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Analysis of Natural Fiber Orientation in Polymer Composites Produced by Injection Molding Process
by
Rajasekaran Karthikeyan
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy
Faculty of Forestry University of Toronto
© Copyright by Rajasekaran Karthikeyan 2017
II
Analysis of Natural Fiber Orientation in polymer composites
Produced by Injection Molding Process
Rajasekaran Karthikeyan
Doctor of Philosophy
Faculty of Forestry
University of Toronto
2017
Abstract
Short fiber reinforced polymer composites (SFRPC) produced by injection molding process have
established a commercial utilization in all sectors due to low cost and lower weight of the
components. The polymers are reinforced with natural fibers to improve their performance. The
orientation of short natural fibers in the polymer composite influences the mechanical
performance. This research thus focused on the prediction of natural fiber orientation using a
theoretical model and then studied the mechanical properties of natural fiber reinforced
composites. The theoretical model was derived by incorporating the shape factor of natural fibers
into the angular velocity of the fluid element in order to predict the orientation during the
injection molding process. The ANSYS- FLUENT software was used to find the velocity
distribution in the fluid domain, from which the angular velocity of the fluid element and the
orientation angle were found numerically. This numerical orientation result was then compared
to the experimental data. The orientation angle of rigid particles rotating at a fixed distance from
III
the inlet gate was measured by an experimental method where a transparent cavity was filled
through an injection molding process
An experimental setup was developed to study the orientation behavior of short natural fibers in
the flowing viscous fluid. Two experimental case studies were conducted to validate the
orientation angles of natural fibers using the derived equation. The case study was performed in
two molds with one of varying section, and another wide area section and the experimental
orientation angles were compared with the numerical predictions. The numerical results of the
flow front and velocity distribution obtained from simulation software were compared with
digitized images of the flow front from the experimental method. The natural fibers have
improved the strength and modulus of the composites. The composite specimens were produced
for different compositions of sisal fiber using compression-molding process and the mechanical
properties of the composites were studied. An increase in tensile strength, tear strength, and
improved hardness was observed in sisal fiber composites. The morphological study using X-ray
tomography and Scanning electron microscopy (SEM) has shown defects, the fiber orientation,
debonding, the fractography and the interfacial adhesion of the fiber and matrix.
IV
Acknowledgments
I would like to express my sincere gratitude and appreciation to my supervisors Dr. M.Sain, and
Dr. S.K.Nayak for their guidance, and relentless support throughout this research thesis . I also
thank my co-supervisor Dr. Jimmi Tjong from M/s Ford motor, Windsor, for his support to
initiate this research. I sincerely acknowledge my committee members, for providing their
valuable suggestions regarding my research work.
I would like to thank Shri. Joseph Bensingh for his constructive support throughout the study and
my heartfelt thanks to the supporting staff and officers of Advance Research School for
Technology and Product Stimulation - ARSTPS Chennai, for their help in conducting the
research. I would like to thank the technical officer, Senior Technical officer, Manager and
supporting staff of Central Institute of Plastics Engineering and Technology - CIPET Chennai,
for helping in the utilization of equipment and continuous support towards my research.
I would like to thank Green Transportation Network (GREET) CoE Project, for the financial
support provided by Department of Chemicals and Petrochemicals (DCPC), Govt. of India and
the Centre for Biocomposite and Biomaterial Processing (CBBP), University of Toronto.
Finally, I would also like to thank my family members and friends for continuous and
uncompromising moral support and patience during my research work.
V
Table of Contents
Abstract ........................................................................................................................................... II
Acknowledgments......................................................................................................................... IV
Table of Contents ............................................................................................................................ V
List of Tables ................................................................................................................................ XI
List of Figures .............................................................................................................................. XII
Chapter 1 : Introduction ..............................................................................................................1
1.1 Overview ..............................................................................................................................1
1.2 Outline of thesis ...................................................................................................................3
Chapter 2 : Literature review and Background...........................................................................6
2.1 Background ..........................................................................................................................6
2.1.1 Natural fiber .............................................................................................................6
2.1.2 Structure of a Natural fiber ......................................................................................7
2.1.3 Characteristic of Natural fiber .................................................................................9
2.1.4 Measurement of shape factor .................................................................................10
2.2 Matrix .................................................................................................................................12
2.3 Flow characteristics for injection process ..........................................................................13
2.3.1 Governing equations ..............................................................................................13
2.3.2 Polymer Viscosity ..................................................................................................14
2.3.3 Theory of fluid flow ...............................................................................................15
2.3.4 Laminar flow ..........................................................................................................16
2.3.5 Steady and un-steady flow .....................................................................................17
2.3.6 Uniform and Non-Uniform Flow ...........................................................................17
2.3.7 Fountain flow .........................................................................................................18
2.4 Basic equation of fluid flow ...............................................................................................18
VI
2.4.1 Flow Kinematics ....................................................................................................19
2.4.2 Newton’s law of motion.........................................................................................19
2.4.3 Curvilinear motion .................................................................................................19
2.4.4 Relative velocity and acceleration .........................................................................20
2.4.5 Principle of linear impulse and momentum ...........................................................20
2.5 Fiber Orientation Distribution............................................................................................21
2.5.1 Orientation in composites ......................................................................................23
2.5.2 Orientation Pattern .................................................................................................24
2.5.3 Fiber aspect ratio ....................................................................................................27
2.5.4 Fiber attrition .........................................................................................................28
2.5.5 Fiber orientation in mould cavity ...........................................................................29
2.5.6 Effect of cavity thickness on orientation ...............................................................32
2.5.7 Convergent and divergent effects ..........................................................................33
2.6 Factors affecting composites property ...............................................................................34
2.6.1 Voids in composites ...............................................................................................34
2.6.2 Moisture absorption ...............................................................................................35
2.6.3 Natural fiber geometry: ..........................................................................................35
2.6.4 Fiber critical length: ...............................................................................................36
2.7 Mathematical model for orientation ...................................................................................36
2.7.1 Assumptions for fiber orientation ..........................................................................36
2.7.2 Existing model for fiber orientation .......................................................................38
2.7.3 Experimental method available for predicting orientation ....................................42
2.7.4 Destructive method ................................................................................................43
2.7.5 Non destructive method .........................................................................................43
2.8 Problem statement ..............................................................................................................44
VII
2.9 Hypothesis..........................................................................................................................45
2.10 Research Objectives ...........................................................................................................45
2.11 Scope of the research work ................................................................................................45
Chapter 3 : Mathematical Model ..............................................................................................47
3.1 Methodology ......................................................................................................................47
3.1.1 Fundamental theory for flow .................................................................................47
3.1.2 Characteristics of Steady flow ...............................................................................48
3.1.3 Assumption made for natural fiber orientation ......................................................49
3.1.4 Fluid domain ..........................................................................................................49
3.1.5 Velocity distribution in fluid domain .....................................................................50
3.1.6 Derivation for angular velocity of fluid elements ..................................................52
3.1.7 Aspect ratio ............................................................................................................55
3.1.8 Shape factor of natural fiber ..................................................................................56
3.1.9 Velocity distribution on natural fiber .....................................................................56
3.1.10 Curling factor .........................................................................................................58
3.1.11 Kinematic rotation of fiber.....................................................................................60
3.1.12 Limitation of the Mathematical model ..................................................................62
Chapter 4 : Computational and Experimental Method .............................................................63
4.1 Method ...............................................................................................................................63
4.1.1 Design of mold cavity ............................................................................................63
4.1.2 Mold cavity for case study .....................................................................................65
4.2 Computational method .......................................................................................................67
4.2.1 Computation method for fiber orientation .............................................................67
4.2.2 CAD model for the Case studies ............................................................................76
4.2.3 Flow analysis in Fluent ..........................................................................................77
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4.2.4 Flow front simulation .............................................................................................80
4.2.5 Numerical approach for orientation .......................................................................81
4.3 Experimental method .........................................................................................................84
4.3.1 Experimental procedure .........................................................................................85
4.3.2 Digital Imaging process for particle in fixed position ...........................................86
4.3.3 Digital imaging process for Case-1........................................................................87
4.3.4 Digital imaging process for Case-2........................................................................89
Chapter 5 : Result and Discussion ............................................................................................92
5.1 Flow Behavior of Viscous Fluid and Orientation of Natural Fiber in the Cavity:
Numerical analysis .............................................................................................................92
5.1.1 Velocity distribution ..............................................................................................92
5.1.2 Flow front comparison ...........................................................................................94
5.1.3 Numerical result of orientation ..............................................................................95
5.1.4 Experimental validation of orientation ..................................................................96
5.2 Flow Behavior of silicone fluid and orientation of Natural Fibers in a Cavity: An
Experimental Method.........................................................................................................97
5.2.1 Velocity distribution ..............................................................................................97
5.2.2 Flow front comparison ...........................................................................................98
5.2.3 Experimental validation of orientation ..................................................................99
5.3 Conclusions ......................................................................................................................101
Chapter 6 : Mechanical Properties and morphological study of Sisal Fiber reinforced
Silicone Composites ................................................................................................................103
6.1 Introduction ......................................................................................................................103
6.2 Experimental ....................................................................................................................105
6.2.1 Materials ..............................................................................................................105
6.2.2 Fiber treatment .....................................................................................................106
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6.2.3 Compounding process and specimen preparation................................................107
6.3 Mechanical Characterization ...........................................................................................107
6.3.1 Tensile test ...........................................................................................................107
6.3.2 Hardness ...............................................................................................................108
6.3.3 Swelling test .........................................................................................................108
6.3.4 Morphological Study ...........................................................................................109
6.4 Results and Discussion ....................................................................................................110
6.4.1 Tensile strength and tensile modulus of the composites by injection molding
process..................................................................................................................110
6.4.2 Comparison of the composite strength by injection and compression process ...111
6.4.3 Tensile Strength of Composites by compression molding process .....................112
6.4.4 Tensile Modulus of the composite by compression molding process .................114
6.4.5 Hardness of Composites ......................................................................................115
6.4.6 Tear Strength ........................................................................................................116
6.4.7 Cross-Linking Density .........................................................................................117
6.4.8 Effect of Fiber Length on Mechanical Property ..................................................119
6.4.9 Morphological Analysis .......................................................................................120
6.4.10 SEM Analysis ......................................................................................................126
6.5 Conclusions ......................................................................................................................129
Chapter 7 : Conclusions and Recommendation ......................................................................130
7.1 Conclusion .......................................................................................................................130
7.2 Study Limitations and recommendations.........................................................................134
7.3 Scientific and engineering contributions of the work ......................................................135
References ....................................................................................................................................136
Appendices ...................................................................................................................................158
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Appendix A: ............................................................................................................................158
Appendix C .............................................................................................................................159
Appendix D: ............................................................................................................................160
Appendix E: ............................................................................................................................161
Appendix F: ............................................................................................................................166
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List of Tables
Table 4.1 : Angular velocity of fluid element at 20 mm from inlet for cavity filling time 8
s .................................................................................................................................. 74
Table 4.2 : Orientation angle of rigid particle at 20 mm from inlet for cavity filling time 8 s ..... 74
Table 4.3 : Angular velocity of fluid element at 20 mm from end for cavity filling time 8 s ...... 75
Table 4.4 : Orientation angle of rigid particle at 20mm from end for cavity filling time 8 s ....... 76
Table 4.5 : Angular velocity of fluid element for Fiber particle P1, P2, P3 complete filling
time 8 s for Case-1 ..................................................................................................... 82
Table 4.6 : Predicted angle of orientation for fiber particles P1, P2, P3 for complete filling
of cavity in 8 s for Case-1 .......................................................................................... 82
Table 4.7 : Angular velocity of fluid element for Fiber particle P1, P2, P3 for complete
filling time 8 s for Case-2 .......................................................................................... 83
Table 4.8 : Predicted angle of orientation for fiber particles P1, P2, P3 for complete filling
of cavity in 8 s for case-2 ........................................................................................... 83
Table 5.1: Numerical and experimental orientation angle of particles at 20 mm from inlet
gate. ............................................................................................................................ 97
Table 5.2 : Numerical and experimental orientation angle of particles at 20 mm from end
of the cavity. ............................................................................................................... 97
Table 5.3 : Comparison of orientation angles obtained experimentally and numerically for
Case-1....................................................................................................................... 100
Table 5.4 : Comparison of experimental orientation angle and numerical orientation angles
