheological parameters; this is because during the process the
temperature was low and the mixing and melting were produced by the high shear rate
created during compounding process. Experimental testing results from HYP/PA11 for
the extrusion processing technique showed a steep decrease in shear viscosity with
increasing shear rate at high temperature, and this melt-flow characteristic corresponds to
shear thinning behavior in HYP/PA11 and due to the high pulp moisture content which
tends to degrade polyamide 11. Results also showed high shear-thinning behavior in
modified HYP/PA11 associated with a high degree of crystallinity and pseudoplasticity;
this was due to the good dispersion of HYP into PA11 and the orientation of the flexible
fibre effects in the direction of the molten PA11.
73
CHAPTER 5
Review of Non-Newtonian Mathematical Models for
Rheological Characteristics of Viscoelastic
Composites
5.1 Abstract
This study presents an overview of viscoelastic characteristics of biocomposites derived
from natural-fibre–reinforced thermoplastic polymers and of predictive models used to
understand their rheological behavior. Various constitutive equations are reviewed for a
better understanding of their applicability to polymer melt in determining viscosity. The
models to be investigated are the Giesekus-Leonov model, the Upper Convected Maxwell
(UCM) model, the White-Metzner model, K-BKZ model, the Oldroyd-B model, and the
Phan-Thien-Tanner models. The aforementioned models are the most powerful for
predicting the rheological behavior of hybrid and green viscoelastic materials in the
presence of high shear rate and in all dimensions.
The Phan-Thien Tanner model, The Oldroyd- B model, and the Giesekus model can be
used in various modes to fit the relaxation modulus accurately and to predict both shear
thinning and shear thickening characteristics. The Phan-Thien Tanner, K-BKZ, Upper
convected Maxwell, Oldroyd-B, and Giesekus models predicted the steady shear
74
viscosity and the transient first normal stress coefficient better than the White-Metzner
model for green-fibre–reinforced thermoplastic composites.
5.2 Introduction
The rheological properties and extrudate behavior of polymer melts are of central
importance in the processing and fabrication of polymer products. The melt-rheological
behavior of short sisal, coir, and pineapple fibre-reinforced polymer systems has been
studied in various works [Anselm et al., 2014; Mohssine et al., 2007]. However, there is
limited research on the effects of parameters such as the fibre length, the fibre-matrix
interaction, and the aspect ratio of green-fibre–reinforced thermoplastic biopolymer
composites on nonlinear rheological behavior [Fengwei et al., 2012; Xiuyang, et al.,
2012].
The mathematical explanation of a viscoelastic fluid is much more complex than its
Newtonian counterparts. In addition to the conservation equations of mass and
momentum, the constitutive equation or rheological equation of state is required; this
relates stress to deformation. For a viscoelastic liquid this relationship is nonlinear, and it
has no standard form universally valid for each fluid in every flow situation. This reality
is one of the reasons why the subject of viscoelasticity is so challenging.
The constitutive equation should not only describe the rheological characteristic of the
polymer melt but also give the final fibre orientation of the composite. For this reason it
is fundamental to evaluate the role of the biocomposite’s rheology and the natural fibre–
polymer interaction. It has been observed that the total stress of the composite increases
75
as fibres are added; consequently, a satisfactory constitutive equation could be achieved
by adding an extra stress term to an already existing constitutive equation, which then
adequately describes the polymer melt [Zhang et al., 2009; Somwangthanaroj, 2010;
Marynowski, 2006].
Accordingly, constitutive equations found in the literature that adequately describe
polymer melt will be explored for their application in biocomposite processing. Particular
focus will be given to nonlinear rheological characteristics of viscoelastic materials. The
power-law, Cross WFL, Casson, Bird-Carreau and Hershel Bulkley models are among
the most preferred rheological models due to their ability to predict velocity and pressure
distributions in uniform flows in addition to their simple representation of shear thinning
behaviour [Marynowski, 2006; Dealy & Wissbrun, 1990; Mahmoud et al., 2012; Owens
& Phillips, 2002]. However, in the case of high shear stress of viscoelastic polymer melt,
the predictive power of these models is considerably reduced [Owens & Phillips, 2002].
In this study, a review of nonlinear rheological models for viscoelastic materials from
natural-fibre–reinforced thermoplastic polymers will be presented by a special review of
the Upper convected Maxwell, Phan-Thien-Tanner (PTT), K-BKZ, Oldroyd-B, Giesekus
and Whhite-Metzner constitutive models.
5.3 Viscoelastic characteristics of materials
Viscoelasticity is the property of a material to demonstrate both viscous and elastic
properties under the same conditions when it undergoes deformation [Han, 2007; Willett
et al., 1995; James, 2009]. Viscous materials present resistance to shear flow and strain
76
linearly with time when a stress is applied [Doraiswamy, 2002; Bird et al., 1987]. The
shear stress of these materials depends on strain: when strain is applied and then released,
they return to their initial configuration [Bird et al., 1987; Tucker & Advani, 1994]. Some
common and well-known viscoelastic materials include paint, blood, ketchup, honey,
mayonnaise, polymer melt, polymer solution and suspension, shampoo, and corn starch
[James, 2009; Jarecki & Ziabicki, 2011].
At constant temperature, water, air, ethanol, and benzene are represented as Newtonian
fluids [Higashitani & Pritchard, 1972; Tuna & Finlayson, 1984; Crochet & Legat, 1992].
This means that the rapport between the shear stress versus shear rate is a straight line
with a constant slope for a fixed temperature that is independent of the shear rate [Tuna &
Finlayson, 1984; Crochet & Legat, 1992; Dealy & Wissbrun, 1999; Doraiswamy, 2002].
In addition, the plot passes through the origin: that is, the shear rate is zero when the
shear stress is zero [Doraiswamy, 2002].
A fluid that does not behave in a Newtonian fashion between shear stress and shear rate
when it undergoes deformation is commonly termed non-Newtonian [Bird et al., 1987;
Tucker & Advani, 1994]. This means that the relation between shear stress and shear is
not a straight line but is non-linear. High-molecular-weight liquids, which include
polymer melts and solutions of polymers, as well as liquids in which fine particles are
suspended, are usually non-Newtonian [Tucker & Advani, 1994; Grafe & Graham, 2003;
Zhou & Kumar, 2010]. In this case, the slope of the shear stress versus shear rate plot will
not be constant as we change the shear rate [Grafe & Graham, 2003; Zhou & Kumar,
2010]. When viscosity decreases with increasing shear rate, the fluid is called shear-
thinning [Jayaraman et al., 2004; Letwimolnun et al., 2007; Collie et al., 2001]. In the
77
opposite case, where the viscosity increases as the fluid is subjected to a higher shear
rate, the fluid is called shear-thickening [Jayaraman et al., 2004; Letwimolnun et al.,
2007; Collie et al., 2001]. Shear-thinning fluids also are called pseudoplastic fluids and
shear-thickening fluids are called dilatants [Da Silva et al., 2012; Mitran & Yao, 2007].
Shear-thinning behavior is more common than shear thickening [Letwimolnun et al.,
2007; Collie et al., 2001].
Another type of non-Newtonian fluid is viscoplastic or “yield stress” fluid [Jayaraman et
al., 2004; Letwimolnun et al., 2007; Collie et al., 2001]. This is a fluid that will not flow
when only a small shear stress is applied. The shear stress must exceed a critical value
known as the yield stress for the fluid to start flowing. Hence, viscoplastic fluids behave
like solids when the applied shear stress is less than the yield stress. Once it exceeds the
yield stress, the viscoplastic fluid will flow just like an ordinary fluid [Letwimolnun et
al., 2007; Collie et al., 2001].
On the other hand, some classes of fluids exhibit time-dependent behavior [Denn, 2008a;
Denn, 2008b; Krutka et al., 2008]. This means that even at a given constant shear rate,
the viscosity may vary with time. This category of material comprises both thixotropic
and rheopectic fluids, whose behaviors in this respect are opposites [Denn, 2008a; Denn,
2008b; Krutka et al., 2008]. The viscosity of a thixotropic liquid will decrease with time
under a constant applied shear stress [Denn, 2008b; Krutka et al., 2008]. However, when
the stress is removed, the viscosity will gradually recover with time as well [Denn, 2008].
By contrast, rheopectic fluid behavior can be observed when the fluid increases in
viscosity with time when a constant shear stress is applied [Denn, 2008b; Krutka et al.,
2008].
78
5.4 Rheological modelling of viscoelastic composites
Mathematical models of viscoelasticity are mostly based on a differential or integral
representation [Tanner, 2000; Denn et al., 1975]. From a mathematical point of view, the
differential representation is easier to handle than the integral one. However, the integral
representation is capable of predicting the time dependence more generally [Tanner,
2000; Denn et al., 1975; Nonaka et al., 2009].
The characteristic feature of linear viscoelastic materials is that the stress is linearly
proportional to the strain history [Nonaka et al., 2009; Da Silva et al., 2012]. Linear
viscoelasticity is usually applicable only for small deformations, low rate, low stress, and
linear materials [Nonaka et al., 2009; Da Silva et al., 2012; Mitran & Yao, 2007].
However, in reality about 90% of fluids are nonlinear, with large deformations, and with
nonlinear response in the presence of such deformations. Nonlinear viscoelastic behavior
is usually exhibited when the deformation is large and most of the time when the material
changes its properties under deformations [Devereux & Denn, 1994; Ellison et al., 2007;
Fisher & Denn, 1977]. Consequently, nonlinear viscoelastic mathematical models are
needed [Fisher & Denn, 1977; Ellyin et al., 2007].
Existing nonlinear mathematical rheological models are often constructed through
modifications and extensions to higher-order stress or strain terms of the linear theory
[Galante, 1991]. As noted earlier, from a mathematical point of view, the integral
representation of a viscoelastic constitutive equation is more difficult to perform than the
differential form. Thus, several models characterized by elastic, viscous, and inertial
nonlinear contributions with various complexities have been developed for describing the
79
nonlinear behavior of these materials [Galante, 1991]. However, in these models, due to
the mathematical complications, only the elastic or viscous nonlinearity is often taken
into account and the inertial contribution is ignored. Moreover, there are only a few
theoretical models formulated with constant-value rheological material parameters.
For these reasons, nonlinear models with constant rheological coefficients are required.
The elastic and viscous nonlinearities are taken simultaneously into consideration through
a simple nonlinear generalized Maxwell fluid model consisting of a nonlinear spring
connected in series with a nonlinear dashpot obeying a power law with constant material
coefficients [Burghardt & Fuller, 1989; Kiriakidis et al., 1989]. According to a previous
study by Bauer (1984), suitable constitutive equations for viscoelastic materials must
relate stress, strain, and their higher time derivatives; or better said, they must take into
consideration the elastic, viscous, and inertial nonlinearities simultaneously [Tan et al.,
2010]. Moreover, various researchers have explored how polymer viscoelasticity affects
the diameter distribution of polymer melt-extrudate fibres and have demonstrated that
increasing the melt viscosity leads to an increase in fibre diameter but has little effect on
the diameter distribution [Tan et al., 2010]. The commonly used Phan-Thien-Tanner
(PTT) and Upper-Convected Maxwell (UCM) constitutive models assume constant shear
stress acting on the fibre surface and neglect the effects of heat transfer [Kiriakidis et al.,
1989; Tan et al., 2010; Jarecki & Lewandowski, 2009]. The K-BKZ type of constitutive
equation has been widely used in various studies on predicting the rheological behavior
of viscoelastic materials. For example, Galante used the constitutive equation to describe
viscoelastic effects in an integral equation of the K-BKZ type, suitable for polymer
solutions and melts [Altan et al., 1989]. The problem with the constitutive equation of K-
80
BKZ is that it is not fully applicable to predicting the nonlinear rheological behavior of
viscoelastic materials [Altan et al., 1989; Marders et al., 1992; Phan-Thien & Tanner,
1977].