for Case-2. ................................................................................................................ 101
Table 6.1:Tensile Properties of Untreated and Treated Fiber Reinforced Composites .............. 113
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List of Figures
Figure 2.1: Physical structure of natural fiber ................................................................................ 8
Figure 2.2: Kink and curl in natural fiber ....................................................................................... 9
Figure 2.3: a) Fiber segment before drying , b) Fiber segment after drying ................................. 10
Figure 2.4: Curling effect in fiber ................................................................................................. 11
Figure 2.5: Fluid flow in layer over flat surface ........................................................................... 15
Figure 2.6 : Streamlines of fountain flow and flow front ............................................................. 18
Figure 2.7: Particle position and motion in vector. ....................................................................... 20
Figure 2.8: Planar motion of Particle in translational and rotational ............................................ 21
Figure 2.9: Single fiber orientation angles .................................................................................... 22
Figure 2.10: Orientation of fiber in skin, core layers of composites. ........................................... 24
Figure 2.11: Orientation of short fiber a) 3D- random isotropic orientation, b) Planar
random c) Aligned ................................................................................................... 25
Figure 2.12: Pictorial representations of fiber orientation ............................................................ 26
Figure 2.13: Fiber distribution in transverse tangential to direction of flow front ....................... 27
Figure 2.14: Fountain Flow, flow front and orientation ............................................................... 31
Figure 2.15: Pinpoint gate and linear gate for analysis of fiber orientation (G.lielens 1999) ...... 32
Figure 2.16: Convergent and divergent zone in mold ................................................................... 33
Figure 2.17: Mathematical model for fiber orientation ................................................................ 40
Figure 2.18: Single fiber P in shear flow ...................................................................................... 41
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Figure 3.1: 2D domain of mold cavity, fiber path line ................................................................. 50
Figure 3.2: (a) 2D Cross sectional of viscous fluid domain (Silicone polymer) with non-
uniform velocity distribution and flow front; (b) Fiber orient due to the effect
of shear .................................................................................................................... 51
Figure 3.3: Fluid element in square shape rotation along flow field ............................................ 52
Figure 3.4: (a) Fluid element at t = t1 s, (b) Fluid element oriented at t = t2 s ............................. 53
Figure 3.5: Natural fiber shapes .................................................................................................... 56
Figure 3.6: a) Velocities distribution over 2D cylindrical shape fiber (b) Induced couple
and orientation of fiber ............................................................................................ 57
Figure 3.7: (a) Non uniform velocities distribution on curling fiber, (b) Velocity
distribution is uniform in horizontal and vertical side ............................................. 58
Figure 3.8: (a) Curliness of fiber fit to sphere, (b) Fiber segment ................................................ 59
Figure 3.9: Angular rate of rotation of single particle ................................................................. 60
Figure 3.10: Kinematic rotation of particle with respect to relative velocity ............................... 61
Figure 4.1: 3D model of mold cavity ............................................................................................ 64
Figure 4.2: Cylindrical particles fixed in Mold cavity .................................................................. 65
Figure 4.3: Transparent Cavity for Case 1 .................................................................................... 66
Figure 4.4: Transparent Cavity for Case 2. ................................................................................... 66
Figure 4.5: (a) 2D mold cavity with particles fixed (b) 2D mesh domain of specimen ............... 68
Figure 4.6: Horizontal velocity distribution on fibers at inlet ..................................................... 69
Figure 4.7: Vertical velocity distribution on fibers at inlet .......................................................... 70
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Figure 4.8: Horizontal velocity distribution on fibers at end ........................................................ 71
Figure 4.9: Vertical velocity distribution on fibers at end ............................................................ 72
Figure 4.10: (a) Flow front, (b) Velocity magnitude distribution in mm/sec ............................... 73
Figure 4.11: 2D model of fluid domain for Case-1 ...................................................................... 76
Figure 4.12: 2D model of fluid domain for Case-2 ...................................................................... 77
Figure 4.13: Meshed domain of Case-1 ........................................................................................ 77
Figure 4.14: Meshed domain of Case-2 ........................................................................................ 78
Figure 4.15: Velocity distribution profile for Case-1 ................................................................... 80
Figure 4.16: Velocity distribution profile for Case-2 ................................................................... 80
Figure 4.17: Experimental setup to view fiber orientation in cavity ............................................ 84
Figure 4.18: Video images of filling process of mold cavity in 8 sec .......................................... 86
Figure 4.19 : (a) Digital image of flow front from CAD (b) Orientation angle of particles ......... 87
Figure 4.20: Digitized image of flow front for case I for each second ......................................... 87
Figure 4.21: Digitized image of path line of fiber particles motion in Case-1 ............................. 88
Figure 4.22: Orientation angle of fiber particles P1, P2, P3 for Case-1 ....................................... 89
Figure 4.23: Digitized image of flow front for Case-2 for each second ....................................... 90
Figure 4.24: Digitized image of path line of fiber particles motion in Case-2 ............................. 90
Figure 4.25: Orientation angle of fiber particles P1, P2, P3 for Case-2 ....................................... 91
Figure 5.1: Velocity profile of fluid flow in domain .................................................................... 93
XV
Figure 5.2: (a) Flow front profile from simulation software (b) Flow front profile from
experimental method. .............................................................................................. 94
Figure 5.3: Velocity distribution of flow front of numerical and experimental ........................... 95
Figure 5.4: (a) Orientation angle of particle at 20 mm from inlet (b) Orientation angle of
particle at 20 mm from end ...................................................................................... 96
Figure 5.5: (a) Flow front developed in experimental method for Case-1, (b) Flow front
developed in ANSYS Fluent for Case-1 .................................................................. 99
Figure 5.6: (a) Flow front developed in ANSYS Fluent for Case-2, (b) Flow front
developed in experimental method for Case-2 ........................................................ 99
Figure 6.1: Schemes of interaction of silane with natural fiber .................................................. 107
Figure 6.2: (a) Tensile strength and Tensile modulus of 15% Silicone/ Sisal fiber
composites by Injection molding process. (b) Tensile strength and Tensile
modulus of 15% Silicone / Sisal fiber composites by Compression molding
Process ................................................................................................................... 111
Figure 6.3: Tensile strength of untreated and treated sisal fiber reinforced silicone
composites ............................................................................................................. 112
Figure 6.4: Tensile modulus of untreated and treated sisal fiber reinforced silicone
composites ............................................................................................................. 114
Figure 6.5: Hardness of untreated and treated sisal fiber reinforced silicone composites .......... 115
Figure 6.6: Tear strength of silane treated and untreated sisal reinforced composites ............... 117
Figure 6.7: (a) Cross-linking density, (b) Swelling coefficient of silicone composites ............. 118
Figure 6.8: (a) Tensile strength for long fiber and short fiber; (b) tensile modulus for long
fiber and short ........................................................................................................ 119
XVI
Figure 6.9: Composites specimen from injection process .......................................................... 120
Figure 6.10: (a) Sisal fiber arrangement in 3D space of composite, (b) Cut Sample of
Sisal/Silicone composites in X-Ray tomography. ................................................. 121
Figure 6.11: a) 3D sample near inlet gate, (b) Front view of Sisal/Silicone composites, (c)
Fiber orientation in 3D space, (d) Fiber orientation in XZ plane .......................... 122
Figure 6.12: X-Ray Tomography - Sliced images of the composites ......................................... 123
Figure 6.13: (a) Long fiber orientation in composites XY plane, (b) Curl fiber orientation
in XZ plane. ........................................................................................................... 124
Figure 6.14: Long fiber planar orientation in 2mm thick specimen ........................................... 125
Figure 6.15: (a) Short fiber orientation in composites XY plane, (b) Short fiber orientation
in XZ plane. ........................................................................................................... 126
Figure 6.16: (a) Untreated fiber, (b) silane treated fiber ............................................................. 127
Figure 6.17: SEM micrographs (a) after tensile fracture; (b) fiber micro-pores and good
adhesion; (c) fiber fracture and poor adhesion; and (d) pullout hole and fiber
tear ......................................................................................................................... 128
1
Chapter 1 : Introduction
1.1 Overview
Globally, production of lightweight components with high strength is necessary in all
manufacturing industries. The component produced in any manufacturing process should be
lightweight with high strength, good aesthetics and low cost. In composites, fibers are
incorporated in a resin to improve strength and modulus. Composites product are developed
using various manufacturing processes such as the injection molding process, the compression
molding process, and the resin transfer molding process. There are various factors influencing
the strength of composites such as fiber orientation, fiber aspect ratio, shape factor, and fiber
resin interfacial interaction (Escalante-Solis, M. A., et al., 2015) .The orientation of the fibers in
the composites varies according to the manufacturing process. The strength of the composites is
inconsistent between different samples due to different orientations of the fibers. Many
researchers have reported that the strength of composites can be improved by chemical treatment
of the fiber surface. They also described the initiation of a crack from the end of a fiber / matrix
interface (Bledzki, A.K., et al. 2002). The transfers of loading from the matrix to the fiber result
in debonding. The stress transfer along the fiber / matrix interface may lead to failure of the
product. Therefore, anticipating the fiber orientation in the composites could give a better
understanding in order to improve the strength and ensure the safety of the product.
2
Fibers can take a deformed structure through curling and kinking. We can describe this structure
with a shape factor that influences the strength of the composite. The stress developed during
tensile loading may initiate cracks at the interface of the deformed fiber and the matrix, and lead
to failure. This motivates us to study the pattern of fiber orientation in composites and to develop
a method to predict the orientation of natural fibers. In this research, a mathematical expression
was developed to find the orientation angle of the natural fibers in the polymer composites. The
pattern of orientation in the skin and core layers of the composites is described for the short and
long fiber composites. The first stage of this project is to understand the flow of polymer in the
mold cavity and to establish the assumptions for the development of the mathematical
expressions describing fiber orientation.
The second stage of the project is to develop a 2D model of the fluid domain in flow simulation
software. The linear velocities were predicted at specific positions in the fluid domain. The
instantaneous velocity acting on the fibers was then used in the mathematical expression to
predict the angular velocity. In the third stage of the project, a laboratory setup was developed
for the experimental validation of the fiber angles predicted numerically. The images of the flow
front and fiber position were digitized for the measurement of orientation angle of the fibers.
Two case studies were performed and the orientation of fibers was experimentally measured. The
case studies were conducted for the wide area cross section and varying section of the mold
cavity. The experimental and numerically predicted orientations were compared.
In the fourth stage of the project, a specimen of sisal fiber reinforced silicone composite was
developed in the injection molding process to study the pattern of orientation. A nondestructive
technique was utilized to observe the orientation of fiber in the skin and core layer of the
3
composites. Also, the silicone composites specimen was developed in the compression molding
process. The morphological study was done on silicone composites through a non destructive
method and found the internal defects, interfacial interaction of fiber/matrix, debonding, fiber
orientation and air blowholes. The mechanical properties and crosslink density were investigated
for different fiber loading of sisal fiber in silicone matrix. .
1.2 Outline of thesis
This thesis describes a mathematical model to predict the orientation of short natural fibers inside
a polymer composite. The predicted orientation of the fibers is evaluated experimentally and the
mechanical properties of sisal fiber/silicone composites are determined experimentally.
Chapter 1 begins with a discussion on the manufacturing processes of composites and the factors
influencing the strength of the composite. This chapter also presents the various stages in the
development of mathematical expressions describing fiber orientation and experimental
validation of the model. This research area focused on the prediction of natural fiber orientation
in polymer composites and briefly described the effect of mechanical properties and morphology
behavior of the composites.
Chapter 2 presents a comprehensive literature review on the physical structure of natural fiber
and the shape factor describing the effect of a curling index in the fibers. This chapter introduces
the fundamental equation of flow and describes the orientation of fibers in the composite. The
rotational and translation motion of fiber in the narrow section of the cavity was briefly
described related to the fiber orientation in the composite. The existing mathematical model for
the glass fiber orientation is briefly described in this chapter. A brief introduction is provided on
4
the factors influencing the strength of the composites. Chapter 2 ends with the significance of
the research objective, hypotheses, problem statement and scope of the research.
Chapter 3 describes the development of a mathematical model for the prediction of natural fiber
orientation in the transient state of the polymer flow. This section describes the assumption of the
fluid element and the shape factor of the natural fiber, for the development of a mathematical
equation. This chapter provides a brief introduction on the fundamental theory of flow,
characteristic of flow parameter, and velocity distribution of the flow front. The assumption was
briefly explained and systematically derived the mathematical expression that includes angular
velocity, curling index of the fiber and tangential effect of flow front motion on the fiber
orientation.
In the Chapter 4, the injection-molded cavity was developed and the orientation angle of the fiber
particles was numerically predicted using the derived equation. In this section, the numerical
calculation was performed and the orientation angle of particles was numerically predicted at a
fixed position of the fluid domain. In addition, two case studies were conducted and
systematically predicted the orientation of fiber particles in a viscous fluid during filling phase of
the cavity. The laboratory experimental setup was developed for the purpose of validation. The
rotational motion of the fiber was digitized and the orientation angle of the fiber during the
filling phase of the mold cavity was measured. The experimental results of the fiber orientation
angle were compared with the numerical results. The part of this chapter was accepted in the
Journal of Natural Fibers.
Chapter 5 begins with the result and discussion about the case studies described in the chapter 4.
In this section, the velocity distribution acting on the fiber particles and flow front effect is
5
compared for two case studies. The orientation angles of two case studies are compared and the
reasons for the deviation in the results are given.
Chapter 6 describes the experimental investigation of sisal fiber reinforced silicone composites
for various percentages of fiber loading. The strength of the composites was compared with
treated and untreated fibers. The cross-linking density of the composites was predicted using
swelling method and briefly explained the mechanical properties and morphological behavior of
the composites. The pattern of orientation in the natural fiber composites was investigated using
X-ray Tomography and optical microscope. The voids, internal structures, fiber adhesion, fiber
orientation, fiber deformation, curling and air blowholes in the composites were also
investigated. The part of this chapter was accepted in the Journal of BioResources.
Chapter 7 presents the conclusion of the research work, study limitations, and recommendations
for future work, and scientific contribution involved in the prediction of fiber orientation in the
polymer composite.
6
Chapter 2 : Literature review and Background
2.1 Background
The injection molding process is applicable for a high production rate of complex shape product
in polymer and short-fiber reinforced composites (SFRC), at a reduced cost. Fibers are added to
polymers to improve properties such as elastic modulus, dimensional stability, and creep
resistance (Agboola, B. O., et. al., 2011). The composites developed from injection moulding
process are anisotropic. This is due to the uneven distribution of short-fiber and uneven
orientation of fibers due to the high shear (Baldwin, J. D., et al., 1997; Zainudin, E. S., et. al.,
2002). The quality of the product depends on the orientation of fiber, where different orientations
lead to variations in tensile strength, stiffness, and thermal expansion (Joshi, M., et al., 1994).
The fiber orientation process takes place in a short period. The complete cycle time for the
injection molding process is comprised of filling stage, holding stage, cooling stage, and ejection
stage to produce complex parts (Park, J. M., et al., 2011). Researchers have tried to predict the
fiber orientation in polymer composites through statistical approaches and developed empirical
models, which are used in commercial simulation software.
2.1.1 Natural fiber
Natural fibers are derived from vegetation such as flax, jute, banana, sisal and jute. The natural
fibers have been classified into bast fiber, seed fiber, leaf fiber, and grass fiber. Examples of leaf
7
fibers are pineapple and sisal fibers, which are soft and flexible in nature (Mohammed, L., et. al.,
2015). There are certain drawbacks in natural fibers such as lower durability, moisture
absorption, variability in fiber properties, curling and kinking in the fiber. Natural fibers are
superior over synthetic fibers in terms of low density, less pollutant production, low cost, high
flexibility, nominal health hazards and biodegradability (Shalwan. A., et al., 2013; Nguong, C.
W., et al., 2013,). Natural fibers in a polymer are eco-friendly and have other advantages such as
reduction in production cycle time, low rate of wear of manufacturing tool, and ease of polymer
recycling (Mishra, S., et al.,2004; Faruk, O., et al., 2012; Joshia, S.V., et. al.,2004; Oksman, K.,
2001). The natural fibers undergoes with high shear during the process of compounding and in
the injection molding process, resulting in fiber breakage and fiber deformation. Fiber length and
aspect ratio are viewed as a factor for the mechanical performance of the composite (Nystrom B,
2007). A fiber greater than the critical length and oriented parallel to the direction of applied load
will enhance higher tensile properties in the composites (Silverman, E.M , 1987; Truckenmuller,
F., et al., 1991; Thomason, J.L., 2002; Affdl, J. C., et al., 1976). The fibers are described as short
fiber and long fiber based on the fiber length. If the fiber length is less than 3mm, then the fibers
are said to be short fiber when used in injection and compression molding process (Chung, D. H.,
et al., 2002; Park, J. M., et al., 2011).
2.1.2 Structure of a Natural fiber
In general, the physical structure of natural fibers consists of cellulose, hemicelluloses, lignin,
pectin and wax. Natural fibers have the tendency to absorb moisture causing weak bonding
between fiber and polymer. A coupling agent is used between natural fibers and the polymer, to
change the functional group of the fiber structure, causing a reduction in moisture and enhancing
compatibility (Ray.S.S et al., 2005). The natural fiber has a complicated cell structure made of
8
microfibrils, where the rigid cellulose fibers are bounded and were embedded in a cross-linked
matrix of lignin and hemicelluloses (Dicker, M. P. et al. 2014).
Figure 2.1: Physical structure of natural fiber
The physical structure of all natural fiber is illustrated in Figure 2.1. It has a complex structure
containing a primary cell wall and three secondary cell walls (S1, S2, S3). The mechanical
properties are determined by the secondary wall where microfibrils are aligned and wound
helically in a long chain. The presence of hydrogen bonding in natural fiber is responsible for the
mechanical strength of the fiber. The primary wall of a single fiber has reinforced cellulose
microfibrils with a matrix consisting of cellulose, hemicelluloses, lignin, and pectin, which holds
the fibrils in a bundle (Fuqua, M.A., et al., 2012). The presence of hemi cellulose in fiber
accounts for moisture absorption and biodegradation of the bio-fiber. The smaller angle of
microfibrillar present in secondary wall enhances the mechanical property of natural fiber. The
9
hollow structure of lumen present at the central axis of natural fiber affects the strength and
flexibility of composite fibers (Azwa, Z. N., et al., 2013).
Cellulose can resist hydrolysis, and degrades on exposure to chemical treatment because of
oxidizing agents. Hemicelluloses of low molecular weight are hydrophilic in nature and are
hydrolyzed by acid and bases. Lignins are hydrophobic in nature, resist from acid and micro-
organism attack and are soluble in alkali on water transportation. The responsibility of Pectin is
to give flexibility to the natural fiber and is a collective name given for heteropolysaccarides
(Azwa, Z. N., et al., 2013).
2.1.3 Characteristic of Natural fiber
The cellulose fibers have excellent bonding ability and are strong enough in various applications
of paper industries. Fibers are rarely straight and curl in pulp during processing of paper. The
fibers are deformed and damaged in the processing stages that influence the strength of the sheet.
The presence of curliness in fibers has a tendency to lower the tensile strength and increase tear
on forming a thin sheet. Slender fibers can have sharp edges known as kinks, angular folds, and
fibrous twists (Johansson, A. 2011). The curl and kink influence the shape of fiber in composites
and could cause poor flowability, fiber agglomeration, and poor dispersion in the matrix (Zarei,
A. 2010; Page, D. H., et al 1985).
Figure 2.2: Kink and curl in natural fiber
10
The curl and kink describe the geometry of the fiber structure and their differences are illustrated
in Figure 2.2. The curl in the fiber describes a non-straight fiber having a certain degree of
curvature, while kinks in a fiber segment are sharp multiple bends caused by mechanical
damages. These two factors affect the tensile stiffness of thin sheet paper (Page, D. H., et al.,
1985; Rauvanto, I. 2003; Hubbe, M. A. 2013).
Figure 2.3: a) Fiber segment before drying , b) Fiber segment after drying
The natural fiber swells by absorbing the moisture from the environment and increases its
weight. The swollen fiber will shrink while drying and enhance the curliness during retting
process. The natural fibers are curly in nature before the drying process and are shown in
Figure 2.3. The fibers are severely beaten up after drying process and are straightened up with
wriggling marks in the micro-compression zone. This weakens the fiber structure resulting in
fiber damage, as shown in Figure 2.3 (Kurakina, T., 2012; Gard, J. 2002; Hubbe, M. A. 2013).
2.1.4 Measurement of shape factor
The morphological structures of a natural fiber are described by five parameters as length, curl,
kink, coarseness and width (Kurakina, T. 2012). The shape factor is defined by the ratio of actual
fiber lengths to projected fiber length and is reported by Jordan (Page, D. H et al. 1985). Page,
11
D.H., et al. have defined a curl index in the form of a ratio, as shown in equation 2.3 and as
represented in Figure 2.4. The occupied area of the curl shaped fiber causes resistance in flow
and interacts with adjacent fibers causing the fibers to agglomerate and be concentrated into a
thin sheet (Zeng, X., 2012; Page, D. H et al. 1985).
The curve representation of fiber is described by a set of coordinate points and is the
summation of discrete points on the Lact = actual length.
The curve representation of fiber is described by a set of coordinate points and is the
summation of discrete points on the actual length, Lact
Figure 2.4: Curling effect in fiber
12
2.2 Matrix
The matrix is a resin used in polymer composites to bond the fibers together and transfer the load
to increase the strength. Silicones are elastomers and exhibit viscoelastic behavior. Silicone is
synthesized from silicon and has a backbone of silicon atoms and oxygen atoms. Silicone has
high-energy Si-O bond and resists to ozone and high temperature. Silicones are recognized as
polyorganosiloxanes and are reinforced with fiber to increase mechanical property and resistance
to higher temperature. The chemical formulation of linear polymer has a unit of Si-O- with
organic group. Silicone has a unique property that allows it to stick to fibers. It is also able to
withstand both low and high temperatures because it has an organic group attached with an
inorganic group of siloxane.
Cross-linking in silicone is performed by room temperature vulcanization (RTV) and is moisture
cured due to presence of oxime represented in the reaction (Allen.K.W et al. 1994).The
activation energy of silicone curing is low and the viscosity is less dependable to temperature.
The formation of a thin layer during wetting process act as a protective membrane that are
followed by oxime curing process in silicone. This may liberate methyl ethyl ketoxime and in the
formation of Si-O-Si bond of flexible siloxane chain (De Buyl, F., et al., 2001; Keshavaraj, R., et
13
al., 1994). They have excellent resistance to the weather, moisture, high temperature and have
low tensile strength. Silicone are employed in application transport, construction, sealing, rapid
tooling and electronic industry because of high-energy absorption.
2.3 Flow characteristics for injection process
In injection molding process, the molten polymer is injected into the mold cavity under high
pressure and shapes the polymer to require product. Molten polymers are viscoelastic in nature
that they flow like a liquid and are deformed when stress is applied. The flow behavior of the
molten polymer is characterized as a combination of both viscous and elastic responses to the
applied stress. Molten polymers exhibit a unique relationship between stress, strain, and time.
The viscosity of the molten polymer is proportional to the shear rate. The material constant of a
viscous polymer is called the viscosity, which is a function of flow rate (Dawson, P. C., 1999).
The small variations in the shear rate of non-Newtonian fluid will cause a large variation in
viscosity. This will lead to improper filling of the cavity and result in inconsistent quality of the
product.
2.3.1 Governing equations
The principle of conservation of three basic quantities, namely mass, momentum, and energy is
the basis of the equations of fluid dynamics. The continuity equation, momentum equation and
the energy equation are the governing equations of fluid flow, used to predict the velocity,
pressure, shear stress and temperature in the fluid domain. The continuity equation and the
momentum equation are coupled to form a differential equation known as the Navier –Stokes
equation (2.6), to predict velocity and pressure in a fluid. The differential form of the equation
14
has been solved by Anderson, (2009) using the finite difference method to find the velocity and
pressure during the transient state in the fluid domain. (Anderson Jr, J. D. 2009)
Conservation of Mass:
Navier –Stokes equation (conservation of momentum)
2.3.2 Polymer Viscosity
The polymer structure is made of long chains of molecules, which leads to complex rheological
behavior in the molten polymer. For elastic materials like metals, shear modulus is the ratio of
shear stress to shear strain and is determined by Hooke’s law. Similarly, for a viscous fluid, the
viscosity η is the ratio of shear stress τ to the rate of shear strain γ and is determined using
Newton’s law, (Dawson, P. C., 1999).
The viscosity is the material constants of the fluid and does not depend on the rate of
deformation. The fluids such as water, oil, silicone have a constant viscosity and do not change
with the rate of flow. The polymer melts are non-Newtonian fluids, where viscosity is not a
constant and the relationship between strain rate and stress is not linear. In polymers, the chains
of molecules are entangled with reversible joints causing an elastic behavior in the molten
15
polymer. Non-Newtonian flow of polymers melt is characterized by shear thinning, where the
viscosity decreases with shear rate (Aho, J., 2011; Kajiwara, T., et al., 1995). Silicone is
considered as a Newtonian fluid having a constant viscosity, and the unit is represented in Nsm-2
or Pa.S.
2.3.3 Theory of fluid flow
The fluid molecules exert a force of attraction on each other keeping the molecules together but
not strong enough to maintain it rigid. Fluids are imagined as packets of layers flowing one over
another. The shearing of one layer over the surface of another layer enables the fluid to flow with
non-uniform velocity. The Figure 2.5 shows the flow of fluid in a layer over a flat surface,
where is the distance above solid surface, is the thickness of each layer, is the length
of the layer, is the elementary distance moved by each layer, is the velocity at a specified
layer, is increase in velocity with respect to the adjacent layer. Each layer slides to a distance
in a time relative to adjacent layers. The ratio of change in distance moved by layer
per unit time is referred as velocity (Van Wazcr, J. R., et al., 1963; Schramm, B., et al.,1980).
Velocity of one layer with respect to another layer in motion is
Figure 2.5: Fluid flow in layer over flat surface
16
The shear force acting on a fluid element enables it to deform in the same direction as the applied
force, and a shear stress τ is produced between the layers correspond to shear strain γ. The shear
strain is defined as
For Newtonian fluid:
2.3.4 Laminar flow
Newtonian fluids have a constant viscosity and flow within a low range of velocities is called
laminar flow. In laminar flow, the pathline of the fluid element remains parallel to neighboring
flow lines and there is no disturbance in the lateral direction. This is defined as streamline
motion. Laminar flow is described an uninterrupted flow of fluid, and the direction of flow at
every point remains constant. The laminar fluid flows with low velocity and tend to flow without
disturbance along the flow direction. There is no slipping effect on the wall boundary for laminar
flow, which also exhibits an increase in fluid velocity from zero to maximum with respect to
distance from the wall. Laminar flow can be described by the Reynolds number and was defined
as the ratio between the inertia forces and the viscous force. Reynolds’s number (equation 2.11)
is denoted by , where ρ - Density in kg/m3, - Velocity in m/sec, –Thickness in m, and μ
– Viscosity in Pa S. The flow of fluid is identified as laminar flow from the Reynolds number.
For the laminar flow, the Reynolds numbers are less than 2000, (Sharp, K. V., et al., 2004)
17
2.3.5 Steady and un-steady flow
If the parameters of fluid flow such as velocity, pressure and area of cross section remain
constant with time, then the flow is said to be a steady flow. The flow of fluid will be laminar
and the properties are constant with time in the flow field. (Tritton, D. J. 2012)
In case of unsteady flow, the flow parameters such as pressure and velocity changes with time
and also with respect to the thickness, as represented in the equation 2.13
2.3.6 Uniform and Non-Uniform Flow
Uniform Flow is the type of flow in which velocity and other flow parameters at any instant of
time do not change with respect to space.
Where indicates that the flow is uniform in ‘y’ and ‘z’ axis. indicates that
the flow is uniform in ‘x’, ‘y’ and ‘z’ directions.
The non-uniform flow has a change in flow parameter such as velocity or pressure at any instant
with respect to space. (Tritton, D. J. 2012)
18
2.3.7 Fountain flow
When a mould cavity is filled with the molten polymer at a high injection pressure, the melt flow
is characterized as fountain flow. The polymer fills the cavity with the flow front shown in
Figure 2.6. The length of fountain flow depends on the injection pressure and flows with high
velocity in the core region of the cavity by making a flow front. The velocity vectors of the
polymer melt are parallel to the wall and progresses to fill the cavity. At the flow front, the fluid
element advances from the frontal flow to the wall of the cavity. The fountain flow follows the
principle of the Lagrangian flow where the fluid elements are relative to the adjacent element in
advancing to flow front (Mavridis, H., et al., 1988).
Figure 2.6 : Streamlines of fountain flow and flow front
2.4 Basic equation of fluid flow
The basic equations of fluid flow obey the three major principles such as conservation of mass,
momentum, and energy, which are called as the continuity equation, the momentum equation and
the energy equation. The continuity equation was derived for finding the unknown velocity of
flow fields in the fluid domain. The momentum equation was used to predict the unknown
parameters like pressure, density, shear stress etc., while the temperature of flow fields was
derived from the energy equation (White, F. M., 1974; Anderson, D. A., et al., 1984).
19
2.4.1 Flow Kinematics
Flow mechanics are concerned with the states of rest and motion of bodies subjected to forces
and are subdivided into statics and dynamics. If the body lies at rest or is moving with uniform
velocity then it is said to be static mechanics. Dynamics deals with the acceleration of a fluid
element and is broadly classified into kinematics and kinetics. The kinematic study of fluid
motion involves the definition of quantities such as displacement, velocity, and acceleration.
Kinetics of fluid flow is based on the definition and description of forces like gravitation,
frictional force, and torque which cause the fluid element to rotate and translate (Hibbeler .R.C,
2009; Chorin , A. J., et al. 1980).
2.4.2 Newton’s law of motion
The acceleration of a particle is directly proportional to the resultant force acting on fluid
particles. If more than one force is acting on a particle, then it can be determined by the
summation of vector forces. The equation of motion is represented as
2.4.3 Curvilinear motion
The curvilinear velocities of fluid particles in a 2D plane are described in a vector form and the
particle position are being described with the position as a function of time, as illustrated in
Figure 2.7. The position of a particle is defined in terms of the distance to a fixed point (r), and a
direction angle θ with respect to the X-axis of the plane. The position can also be defined in
vector form: . The velocity of a particle changes with time and the velocity vector
remains tangential to the curve path (Hill, R., et al., 2014; Chorin, A. J., et al., 1980). The
particle position changes with respect to time at a certain velocity and are represented in a
20
derivative form as: , where velocity
. The summation of all the velocity
components is termed as average velocity
.
Figure 2.7: Particle position and motion in vector.