The behavior and properties of a non-Newtonian fluid with incompressible flow are
provided by the conservation of mass and momentum equations, respectively.
5.5 Governing Equations
The governing equations for the annulus flows are presented as follows.
Continuity equation for incompressible fluids:
(5.1)
where v is the velocity vector.
Equation of momentum:
( + V. = - (5.2)
Where the density, p is the pressure, and is the stress tensor.
81
5.6 Constitutive equations
There are many numerical representations for viscoelastic models. The most common
models are Upper-Convected Maxwell (UCM), Phan-Thien-Tanner (PTT), Oldroyd-B,
Giesekus, K-BKZ and White-Metzner.
5.6.1 K-BKZ model
The K-BKZ integral constitutive equation with multiple relaxation times describes and
predicts the stresses within a fibrous suspension, solution, or molten polymer. Also, an
extra term is added to the constitutive equation to account for the extra stresses due to the
presence of fibres and to predict the orientation of a given fibre undergoing stresses
within the suspension or molten [Phan-Thien, 1978]. The motivation for developing such
a constitutive equation with these two considerations is to present an equation that can
describe the rheological behavior of polymeric fibrous solutions and moltens while also
to have a model, which can be used in numerical simulations:
τc = τf + τp (5.3)
The fibre equation is:
(γ) (5.4)
Where η(γ) is the viscosity of the polymer, γ is the shear rate, f is the fibre volume
fraction, D and L are the diameter and length of the fibre, n is the number of the
suspension, and h is the average distance from a given fibre to its nearest neighbor
82
[Wellington et al., 2007]. Dinh and Armstrong proposed the following expression to
calculate the distance between two fibres:
h = for aligned systems
h = (n )-1 for random systems
Orientation tensor:
= (5.5)
The polymer equation is:
(5.6)
Where τp is the shear stress for the polymer, λk and Gk are the relaxation times and
relaxation moduli, N is the number of relaxation modes, is the finger strain tensor,
and is its first and second invariants. H is the strain memory function, and the
following formula is used, proposed by Papanastasiou et al.:
H( (5.7)
83
For simple shear flow, the strain-memory function is given as:
H( (5.8)
( (5.9)
where are nonlinear model constants to be determined from shear and
elongation flow data, respectively. The strain-memory function in
simple shear flow is dependent on . This is expected since is viewed as
a shear-thinning parameter, while is viewed as an elongational-thinning parameter
[Phan-Thien, 1978; Wellington et al., 2007].
5.6.2 Upper-Convected Maxwell model (UCM)
The UCM model is a differential generalization of the Maxwell model for the case of
large deformations based on the upper-convected time derivative. The model can be
written as:
(5.10)
D = (5.11)
84
D is the tensor of the deformation rate
(5.12)
where λ is the relaxation time, η is zero shear viscosity, and is the upper-convected time
derivative of the stress tensor, which is expressed as:
= τ + V. τ – .τ – τ ( (5.13)
The UCM constitutive model incorporates memory effects of materials, but its viscosity
is constant at various shear rates [Giesekus, 1982; Giesekus, 1985; Mostafaiyan et al.,
2004].
5.6.3 White-Metzner Model
The White-Metzner model is derived from the network theory of polymers (White and
Metzner 1963). Modification of the viscosity and relaxation parameters as a function of
the shear rate, leads to the White-Metzner model. This model exhibits shear thinning,
not because of non affine motion, but because the relaxation is accelerated at high strain
rates, where the relaxation is faster than any deformation [Isaki et al., 1991]. The
viscoelastic differential constitutive model takes the form: τ1 + λ(γ) = 2η(γ)D, where
η(γ) can be obtained from the experimental shear viscosity curve and the function λ(γ)
can be obtained from the experimental first normal stress difference curve.
85
5.6.4 Phan-Thien-Tanner model (PTT)
The PTT model refers to a quasi-linear viscoelastic constitutive equation, which is widely
used in simulation of polymer solution flows. The original Phan-Thien-Tanner equation
was written using both of the following modifications simultaneously: the Gordon
Schowalter derivative and segment kinetics. It employs specific forms for the creation
and destruction rates of the network junctions in the network theory of Lodge and
Yamamoto [Yarin et al., 2010; Sebastien et al., 2011]. Although the Phan-Thien Tanner
model overpredicts both the shear viscosity at higher shear rates and the transient and
extensional properties, it accurately predicts the zero shear viscosity and seems suitable
for numerical simulations of polymer melts. It is worth noting that, compared to integral
models such as the Bird-Carreau and Wagner models, differential models such as the
PTT model provide robust numerical algorithms and exhibit good behavior in FEM
simulations [Yarin et al., 2010]. The interested reader is referred or more accurate
comparison between the K-BKZ (as integral model) and the PTT model.
In the PTT model, the extra stress tensor is considered as the sum of the viscoelastic
component , and the purely Newtonian component .
+
in which is given by:
86
= 2 D (5.14)
where D is the strain rate tensor.
The complete form of the PTT constitutive equation for the viscoelastic component is:
f(trτ) τ + λ + λ(γτ + τγ) = η (5.15)
or
+ ) + (5.16)
where the Oldroyd’s upper convective derivative is defined by:
= - . (5.17)
where V represents the velocity matrix, is the transpose of the velocity matrix, and
D(V)/Dt is the material derivative of the velocity matrix.
Analyzing the expression above, the first term represents the stress tensor transport and
the transient part of the flow [Sebastian et al., 2011]. In the second term, the slipping
between the fluid polymeric chains is computed. The third term includes the elastic
effects. Finally, the term on the right side of the equality represents the diffusive effects:
87
τ is the stress tensor, D the deformation-rate tensor, λ the fluid relaxation time, and G the
relaxation module. The parameter ξ controls the amount of movement between the fluid
polymeric chains [Oldroyd J.G, 1950]. For ξ = 0 the model is named PTT Affine and the
slipping between the polymeric chains is neglected. The function Y depends on the rate of
creation and destruction of the links between the chains. Moreover, the PTT model
incorporates the memory effect of materials and its viscosity can vary with the change of
the shear rate. When ξ is zero, PTT constitutive equation reduces to its simplified form
(SPTT) [Yarin et al., 2010; Sebastien et al., 2011]:
f(tr(τ))τ + λ = η (5.18)
Phan-Thien and Tanner assumed specific forms for the creation and destruction rates of
the network junctions and derived a constitutive equation containing two free parameters,
and ξ [Cirulis, 2010]. The exponential constitutive model takes the following form:
exp + = 2 (5.19)
and are the adjustable parameters of the model.
The parameters η and λ are the viscosity and relaxation time respectively, measured from
the equilibrium relaxation spectrum of the fluid. They are not considered as adjustable
parameters of the model. The PTT model can be solved using a single relaxation time or
multiple relaxation times, similar to the Giesekus model. The linear form of the PTT
88
model predicts shear thickening at high elongational rates, after which a plateau is
reached [Isaki et al., 1991; Sebastian et al., 2011].
5.6.5 Giesekus-Leonov model
Giesekus proposed a constitutive model based on a concept of configuration-dependent
molecular mobility. In this model, the viscoelastic component of the extra stress tensor is
represented with the following parameters . Owing to the highly nonlinear
nature of the model equations, all of the properties need to be obtained numerically.
+ - + = 0 (5.20)
The α parameter is the dimensionless Giesekus-model mobility factor and controls the
extensional viscosity and the ratio of the second normal stress difference to the first one.
The dimensionless Giesekus-model mobility factor used to evaluate the anisotropic drag
is represented by 0 < α < 1. For α = 0 the model becomes the isotropic UCM model,
while for α =1 the model is merely an anisotropic drag, and for α > 0 the model
represents shear-thinning behavior. The Giesekus model predicts the tension-thickening
region for elongational flow, after which a plateau is reached; but it shows the existence
of a tension-thinning region at high strain rates [Luo & Tanner, 1987; Chauvière &
Owens, 2002; Cirulis et al., 2910; Oldroyd, 1950].
89
5.6.6 Oldroyd-B Model
The Oldroyd-B model is a principal form of viscoelastic model:
- 2 (d - = 0 (5.21)
where d is the rate of deformation tensor, is the shear viscosity, is the relaxation
time, and is the second relaxation parameter [Oliveira, 2009; Byron et al., 2011;
Trebotich et al., 2005]. The Oldroyd-B model is mostly used to describe the rheological
characteristics of polymer liquids composed at low concentration and moderate shear
rates for high-viscosity Newtonian molecular-weight polymer.
1) At the model simplifies to a second-order fluid with a vanishing second normal
stress coefficient.
2) At the model reduces to the convected Maxwell model.
3) At the model reduces to a Newtonian fluid with viscosity
5.7 Conclusion
Understanding the complex behaviour of polymer materials and interpreting it as one
general equation requires a vast knowledge of the characteristics and formation of this
90
complex type of material. Since rheometers do not provide the necessary information for
all important rheological properties, constitutive equations are the best available tools for
effective process control.
The development of valuable models for composite behavior and the exploration of
appropriate constitutive equations to describe this complex behavior has been a high
priority for many researchers. However, understanding the rheological behavior of
viscoelastic composites is a redoubtable challenge.
The K-BKZ, PTT, Oldroyd-B, and Giesekus models was widely studied for future
implementation works. These models can be applied to the prediction and determination
of the shear viscosity of viscoelastic composites as a function of shear stress and shear
rate during extrusion and injection moulding processes.
91
CHAPTER 6
Modeling the Rheological Characteristics of Flexible
High Yield Pulp-Fibre–Reinforced Bio-Based Nylon
11 Bio-Composite
6.1 Abstract
The aim of this work was to develop a mathematical model to investigate the rheological
characteristics of viscoelastic pulp fibre composite materials. The rheological properties
of High Yield Pulp (HYP) reinforced bio-based Nylon 11 (Polyamide 11 or PA11)
composite (HYP/PA11) were investigated using a capillary rheometer. Novel predicted
multiphase rheological-model–based polymer, fibre, and interphasial phases were
developed. Rheological characteristics of the composite components influence the
development of resultant microstructures; this in turn affects mechanical characteristics
of a multiphase composite. The main rheological characteristics of polymer materials are
viscosity and shear rate. Experimental and theoretical test results of HYP/PA11 show a
steep decrease in apparent viscosity with increasing shear rate, and this melt-flow
characteristic corresponds to shear thinning behavior in HYP/PA11. The nonlinear
mathematical model to predict the rheological behavior of HYP/PA11 was validated
experimentally at 220˚C and 5000S-1 shear rate. Finally, predicted and experimental
viscosity results were compared and found to be in strong agreement.