2.4.4 Relative velocity and acceleration
In planar motion, the fluid particles flow in both rotational and translational motion in a 2-D
plane, as indicated in the Figure 2.8. If the flow of fluid particles has only translation then it is
described by position, velocity and acceleration. In addition to translation motion, if the particle
undergoes rotation then the particles are described by linear position, angular position and
angular acceleration. A particle at point A undergoes translation with respect to point B, and has
a rotation around point B. The vectorial representation of the velocity is given as
vA = vB + vA/B = vB + ω x rA/B., and the acceleration was represented in the form aA = aB + (aA/B)t +
(aA/B)n = aB + α x rA/B - ω2rA/B. (Hill, R., et al., 2014).
2.4.5 Principle of linear impulse and momentum
The equation of motion for a particle, of mass moves with a velocity and a force
acting on the fluid in time is given by
21
Figure 2.8: Planar motion of Particle in translational and rotational
The principle of linear impulse momentum of a fluid particle is represented by
2.5 Fiber Orientation Distribution
The fiber’s role in determining the mechanical properties of fiber-reinforced composites operates
through four major factors: the fiber volume fraction, fiber orientation, aspect ratio, and
fiber/polymer matrix interaction (Zak, G., et al., 2001). The orientations of the fiber in the
composites are predicted by probability distribution function and further the model was
improvised by tensor method (Advani, S. G., et al., 1987). The accuracy of the models was
22
further improvised by considering the fiber - fiber interaction and predicted the orientation of
fiber (Chung, D. H, et al., 2002; Mlekusch, B., et al., 1999).
Figure 2.9: Single fiber orientation angles
The statistical characterization of fiber orientation distribution (FOD) in a short fiber composite,
described in terms of the two angles and as shown in Figure 2.9, is called the probability
distribution function (Jain, L. K., et al., 1992).
The orientation of fibers is represented in form of a probability distribution function where the
single fiber orientation is described by a unit vector with spherical coordinates and (Bay,
R. S. et al., 1992). The probability of fiber angles is represented by
23
The orientation angles and are measured experimentally for a number of fibers and the
samples are drawn to fit distribution function , with an average value of the orientation angle.
Advani and Tucker 1987 have described the orientation by a second order tensor method Aij , by
considering the average orientation of all fibers in a sample. There are nine components of
orientation in the orientation tensor, in which denotes the orientation of fiber in the X
direction and denotes orientation in the Z direction. The tensor is symmetrical
, and the number of tensor components is thus reduced from nine to six; one diagonal
component is eliminated under the condition of normalization of unit value
.There have five independent tensor components such as
(Bay, R. S., et al., 1992). The tensor indicates the
fibers are perfectly oriented in horizontal X-direction and indicates fibers are oriented
vertically in Y direction, whereas varies from -0.5 to 0.5 indicates angular
orientation.
2.5.1 Orientation in composites
The microstructure of the composites shows, that the orientation of fiber in each layer varies
from the core region to the wall, as shown in Figure 2.10. The fibers are parallel near the wall
and randomly oriented in the center region. This causes anisotropic properties in the composite
structure (Wielage, B et al., 1999). The orientation of long fiber was examined by Bailey.R et al.,
and described the internal structure of the composites has three regions of orientation (Bailey, R.
et al., 1991; Toll, S. et al., 1993). The topmost layer is called the skin layer; it has a thickness of
15-20% of the total part thickness (Karger-Kocsis, J., et al., 1987) and is created by rapid
cooling due to extensional deformation during fountain flow. The fibers in the skin layer lie
parallel to the wall of the cavity in a thin layer, and fibers are less oriented along the direction of
24
flow than the fibers in the shell layer. The skin region is adjacent to a thick shell layer known as
the shear zone, where the fibers lie parallel to the wall. Fibers in the shell region undergo large
shear strain near the mold wall and shear flow of the fluid makes the fibers align parallel to the
wall, as shown in Figure 2.10. The next region in the middle of the composite is called the core
layer; it has a thickness of 60-70% of the total part thickness (Karger-Kocsis, J., et al., 1987) and
the fibers are oriented transverse to the direction of flow. The orientations of fibers in this region
are random and are determined by velocity gradient in line with the position of inlet gate size
(Bright, P. F., et al., 1978; Gerard, P., et al., 1998; Akay, M., et al., 1991; Yang, C., et al., 2010).
Figure 2.10: Orientation of fiber in skin, core layers of composites.
2.5.2 Orientation Pattern
Various patterns of fiber orientation are shown in Figure 2.11 and the aligned fibers are shown
in Figure 2.11(c), where the fibers are parallel to each other. This parallel orientation of fibers in
the composites results in high tensile strength. The Figure 2.11 (b) shows the planar orientation,
where the fibers near the plane surface are horizontally oriented and the same fibers remain
randomly oriented in the lateral plane. A random orientation is shown in Figure 2.11(a), where
fibers are oriented randomly with respect to the reference planes (Chung, D. H. et al., 2002)
25
Figure 2.11: Orientation of short fiber a) 3D- random isotropic orientation, b) Planar
random c) Aligned
The stress applied on the composite is distributed at the interface of the fiber and the matrix, and
the transfer of load from the matrix to the fiber increases the mechanical properties of the
material. The shearing of the fluid element changes the orientation of the fibers and forms a
different pattern of orientation in the composites (Oumer, A. N., et al., 2013). The longitudinal
orientation of the composite shown in Figure 2.12(a), such that the applied stress lies parallel to
fibers direction, which achieves high tensile strength. However, the fiber direction lies transverse
to the applied force in Figure 2.12(c), where the stress is imposed on the lateral surface of fiber
gives lower strength. The stress applied to the specimen in the angular orientation shown in
Figure 2.12(b) may have optimized strength compared to the longitudinal and transverse
orientations. Therefore, the strength of the composites varies and depends on the pattern of fiber
orientation.
26
Figure 2.12: Pictorial representations of fiber orientation
In addition, the volume fraction of fibers in the composites has an effect on mechanical
properties. Higher concentration of fiber (more than 20% by weight) in a polymer composite will
increase strength and modulus, but may also increase the viscosity of the molten polymer. This
causes a significant change in the velocity profile with a low rate of shear and increases the
degree of pseudo-plasticity. It is also difficult to predict the orientation distribution at high fiber
content because of fiber interaction in the composite (Zainudin, E. S. et al., 2002; Yang, C., et
al., 2010).
In short fiber composites, the fibers are distributed along the direction of fountain flow and are
oriented transverse to flow front in the core region, which was experimentally verified by Gupta
and Wang. The Figure 2.13 shows the thin section of injection-molded parts, the fibers
predominantly lie in the plane surface of the part. The shear-dominated flow near the surface of
the wall tends to align the fiber along the flow (shell region). Further, the extension of fiber flow
near the mid-plane of the cavity tends to align the fibers transversely to the flow in the core
region (Jackson, W. C., et al. 1986; Yang, C., et al., 2010).
27
Figure 2.13: Fiber distribution in transverse tangential to direction of flow front
A high shear rate takes place at the narrow gates of the thin injection molded parts and causes
fibers to align along the wall. Further, the fibers move with high velocity due to injection
pressure, orienting the fibers in a transverse direction at the core region. The fountain flow aligns
the fiber along the parabolic profile across the cavity thickness. Thus, orientation depends on the
thickness of the cavity, temperature of the molten polymer and the concentration of fibers. On
the other hand, solidification rate increases from the wall of the cavity to the core region by
reducing the cross section of fluid flow. This increases the shear on filling the cavity and reduces
the degree of orientation (Bay, R. S. et al., 1992; Altan, M. C. 1990).
2.5.3 Fiber aspect ratio
The rheological behavior of polymer composites is influenced by the fiber aspect ratio and
affects the pattern of fiber orientation. The high aspect ratio fibers suspended in the fluid medium
may affect the local flow by causing, stresses in the system and influence the rheological
behavior. The fibers are assumed to be uniform, axis-symmetric, and characterized by the aspect
ratio ar = l/d. The fibers are suspended in a solvent and the characteristics of the suspension are
28
expressed by the volume fraction and aspect ratio of the fiber particles (Chung, D. H. et al.,
2002).
The suspended fibers are characterized in the polymer melt by fiber length (L), fiber diameter
(D), the number of fibers per unit volume (n), and are classified into three regimes as diluted,
semi-diluted, and concentrated.
Diluted
Semi-diluted
Concentrated
Where
These concentration regimes are related to the rheological characterization of the polymer melt
in terms of the coupled effect between fiber particle and fluid motion.
2.5.4 Fiber attrition
The fiber breakage during molding process affects the fiber length and reduces the mechanical
properties of the composite. There are three mechanisms of breakage: fiber – flow interaction,
fiber – fiber interaction, and fiber – wall interaction in the mold cavity (Von-Turkovich. R., et
al., 1983; Gupta., V.B. et al., 1989)
29
Fiber-flow interactions: The fluid flow in an injection molding process is a combination of
elongation and shear deformation. During the elongation flow, fibers tend to align along the
direction of stretch and undergo tension, which may cause fiber breakage. The shearing of fiber
during the flow tends to rotate the fibers along the streamlines and deform the fiber to a critical
radius of curvature (Karger-Kocsis, J. et al., 1988; Bailey. R, et al., 1991).
Fiber-fiber interactions: The overlapping of fibers induces bending stresses on the fiber and
restricts the flow to break the fibers. Turkovic and Erwin, 1983, did the study on the effect of
fiber volume fraction and the breakage of fibers during compounding Process. The lengths of
glass fibers are found identical in length for the volume fractions of 1 to 20% (Von Turkovich,
R.,. et al., 1983). The increase in fiber –fiber interaction could cause agglomeration and decrease
the interaction between fiber and matrix. The weak interaction initiates the crack and propagates
the crack growth along the direction of fiber orientation. The fiber also resists the growth rate of
cracks in the composites. The crack growth rate of the composites decreases with the number of
fibers oriented perpendicular to the crack tip (Hine, P. J., et al. 2004).
Fiber-wall interactions: The fiber length is reduced during the shearing action of the twin-screw
co-rotator in the compounding process. The fiber flow through the narrow gate may reduce its
original length and break the fiber at its weaker region due to high injection pressure. The flow
also exhibits a high shear rate near the surface of the mold, which can affect the fibers interacting
with the wall (Denault, J., et al., 1989; Bailey, R. et al. 1991; Singh, P., et al., 1989).
2.5.5 Fiber orientation in mould cavity
The orientation of fibers has been predicted by considering a single fiber orientation in statistical
methods with the Smoluchowski equation (Vélez-García, G. M., et. al., 2012). The fiber
30
orientation and fiber distribution depend on the mold gating system, which controls the flow
pattern of the fiber inside the mold cavity. The fibers align longitudinally in the narrow section
of the sprue area and the runner area of the injection-molded cavity. When the fibers exit from
the narrow gate to the wider area of the cavity, the divergence effect could cause the fiber to
orient transverse to the direction of flow in the core region. Figure 2.14 shows the flow pattern
and flow front of the molten polymer as well as fiber orientation in the core and skin layers of
the mold cavity. Redjeb. A., et al., has stimulated the orientation of fibers in the narrow area of
the sprue and in the gate of the mold cavity by the computational approach. The flow kinematics
and the tensor method of fiber orientation were coupled using a computational method. The
computation was performed in two stages: in the first stage, FEM was used to calculate the
various stress terms in the flow equation. In the second stage, velocity distribution in the domain
was considered for computing fiber orientation at each time step (Han, K. H. et al., 2002; Redjeb.
A., et al., 2005; Gillissen, J. J. J., et al., 2007; Dou, H. S., et al., 2007). The computational
approach has coupled the orientation of the fiber and pathline of a fluid flow using FEM for
small intervals of time in mold filling (Dantzig, J. A., et al., 2001; Bay .R.S, et al., 1992).
The Figure 2.14 shows the fountain flow with flow front along the thickness of the cavity in the
XZ plane and the orientation of fibers in the gate region, skin layer, and core layer of the mold
cavity. Also, the orientations of fibers are represented along the flow front in the XY plane of
the cavity, as shown in the Figure 2.14. The polymer flows with a nonuniform velocity creating
a flow front with a parabolic profile during filling phase of the cavity. The polymer melts in the
core region flow with high velocity due to the start of solidification from the wall to the core
region. Unlike thermosetting polymers, the formation of cross-links occurs at a slower rate and
31
the flow front orients the fibers during filling phase of the mold cavity (Dantzig, J. A., et al.,
2001; Bay, .R.S, et al., 1992; Folkes, M. J. et al. 1980).
Figure 2.14: Fountain Flow, flow front and orientation
The solidification of the layer near the wall is faster and resists the flow of polymer at slower rate
results in a high shear rate. This causes a higher degree of fiber orientation along the direction of
flow near the wall of the cavity. The fountains flow forms an elliptical shape to advances frontal
flow in a radial direction. The flow front of molten polymer moves fibers towards the mold wall
and aligns the fibers parallel to the wall surface to have translatory motion (Bay R.S, et al., 1992;
Jackson, W. C.,et al., 1986). The shear rate of the polymer melt in the core region is
comparatively lower and flows with high velocity. This results in a transverse alignment of the
fibers at the gate portion and in the core region of the mold cavity, as illustrated in Figure 2.14.
32
Figure 2.15: Pinpoint gate and linear gate for analysis of fiber orientation (G.lielens 1999)
The fiber distribution and orientation were considered in a dumbbell shaped part for two types of
gates, such as pinpoint gate and linear gate as shown in Figure 2.15 (Lielens, G. 1999). The
gating design greatly affects the fiber breakages, fiber agglomeration, and fiber orientation. The
cavity having a pinpoint gate produces a diverging flow during the initial stage of filling of the
cavity. This causes fibers to flow parallel to the flow fronts. Subsequently in the converging flow
of polymer, the fibers are partially oriented along the direction of flow causing a non–
homogeneous pattern of orientation. On the other hand, a gate located at a linear edge results in
partial orientation in the converging zone for short and long fiber, and results in spatially
homogeneous orientation. (Lee, S. C., et al.1997; Lielens, G. 1999; Zainudin, E. S. et al., 2002).
2.5.6 Effect of cavity thickness on orientation
The pattern of the flow front in the injection molding process is affected by cavity thickness and
other factors such as flow behavior, melt temperature, fiber content, and matrix. The injection
pressure and gating system changes the flow rate and affects the fiber alignment in the thin
cavity. The reduction in thickness of the cavity results in a planar orientation of the fibers with
the flow front (Baldwin, J. D. et al, 1997).The Moldflow® software was used to predict the
orientation and distribution of short glass fibers by considering the effect of injection speed and
33
thickness of the specimen. If the thickness of the cavity is larger than the fiber length, then there
will be a small degree of fiber orientation when the injection time is longer, whereas there will be
high degree of planar orientation in a thin cross section of cavity part (Wang, J., et. al., 2010). In
order to achieve a smooth surface and complete filling of the mold cavity, it is recommended to
increase the injection speed, injection pressure and melt temperature. (Lee, S. C., et. al., 1997;
Bright, P. F., et al., 1978; Folkes, M. J. et al. 1980).
2.5.7 Convergent and divergent effects
The mold cavity consists of narrow size and wide areas in the section. In the convergent section
has a narrow area, where the fibers align due to high shear and the fibers become parallel to the
narrow gate. However, in the divergent area of the cavity, fluctuating velocities of the melt orient
the fibers transversely to the direction of flow. In the convergent and divergent regions, it is
found that the fibers have a tendency to orient to a higher degree near the wall (Papthanasiou, T.
D., et al. 1997).
Figure 2.16: Convergent and divergent zone in mold
34
The Figure 2.16 indicates the orientation of fibers in convergent and divergent area of fluid flow
in the mold cavity. In the convergent area of flow will increase the velocity and make fibers align
along the surface to form a longitudinal orientation. Whereas, in the divergent area has a wider
volume to decrease the velocity and orient the fiber in an angle to flow direction. The orientation
produced by fan gate depends on the injection rate and fibers are oriented transverse to flow
direction than edge gate. Therefore, orientation can be controlled by varying the cross section
through integrating converging and diverging section the mold design. The fiber oriented in the
narrow section has an effective transfer of stress from the matrix to fiber when the fibers are
oriented longitudinally that enhances strength in reinforced composites. On the other hand, the
stress transfer in transverse orientation results in fracture at lower tensile stress due to the large
stress transfer on the lateral surface of the fibers (Silva, C. A.,et al. 2006; Kulkarni, A, et al.
2012).
2.6 Factors affecting composites property
The mechanical properties of a composite are enhanced by controlling the aspect ratio,
agglomeration, and orientation of fibers. The composite strength is a function of fiber length,
fiber volume fraction, fiber distribution, and fiber orientation. The load applied to the matrix will
be transferred in shear to the interface with the fiber. The stress on the fiber depends on the
length of the fiber, and on its orientation relative to the applied load (Joshi, M., et al., 1994;
Joseph, K. et al., 1993).
2.6.1 Voids in composites
The presence of micro-voids at the interface of fiber and matrix causes an adverse effect on the
mechanical properties of composites. These voids are formed at the interface of fibers with the
35
matrix and the presence of volatile substances produced by a condensation reaction. Air
entrapment in the matrix and higher content of fibers in the matrix may lead to the formation of
voids and has low fatigue resistance (Alomayri, T. et al., 2014; Anderson, J., et al., 2014).
2.6.2 Moisture absorption
Natural fibers are hydrophilic in nature and absorb moisture by breaking the hydrogen bond
present at the cell wall. The fibers in composites swell because of moisture absorption and
weakening the bonding between fiber and matrix. This will cause cracking in the matrix,
dimensional instability and poor mechanical properties (Ho, M. P., et al., 2012). The surfaces of
the natural fibers covered in wax, contamination and with high moisture absorptivity, were
removed by chemical treatment such as the alkali treatment, silane treatment, and peroxides
treatment. In addition, the treatment removes hydroxyl bonds from the surface of fibers (Ali, A.,
et al., 2016).
2.6.3 Natural fiber geometry:
The fiber geometry such as diameter, length, curling and kinking, is a major parameter that
affects the mechanical properties of natural fiber reinforced composites. According to analytical
relations, the tensile strength of the composite is enhanced by increasing the fiber volume
fraction and fiber length (Bongarde, U. S., et al., 2014). The fiber surface can be made rough by
removing volatile substances and waxes in the chemical treatment process. The rough surface of
the fiber improves the bonding interface between the fiber and matrix. The flexibility and
varying diameter of the fiber can affect breakage and influences the fiber transfer of stress from
the matrix to fiber.
36
2.6.4 Fiber critical length:
The chopped natural fibers used in the injection molding process should be above the critical
length and the interfacial bonding should be good for transferring the stress in the polymer to the
fiber. However, fiber lengths after the injection molding process are limited to 3 mm because of
high shear rates in the injection barrel. Therefore, gate size must be 40% of part thickness. It also
depends on pressure and temperature distribution in the mould cavity (Beck, R. D., 1970; Zhai,
M., et al., 2006). The fibers length shorter than the critical length may be unable to carry
effective loads. This establishes a poor interfacial bonding that can also lower the load capacity
(Fu, S. Y., et al., 1996). A fiber longer than the critical length would increase the fracture load
and result in fiber fracture prior to matrix failure. Hence, it is required to determine the fiber
critical length for the injection molding process to avoid fiber attrition. Together with an increase
in fiber content and preventing the fiber attrition could improve composite strength, as predicted
by theoretical models. The quantity of fiber, however, could be limited in the injection molding
process because of the fiber/polymer viscosity, cluttering of fibers, inlet gate size, and a narrow
runner (Ho, M. P. et al., 2012; Fu, S. Y., et al., 1996).
2.7 Mathematical model for orientation
2.7.1 Assumptions for fiber orientation
A viscous fluid is flowing inside the mold cavity exhibits shears along the wall and flows with
non-uniform velocities. The shear force of the fluid acting on the fibers induces a rotational and
translation motion during filling the mold cavity. There are many researchers have developed the
model by stating the assumption and their limitations. Jeffery (1922) has described the particle
as being ellipsoidal and exhibiting a periodical rotation characterized by the Jeffery orbits. He
assumed that fiber particles are rigid and that the inertia forces acting on the fiber particles were
37
negligible (Jeffery G.B., 1922). The assumptions were further modified, based on the moment
acting on the rigid fiber due to interaction with the fluid as well as a small amount of bending
and torsion in the fiber (Joung C.G. et al., 2001; Zhou, K., et al., 2007). The motion of viscous
fluid was assumed to have a constant shear and to induce an impulse moment on the ellipsoid
single fiber, causing it to rotate (Joung C.G. et al., 2001; Shanley, K. T., et al., 2011). The flow
of a single ellipsoidal fiber was determined by the non-uniform shear in the viscous fluid across
the volume of the cavity. The non-uniform shear force has a tendency to move the particles in a
translational and rotational motion. In another study, the flow was assumed to be in the transient
state of low laminar flow, with a hydrodynamic force acting on the fiber, causing translation
motion inside the cavity (Nouri J. M. et al., 1993; Lovalenti, P. M., et al., 1993). The angular
velocity was predicted in the annular duct for axial flow of a Newtonian fluid. The author has
considered the flow to be laminar, steady-state, and incompressible in the duct. And also the
angular velocity in an annular duct has an axial velocity profile for the pipe eccentricities of 0.2
and 0.4 (Al-maliky, R. F. 2013). Rao et al. have investigated the orientation of fibers in the
convergent region and divergent region of the mold cavity, by assuming the flow to be a steady
flow and the fluid to be Newtonian (Rao, B.N., et al., 1991).
In another study, a computational model was developed for an incompressible flow of non-
Newtonian fluid, where the velocity profile and fiber orientation for suspended short fibers was
predicted through the finite difference method (Shanley, K.T., et al., 2011). The second order
tensor of orientation was numerically solved through the Runge – Kutta method to predict the
fiber orientation (Oumer, A. N. et al., 2009). Shanley, et al has implemented the tracing
technique and traced the flow path of the suspended particle for predicting the orientation of the
particle. (Shanley, K.T., et. al., 2011). Folgar et al., 1984 developed an analytical expression for
38
a single fiber orientation through a statistical distribution function. Advani et al., 1986 has
introduced the tensor method to find the degree of fiber orientation in the specified region of the
fluid domain (Rao, B.N., et al., 1991).
2.7.2 Existing model for fiber orientation
There are various models developed by researchers for polymer flow that have been
implemented in simulation software to optimize the flow rate and process parameters for the
injection molding process. In simulation software such as Autodesk Moldflow® Insight, the
Folgar-Tucker model is employed to predict the orientation of fibers inside the cavity. A
mathematical equation was derived for flow analysis to obtain the pressure and velocity
distributions. The momentum and energy conservation equation have been considered to find
pressure for the thermoplastic material in the mold cavity (Greene, J. P., et al., 1997). The flow
of the polymer in the cavity was modeled for non-isothermal flow of a non-Newtonian material
between two walls and is governed by the equations of continuity, momentum, and energy
transport, as follows:
Where is the velocity vector, is the shear stress tensor, is the pressure, is the gravity
term,
denotes the material time derivative, T is the temperature, and ρ, η, Cp, k are the fluid
density, viscosity, heat capacity, and thermal conductivity, respectively.
39
In the injection molding process, molten plastics are viscoelastic materials in nature and behave
as non-Newtonian fluids. Previous researchers have considered the molten material of plastics as
a Newtonian fluid instead of a non-Newtonian fluid for the sake of simplicity (Joung, C.G, et al.,
2001; Fan, X., et al., 1998; Yamane, Y., et al., 1994). Various models have been developed for
the orientation of short glass fiber in polymer composites described through a probability density
function. Further, the investigation (Folgar and Tucker, 1984) was pursued towards the
improvement of accuracy in prediction of fiber orientation. The current progress of the model
developments is presented in Figure 2.17. In 1922, Jeffery’s model was developed by
considering a simple shear flow on a rigid ellipsoid fiber motion in a Newtonian fluid and
characterized the motion of the fiber particle in a periodic motion called Jeffery orbit, shown in
Figure 2.18. The trajectory of the fiber around the vorticity axis was characterized by a periodic
tumbling motion in an ellipsoid path resting along the direction of shear (Phelps. J.H, 2009;
Jeffery, G. B., 1922).
Jeffery obtained a differential equation for the motion of an ellipsoidal fiber where the
orientation was represented by a unit vector P, as follows (Joung, C. G., et al., 2001):
Where
is Fiber aspect ratio,
P is unit vector representing the ellipsoidal fiber orientation,
is the derivative of fiber orientation.
- Shape correction factor for cylindrical rod fiber
40
- Vorticity tensor
- Deformation or strain rate tensor
= Velocity vector
Figure 2.17: Mathematical model for fiber orientation
The Jeffery periodic orbital time is given by
41
Where is a function of shear rate.
Figure 2.18: Single fiber P in shear flow
The Jeffery model was accepted as a general method to predict single fiber orientation in a
Newtonian fluid. However, this model cannot be applied to dense fibers suspended in a
composite because the effect of fiber-fiber interaction is not considered (Joung C.G., et al.,
2001). Folgar and Tucker improved the Jeffery model by adding the effect of fiber- fiber
interaction and introducing a coefficient of interaction in the model, called rotary
diffusion
. The incorporation of rotary diffusion has improved the prediction of the
orientation rate of the fiber unit vector (Folgar .F, et al., 1984).
Where a distribution is function and is a parameter describing fiber- fiber interaction,
which can be determined by an empirical method. Furthermore, Folgar and Tucker assumed that
can be expressed as where is the shear rate of flow since the intensity of
42
interaction is proportional to the shear rate of flow. is the coefficient of interaction and is
described with a tensor instead of a scalar to reflect the anisotropic nature of suspended fibers in
a composite. Folgar and Tucker assumed the controlling parameter of fiber-fiber interaction
and determine through tensor method by introducing orientation tensor and .
The second order tensor equation for fiber orientation in a large population of fibers is given by:
Where
is material derivative
2.7.3 Experimental method available for predicting orientation
The composite specimen was prepared by an experiment using the injection molding process.
The sample is cut at a specific position and the orientation of fibers is measured under an
electron microscope. The orientation angle of the fiber is found using the sampling method in the
cut section of the specimen (Meyer, K. J., 2013). The theoretical model is developed from
reliable data obtained from experimental results. However, it is difficult to ascertain the fiber
orientation through micro-radiography, since the orientation of fibers varies along the length,
diameter, and thickness of the sample (Meyer, K. J., 2013). An image analysis technique was
used on the cut specimen and the orientation of fibers was predicted in each section. A statistical
method was used and derived the distributive function for the orientation of fibers (Gadu-Maria,
et al., 1993). Phelps, J.H., used an image analysis technique on the sample under an optical
microscope (Axiovert 40 MAT; Carl Zeiss LLC) and acquired several images. The images were
43
joined to form single images and the orientation was predicted using a statistical method. Also
represented the horizontal orientation of fiber in percentage and described in a graphical format
along the thickness of the cavity (Phelps.J.H, 2009). Gadala-Maria., F, et al., 1993, have utilized
image acquisition technique to digitize the acquire image on the monitor and orientation of fiber
was determined by the gradient vector at each pixel enabled on the edges of the fiber.
2.7.4 Destructive method
The orientations of fiber in the composites can be evaluated using destructive techniques by
cutting a section from the composite specimen. The destructive approach causes damage to the
sample and image analysis method was used only for sampling process (Meyer, K. J., 2013). In
addition, surface characteristics can be inspected through this microscopy. There are various
types of equipment used in destructive methods such as low range optical microscope, CNC
vision mission microscope, and high range magnification of scanning electron microscope. The
micrograph of SEM can be used to find the macroscopic orientation of fiber, microfibrils
orientation, voids, cracks and the fiber matrix interface (Fischer, G., et al., 1988).
2.7.5 Non destructive method
The non-destructive method was utilized to inspect the macroscopic dimensions of fibers and to
quantify the orientation of fibers in the composites. Radiography and X-ray tomography
equipment are employed in the non-destructive method. In this method, the specimen is not
damaged and it is polished to find the defects (Bernasconi, A., et al., 2012). The radiography
approach is based on projection and absorption of X-ray images falling on the plane surface of
the sample. Radiography can give the orientation of fibers projected on the plane. The series of
radiographic images is reconstructed using computed tomography and 3D views of the fiber
44
orientation are obtained. The voids, internal structure and fiber orientation in each section of the
composite is examined. This method is employed to assess the fiber content in composites and to
view air bubbles in the composite (Bernasconi, A., et al., 2012; Schilling, P. J., et al., 2005).
2.8 Problem statement
The physical structure of natural fiber includes curling and kinking, which may affect
the pattern of orientation in the polymer composites. This makes developing a
mathematical expression to find the orientation of fibers in polymer composites
challenging.
The flow of molten polymer in the mold cavity has non-uniform velocities. The fluid
flows in a transient state during the filling phase of the cavity. It is a challenging
issue to find the velocities of fluid elements in the fluid domain.
The deformed nature of natural fibers causes a distinct pattern of orientation in the
composites. This may result in non-uniform distribution of fibers and agglomeration,
affecting the strength of the composite. It is a challenging task to understand the
pattern of natural fiber orientation in the composites.