92
6.2 Introduction
The study of the rheological behavior of viscoelastic polymer composites is mostly
limited to a two-phase fibre-polymer. The so-called interphase zone appears in the
viscoelastic damping of polymer composite processing [Pervaiz & Sain, 2003]. This
deformation significantly affects the predicted overall rheological characteristics of
natural-fibre–reinforced thermoplastic composites [Bourmaud & Baley, 2009]. During
processing, fibre-reinforced polymers are subjected to rigorous deformations that cause
fibres to translate, agglomerate, bend, and rotate with the flow of the fibre matrix [George
et al., 2001; Gu & Kokta, 2010; Bajpai, 2010; Thomen, 2001; Plackett et al., 2010;
Uhlherr et al., 2005]. This strongly influences the rheological and mechanical properties
in different parts of the final product because of the close dependence of these properties
on the orientation state of the fibres. Likewise, rheological properties that are a function
of the flow-induced fibre configuration in the matrix also influence the physical
properties of fibre-reinforced polymer composite [Liu et al., 2000; Kaw & Besterfield.,
1998].
The effect of the interphasial zone has been already studied by Kaw and Besterfield
[1998] and Yeh [1992] as a third constituent of the predictive models with respect to the
elastic behavior of fibre-reinforced polymer composites. Gohil and Shaikh [2010] and
Kari et al. [2005] have investigated the interphasial effect in wood-fibre-reinforced
polymer composites. It was demonstrated that the interphase, considered as a
homogeneous and isotropic material, has a significant effect on the loss factor and on the
prediction of the elastic properties of three phases: fibre, interphase, and polymer
93
composite. Other work by Lamnawar and Maazouz [2008], and Larache, Agbossou, and
Pastor [1994] used theoretical and experimental approaches based on shear lag and shear
modulus to show the role of the interphase in the elastic properties of composite
materials. However, no studies have been found in the literature that consider these three
phases in investigating the effect of the interphase on prediction of the rheological
characteristics of viscoelastic pulp-fibre–reinforced thermoplastic polymer composites.
The rheological characteristics of such composites are vital to their final mechanical
properties. Although natural-fibre–reinforced polymer composites and their processing
have been partially reviewed in several papers [Lamnawar, & Maazouz, 2008; Larache et
al., 1994; Deshpande, 2004], models of their rheological behavior and analysis of the
rheology–processing parameter relationships have been neither investigated nor reported.
This study reports on the state-of-the-art technology in the rheology of biocomposites
from green-fibre polymers, including their viscoelasticity and complex rheological
behaviors as influenced by different conditions. Hence, an overview of the viscoelastic
properties of biomaterials derived from pulp-fibre-reinforced thermoplastic polymers is
presented in order to analyze their rheological behavior as part of predicting the viscosity
of polymer melts.
Giesekus proposed a constitutive model based on a concept of configuration-dependent
molecular mobility [Lamnawar, & Maazouz, 2008; Larache et al., 1994; Hosseinalipour
et al, 2012]. In this model, the viscoelastic component of the extra stress tensor is
represented with the parameters ; due to the highly nonlinear nature of the
94
model equations, all the properties need to be obtained numerically. Moreover, this
model is only able to predict low load and low shear rate in the presence of fibre.
The purpose of this study, therefore, is to present experimental and predicted results of
HYP/PA11 and to validate this novel rheological modeling approach. First, we fully
explored the viscoelastic-polymer-based Giesekus constitutive model. Second, we
introduced the fibre and interphasial phases in function of fibre diameter and aspect ratio
to the Giesekus model, considering the effect of fibre entanglement and agglomeration on
the variation of the viscosity with shear rate. Finally, the model was validated by
obtaining the experimental data needed to evaluate the model’s predictions.
6.3 Mathematical model
6.3.1 Governing Equations
The equations governing the flow are the mass and momentum conservation equations.
0 (1) (6.1)
(6.2)
where v is the velocity vector, ρ the polymer melt density, τ the polymeric extra stress
contribution, p the pressure, and g the gravitational velocity.
For polymer melts exhibiting Newtonian rheology, τ takes the form
g
95
= 2μD,(3) (6.3)
where μ is the melt viscosity and D = (∇u + (∇u)T)/2 is the rate-of- strain tensor. For
viscoelastic polymer melts, the stress tensor depends on the deformation history.
6.3.2 Assumptions and boundary conditions
The model was designed on the assumption that it should describe rheological behavior
as a function of the rate of deformation according to different conditions like fibre
flexibility, interphasial zone and aspect ratio, and anisotropic parameter. In addition, to
obtain a closed-form analytical expression for the velocity distribution as a function of
the viscoelastic parameters, the following assumptions and boundaries conditions were
introduced:
The flow of fibre-reinforced thermoplastic composites is assumed to be an
incompressible fluid during the extrusion and injection molding processes;
The velocity field is steady and fully developed, i.e., u = u(y), v = 0;
The isothermal viscosity laws are applied, i.e., the viscosity is only a function of shear
rate;
The components of the composite are anisotropic, then nonlinear viscoelastic models;
The flow is in a closed system and is driven only by applying load (zero pressure
gradient, i.e., ∇P = 0);
96
Given the high viscosity of the polymer melt, inertia is negligible.
6.3.3 Model development
A single Giesekus model derived from a Maxwell element would be sufficient to model
the observed relaxation-time behavior, the shear stress, and the viscosity of polymer
material. However, the strong nonlinear viscoelastic expression of shear viscosity in
function of high shear rate of HYP-fibre-reinforced polymer composite required the
extension of the model to include more parameters. Hence, in addition to the polymer
phase, the fibre and interphase phases have been formulated into the Giesekus base
model.
The literature offers various concepts for modeling change in the viscous properties. It
has been pointed out that only the viscous overstress and the strain rate are suitable
dependencies for formulating a viscosity function.
Figure 6.1. HYP fibre of length L before load is applied
Figure 6.1 shows the surface area of the flexible HYP at different points. Assuming that
the fibre is flexible, when shear is applied the fibre is agglomerated at the point of
diameter “D”.
L
97
The surface area of fibre before agglomeration is maximum, and is calculated as follows:
AMax = πDL (6.4)
At the agglomerated point, the surface area is minimum, and we obtain:
AMin = πD²∕4 (6.5)
Assuming that the composite material has three phases and that the fibre is
flexible, the total stress or the stress of the composite is represented as:
(6.6)
The shear stress of the polymer phase:
(6.7)
where α is a model parameter attributed to anisotropic Brownian motion or anisotropic
hydrodynamic drag on the constituent polymer molecules. It is required that 0 < α < 1 as
discussed by Giesekus [1982].
The shear stress of the fibre phase:
(6.8)
For
98
(6.9)
The shear stress at the interphasial phase:
(6.10)
By rearrangement, we have:
(6.11)
Substituting equations 7, 9 and 11 into (6) and rearranging it, we arrive at:
(6.12)
Predicting the shear viscosity during the extrusion process and using the capillary
rheometer involves a coupled analysis of flow, shear rate, aspect ratio, and interphasial
effect. The resultant equation is highly nonlinear due to the viscosity, which depends on
the shear rate, fibre aspect ratio, and process parameters; these nonlinearities have been
solved by the Newton-Rapson method of numerical approach.
99
6.4 Materials and Methods
6.4.1 Materials
The matrix biopolymer bio-based Nylon 11, density 1.03, MFI 11, was supplied by
Arkema, France. Aspen HYP fibres were supplied by Tembec (Montreal, QC). The HYP
is the type used in wood-free printing and in writing-paper grades and multiple-coated
folding-board grades; fibre length is 0.230 to 0.85mm. Finally, the pulp-fibre length was
reduced by using a mechanical crib in order to investigate the aspect-ratio effect on the
rheological behavior of the HYP/PA11.
6.4.2 Experiment
The experiment was processed using a conical twin extruder. In the mixing method, the
HYP fibre was dried at 80˚C for 6 hours and then added to the corresponding PA11 and
well mixed before it was introduced to the extruder. The average temperature of the
barrel was 200˚C.
6.4.3 Rheological Measurements
The rheological measurements of the composites’ melt-flow properties were carried out
in a twin-bore Rosand Capillary Rheometer model RH2000. (The standard RH2000 range
supports temperatures from -40˚C to 500˚C. The standard maximum force applied is
12kN.) The composite samples for testing were cut into very small pieces, then placed
inside the barrel and forced down into the capillary with the plunger attached to the
moving cross-head. Representative steady-shear viscosity versus high shear rate is
presented in the figures below for HYP/PA11, which was processed at the average
100
extrusion temperature of 200˚C. The apparent viscosity of the sample was obtained from
steady-shear measurements for different fibre aspect ratios, with the rate ranging from 50
to 5000 S-1. The rheology viscosity data presented in this paper represent an average
value of three measurements.
6.5 Results and discussion
The novel nonlinear viscoelastic material model was explored in order to simulate the
nonlinear rheological behavior of HYP/PA11. In this study, both experimental and
predictive results on HYP/PA11 were investigated in order to understand the power,
validity, and capabilities of the novel rheological model developed. The detailed
rheological properties are the major focus of this work.
6.5.1 Experimental Results
Rheological characteristics of the polymer, fibre, and interphasial phases influence the
final characteristics of the resultant microstructure of composite materials; these
characteristics in turn affect the mechanical properties of a multiphase polymer
composite system. Experimentally, the apparent viscosity as function of the steady-shear
rate of HYP/PA11 at 200˚C is shown in Figure 6.2. (As noted, these results are the
average of three different experimental tests.)
101
Figure 6.2. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
As noted, the composite material used in the experimental study had a fibre length of
0.73 mm, and the experiment was conducted at 200˚C. The experimental results showed
that the apparent viscosity of HYP/PA11 composite decreases with increasing shear rate.
This decrease in the shear viscosity with the increase in shear rate corresponds to the
pseudoplastic fluid characteristic of the composites. This pseudoplastic behavior (also
referred to as shear-thinning behavior) plotted in Figure 6.2 is mainly influenced by the
orientation of the polymer molecules, the agglomeration of the flexible fibre, and the
entanglements within the polymer chains in the capillary rheometer. Due to the flexibility
of HYP, when shear is applied to the material, the orientation of the fibre changes its
configuration from rectangular to spherical; such modifications are produced in the fibre
length and the surface area of the fibre once the orientation is completed at high shear
rate. On the other hand, the chain agglomerations are produced simultaneously with
collapsing one chain onto another chain. The entanglement of the chains followed by
0
100
200
300
400
500
600
700
800
0 1000 2000 3000 4000 5000
Sh
ea
r vis
co
sit
y (
Pa
.S)
Shear rate (s-1)
102
agglomerations, as well as the entanglements within the chains, are caused by the
Brownian motions and low relaxation of HYP. The high shear-thinning behavior obtained
for HYP/PA11 can be also associated to the thermal degradation of HYP during the
rheological testing. The molten polymers tend to arrange themselves with their major
axes in the direction of shear, and thereby points of entanglement are reduced. As a
result, the viscosity decreases. In other words, in this case of non-Newtonian flow
behavior of polymer melts, the decrease in viscosity when the shear rate is increased by
applying load is associated with high shear-thinning behavior and with viscoelastic
characteristics of biocomposite materials. However, at very high shear rates (from 3000
to 5000 S-1), the molten HYP/PA11 showed a less restrained decrease in apparent
viscosity. Such high decrease in the shear viscosity is associated with high shear-thinning
behavior. This non-Newtonian behavior is associated with the alignment and orientation
of the fibre in the polymer chains and the effect of the fibre aspect ratio. At low as at high
shear rates, the formation of agglomerates is evident; therefore, HYP molecules are
completely oriented due to the good green-HYP dispersion in the bio-based PA11 matrix.