The dynamic behaviour of fiber movement and the formation of the flow front are
difficult to visualize inside the mold cavity. The challenging task is to digitize the
fiber motion and find the orientation angle during the filling phase of the cavity.
An experimental setup is required to validate the mathematical model and to predict
the orientation of fibers in the transient state of fluid flow.
It is challenging to understand the orientation of natural fibers, void formation and
fiber-matrix interfacial interaction in the composite using a non-destructive method.
45
Based on the problem identified from the literature, the objective, and the hypothesis have
been stated for the analysis of the fiber orientation in the composites.
2.9 Hypothesis
The hypothesis of this research is that during the injection molding process, the curling of short
natural fibers leads to planar orientation in the skin layer and random orientation in the core layer
of the composite.
2.10 Research Objectives
To develop a mathematical model to predict fiber orientation in polymer composites
produced by injection molding process.
To design an experimental setup to visualize the orientation and flow behaviour of
natural fibers in a mold cavity.
To examine the pattern of fiber orientation for short and long fibers in the injection
molding process.
To examine the mechanical properties of natural fiber composites for different
percentages of fiber loading.
2.11 Scope of the research work
The primary goal of the project is to derive a mathematical model for predicting the natural fiber
orientation during the filling phase of the cavity. The mathematical expression was derived by
assuming a curling index and aspect ratio of the fibers.
To find the orientation of natural fiber in the specific location of the composites
46
To predict the angular velocity of fluid elements in the fluid domain of the cavity
To customise the source codes for the developed model into flow simulation software
to predict the orientation of fiber in the composite parts.
To enhance the planar orientation to improve the strength of the composites by
implementing a tab gate.
To anticipate the orientation of fibers in the critical area of the composite and to find
the effect of fiber loading on the composite strength.
47
Chapter 3 : Mathematical Model
3.1 Methodology
A mathematical model was developed to find the orientation angle of natural fibers during the
filling phase of a molding cavity by considering the curled nature of the fiber. The assumption is
made to derive the model was described in this section. The rotational effect of the fluid element
was assumed during the flow of fluid in the mold cavity. A systematic approach was used to
derive the angular velocity of the fluid and the orientation of the fibers.
3.1.1 Fundamental theory for flow
The flow of fluid in any domain follows the three fundamental laws of physics on conservation
of mass, momentum, and energy, which can be used to find the velocity, pressure, and
temperature of the fluid. The basic equations for the flow are given as the following:
Continuity:
Momentum:
Energy:
Where P is the pressure, T is the temperature, ρ is the density, Cp is the specific heat at constant
volume, S is the rate of heat generation, q is the heat flux, τ is the shear stress, D/Dt is the
48
substantial derivative and is the gradient operator. The continuity equation (3.1) and the
momentum equation (3.2) are coupled and derive an equation for finding pressure and velocities
through the stream vorticity approach (Wang, J., et al., 2008; Hu, H. H., et al., 1992; Zhang, D.
et al., 2011; Sugihara-Seki, M. 1996; Anderson Jr, J. D., 2009). The equations were used to
calculate pressure and velocities by solving the partial differential equation in finite difference
method by considering the boundary values of the fluid domain.
3.1.2 Characteristics of Steady flow
The velocity of the fluid flow inside the mold cavity describes the characteristics of flow. The
velocity at every point of flow assumed to remain constant with time for steady state flow. The
Reynolds number Re defines the characteristics of flow as Re = U.H/υ, where U is the velocity
of fluid, H is the cross section height of the fluid domain and is the kinematic viscosity of the
fluid. If the Reynolds number is less than 2000, then the fluid flow is characterized as laminar
flow and the fluid elements shear along the direction of flow (Bretherton, F. P., 1962; Sugihara-
Seki, M. 1996). The molten polymer is having a viscous nature and assumed to flow inside the
cavity with low shear. Therefore, it is characterized as a low laminar flow with a Reynolds
number less than 100 (Jeffery. G.B., 1922; Tooby, P. F. at el. 1997). The low laminar (Stokes)
flow assumes streamlined flow; the suspended short fibers are assumed as very small masses
floating on the fluid elements (Shanliang, Z., et al., 2007; Bellani, G., 2008; Chwang, A. T., et
al., 1975). It is assumed that the fluid elements of the viscous fluid act as a carrier for the
suspended short fiber particles and they cause rotational motion due to the non-uniform
velocities across the cavity. The dynamic motion is described by the change in position of the
fluid elements with respect to time and exhibits a rotational and translational motion (Anderson
Jr, J. D., 2010; Jensen, K. D. 2004).
49
3.1.3 Assumption made for natural fiber orientation
The following assumptions were made to derive a model for predicting the orientation of natural
fiber in a polymer composite during filling of the cavity.
1. The viscous fluid is assumed to be Newtonian and flows with low laminar flow.
2. Fluid is assumed to have finite elemental square shape and flows with rotational and
translational motion.
3. Natural fiber size is less than 3mm and has a negligible mass, floating on the viscous
fluid element.
4. Fluid elements act as carriers of the fiber particle, which are assumed to rotate relative to
the fiber geometrical centre.
5. Natural fibers are assumed to have a constant curling factor that depends on their shape.
The mathematical model is derived by incorporating the geometrical factor of the natural fiber
with the angular velocity of the fluid element to find the orientation angle of the particle inside
the viscous fluid during the filling phase. The dimension of the mold cavity was considered for a
size of (165X18X3) mm.
3.1.4 Fluid domain
In order to derive an equation for the angular velocity of the viscous fluid, a rectangular 2D fluid
domain is considered as a cross-sectional thickness of the polymer component. The silicone
polymer was chosen because of its viscous nature. The silicone polymer is injected into a cavity
and the velocity fields of the fluid element are oriented along the direction of flow in filling the
cavity. The flow of fluid along the domain has a non-uniform velocity, resulting in a flow front
and shear along the direction of flow. Figure 3.1 shows the 2D cross-section of the mold with
50
the inlet, outlet, boundary walls and the fluid elements flowing along the path line. (John D.
Anderson Jr., 2010; Jensen, K. D. 2004).
Figure 3.1: 2D domain of mold cavity, fiber path line
3.1.5 Velocity distribution in fluid domain
The fluid element flows in a streamlined motion by laminar flow carrying the suspended
particles along the direction of motion (Shanliang, Z. et al., 2007; Hu, H. et al., 1992). The fluid
elements have varying velocities across the domain from zero in the boundary wall to maximum
velocity in the core layer of the flow domain as showed in Figure 3.2(a). The non-uniform
velocity distribution across the fluid domain causes a low shear rate in the core layer and a high
shear rate near the wall boundary (Shanliang, Z. et al., 2007; Bretherton., F.P., 1962).The high
shear rates occur in the XZ plane and have a 3D orientation effect in the flow domain. This
causes the fiber to turn in XY plane because of the larger area compared to the XZ plane of the
cavity (Jackson, W.C. et al., 1986). The higher shear pulls the fiber to a region of lower shear in
the XY plane so as to cause uniform shear on the surface of the fiber, as shown in Figure 3.2 (b).
The basic principle of orientation depends on the shearing effect by establishing a difference in
velocities in the fluid domain (Yasuda, K., 2004; Jackson, W.C., et al., 1986).
51
Figure 3.2: (a) 2D Cross sectional of viscous fluid domain (Silicone polymer) with
non-uniform velocity distribution and flow front; (b) Fiber orient due to the effect of
shear
The fluid elements flow with rotational and translation motion. The rotational effect of the fluid
element takes place due to non-uniform velocities acting along the direction of flow (John D.
Anderson Jr., 20105; Aris, R., 2012). Therefore, the angular velocity of the fluid element is
determined by local changes in the velocity gradient at specific positions in the X and Y-axis.
Figure 3.3 shows the rotation of a fluid element with respect to its center, which causes a
shearing effect on the square surfaces of fluid elements along the flow path. The fluid flows in
low laminar regime following Stokes flow and the suspended particles like fibers are being
carried away by fluid elements in rotation with respect to its geometrical center (Götz, T. 2005;
Wang, W., et al., 2012; Tornberg, A. K.,et al., 2004 ).
52
Figure 3.3: Fluid element in square shape rotation along flow field
3.1.6 Derivation for angular velocity of fluid elements
A rectangular cross sectional of the mold cavity is considered as a two dimensional domain of
viscous fluid. The fluid flows along the path with translational and rotational motion. The fluid
elements are assumed to be square shape PQSR, where and are the lengths of the
horizontal and vertical side of the fluid element, as shown Figure 3.4(a). The velocities and
are the initial velocities of the fluid element at point P along the X and Y direction flow, at
time t1. They undergo a small change in velocity at point R along the Y-axis of the fluid element
by
and also undergo a change in velocity at point along the axis of the fluid
element of
at , as shown in Figure 3.4(b). The change in velocity at Q along the X-
axis and the Y-axis is given by
and
, respectively, and the fluid
element rotates along the flow path from seconds to seconds, as shown in Figure 3.4(b).
53
Figure 3.4: (a) Fluid element at t = t1 s, (b) Fluid element oriented at t = t2 s
The sides and are rotated in clockwise and anticlockwise direction through an angle of
and , respectively. The changes in velocities
and
, correspond to
and , where the fluid element P moves to P' along the Y direction for a time increment of
by a distance of . Similarly, S moves along Y direction for time increment of , which
is given by
with net displacement in Y direction from ,
.
Consider the triangle from Figure 3.4(b), where the side is rotated to by a small
angle θ , with the positive sign indicating rotation in an anticlockwise direction.
Assume for small angle that . By re-arranging the equation (3.4):
54
By considering a triangle from Figure 3.4(b), the side is rotated to in a clockwise
direction by a small angle , where the negative sign indicates the clockwise direction of
rotation. The fluid element at point is translated to as shown in Figure 3.4(b) in a time
and the fluid element at point is moved to with a change in velocity along the axis given
by
. The point P of the fluid element PQRS moves along the X
direction with a velocity
in a time increment of given by and the point S moves along the X direction with a
small change in velocity from initial velocity for an incremental time of given
by
. The side is rotated to in clockwise by a small change in angle -
with a negative sign indicating rotation in the clockwise direction.
By rearranging the equation (3.6):
The average rate of change of the fluid element angle along the direction of flow during filling of
cavity in 2D domain is given by
Substituting the values of equation (3.5) and equation (3.6) into equation (3.7), the angular
velocity of the fluid element along the axis of the plane of the 2D domain of flow in the
cavity is obtained to be:
55
3.1.7 Aspect ratio
The aspect ratio is defined as the geometrical ratio of length to width of the fluid element of
rectangular shape. It is denoted by . If the aspect ratio of the fluid element is unit,
then, the length and width of the fluid element are equal and the fluid element is assumed to have
a square shape. In the dynamics of fluid theory, fluid element flows with translation and rotation
along the flow field. The unit value was assumed for the aspect ratio of the fluid element and the
fluid flows in streamline motion (Anderson Jr, J. D., 2010; Fox, R. W., et al., 1985). The aspect
ratio is considered in determining the angular velocity of a rotating fluid element, assuming that
the fluid element rotates locally with respect to its center, as showed in Figure 3.3. The non-
uniform velocities across the section of the fluid domain induce a couple on fluid elements
enabling a rotational motion. The angular rate of rotation of the fluid element with respect to its
center is given by:
If then the shape of the fluid element is represented as square (L=D), and the angular
velocity is given as:
56
According to Stokes’ law, the frictional force exerted on the suspended fiber particles for small
Reynolds number of laminar flow carries the fiber over the fluid element along the direction of
flow. The suspended short fibers are rotated due to the shearing action of the viscous fluid during
filling of the cavity (Gotz, T., 2005; Andric, J., et al., 2013).
3.1.8 Shape factor of natural fiber
Short natural fibers with low density consisting of cylindrical fibrils with curls and kinks float on
the viscous fluid and rotate because of shear. The fibrous structure in the polymer matrix affects
the flow behavior of the viscous fluid (Epstein, M., et al., 1995; Tornberg, A. K., et al., 2004).
The ideal geometry of natural fiber is considered to be cylindrical in shape with an aspect ratio of
fiber defined as the ratio of fiber length to its diameter
. Figure 3.5 shows
schematic 2D images of a natural fiber in various shapes and are spinning around the self-center
of the fiber geometry (Zeng, X., et al., 2012; Edlind, N. 2003).
Figure 3.5: Natural fiber shapes
3.1.9 Velocity distribution on natural fiber
The flow of molten polymer inside the cavity exhibits a flow front and has non-uniform
velocities distributed on the surfaces of the fibers. Figure 3.6(a) shows the non-uniform
velocities acting on the vertical side and the horizontal side of the cylindrical fiber that induces a
57
torque with respect to the geometrical center of the fiber. The fiber rotates with respect to its
center due to non-uniform velocities and to the shape factor of fiber. The short fiber rotates at a
maximum angle, where the velocities acting on the fiber in the X and Y directions are equal. The
fiber remains tangential to the flow front of the viscous fluid shown in Figure 3.6(b).
Figure 3.6: a) Velocities distribution over 2D cylindrical
shape fiber (b) Induced couple and orientation of fiber
The non-uniform velocities acting on the vertical side of a cylindrical fiber decrease, while those
along the horizontal side increase, enabling rotation until the fiber reaches steadiness in velocity.
Figure 3.7(a) shows the non-uniform distribution of velocity acting on the vertical and the
horizontal sides of a curled fiber causing it to rotate to a maximum angle of orientation, until the
fluid element become tangential to the flow front as shown in Figure 3.7(b).
58
Figure 3.7: (a) Non uniform velocities distribution on
curling fiber, (b) Velocity distribution is uniform in
horizontal and vertical side
3.1.10 Curling factor
It is hypothesized that the curliness of a natural fiber causes an influencing factor that resists the
orientation of the fiber along the orientation of the fluid element. This curling effect in natural
fibers induces a resisting factor in the angular velocity of fiber motion, which must be accounted
for the prediction of fiber orientation. The curl is defined as the ratio between the shortest
distances between the ends of fiber to the contour (true) length of the fiber, which is fit to the
spherical diameter of the curve shaped fiber, as shown in Figure 3.8(a). The curling index is
the ratio of circumference length of curling fiber to the length in curve shaped fiber shown
in the Figure 3.8, denoted by diameter of spherical geometry (Edlind., N. 2003) and curling
factor is given by
59
Figure 3.8: (a) Curliness of fiber fit to sphere, (b) Fiber segment
The curliness in the fiber has multiple segmental arcs that can form a slender curved fiber, as
shown in Figure 3.8(b), where indicates the radius of a single fiber segment and is the
angle of the arc spanning the fiber of length , is given by:
The aspect ratio of the fluid element is assumed to have a unit value for the ideal case so as to
predict the angular velocity at a specific position. The small fiber particle floating over fluid
element is assumed to have a resisting factor, so the curling index parameter was added to the
aspect ratio (L/D) of a fluid element, in the equation (3.12) (Gotz, T. 2005).