This means that the breakage of the fibre length allows the maintenance of an accurate
fibre-aspect ratio when the diameter of flexible HYP is kept unchangeable during the
process. The shorter length of the fibres will also support their alignment in the direction
of the flow, thus reducing the fibre-fibre collisions and leading to a larger decrease in the
apparent viscosity.
103
6.5.2 Variation of the viscosity with a function of shear rate of
HYP reinforced PA11 at various temperatures
The variation of the apparent viscosity in function of the shear rate of HYP-reinforced
PA11 at various temperatures was investigated; the rheological test results are presented
in the figure 6.3. The rheological conditions were kept constant while different tests were
run for 190˚C, 200˚C, and 210˚C.
Figure 6.3. Variation of the viscosity with a function of shear rate of HYP/PA11 at various temperatures.
0
200
400
600
800
1000
0 1000 2000 3000 4000 5000
Sh
ear
vis
co
sit
y (
Pa.s
)
Shear rate (s-1)
190 degree
200 degree
210 degree
104
The apparent viscosity of the HYP/PA11 depended on the rate of shear at which it was
measured and presented. The shearing effects decreased as the temperature increased;
that is, the HYP/PA11 became more non-Newtonian in the higher temperature region. At
higher temperature the reduction of the shear viscosity was more pronounced at
intermediate shear rate, while for 190˚C, the reduction of the shear viscosity reached a
maximum at higher shear rates (from 3000 to 5000 S-1). This characteristic is due to the
fact that the HYP-reinforced PA11 fibres were agglomerated and entangled at low
temperature and low and intermediate shear rate; this made flow deformation difficult.
(At this point this rheological behavior is called near-Newtonian.) At high shear rate, the
shearing effects increased while the effect of temperature was less pronounced, and flow
deformation was mostly dominated by the shearing effect. However, from 3000 to 5000
S-1 all the apparent viscosity variations in function of shear rates followed the same rate
of deformation for different temperature profiles; this corresponds to shear-thinning
behavior.
6.5.3 Effect of fibre content on the rheological behavior of
HYP/PA11
The effect of the fibre content on the rheological characteristics of the composite was
investigated. Figure 6.4 shows the experimental results for 10%, 20%, and 30%
HYP/PA11. These curves are typical of pseudoplastic materials, which show a decrease
in viscosity with increasing shear rate. At high fibre content, the material offers higher
shear viscosity even for high shear rate. In general, the incorporation of fibres in polymer
systems increases the viscosity and increases further with fibre content.
105
Figure 6.5. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
The difference is not very significant for 10% and 20% fibre for intermediate and high
shear rate. At low HYP content, the shear viscosity was expected to increase rapidly with
increasing concentrations of the fibres because of the rapidly increasing interactions
between particles as they become packed more closely to each other. Nevertheless, at
very high fibre content, random anisotropic structures of fibres in the polymer melt were
created. The increase in shear viscosity was found to be more predominant at lower shear
rates where fibre and polymer molecules were not completely oriented.
6.5.4 Effect of the fibre aspect ratio on the rheological property
The results from the study of the effect of the aspect ratio of flexible-pulp–fibre-
reinforced bio-based Nylon 11 are presented below in Figure 6.5.
0
200
400
600
800
1000
0 1000 2000 3000 4000 5000
Sh
ea
r vis
co
sit
y (
Pa
.s)
Shear rate (s-1)
10%HYP/PA11
20%HYP/PA11
30%HYP/PA11
106
At low fibre aspect ratio, the decrease in viscosity as a function of the shear rate was
greater for both low and high shear rate. Contrarily, at higher fibre-aspect ratio the shear
viscosity shows a moderate decrease for low and intermediate shear rate.
Figure 6.6. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
At low and intermediate shear rate, the viscosity curves are slightly decreased and the
distance between each viscosity curve remains large. However, at high shear rate the
viscosity plots are tightly close. This is because fibre agglomeration and entanglement are
not pronounced at high shear rate or frequency, due to the complete orientation of the
fibre and polymer molecules. Much as with high fibre content, the increase in shear
viscosity is found to be greater at lower shear rates, where fibre and polymer molecules
are not completely oriented.
0
200
400
600
800
1000
1200
1400
0 1000 2000 3000 4000 5000
Shear Rate (s-1)
Ar1 Ar3 Ar2
107
6.5.5 Predicted results
In this section, the numerical plot below shows the results of the mathematical predictive
model for representing the rheological characteristics of the material and the influence of
processing conditions on the material’s resultant microstructure.
To verify the applicability of the formulated viscoelastic-material model, certain
rheological tests were simulated and compared with the experimental data. The
comparisons show that the newly developed rheological viscoelastic-material model is
capable of simulating not only the dependence of shear viscosity on the material’s shear
rate, but also the variation in the slope of the material’s rheological responses. The shear
viscosity curve observed for HYP/PA11 is depicted in Figure 6.6 for 30% HYP fibre.
Figure 6.6 shows that HYP/PA11 biocomposite acts as a pseudoplastic fluid and that the
shear viscosity plots have a tendency to decrease for high shear rates. The various
assumptions considered in these models, in fact, were well fitted to the fluid’s actual
behavior. The fibre-agglomeration effect considered when the model was first conceived
is a primary contribution to the originality of this study. Accordingly, both predicted and
experimental results showed how the flexibility and entanglement of HYP fibre
contribute to the change in the fibre’s total surface area and the resultant influence on the
rheological characteristics of HYP/PA11composite.
108
Figure 6.7. Prediction of shear viscosity vs. shear rate of HYP/PA11at 200˚C
The entanglement and agglomeration of the fibre are manifested at high shear rate, where
the decrease in the fibre’s surface area increases the material’s shear viscosity and
consequently shows a non-Newtonian behavior. Figure 6.6 demonstrates that the
flexibility and diameter of the pulp fibres affects the viscoelasticity of the resultant
composite. Another observation is that the interphase interaction also influenced the
viscosity behavior with the changing shear rate of HYP/PA11, together with the change
in the aspect ratio, which was mostly present in the interphase. The interphase interaction
in pseudoplastic fluid behavior is significant in the study of the shear viscosity with the
increase in shear rate of high-fibre–content reinforced polymer composite. The observed
decrease in the shear viscosity of composite material from the plot map of the predicted
model is associated with the high degree of pseudoplasticity due to perfect dispersion of
high-yield pulp fibre into the composites; this gives rise to the good reinforcing effect of
HYP on PA11.
0
100
200
300
400
500
600
700
800
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Shear rate (s-1
)
Sh
ea
r v
isc
os
ity
(P
a.s
)
109
6.5.6 Modeling results versus experimental results
In this section, the comparisons between the theoretical predictions and experimental
measurements are detailed. In the experiments, the shear viscosity was determined to be a
function of high shear rate while polymer flow rate and processing temperature were kept
constant. Experimental and predictive results from HYP/PA1 are shown in Figure 6.7.
The average shear viscosity at the initial shear rate was about 800 Pa. s for 200˚C for low
fibre aspect ratio and about 1000 Pa. s for intermediate and high fibre aspect ratio, and at
this point the melt exhibited both experimentally and predictively a shift from Newton to
non-Newtonian rheological characteristics. However, as the shear increased, HYP/PA11
showed highly non-Newtonian behavior, corresponding to high shear-thinning behavior.
The accuracy of the predictive model derived from the experimental testing results and
used for calculating the previous shear viscosity was high. Experimentally and
mathematically, the shear viscosity as function of steady-shear rate of HYP/PA11 at
200˚C is shown in Figure 6.7 (where Exp. = experiment and M. = modeling): Ar1, Exp.
Ar2, and Exp. Ar3 represent the fibre aspect ratio 1, 2, and 3; and Ar1 < Ar2 < Ar3.
110
Figure 6.8. Shear viscosity vs. shear rate of HYP/PA11 at 200˚C.
Despite the discrepancy between the values for viscosity obtained by the predictive
model and those from experiments from 2000 to 2500 S-1, the agreement between the
model’s predictions and experimental data is remarkable given the simplicity and
accuracy of the model, the exactitude of the material properties and parameters, and the
fitness of the proposed boundary conditions. At both low and high shear rate, good
agreement is evident from the results; hence, this novel mathematical predictive
rheological model is well fitted to the extrusion of viscoelastic biocomposite materials.
From 3000 to 5000 shear rate, both experimental and predictive results show a regular
decrease in the shear viscosity, which may be due to the fact that fibre distribution and
orientation are complete, and that the viscosity is mainly dependent on the mobility of the
polymer chains in the composite structure. The model’s plot of shear viscosity versus
shear rate is evidence that the model is applicable to mathematically representing the
0
200
400
600
800
1000
1200
0 1000 2000 3000 4000 5000
Shea
r vi
sco
sity
(P
a.s)
Shear rate ( S-1)
Exp. Ar1 Exp. Ar2 Exp. Ar3
M.Ar1 M. Ar2 M. Ar3
111
rheological behavior of a variety of natural-fibre–reinforced thermoplastic viscoelastic
composite materials.
6.6 Conclusions
In this study, a novel rheological model for viscoelastic materials was developed in order
to predict rheological properties and then compared with experimental results on
HYP/PA11. This nonlinear rheological model was developed for constant material
parameters, simultaneously considering viscous, elastic, and inertial nonlinearities and
interphasial phase variables and parameters. The predictive results indicated that the
developed model well supports the determination of rheological characteristics of the
investigated material, such as viscosity and shear stress. In addition, the rheological
model was plausibly demonstrated and validated based on the experimental results of
shear viscosity versus shear rate. Both experimental and predictive results showed high
shear-thinning behavior in HYP/PA11 associated with a high degree of pseudoplasticity
due to the good dispersion of HYP into PA11 and the orientation of the flexible fibre
effects in the direction of the molten PA11. The model was validated for different fibre
aspect ratios and high shear rate, up to 5000 S-1. Due to its consistency and its high
predictive ability, the model may be applied in rheological studies and investigations of
viscoelastic materials, particularly in the automotive, construction, and aerospace
industries.
112
CHAPTER 7
Conclusions and Recommendations
7.1 Conclusions
Stress and viscosity relation of high-yield-pulp fibre–reinforced bio-based PA11
composite by both the extrusion process and the batch mixing process has been
studied.
Fibre burning was observed as the fibre content increase from 10% to 20 and 30% using
the extrusion process.
A co-factor, 3% inorganic salt such as lithium chloride, was used to decrease the melting
temperature of PA11 from 188 ˚C to 175˚C.
Addition of the co-factor, LiCl, increased shear viscosity and enabled low temperature
processing.
The viscosity of HYP/PA11 at high shear rate have been investigated and found to be
increased for higher fibre content and aspect ratio.
The rheological tests were performed at very high shear rate (5000/S) and at steady
state. With both processing techniques used and with the different fibre parameters,
shear-thinning behavior was present in all formulations used during this thesis research
study.
A novel mathematical model was developed to predict the rheological characteristics of
viscoelastic materials. The model was validated experimentally for established boundary
conditions and assumption.