The curling index value from equation (3.13) is substituted into equation (3.15). Hence the
rotational rate of the fiber with the curling effect was included in the aspect ratio of the fluid
element is given by
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The equation (3.10) represents the instantaneous angular velocity of the rotating object that is
used to predict the orientation angle of the fiber at a filling time t sec, given by:
3.1.11 Kinematic rotation of fiber
The non-uniform flow front moves in a closed cavity with a radial velocity as shown in
Figure 3.9. The flow front of the fluid establishes an impulse force on the fixed particle at
specific positions and rotates it with respect to its geometric center.
Figure 3.9: Angular rate of rotation of single particle
The fluid shear force creates a moment on the particle that turns with respect to its geometric
center. Figure 3.10 shows the velocity and acting on the particle in horizontal and
vertical directions. The impulse moment rotates the particles until it reaches an equilibrium
position, where the horizontal velocity and the vertical velocity are balanced.
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Figure 3.10: Kinematic rotation of particle with respect to relative velocity
The fiber rotates due to the non-uniform velocity and the degree of orientation depends on the
shear rate of fluid flow across the fluid domain. The impulse force acts on the fiber particles
causing an instant rotation of the fiber particles that become tangential to the flow front. Thus,
the rotational motion of the fiber particle flow along the direction of fluid flow has a relative
velocity and direction angle ϕ with respect to the inlet gate is given by
Radial Velocity =
The angle predicted through the relative velocity of fluid flow is due to the impulse moment
acting on the fiber particle. The fiber remains tangential to the flow front because velocities
acting on the surface of the fiber are uniform. The immersed fiber in the viscous fluid flows
along the flow front and becomes oriented tangential to the flow front in the XY plane.
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The orientation of the fiber during flow in the mold cavity is given by an equation as
3.1.12 Limitation of the Mathematical model
The derived model was limited to the rectangular shaped cavity having a wide area
cross section and varying cross section
The model is limited to constant curling factor; the flexibility of the natural fiber was
not considered.
The Derived model depends on velocities of the viscoelastic polymer rather than the
viscosity and pressure of the polymer.
The model is limited to laminar flow of polymer and the fiber interaction coefficient
and turbulent flow are not considered.
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Chapter 4 : Computational and Experimental Method
4.1 Method
In this section, the injection cavity was designed and the prototype of the mold cavity was
developed for the model validation. The orientation of fiber particles was numerically predicted
using the derived model. Two case studies were carried out to investigate the orientation of fiber
particles in a viscous fluid during the filling phase of the cavity. The laboratory scale model was
developed and the flow front images were digitized to measure the fiber orientation angle.
4.1.1 Design of mold cavity
The cavity was designed as per the standard of the tensile specimen, and the position of the inlet
gate was fixed at the bottom of the cavity as showed in Figure 4.1. The sprue was designed
perpendicular to the inlet gate in such a way that the injection of viscous polymer is
perpendicular to the cavity (Figure 4.1). The 3D model of the cavity was designed in CAD
software (CATIA V5 R10) and the wide area of the cavity was defined as the XY plane. The
thickness of the cavity was considered as the XZ plane. High shear forces are present in this
plane. The orientation of the fibers in 3D space due to the shearing effect which causes the fiber
to turn in XY plane. In addition, it is difficult to view the fiber orientation and flow front in a
3mm thick cavity. Therefore, XY plane was considered and the orientation angle was predicted
for the purpose of model validation.
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Particles of cylindrical shape were designed in CAD software with size of length 3mm and
radius 0.25mm. The designed fiber particle has a hole at the center of geometry to rotate freely.
The prototype of silicone-based fiber was developed using a rapid prototyping process for
validating the orientation angle of fiber particles in viscous fluid flow.
Figure 4.1: 3D model of mold cavity
The CAD model of the mold cavity was designed with provision of holes at 20mm from inlet
gate and 20mm at the exit end of the cavity to insert a pin. The designed CAD model of the
cavity was transformed into STL file using rapid prototyping software. The 3D model was sliced
using slicing software of PolyJet 3D printer and the mold cavity was built. The top mold was
printed using rigid transparent material in PolyJet Printer (model – Eden 350V; manufacturer –
OBJECT; Country- US). The cylindrical particles were printed using flexible rubber material in
PolyJet printer. The pin was inserted in the holes provided in the mold cavity and the cylindrical
particles with hole was inserted in the pin to rotate the particle freely in the mold cavity, as
shown in Figure 4.2.
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Figure 4.2: Cylindrical particles fixed in Mold cavity
4.1.2 Mold cavity for case study
Two transparent cavities were developed in rapid prototyping machine to visualize the
orientation of free flowing fibers. The transparent cavity of varying section representing Case-1
of ASTM D 638 –Type I, is shown in Figure 4.3 and another cavity was designed to have a wide
area cross section representing Case-2 with dimensions 150 x 50mm, shown in Figure 4.4.
In the Case-1 cavity, a photo- bleaching process was done on the veroclear material of the
PolyJet printer (model –Eden 350V) to improve the transparency of photo-polymer material.
The injection path of the fluid flow was designed for inward flow and the inlet gate remains
normal to the injection point. A separate guide way was developed from epoxy material to hold
the nozzle and to guide the viscous fluid into the injection sprue. The vent hole is provided at the
exit end of the transparent cavity and the cavity pressure was released during filling shown in the
Figure 4.3.
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Figure 4.3: Transparent Cavity for Case 1
The wide area cavity was developed and the vent hole was placed at the exit of the transparent
cavity. The injection point was designed normal to the inlet gate as showed in the Figure 4.4.
The cavity was designed to have a uniform section and the fiber orientation was visualized along
with the flow front in the XY plane.
Figure 4.4: Transparent Cavity for Case 2.
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4.2 Computational method
4.2.1 Computation method for fiber orientation
The computational fluid dynamics (Fluent 14.5) software was employed to study the velocity
distribution inside the cavity during the filling period. The computational methods used a
decoupled approach in two stages to find the orientation angle of the fibers (Redjeb. A., et al.,
2005). The first stage was used to determine the velocity distribution acting on the fiber particles
in the fluid domain. In the second stage, the mathematical equation was used and the velocity
gradient was numerically obtained from the simulation result, to predict the orientation of fiber
particles.
4.2.1.1 CAD model of the mold cavity
The 2D model of ASTM 638D- mold cavity was developed to study the fluid flow analysis
inside the cavity. The 2D cavity was designed in such a way that the cylindrical fiber particles
are fixed at a distance 20mm from the inlet gate and also 20mm from the end portion of the
cavity, as shown in Figure 4.5(a). The 2D fluid domain of the cavity was meshed using gambit
software for a mesh size of 0.5 units, shown in Figure 4.5(b) and imported to ANSYS Fluent
14.5 to analyze the velocity distribution over the fibers positioned 20mm from inlet. The analysis
was executed for a fill time of 8 seconds to find the velocity magnitude in the mold cavity. The
flow of fluid was considered as transient, laminar and gravity-based flow. Therefore, the k-kl-
transition flow model was chosen in the simulation software and to find the velocity of fluid
based on the characteristic of the boundary condition. (Aftab, S. M. A., et al. 2016). The analysis
was performed on 2D domain and 2D mesh was generated to predict the velocity distribution
acting on the fibers fixed at specified positions.
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Figure 4.5: (a) 2D mold cavity with particles fixed (b) 2D mesh domain of specimen
The viscous silicone polymer was selected with a Reynolds number as Re=100, causing laminar
flow. The inlet velocity was assigned to 0.02 m/sec while the outlet pressure is at atmospheric
conditions. The polymer was allowed to fill the cavity in 8sec and the flow of polymer was
considered as laminar flow. The velocities acting on the fiber particles were measured by
assigning the following boundary condition for the fluid domain.
Polymer : Silicone
Viscosity of the fluid : 130Pa.s
Inlet velocity : 0.02 m/sec
Outlet pressure : gauge pressure (101.325 pa)
Boundary Velocity : zero (wall effect)
The pressure – velocity coupling option and second order momentum equation were employed
for analysis and to find the velocity distribution over particles in P1, P2, P3, P4 and P5, P6, P7,
P8 locations.
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4.2.1.2 Velocity distribution
The CFD analysis was performed to obtain the velocity distribution at 20mm from the inlet and
20mm from the end of the cavity. The non-uniform velocities acting on the 2mm length of short
particles was obtained from numerical calculation to find the orientation angle. Figure 4.6 and
Figure 4.7 shows the horizontal and vertical distribution of velocities over each particle
during a filling period of 8 second. The horizontal velocity distribution on the particles P1, P2,
P3 and P4 varies along the length of the particles and the horizontal velocity profile is shown in
the Figure 4.6. The particles P1 and P4 positioned near the wall of the cavity have a maximum
variation in velocities along the length of the particle. The particles P2 and P3 positioned near
center region of the cavity have a minimum variation of velocities along the length of the
particles.
Figure 4.6: Horizontal velocity distribution on fibers at inlet
The horizontal velocities acting on the Particle P1of length 2mm positioned near the inlet
gate gradually decrease from the lower end of the particle to the upper end. Also, the horizontal
velocities acting on the particle P4 positioned near the wall gradually increase from the
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lower end of the particles to the upper end. The velocity near the wall is minimum because the
fluid layers are in contact with the wall surface. The velocities vary from a maximum 0.4mm/sec
to a minimum 0.06mm/sec for Particles P1 and P4. Similarly, the vertical velocities vary from a
minimum 0.04mm/sec to a maximum 0.4mm/sec along the length of the 2mm particles P2 and
P3.
Figure 4.7: Vertical velocity distribution on fibers at inlet
The vertical velocities acting on the diameter of particle P1, P2, P3 and P4, are shown in the
Figure 4.7. The variation of velocities acting on the diameter of the particles is varied from
0.04mm/sec to 0.4mm/sec. The particles P1, P2, P3, and P4 are exposed to uniform variation of
velocities in the Y direction.
The horizontal distribution of velocities acting on particles P5, P6, P7, P8 at a position 20mm
from the end of the cavity are shown in the Figure 4.8. Each particle exhibits a minimum
1.2mm/sec to a maximum velocity of 2.7mm/sec. The particles P8 and P5 are positioned near the
wall of the cavity and the particles are exposed to a variation in velocities. The particles in P6
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and P7 position near the center region of the cavity have a same variation in velocities due to the
vent hole at the exit end of the cavity.
Figure 4.8: Horizontal velocity distribution on fibers at end
The Figure 4.9 shows the vertical velocity distribution acting on the particles P5, P6, P7 and
P8. The vertical velocities vary from a negative value of -1.5mm/sec to a positive value of
1.5mm/sec. The negative value of the vertical velocity is due to the entrapment of air in the
cavity and the flow of fluid creates a circulation at the end of the cavity. Therefore, the degree of
rotation of particles at the end of the cavity is unpredictable due to the negative velocity.
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Figure 4.9: Vertical velocity distribution on fibers at end
The flow front and velocity magnitude distributions inside the 2D domain of the cavity are
shown in Figure 4.10(a). The Figure 4.10(b) shows the velocity distribution at a distance 20mm
from the inlet for the particles P1, P2, P3, and P4 and the velocity magnitude at varying cross-
sections of the cavity. The variation of the velocity vectors at the inlet gate region forms a
varying flow front and gradually decreases along the area of cross section. The flow fronts are
varying along the direction of flow, with respect to the 2D section of the cavity. The velocity
vector acting on the fixed particles is shown in Figure 4.10(a) and the magnitudes of the
velocities are numerically predicted for calculating the angular velocity of a fluid element.
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Figure 4.10: (a) Flow front, (b) Velocity magnitude distribution in mm/sec
4.2.1.3 Numerical approach for orientation
The numerical calculations for angular velocity of the fluid field were calculated for the particles
positioned at 20mm from the inlet and are shown in the Table 4.1. The maximum (Vx max) and
minimum (Vx min) horizontal velocity acting on the rigid particle were determined numerically
from Fluent software. Similarly the maximum (Vy max) and minimum (Vy min) vertical velocity
acting on the rigid particle was also determined numerically for a 2D particle with the size of
2mm X 0.4mm (L×W). The manual calculation was performed using the derived mathematical
model to find the orientation angle of particles at 20mm from the inlet and is shown in Table 4.1
and Table 4.2. The similar numerical calculations for angular velocity and orientation angle were
calculated for all the particles positioned at 20mm from the end of cavity and are shown in the
Table 4.3and Table 4.4.
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Table 4.1 : Angular velocity of fluid element at 20 mm from inlet for cavity filling time 8 s
S no.
Fill Time
Particles
Vx max
Vx min
Vy max
Vy min
Delta Vx
Delta Vy
Delta x
Delta y
w= 0.5*(dVy/dx-dVx/dy)
sec mm/s mm/s mm/s mm/s mm mm mm mm rad/sec
1 8 P4 2.88 5.53 0.02 0.10 -2.65 -0.08 0.4 2 0.56
2 8 P3 7.14 7.64 0.02 0.32 -0.50 -0.29 0.4 2 0.24
3 8 P2 7.82 7.59 0.03 0.24 0.23 -0.21 0.4 2 0.32
4 8 P1 6.23 3.75 0.10 0.02 2.48 0.08 0.4 2 -0.52
From the Table 4.1, the maximum horizontal velocity of silicone fluid acting on the diameter
0.4mm (Delta-x) of particle P1 (Vx- max) is 6.23mm/s and the minimum velocity (Vx-min) is
3.75mm/s. Similarly, the maximum vertical velocity of fluid acting on length 2mm (Delta-y) of
particle P1 (Vy-max) is 0.10mm/s and minimum velocity (Vy-min) is 0.02mm/s. The results are
tabulated and the angular velocity of the fluid element was calculated by assuming a unit value
for aspect ratio.. Similarly, the angular velocities were calculated for the particles P2, P3, and P4
positioned at 20mm from the inlet.
Table 4.2 : Orientation angle of rigid particle at 20 mm from inlet for cavity filling time 8 s
S no.