113
Shear-thinning behavior was observed experimentally and mathematically. This shear-
thinning behavior or pseudoplastic property, which corresponds to non-Newtonian fluid
behavior, was more pronounced at high shear rate.
7.2 Scientific and engineering contribution of this thesis
During the past decade, scientific computation has become increasingly important in
applied mathematics, providing insight into many problems that would preclude a simple
analytical description. Since biomaterials exhibit a complicated viscoelastic behavior that
cannot be predicted using a Newtonian approach, and since they show both atomistic
effects and macroscopic ones, they are ideally suited to being studied by means of non-
Newtonian models. At the most general level, this thesis has made use of applied
mathematical models from a variety of different perspectives to examine aspects of flow
characteristics and the effect of the pulp-fibre aspect ratio under shearing effects that
would be difficult to address either by pure theory or by experiment.
The final objectives of this work were to develop lightweight composites from HYP-
fibre–reinforced bio-based nylon11 for automotive applications in order to decrease the
weight of vehicles and consequently decrease their fuel consumption and emissions.
7.3 Study limitations
Processing HYP-fibre–reinforced bio-based PA11 composite through the extrusion
process is challenging, and there is not much in the literature about this problem.
This model can be only used for multiphase flexible fibre reinforced thermoplastic
polymer composites.
114
Numerical simulations of the rheological-characteristic studies of flexible multiphase
natural-fibre–reinforced bio-based thermoplastic composites using the Navier-Stokes
governor equation have not been developed to help in the conception of the
mathematical model.
7.4 Recommendations
1. Further attempts should be made to accelerate the production of green composite fibres
from pulp-reinforced bio-based polyamide composite materials.
2. A more detailed study is required in order to better understand the formation
mechanism of HYP-fibre–reinforced PA11 composites.
3. The mechanical performance of high-yield-pulp–reinforced bio-based PA11
composites should be studied to better understand their applicability as structured
composite materials for the automotive and aerospace sectors.
4. The model should be more refined and simple in order to widen exploration for the
prediction of viscoelastic properties of composite materials.
5. Finally, the novel predicted model should be used for the simulation and optimization
natural fibre reinforced bio-based polymer materials processing.
115
7.5 Publications and Conferences
Articles published
Cherizol, R., Sain, M. and Tjong, J. (2015) Modeling the Rheological Characteristics of
Flexible High-Yield Pulp-Fibre-Reinforced Bio-Based Nylon 11 Bio-Composite.
Journal of Encapsulation and Adsorption Sciences, 5, 1-10.
http://dx.doi.org/10.4236/jeas.2015.51001.
Cherizol, R., Sain, M. and Tjong, J. (2015) Review of Non-Newtonian Mathematical
Models for Rheological Characteristics of Viscoelastic Composites. Green and
Sustainable Chemistry, 5, 6-14.
http://dx.doi.org/10.4236/gsc.2015.51002.
Cherizol, R., Sain, M. and Tjong, J. (2015) Evaluation of the Influence of Fibre Aspect
Ratio and Fibre Content on the Rheological Characteristic of High-Yield Pulp-
Fibre–Reinforced Polyamide 11 “HYP/PA11” Green Composite. Open Journal of
Polymer Chemistry, 5, 1-8. http://dx.doi.org/10.4236/ojpchem.2015.51001.
Cherizol, R., Sain, M. and Tjong, J. (2016) Effect of Lithium Chloride on the Fibre
Length Distribution, Processing Temperature and the Rheological Properties of
High-Yield-Pulp-Fibre–Reinforced Modified Bio-Based Polyamide 11
Composite.
Conference: Oral presentation
13th International Symposium of Bioplastics, Biocomposites and Biorefining (ISBB)
Guelph 2014.
116
Predicting the Rheological Behavior of Flexible Bleached Chemithermomechanical Pulp
Reinforced Nylon 11 Green Composite.
117
References
Abraham, T. N., & George, K. E. (2007). Short Nylon Fibre Reinforced PP: Melt
Rheology. Polymer-Plastics Technology and Engineering, 46(3), 321–325.
Ackley, D. E., & Rudder, S. L. (2004). Filler reinforced thermoplastic compositions and
process for manufacture. Michigan State University, United States, 1(61).
http://doi.org/US20100322867A1.
Adekunle, K., Cho, S.W., Patzelt, C., Blomfeldt, T., & Skrifvars, M. (2011). Impact and
flexural properties of flax fabrics and Lyocell fiber-reinforced bio-based
thermoset. Journal of Reinforced Plastics and Composites, 30(8), 685–697.
http://doi.org/10.1177/0731684411405874.
Agarwal, N. (2009). Transient Shear Flow Rheology of Concentrated Long Glass Fiber
Suspensions in a Sliding Plate Rheometer. Virginia Polyclinic Insitute and State
University, Master Thesis.
Altan, M.C., Advani, S.G., Guceri, S.I., Pipes, R.B. (1989). J. Rheol., 33:1129–1155.
Aminabhavi, T. M., Biradar, N. S., Cassidy, P. E., Texas, S., & Marcos, S. (1987).
Polymer Reviews Versatile Lightweight Polymer Composites. Journal of
Macromolecular Science , Part C, 37–41.
Ananinedjiwala, R. D., Blouw, S., Area, T. C. (2011). Composites from Bast Fibres
Prospects and Potential in the Changing Market Environment. Journal of Natural
Fibers, 37–41.
Ansari M., Alabbas A., Mitsoulis E, Hatzikiriakos, S.G. (2010). Entry flow of
polyethylene melts in tapered dies. Int. Polym. Proc.,25: 287–296.
118
Ansari, M., Hatzikiriakos, S. G., & Mitsoulis, E. (2011). Slip effects in HDPE flows.
Journal of Non-Newtonian Fluid Mechanics, 167-168, 18–29.
http://doi.org/10.1016/j.jnnfm.2011.09.007.
Anselm O.O., Joseph N. A., Nduji A.A. (2014). Characterization and comparison of
rheological properties of agro fiber filled high-density polyethylene bio-
composites. Open Journal of Polymer Chemistry, 4:12-19.
http://dx.doi.org/10.4236/ojpchem.2014.41002.
Argyris, J., St. Doltsinis, I., & Da Silva, V. D. (1991). Constitutive modelling and
computation of non-linear viscoelastic solids. Part I: Rheological models and
numerical integration techniques. Computer Methods in Applied Mechanics and
Engineering, 88(2), 135–163. http://doi.org/10.1016/0045-7825(91)90252-2.
Assie, A., E., Eltaher, M., & Mahmoud, F. (2011). Behavior of a viscoelastic composite
plates under transient load. Journal of Mechanical Science and Technology,
25(5), 1129–1140. http://doi.org/10.1007/s12206-011-0302-6.
Awal, A., Ghosh S., & Sain, M. (2010). Thermal properties and spectral characterization
of wood pulp reinforced bio-composite fibers. Journal of Thermal Analysis and
Calorimetry, 99(2):695- 701.
Awal, A., Ghosh, S., & Sain, M. (2009). Development and morphological
characterization of wood pulp reinforced biocomposite. Journal of Materials
Science, 44(11):2876-81.
Ayroud, A. (1983). M. High yield and very high yield pulping. D.V. Ingruber, M.J.
Kocurek, and A. Wong Eds., in “Pulp and Paper Manufacture,” Vol. 4, Sulfite
Science and Technology, CPPA, Montreal.
119
Bajpai, P. (2012). Brief description of the pulp and paper making process. Biotechnology
for Pulp and Paper Processing, 10.1007/978-1-4614-1409-4_2.
Banks, H.T., Hood, J.B., Medhin, N.G., and Samuels, J.R. (2006). A stick-slip/Rouse
hybrid model for viscoelasticity in polymers, Technical Report CRSC-TR06-26,
NCSU, Nonlinear Analysis: Real World Applications, 9;2128–2149.
Barkoula, N. M., Alcock, B., Cabrera, N. O., & Peijs, T. (2008). Fatigue properties of
highly oriented polypropylene tapes and all-polypropylene composites. Polymers
and Polymer Composites, 16(2), 101–113.
Barkoula, N. M., Garkhail, S. K., & Peijs, T. (2009). Effect of Compounding and
Injection Molding on the Mechanical Properties of Flax Fiber Polypropylene
Composites. Journal of Reinforced Plastics and Composites, 29(9), 1366–1385.
http://doi.org/10.1177/0731684409104465.
Batchelor, G. K. (1967). An Introduction to Fluid Dynamics, Cambridge Universisity
Press, London, United Kingdom.
Behzad, T. (2007). Loose fiber molding: cure and product design fundamentals: PhD
thesis, University of Toronto.
Bhatnagar, N., Bhardwaj, R., Selvakumar, P., & Brieu, M. (2007). Development of a
biaxial tensile test fixture for reinforced thermoplastic composites. Polymer
Testing, 26(2), 154–161. http://doi.org/10.1016/j.polymertesting.2006.09.007.
Bird, R.B., Armstrong, R.C., & Hassager, O. (1987). Dynamics of polymeric liquids.
Fluid Mechanics, vol. 1. Wiley, New York.
Botelho, E. C., & Rezende, M. C. (2009). Evaluation by free vibration method of
moisture absorption effects in polyamide/carbon fiber laminates. Journal of
120
Thermoplastic Composite Materials, 23(2), 207–225.
http://doi.org/10.1177/0892705709342614.
Botha, A. F., & Hunter, L. (2010). The measurement of wool fibre properties and their
effect on worsted processing performance and product quality. Part 1: The
objective measurement of wool fibre properties. Textile Progress, 42(4), 227–339.
http://doi.org/10.1080/00405167.2010.486932.
Bourmaud, A. & Baley, C. (2009). Rigidity analysis of polypropylene/vegetal fibre
composites after recycling. Polymer Degradation and Stability, 39:297-305.
Brandl, W., Marginean, G., Chirila, V., & Warschewski, W. (2004). Production and
characterisation of vapour grown carbon fiber/polypropylene composites. Carbon,
42(1), 5–9. http://doi.org/10.1016/j.carbon.2003.09.012.
Burghardt, W.R. & , Fuller, G.G. (1989). Note: End effects in flow birefringence
measurements. J. of Rheol., 33(5):771-779.
Byron R., Bird R., Robert C. Armstrong, and Ole H. (1987). Dynamics of Polymeric
Liquids, Volume 1: Fluid Mechanics, 2nd Ed. New York: John Wiley & Sons.
Chen, H., Ding, Y., & Tan, C. (2007). Rheological behaviour of nanofluids. New Journal
of Physics, 9(10), 367–367. http://doi.org/10.1088/1367-2630/9/10/367.
Chhhabra, R. P. (2010). Non-Newtonian Fluids: An Introduction, Department of
Chemical Engineering, Indian Institute of Technology Kanpur. SERC School-
cum-symposium on rheology of complex fluidss; 1–33.
Chhabra, R.P., Richardson, J.F. (2008). Non-Newtonian flow and applied rheology. 2nd
edn. Butterworth-Heinemann, Oxford.
121
Chopra, M.; and Larson, R. G. (2002). “Brownian Dynamics Simulations of Isolated
Polymer Molecules in Shear Flow near Adsorbing and Nonadsorbing Surfaces”,
Journal of Rheology, 46:4, 831.
Conshohocken, W. (2010). Standard Test Method for Melt Flow Rates of Thermoplastics
by Extrusion plastomer, 1–15. http://doi.org/10.1520/D1238-10.
Crochet M. J. & Legat V. (1992). J. Non-Newtonian Fluid Mech., 42:283-299.
Da Silva, L. J., Panzera, T. H., Velloso, V. R., Christoforo, A. L., & Scarpa, F. (2012).
Hybrid polymeric composites reinforced with sisal fibres and silica
microparticles. Composites Part B: Engineering, 43(8), 3436–3444.
http://doi.org/10.1016/j.compositesb.2012.01.026.
Dealy, J. & Wissbrun, K. (1999). Melt rheology and its role in plastics processing:
theory and applications. Dordrecht, The Netherlands: Kluwer Academic
Publishers.
Dealy, J.M. & , Wissbrun, K.F. (1990). Melt Rheology and its Role in Plastics Processing
–Theory and Applications, Van Nostrand Reinhold, New York.
Denn, M.M. (2008). Continuous drawing of liquids to form fibers. Annual Revue Fluid
Mech., 12:365–387.
Denn, M.M. (2008). Polymer Melt Processing: Foundations in Fluid Mechanics and Heat
Transfer. Cambridge University Press, New York.
Denn, M.M., Petrie, C.J.S., & Avenas P. (1975). Mechanics of steady spinning of a
viscoelastic liquid. AIChE Journal, 21:791–799.
Devereux, B.M. & , Denn, M.M. (1994). Frequency response analysis of polymer melts
spinning. Ind. Eng. Chem. Res., 33:2384–2390.
122
Dittenberg, D. B., & Gangarao, H. V. S. (2012). Critical review of recent publications on
use of natural composites in infrastructure. Composites Part A: Applied Science
and Manufacturing, 43(8), 1419–1429.
http://doi.org/10.1016/j.compositesa.2011.11.019
Dealy J, Wissbrun K. (1999). Melt rheology and its role in plastics processing: theory and
applications. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Deitzel, J.M., Kleinmeyer, J., Harris, D., Beck, Tan, N.C. (2001). The effect of
processing variables on the morphology of electrospun nanofibers and textiles.
Polymer;42(1):261-72.
Doraiswamy, D. (1998). The Origins of Rheology: A Short Historical Excursion. DuPont
Technologies, Experimental Station Wilmington, DE 19880-0334.
Eder, R.H.J., Winckler, S.J. (2001) Processing of advanced thermoplastic composites
using cyclic thermoplastic polyesters. In: Proceedings of 22nd SAMPE Europe
conference, Paris, France. p. 661–72.
Dominkovics, Z, Danyadi, L, & Pukanszky, B (2007). Surface modification of wood
flour and its effect on the properties of PP/wood composites. Composites Part A:
Applied Science and Manufacturing. 38(8):1893-901.
Doraiswamy, D. (1988). The origins of Rheology, Dupont Technologies, Wilmington,
DE 19880-0334.
Duc, A., Vergnes, B., & Budtova, T. (2011). Polypropylene/natural fibres composites:
Analysis of fibre dimensions after compounding and observations of fibre rupture
by rheo-optics. Composite A; 42: 1727-1737.
123
Eberle A. (2008). The dynamic behavior of a concentrated composite fluid containing
non-Brownian glass fibers in rheometrical flows. Blacksburg: PhD Thesis,
Virginia Tech.
Eberle A., Baird D., Wapperom P., Vélez-García G. (2009). Obtaining reliable transient
rheological data on concentrated short fiber suspensions using a rotational
rheometer. J. Rheol. 53(1049-1068).
Eberle, A., Baird, D., Wapperom, P. (2008). Rheology of non-Newtonian fluids
containing glass fibers: A review of experimental literature. Ind. Eng. Chem. Res,
47, (10), 3470- 3488.
Eberle, A., Baird, D., Wapperom, P., & Vélez-García, G (2009).Using transient shear
rheology to determine material parameters in fiber suspension theory. Journal of
Rheology, 53, 685.
Ellison, C.J., Phatak, A., Giles, D.W., Macosko, C.W., Bates, F.S. (2007). Melt blown
nanofibers: Fiber diameter distributions and onset of fiber breakup. Polymer.
48:3306–3316.
Ellyin, F., Vaziri, R., & Bigot, L. (2007). Predictions of two nonlinear viscoelastic
constitutive relations for polymers under multiaxial loadings, Polymer
Engineering & Science.
Elsevier (2009). The curauá challenge: optimizing natural fibres. Plastics, Additives and
Compounding, 11(5), 12–17. http://doi.org/10.1016/S1464-391X(09)70134-5.
Fengwei, X., Peter, J. H., Luc, A. (2012). Rheology to understand and optimize
processibility, structures and properties of starch polymeric materials. Progress in
Polymer Science. 595–623.
124
Fisher, R.J. & , Denn, M.M (1977). Mechanics of nonisothermal polymer melt spinning.
AIChE Journal. 23:23–28.
Fornes, T.D. and Paul, D.R. (2004). Structure and Properties of Nanocomposites Based
on Nylon-11 and -12 Compared with Those Based on Nylon-6, Macromolecules,
37(20): 76987709.
Gad-el-Hak, M. (1999). The Fluid Mechanics of Microdevices — The Freeman Scholar
Lecture. Journal of Fluids Engineering, 121(March), 5 – 33.
http://doi.org/10.1115/1.2822013.
Galante, S.R. (1991). An investigation of planar entry flow using a high resolution flow
birefringence method. Carnegie Mellon University, Pennsylvania (USA), PhD
thesis.
Gava, A. (2012). On the performance of a viscoelastic constitutive model for micro
injection moulding simulations. Express Polymer Letters, 6(5), 417–426.
http://doi.org/10.3144/expresspolymlett.2012.44.
George, J., Sreekala, M.S., & Thomas, S. (2001). A review on interface modification and
characterization of natural fiber reinforced plastic composites. Polym. Eng. Sci.
41(9):1471–85.
Giesekus, H. (1982). A simple constitutive equation for polymer fluids based on the
concept of deformation-dependent tensorial mobility. J. Non-Newtonian Fluid
Mech.11:69–109.
Gilles, H., Wagner, J., & Mount, E. (2004). Extrusion: The definitive extrusion
processing guide and handbook. Library of Congress Cataloging-in-Publication
Data. ISBN:0-8155-1473-5.
125
Gohil, P. & Shaikh, A. (2010). Analytical investigation and comparative assessment of
interphase influence on elastic behavior of fiber reinforced composites. Journal of
Reinforced Plastics and Composites. 5(29).
Goodwin, J.W., Hughes, R.W. (2008). Rheology for chemists: An introduction. The
Royal Society of Chemistry, Cambridge.
Graessley, W.W. (2004). Polymer liquids and networks: structure Structure and
properties. Garland Science, New York.
Grafe, T. & Graham, K. (2003). Polymeric nanofibers and nanofiber webs: A new class
of nonwovens. Int. Nonwovens J. 12:51–55.
Gu, R. & Kokta, B. (2010). Mechanical properties of PP composites reinforced with
BCTMP aspen fiber. J Reinf. Plast. Compos. 23.
Guo, R., Azaiez, J., & Bellehumeur, C. (2005). Rheology of fiber filled polymer melts:
Role of fiber-fiber interactions and polymer-fiber coupling. Polymer Engineering
& Science, 45(3), 385–399. http://doi.org/10.1002/pen.20285.
Han, C. (2007). Rheology and processing of polymeric materials, vol. 2. Oxford, UK.
Oxford University Press.
Herrera-Franco, P., & Valadez-González, A. (2004). Mechanical properties of continuous
natural fibre-reinforced polymer composites. Composites Part A: Applied Science
and Manufacturing, 35(3), 339–345.
http://doi.org/10.1016/j.compositesa.2003.09.012.
Higashitani, K. & , Pritchard, W. G. (1972). A kinematic calculation of intrinsic errors in
pressure measurements made with holes. Trans. Soc. Rheol.16:687.
126
Ho, M., Wang, H., Lee, J.-H., Ho, C., Lau, K., Leng, J., & Hui, D. (2012). Critical factors
in manufacturing processes of natural fibre composites. Composites Part B:
Engineering, 43(8), 3549–3562. http://doi.org/10.1016/j.composites
b.2011.10.001.
Huq, A. & Azaiez, J. (2006). Modeling of fiber-polymer coupling for suspensions of.
mono-modal fiber http://doi.org/10.1002/pc.
Huq, A.M.R. & , Azaiez, J. (2005). Effect of length distribution on the steady shear
viscosity of semiconcentrated polymer-fiber suspensions. Poly. Eng. Science.
Isaki, T., Takahashi, M., Takigawa, T., Masuda, T. (1991). Comparison between uniaxial
and biaxial elongational flow behavior of viscoelastic fluids as predicted by
differential constitutive equations. Rheol. Acta. 30:530–539.
James D. F. (2009). Boger fluids. Annual Review of Fluid Mechanics. 41:129–142.
Jarecki, L., .& Lewandowski, Z. (2009). Mathematical modelling of pneumatic melt
spinning of isotactic polypropylene. Part III. Computations of the process
dynamics. Fibres Text. East. Eur. 17:75–80.
Jarecki, L. & , Ziabicki, (2011). A. Mathematical modelling of pneumatic melt spinning
of isotactic polypropylene. Part II dynamic model of melt blowing. Fibres Text.
East. Eur.16:17–24.
Jayaraman K., Kotaki M., Zhang Y., Mo X., Ramakrishna S. (2004). Recent advances in
polymer nanofibers. J. NanoSci. Nanotechnoly. 52–65.
John, M., & Thomas, S. (2008). Biofibres and biocomposites. Carbohydrate Polymers,
71(3), 343–364. http://doi.org/10.1016/j.carbpol.2007.05.040.
127
Kari, S., Berger, H., Rodriguez, R.R., & Gabbert, U. (2005). Computational evaluation of
effective material properties of composites reinforced by randomly distributed
spherical particles. Compos. Struct. 71: 397–400.
Kaw, A. & , Besterfield, G. (1998). Effect of interphase on mechanical behavior of
composites. J. Eng. Mech. 117(11): 2641-2658.
Keshtkar, M.; Heuzey, M.; Carreau, P. (2009). Rheological behavior of fiber-filled model
suspensions: Effect of fiber flexibility. Journal of Rheology. 53-631(29).
Khor, C. Y., Ariff, Z. M., Ani, F. C., Mujeebu, M. A., Abdullah, M. K., Abdullah, M. Z.,
& Joseph, M. A. (2009). Three-dimensional numerical and experimental
investigations on polymer rheology in meso-scale injection molding.
International Communications in Heat and Mass Transfer, 8–16.
http://doi.org/10.1016/j.icheatmasstransfer.2009.08.011.
Kiriakidis, D.G., Park, H.J., Mitsoulis Mitsoulis, E., Vergnes B., Agassant, J.-F. (1989).
A study of the stress distribution in contraction flows of an LLDPE melt. J.our.
Non-Newtonian Fluid Mechanics. 47:339-356.
Krigstin, S. and M. Sain. 2006. “Characterization and potential utilization of recycled
paper mill sludge.” Pulp and Paper Canada 107(5):29–32.
Krutka, H.M., Shambaugh, R.L., & Papavassiliou, D. (2008). Effects of the polymer fiber
on the flow field from a slot melt blowing die. Ind. Eng. Chem. Res. 47:935–945.
Ku, T. & , Lin, C. (2005). Shear flow properties and melt spinning of thermoplastic
polyvinyl alcohol melts. Textile Research Journal. 75(9):681.
Kucharczyk, P., Otgonzu, O., Kitano, T., Gregorova, A., Kreuh, D., Cvelbar, U., Saha, P.
(2012). Correlation of Morphology and Viscoelastic Properties of Partially
128
Biodegradable Polymer Blends Based on Polyamide 6 and Polylactide
Copolyester. Polymer-Plastics Technology and Engineering. 51(14), 1432–1442.
http://doi.org/10.1080/03602559.2012.709296.
Kundu, P. K. (1990). Fluid Mechanics. Academic Press, NY.
La Mantia, F. P., & Morreale, M. (2011). Green composites: A brief review. Composites
Part A: Applied Science and Manufacturing, 42(6), 579–588.
http://doi.org/10.1016/j.compositesa.2011.01.017.
Lamnawar, K. &, Maazouz, A. (2008). Rheology at the interface and the role of the
interphase in reactive functionalized multilayer polymers in coextrusion process.
American Institute of Physics. 978: 7354-0549.
Landau, L. D., and Lifshitz, E. M. (1987). Fluid Mechanics, Second Edition, Pergamon
Press, Oxford, United Kingdom.
Larache, M., Agbossou, A., & Pastor, J. (1994). Role of interphase on elastic behavior of
composite materials: theoretical and experimental analysis. J. Compos. Mater.
28:1141–57.
Larson, R. G. (2005). The rheology of dilute solutions of flexible polymers: progress
Progress and problems. J. Rheology, 49 1–70.
Larson, R.G. (1999). The structure and rheology of complex fluids. New York: Oxford
University Press.
Lau, K., Ho, M., Au-Yeung, C., & Cheung, H. (2010). Biocomposites: Their
multifunctionality. Int. J. Smart and Nano Materials, 1(1), 13–27.
http://doi.org/10.1080/19475411003589780.
129
Le Moine, N., Oever, M.v.d, & Budtova, T. (2011). A statistical analysis of fibre size and
shape distribution after compounding in composites reinforced by natural fibres.
Composites Part A: Applied Science and Manufacturing. 42(10), 1542–1550.
http://doi.org/10.1016/j.compositesa.2011.07.012.
Le Moine, N., Oever, M.v.d, & Budtova, T. (2013). Dynamic and capillary shear
rheology of natural fiber-reinforced composites. Poly. Eng. Sc.
Letwimolnun, W., Vergnes, B., Ausias, B., Carreau, P.J. (2007). J. Non-Newtonian Fluid
Mech. 141- 167.
Li, J., & Renardy, Y. Y. (2000). Shear-induced rupturing of a viscous drop in a Bingham
liquid. Journal of Non-Newtonian Fluids Mechanics, 235–251.
Likhtman, A. E., & and Graham, R. S. (2003). Simple constitutive equation for linear
polymer melts derived from molecular theory: Rolie–Poly equation. Journal of
Non-Newtonian Fluid Mechanics, 114(1), 1–12. http://doi.org/10.1016/S0377-
0257(03)00114-9.
Liu, H., Wu, Q., & Zhang, Q. (2009). Preparation and properties of banana fiber-
reinforced composites based on high density polyethylene (HDPE)/Nylon-6
blends. Bioresource Technology, 100(23), 6088–97.
http://doi.org/10.1016/j.biortech.2009.05.076.
Liu, T., Lim, K.P., Tjiu, W.C., Pramoda, K.P. and Chen, Z.K. (2003). Preparation and
Characterization of Nylon11/Organoclay Nanocomposites, Polymer, 44(12):
35293535.
130
Liu, Y.J., Xu, N., & Luo, J.F. (2000). Modeling of interphases in fiber-reinforced
composites under transverse loading using boundary element method. J. Appl.
Mech. 67:41.
Lodge, A.S. (1998). Normal stress difference from hole pressure measurements. In:
Collyer and, Clegg DW, [editors]. Rheological measurements. London, UK:
Elsevier Applied Science. 345–82
Ludvik, C. N., Glenn, G. M., Klamczynski, a. P., & Wood, D. F. (2007). Cellulose
fiber/bentonite clay/biodegradable thermoplastic composites. Journal of Polymers
and the Environment, 15(4), 251–257. http://doi.org/10.1007/s10924-007-0072-5
Luo, X.-L. &, Tanner, R.I. (1987). A pseudo-time integral method for non-isothermal
viscoelastic flows and its application to extrusion simulation, Rheol. Acta.
26:499–507.
Mahmoud A., Savvas G. H., Evan M. (2012). Slip effects in HDPE flows. J. of Non-
Newtonian Fluid Mechanics. 167–168:18–29.
Malkin, A.Y., Isayev, A.I. (2006) Rheology: Concepts, methods and applications. Chem.
Tech. Toronto.
Marders, H., Vergnes, B., Demay, Y., Agassant, J.-F. (1992). Steady flow of a White-
Metzer fluid in a 2-D abrupt contraction: computation Computation and
experiments. J. Non-Newtonian Fluid Mech. 45:63-80.
Marynowski, K. (2006). Two-dimensional rheological element in modelling of axially
moving viscoelastic web. European Journal of Mechanics A/Solids. 25:729–744.
131
Mason, T. G. (2006). Rheology of soft materials: Outline affine and non-affine shear
deformations. Department of Chemistry and Biochemistry Department of Physics
and Astronomy California NanoSystems Institute UCLA; 1–16(2006).
Mitran, S.M. &, Yao, L. (2007). A double projection method for incompressible
viscoelastic flow. Technical report, Department of Mathematics University of
North Carolina, November 1, Chapel Hill, USA.
Mohanty, A. K., M. Misra & L. T. Drzal. (2002). “Sustainable bio-composites from
renewable resources: opportunities and challenges in the green materials world.”
Journal of Polymers and the Environment 10(1/2):19–26.
Mohssine, M., Yves, F., & Mario, F. (2007). A global rheological model of wood
cantilever as applied to wood drying. Wood Sci. Technol. 41:209–234.
Mostafaiyan, M., Khodabandehlou, K., & Sharif, F. (2004). Analysis of a viscoelastic
fluid in an annulus using Giesekus model. J. Non-Newtonian Fluid Mech. 118:49–
55.
Moutee, M., Fortin, Y., & Fafard, M. (2006). A global rheological model of wood
cantilever as applied to wood drying. Wood Science and Technology, 41(3), 209–
234. http://doi.org/10.1007/s00226-006-0106-5.
Mukhopadhyay, S., Deopura, B. L., & Alagiruswamy, R. (2003). Interface Behavior in
Polypropylene Composites. Journal of Thermoplastic Composite Materials,
16(6), 479–495. http://doi.org/10.1177/089270503038223.
Müller, S., Kästner, M., Brummund, J., & Ulbricht, V. (2011). A nonlinear fractional
viscoelastic material model for polymers. Computational Materials Science,
50(10), 2938–2949. http://doi.org/10.1016/j.commatsci.2011.05.011.
132
Nahar, S., Khan, R., Dey, K., Sarker, B., Das, K., & Ghoshal, S. (2011). Comparative
studies of mechanical and interfacial properties between jute and bamboo fiber-
reinforced polypropylene-based composites. Journal of Thermoplastic Composite
Materials, 25(1), 15–32. http://doi.org/10.1177/0892705711404725.
Nonaka, A., Trebotich, D., Miller, G.H., Graves, D.T., Colella Colella, P. (2009). A
higher-order upwind method for viscoelastic fluids. Comm. App. Math. and
Comp. Sci. 4:57–83.
Ojo, A., & Akanbi, C. T. (2006). Rheology of Soy-Ogi: effect of concentration and
temperature. Journal of Food Engineering, 72(2), 141–146.
http://doi.org/10.1016/j.jfoodeng.2004.11.030.
Oldroyd, J.G. (1950). On the formulation of rheological equations of state. Mathematical
and Physical Sciences. 200:523–541.
Oliveira, P. J. (2009). Alternative derivation of differential constitutive equations of the
Oldroyd-B type. Journal of Non-Newtonian Fluid Mechanics, 160(1), 40–46.
http://doi.org/10.1016/j.jnnfm.2008.11.013
Owens, R. G. & Phillips, T. N. (2002). Computational Rheology. Imperial College Press.
Panton, R. L. (1996). Incompressible Flow, Second Edition, Wiley-Interscience, NY.
Park, H., Lim, S., Smillo, F., Dealy, J., & Robertson, C. (2008). Wall slip and spurt flow
of polybutadiene. Journal of Rheology. 52, 1201.
Parlevliet, P. P., Bersee, H. E. N., & Beukers, A. (2006). Residual stresses in
thermoplastic composites—A study of the literature—Part I: Formation of
residual stresses. Composites Part A: Applied Science and Manufacturing, 37(11),
1847–1857. http://doi.org/10.1016/j.compositesa.2005.12.025.
133
Peltola, H., Madsen, B., Joffe, R., & Nättinen, K. (2011). Experimental study of fiber
length and orientation in injection molded natural fiber/starch acetate composites.
Advances in Materials Science and Engineering.
http://doi.org/10.1155/2011/891940.
Pervaiz, M. & Sain, M. (2003). Carbon storage potential in natural fibre composites.
Resources, Conservation and Recycling. 39(4):325-40.
Phan-Thien, N. & , Tanner, R. I. (1977). J. Non-Newtonian Fluid Mech. 2: 353-365.
Phan-Thien, N. (1978). Trans. Soc. Rheol., 22:259-283.
Plackett, D., Torgilsson, R., & Andersen, T. (2010). Influence of fiber type, fiber mat
orientation, and process time on the properties of a wood fiber/polymer
composite. International Journal of Polymeric Materials. 51:1005-1018.
Qiao, X., Li, W. E. I., Watanabe, H., Sun, K., & Chen, X. (2009). Rheological Behavior
of Biocomposites of Silk Fibroin Fiber and Poly (e-caprolactone): Effect of Fiber
Network, 1957–1970. http://doi.org/10.1002/polb.
Ramani, K., Bank, D., & Kraemer, N. (1995). Polymer Composites. 16, 258-267.
http://doi.org/10.1016/j.progpolymsci.2011.07.002.
Rao, M.A. (2007). Rheology of food gum and starch dispersions. In: Rao, M.A. [, editor].
Rheology of fluid and semisolid foods: Pprinciples and applications. New York,
NY: Springer. 174–203.
Rilsan Polyamide 11 Technical Data Sheet, Arkema Inc., France. (2015).
Sadeghian, N. &, Golzar, M. (2008). PVT Measurement system for wood plastic
composite melt in an extrusion process. J. Reinf. Plast. Compos. 27: 739–750.
134
Saheb, D.N., Jog, J.P. (1999). Natural fiber polymer composites: A review. Advances in
Polymer Technology. 18(4):351-63.
http://doi.org/10.1016/j.compositesb.2011.10.001.
Sahoo, S., Misra, M., & Mohanty, A. K. (2011). Enhanced properties of lignin-based
biodegradable polymer composites using injection moulding process. Composites
Part A: Applied Science and Manufacturing, 42(11), 1710–1718.
http://doi.org/10.1016/j.compositesa.2011.07.025.
Saravana Bavan D., & Mohan Kumar, G. (2010). Potential use of natural fiber composite
materials in India. Journal of Reinforced Plastics and Composites, 29(24), 3600
Sepehr, M., Ausias, G., & Carreau, P. (2004). Rheological properties of short fiber filled
polypropylene in transient shear flow. J. Non-Newt. Fluid Mech. 123: 19-32.
Segerholm, B. K., Walkenström, P., Nyström, B., Wålinder, M. E. P., & Larsson Brelid,
P. (2007). Micromorphology, moisture sorption and mechanical properties of a
biocomposite based on acetylated wood particles and cellulose ester. Wood
Material Science and Engineering, 2(3-4), 106–117.
http://doi.org/10.1080/17480270801906175.
Selvakumar, P., & Bhatnagar, N. (2009). Studies on polypropylene/carbon fiber
composite foams by nozzle-based microcellular injection molding system.
Materials and Manufacturing Processes, 24(5), 533–540.
http://doi.org/10.1080/10426910902742738.
Sengupta, R., Chakraborty, S., Bandyopadhyay, S., Dasgupta, S., Mukhopadhyay, R.,
Auddy, K., & Deuri, a S. (2007). A short review on rubber / clay nanocomposites
135
with emphasis on mechanical properties. Engineering, 47, 21–25.
http://doi.org/10.1002/pen.
Sepehr M., Ausias G., & Carreau P. (2004). Rheological properties of short fiber filled
polypropylene in transient shear flow. J. Non-Newt. Fluid Mech. 123: 19-32.
Sepehr, M., Carreau, P. J., Moan, M., and Ausias, G. (2004). Rheological properties of
short fiber model suspensions, J. Rheol. 48, 1023–1048.
Severini, F., Formaro, L., Pegoraro, M., & Posca, L. (2002). Chemical modification of
carbon fiber surfaces. Carbon, 40(5), 735–741. http://doi.org/10.1016/S0008-
6223(01)00180-4
Sherman, F. S. (1990). Viscous Flow. McGraw-Hill, NY.
Sin, L.T., Rahmat, A.R., Rahman, W., Sun, Z.Y., Samad, A.A.(2010). Rheology and
thermal transition state of polyvinyl alcohol–cassava starch blends. Carbohydr
Polym; 737–9.
Snijkers, F., D’Avino, G., Maffettone, P. L., Greco, F., Hulsen, M.A., & Vermant, J.
(2011). Effect of viscoelasticity on the rotation of a sphere in shear flow. Journal
of Non-Newtonian Fluid Mechanics, 166(7-8), 363–372.
http://doi.org/10.1016/j.jnnfm.2011.01.004.
Sobczak, L., Lang, R. W., & Haider, A. (2012). Polypropylene composites with natural
fibers and wood: General mechanical property profiles. Composites Science and
Technology, 72(5), 550–557. http://doi.org/10.1016/j.compscitech.2011.12.013.
Soulages, J., Schweizer, T., Venerus, D. C., Kröger, M., & Öttinger, H. C. (2008).
Lubricated cross-slot flow of a low density polyethylene melt. J. Non-Newtonian
Fluid Mech. 154(1), 52–64. http://doi.org/10.1016/j.jnnfm.2008.02.007.
136
Sperling, L.H. (2006). Multicomponent polymeric material. In Introduction to Physical
Polymer Science, Wiley, 702.
Switzer, L..& Klingenberg, D. (2003). Rheology of sheared flexible fiber suspensions via
fiber- level simulations. Journal of Rheology, 47, 759.
Somwangthanaroj, A. (2010). Rheology and polymer characterization. Powerpoint
presentation. http://pioneer.netserv.chula.ac.th/~sanongn1/course.html.
Stamboulis, A., Baillie, C. A., Garkhail, S. K., van Melick, H. G. H. and Peijs, T. (2000).
Environmental Durability of Flax Fibers and Their Composites Based on
Polypropylene Matrix, Applied Composite Materials, 7 : 273–294.
Stewart, R. (2011). Rebounding automotive industry welcome news for FRP. Reinforced
Plastics, 55(1), 38–44. http://doi.org/10.1016/S0034-3617(11)70036-4.
Tadmor, Z.& Gogos, C. G. (1979). Principles of Polymer Processing, John Wiley & Son,
New York, NY.
Takase, S. Shiraishi, N. S. (1989). Journal of Applied Polymer Science, 37, 645-659.
Talreja, R. & Manson, J.A. (2001). Polymer matrix composites. Oxford: Elsevier Science
Ltd.
Tan, D.H., Zhou, C., Ellison, C.J., Kumar, S., Macosko, C.W., Bates, F.S. (2010).
Meltblown fibers: Influence of melt viscosity and elasticity on the diameter
distribution of melt blown fibers. J. Non-Newtonian Fluid Mech. 165:892–900.
Tanner, R.I. (2000). Engineering Rheology, second ed., Oxford University Press, Oxford.
Taylor, P. (2006). Engineering the Interface in Composites and Bonded Components
Engineering the Interface in Composites and Bonded Components. The Journal of
adhesion, 37–41.
137
Taylor, P., Zhu, Y., Wilding, M. A., & Mukhopadhyay, S. K. (2011). Fibre-on-fibre
Abrasion in Oxidised Polyacrylonitrile Fibre-on-fibre Abrasion in Oxidised
Polyacrylonitrile. Journal of the textile Institute, 37–41.
Technical Association of the Pulp and Paper Industry. (2007). Forming hand sheets for
physical tests of pulp. TAPPI Test Methods, TAPPI, Norcross, GA.
Thomen, H. (2001). Modeling the physical processes in natural fiber composites during
batch and continuous pressing. Thesis. Oregon State University.
Thumm A. & Dickson A. (2013). The influence of fibre length and damage on the
mechanical performance of polypropylene/wood pulp composites. Composite A,
46: 45-52.
Tong, X., Liu, C., Cheng, H-M., Zhao, H., Yang, F., Zhang, X. (2004). Surface
modification of single-walled carbon nanotubes with polyethylene via in situ
Ziegler–Natta polymerization. J. Appl. Polym. Sci.,92(6):3697–700.
Trebotich D., Colella P., Miller G.H. (2005). A stable and convergent scheme for
viscoelastic flow in contraction channels. J. Comput. Phys., 205:315–342.
Tucker, C. L. &, Advani, S. G. (1994). Processing of short fiber system: Flow and
rheology in polymer composites manufacturing. Elsevier, Amsterdam, pp.147-
202.
Tuna N. Y. & Finlayson, B. (1984). On the description of the orientation state for fiber
suspensions in homogeneous flows. J. Rheology, 2879:93.
Uhlherr P.H.T., Guo J., Zhang, X.M., Zhou J.Z.Q., & Tiu, C. (2005). The shear-induced
solid-liquid transition in yield stress materials with chemically different
structures. J. Non-Newt. Fluid Mech., 125:101-119.
138
Valenti, B., Bianchi, E., Greppi, G., & Ciferri, a. (1973). Bulk properties of synthetic
polymer-inorganic salt systems. Melting behavior of salted poly (caproamide). J.
Phys. Chem., 77(12767), 389–395.
http://pubs.acs.org/doi/abs/10.1021/j100622a017.
Van Rijswijk, K. & Bersee, H.E.N. (2007). Reactive processing of textile fiber-reinforced
thermoplastic composites – An overview. Composites Part A: Applied Science
and Manufacturing, 38(3), 666–681.
http://doi.org/10.1016/j.compositesa.2006.05.007.
Wang, J., & Birgisson, B. (2007). A time domain boundary element method for modeling
the quasi-static viscoelastic behavior of asphalt pavements. Engineering Analysis
with Boundary Elements, 31(3), 226–240.
http://doi.org/10.1016/j.enganabound.2006.09.007.
Wang, X., Chen, L., Li, X., Xie, F., Liu, H., and Yu, L. (2011). Thermal and rheological
properties of breadfruit starch. J. Food Sci., 76:E55–61.
Willett J. L., Asberg B. K., Swanson C.L. (1995). Rheology of thermoplastic starch:
effects of temperature, moisture content, and additives on melt viscosity. Pol.
Eng. Sci.,35:202–10.
Xie, F., Halley, P. J., & Avérous, L. (2012). Rheology to understand and optimize
processibility, structures and properties of starch polymeric materials. Progress in
Polymer Science, 37(4), 595–623.
Xiuying Q., Wei L., Hiroshi W., Kang S., Xiaodong, C. (2009). Rheological Behavior of
Biocomposites of Silk Fibroin Fiber and Poly (e-caprolactone): Effect of Fiber
Network. Wiley InterScience.
139
Xu, C., Jia, Z., Wu, D., Han, Q. and Meek, T. (2006). Fabrication of Nylon-6/Carbon
Nanotube Composites, J. Elect. Mater., 35(5): 954957.
Yarin, A.L., Sinha-Ray, S., & Pourdeyhimi, B. (2010). Melt blowing: II—linear and
nonlinear waves on viscoelastic polymer jets. Phys. Fluids, 108:034913.
doi.org/10.1063/1.3457893doi.org/10.1063/1.3457893.
Yeh, J.R. (1992). The effect of interphase on the transverse properties of composites. Int
J Solid Stress, 29:2493–502.
Yi Zhuang Xu et. al. (2000). Journal of. Applied Polymer Science, 77: 2600 - 2685.
Ying, Q., Wei, L., Watanabe, H., Sun, K., Chen, X. (2009). Rheological Behavior of
Biocomposites of Silk Fibroin Fiber and Poly (e-caprolactone): Effect of Fiber
Network. Wiley InterScience.
Young, R. J., & Montes-Moran, M. A. (2002). Raman spectroscopy study of high-
modulus carbon fibres; effect of plasma-treatment on the interfacial properties of
single-fibre – epoxy composites Part II: Characterisation of the fibre – matrix
interface. Carbon, 40, 857–875.
Young, R. J., & Montes-Moran, M. A. (2002). Raman spectroscopy study of high-
modulus carbon fibres; effect of plasma-treatment on the interfacial properties of
single-fibre–epoxy composites Part II: Characterisation of the fibre–matrix
interface. Carbon, 40, 857–875.
Zhang Y., Lim C.T., Ramakrishna S., Huang Z.M. (2005). Recent development of
polymer nanofibers for biomedical and biotechnological applications. J. Mater.
Sci. Mater. Med.,16:933–946.
http://pioneer.netserv.chula.ac.th/~sanongn1/course.html.
140
Zhang, X., Yang, G. and Lin, J. (2006). Synthesis, rheology, and morphology of nylon-
11/ layered silicate nanocomposite, J. Polym. Sci. Part B: Polym. Phys., 44(15):
21612172.
Zhou, C. & , Kumar, S. (2010). Thermal instabilities in melt spinning of viscoelastic
fibers. J. Non-Newtonian Fluid Mech., 165: 879–891.
http://doi.org/10.1080/03602550601155880.
Zhou, C., Tan, D. H., Janakiraman, A. P., & Kumar, S. (2011). Modeling the melt
blowing of viscoelastic materials. Chemical Engineering Science, 66(18), 4172–
4183. http://doi.org/10.1016/j.ces.2011.05.051.