Fill Time
Particles
Fiber Length L
Fiber Dia - D
Curl length CL
Curling factor
Teta = t. (Curl factor).w
Teta Degree ranging from 0-180
sec mm mm mm (L/CL)-1 Rad Deg Deg
1 8 P4 2 0.4 1.5 0.33 1.51 86.35 86.35
2 8 P3 2 0.4 1.5 0.33 0.64 36.87 36.87
3 8 P2 2 0.4 1.5 0.33 0.84 48.42 48.42
4 8 P1 2 0.4 1.5 0.33 -1.40 -80.09 9.91
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From the Table 4.2, the curling length of fiber particle was assumed for a constant length of
1.5mm (CL) from which the curling factor was used and calculated the orientation angle. The
orientation angle of particle P1 is calculated by multiplying the angular velocity and the curling
factor for a complete fill time of 8 sec. Finally, the orientation angle is converted from radiant to
degree and the predicted angles are converted to a range from 0° to 180°. Similar method is
adopted for the particles P2, P3, and P4.
Table 4.3 : Angular velocity of fluid element at 20 mm from end for cavity filling time 8 s
S no.
Fill Time
Particles
Vx max
Vx min
Vy max
Vy min
Delta Vx
Delta Vy
Delta -x
Delta -y
w= 0.5*(dVy/dx - dVx/dy)
sec mm/s mm/s mm/s mm/s mm mm mm mm rad/sec
1 8 P8 2.69 2.18 -1.20 1.26 0.51 -2.46 0.40 2.00 -3.20
2 8 P7 2.71 2.75 -1.26 1.39 -0.04 -2.66 0.40 2.00 -3.31
3 8 P6 2.75 2.69 -1.33 1.37 0.05 -2.70 0.40 2.00 -3.39
4 8 P5 1.96 2.63 -1.06 1.27 -0.67 -2.33 0.40 2.00 -2.74
The angular velocity of the particles was calculated for particles P5, P6, P7 and P8 located at a
distance of 20mm from the end of the cavity and is tabulated in Table 4.3. Furthermore, the
curling factor is calculated for an assumed constant curling length of 1.5mm and the orientation
of the particle is predicted. For an angle exceeding 360°, the result was converted to be within
the range from 0° to 180°. The results are shown in Table 4.4.
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Table 4.4 : Orientation angle of rigid particle at 20mm from end for cavity filling time 8 s
S no.
Fill Time
Particles
Fiber Length L
Fiber Dia - D
Curl length CL
Curl factor
Teta = 1/2. t. (Curl
factor).w
Teta Degree ranging from 0-180
sec mm mm mm (L/CL)-1 Rad Deg Deg
1 8 P8 2 0.4 1.5 0.33 -8.53 -488.90 128.90
2 8 P7 2 0.4 1.5 0.33 -8.83 -506.10 146.10
3 8 P6 2 0.4 1.5 0.33 -9.04 -517.94 157.94
4 8 P5 2 0.4 1.5 0.33 -7.31 -419.02 59.02
4.2.2 CAD model for the Case studies
The case studies were performed for free flow of fibers in silicone fluid during the filling phase
of the cavity. The mathematical equation was used and to numerically predict the orientation
angle of free flowing fibers. Two case studies were performed for finding the orientation angle of
fibers at varying sections (Case-1) of the cavity and wide area uniform section (Case-2) of the
cavity. The 2D model of fluid domain was designed in CAD software for Case-1 and Case-2
cavities and is shown in Figure 4.11 and Figure 4.12.
Figure 4.11: 2D model of fluid domain for Case-1
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Figure 4.12: 2D model of fluid domain for Case-2
4.2.3 Flow analysis in Fluent
The CAD model was developed for a 2D fluid domain and was meshed using the meshing
software to numerically simulate the flow in the cavity, shown in Figure 4.13 and Figure 4.14.
The internal fluid region is meshed using quadrilateral cell element with the pave algorithm of
gambit.The flow domain has meshed with a unit size interval of 0.5 and generated 35813
elements and 36554 nodes (Hanzlik, J. A. 2008). The edges of the geometrical surfaces were
converted into face and the boundary conditions were applied to the fluid domain. The inlet
velocity is defined and velocity in the wall is considered to be zero.The fluid assigned for flow
analysis is silicone and the Fluent5/6 solver was selected to predict the velocity in the fluid
domain.
Figure 4.13: Meshed domain of Case-1
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Figure 4.14: Meshed domain of Case-2
4.2.3.1 Procedure to obtain velocity distribution using FLUENT analysis
Step 1: To analyze the 2D mold cavity, the mesh file was imported into Fluent 12.5 and
analyzed by using Ansys 14.5 software.
Step 2: The mesh geometry of fluid domain model in *.dbs file was exported to a 2D file format
of *.msh . The mesh file option in the software was enabled and the quality and size of the mesh
were checked.
Step 3: The velocity in the fluid domain was predicted by enabling transient nature of the flow,
density and a transition flow model was selected for the analysis. The model was
used for the application of low Reynolds number, transitional flow and shear flow (El-Behery, S.
M., et al., 2009).
Step 4: The flow of fluid along the surface of the wall and resistance over the wall was
considered by enabling the wall treatment option in the Fluent software.
Step 5: Fluid properties are assigned based on silicone material available in the Fluent software
and customized other variables required for the analysis.
Step 6: The boundary condition was applied based on the inlet velocity and the wall effect on
fluid flow in the fluid domain.
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Step 7: The process was carried out for a defined outlet flow with gauge pressure condition
exposed to the atmosphere.
Step 8: The Reynolds Average Navier-Stokes model was selected to predict the velocity and
pressure in the fluid domain. The second order momentum equation was used for 1000 iterations
to the set value of 0.001 to obtain a converged result of velocity.
Step 9: The flow-lines in the fluid domain were obtained after convergence of 1000 iterations
and the line was marked at position X=20mm and X=145mm in the cavity by creating line
option. A data file was produced that can be exported for numerical validation.
Step10: To create the image of the velocity magnitude, vorticity magnitude, stream function and
the vector diagram at 20mm at 145mm, the velocity distribution diagram was obtained and is
saved in an image format.
Step 11: The case file and data file format can be saved to retrieve the data for verification.
4.2.3.2 Boundary conditions
Property of the viscous fluid : silicone
Viscosity of the fluid : 130 Pa S
Inlet velocity : 0.02 mm/sec
Outlet pressure : gauge pressure (101.325 pa)
Outlet boundary : wall
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4.2.4 Flow front simulation
The CFD analysis was performed to obtain the velocity distribution at various positions of the
cavity for Case-1 and Case-2 shown in Figure 4.15 and Figure 4.16. The non-uniform velocities
acting at specified positions are considered for the numerical calculation of velocities and
in the fluid domain for the complete filling of the cavity in 8 seconds. The horizontal and
vertical velocities gradients was found to predict the fluid element rotation at specific locations
and to find the orientation angle of the fluid element during the dynamic flow of the fluid.
Figure 4.15: Velocity distribution profile for Case-1
Figure 4.16: Velocity distribution profile for Case-2
There are two parts of the angle, used to predict fiber orientation using mathematical
equation 3.22, where is the orientation angle predicted by instant rotation due to the local
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velocity difference acting on the fiber and is the angle predicted based on the relative
velocity of flow front at the specified position. The orientation angle of the fiber particle was
predicted by coupling orientation angle ( shown in the equation 3.22.
4.2.5 Numerical approach for orientation
The numerical calculation for the angular velocity of the fluid field was performed using
Equation 3.17 for fibers P1, P2, and P3 at different times (2 , 4 , 6, and 8 s) at the corresponding
positions in the cavity and is shown in Table 4.5. The maximum (Vx max) and minimum (Vx min)
horizontal velocities acting on the fluid element were determined numerically from Fluent
software. Similarly, the vertical velocities maximum (Vy max) and minimum (Vy min) acting on the
fluid element were also calculated numerically for an imaginary boundary around the 2D fluid
element of size (2×2 mm2) (L x W). The orientation angle of the fiber in the mold was calculated
using a mathematical equation for a filling time of 8 sec and is shown in Table 4.5 and Table 4.6.
The similar method of numerical calculation was done for fiber particles P2 and P3 to obtain the
angular velocity and the orientation angle of the fiber inside the mold cavity.
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Table 4.5 : Angular velocity of fluid element for Fiber particle P1, P2, P3
complete filling time 8 s for Case-1
Table 4.6 : Predicted angle of orientation for fiber particles P1, P2, P3
for complete filling of cavity in 8 s for Case-1
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The similar process was followed for the Case-2 mold cavity and the angular velocity of the fluid
element was numerically calculated, as showed in Table 4.7. The calculation was further
extended to predict the orientation of fiber particles by including a curling factor for the
complete 8 sec. The orientation angles are shown in Table 4.8.
Table 4.7 : Angular velocity of fluid element for Fiber particle P1, P2, P3 for
complete filling time 8 s for Case-2
Table 4.8 : Predicted angle of orientation for fiber particles P1, P2, P3 for
complete filling of cavity in 8 s for case-2
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4.3 Experimental method
The experimental setup was designed to visualize the flow of fluid and the rotational rate of fiber
particles. The lab simulation model consists of a compressor, solenoid valve, pneumatic cylinder,
syringe pump, transparent mold cavity, and viscous fluid (silicone). The air compressor
converted electric energy into kinetic energy and compressed air from the compressor was
connected to pneumatics cylinder through a pneumatic control valve. The high-pressure plunger
of the pneumatics cylinder piston pushes the ram of the syringe pumps to a nozzle. The syringe
pump containing viscous fluid was injected into the transparent cavity. The pressure in the
syringe was maintained to fill the cavity with laminar flow by controlling the pneumatics control
valve.
Figure 4.17: Experimental setup to view fiber orientation in cavity
The simulation model is shown in Figure 4.17. The viscous fluid was filled in the syringe pump
and injected into the cavity for the specified time in ‘ sec. The digital camera was focused on
the XY plane of the transparent cavity and the fluid flow and rotational rate of fiber particle in‘
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second was recorded. The animation of fluid flow was analyzed for each interval of time, to find
the orientation angle of fibers.
4.3.1 Experimental procedure
Step 1: The silicone polymer was considered as a viscous fluid and has a transparent nature with
a viscosity of 130Pa S. The silicone polymer was injected into the cavity containing cylindrical
particles fixed at position 20mm from the inlet and 20mm from the end. The viscous fluid was
injected in 8 seconds and the rotation of cylindrical particles during filling of the cavity was
visualized.
The two case studies (Case-1 and Case-2) were carried out by mixing silicone polymer with
natural fibers of 2mm in length placed in the syringe-pump. The viscous fluid with fiber was
injected to fill the cavity in 8 seconds and the orientation of fiber in the XY plane was visualized.
Step 2: The high-pressure plunger was activated using the compressor with a pneumatic control
valve, as showed in Figure 4.17. The compressed air was supplied to the pneumatic cylinder to
compress the piston of the cylinder.
Step 3: The natural fiber mixed with silicone polymer and placed in the cylinder. The plunger of
the syringe pump has compressed the cylinder and injected into the transparent cavity.
Step 4: The video camera was attached to the experimental setup and recorded the fluid flow.
The camera data were recorded in an attached system to study the image frames of the flow.
Step 5: The video recording was digitized by using CAD software to obtain the flow front for
every second and predict the angle of fiber at every instant of flow.
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Step 6: The orientation angle of fiber obtained from the experiment method was used to validate
the mathematical expression.
4.3.2 Digital Imaging process for particle in fixed position
The digital camera fixed on the injection system captures the video image of the fluid flow and
fiber orientation. The frame grabber option was used to position the fluid flow in the cavity and a
motion controller manages the image acquisition set-up. Afterward, the image was digitized for
each second and the frames were pasted on model space of CAD software, as showed in
Figure 4.18.
Figure 4.18: Video images of filling process of mold cavity in 8 sec
The curve lines were traced on the image frames and the flow front curve was drawn, indicating
the velocity profile, as shown in Figure 4.19(a). The orientation angles of each particle were
measured and dimensioned using CAD software, as shown in Figure 4.19(b).
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Figure 4.19 : (a) Digital image of flow front from CAD (b) Orientation angle of particles
4.3.3 Digital imaging process for Case-1
In the Case-1 study, the fiber / silicone polymer mixture was injected into a cavity of varying
section to view the orientation of fibers, flow front, and the flow field. The digital camera was
focused on the transparent cavity and captured the video image of the fluid flow and fiber
orientation. The video image was digitized at every second, the frames were inserted into model
space of CAD software, and the flow front for each second was manually traced. The orientation
angles of fibers were digitized to find the angle at each second, to verify the theoretical angle of
orientation shown in Figure 4.20
Figure 4.20: Digitized image of flow front for case I for each second
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Figure 4.21 shows the digitized image of fiber particles flowing along the pathline trace from the
experimental method. The flow field of fiber particle P1 flows along the wall of cavity and
pathline shows the streamline motion. The image clearly shows the fiber particles near the wall
of the cavity were aligned during the flow and the fiber particles in the center region, flows with
high velocity in a random orientation.
Figure 4.21: Digitized image of path line of fiber particles motion in Case-1
The orientation angles for the selected particles P1, P2, P3 for the Case-1 were measured and are
shown in Figure 4.22. The flow front of the viscous fluid was digitized for every 2 sec and
measured the fiber position and angle for the same interval of time on filling the cavity. The fiber
P1, P2, P3 positions and angular rotation are digitized for every 2 sec for complete filling of the
cavity in 8 sec. The fiber particle P3 moves with rotation from the inlet to the wall boundary and
remains horizontal to the wall with translational motion. The fiber particle P2 position at the
center of the cavity moves with high velocity and remains transverse to the direction of flow.
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Figure 4.22: Orientation angle of fiber particles P1, P2, P3 for Case-1
4.3.4 Digital imaging process for Case-2
In the Case-2 study, the fiber / silicone polymer mixture was injected into a uniform section of
the cavity. The flow front, fiber orientation, and the flow fields were digitized from the motion
controller of image acquisition. The video image was digitized for every second and the frames
were inserted into model space of CAD software. The flow front and fiber position were
manually traced for each second. The orientation angles of fibers P1, P2 and P3 were digitized
and measured the angle for each second as showed in Figure 4.23.
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Figure 4.23: Digitized image of flow front for Case-2 for each second
Figure 4.24 shows the digitized image of fiber particles flowing along the pathline trace from the
experimental method. The flow field of fiber particle P1 flows along the wall of the cavity and
fiber particles were aligned with the flow. The fiber particles in the center region flow with high
velocity in a random orientation and remain transverse to the direction of flow. The fiber P2
shown in the Figure 4.24, flow in a different path and orient angularly to the direction of flow.
Figure 4.24: Digitized image of path line of fiber particles motion in Case-2
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The Case-2 transparent cavity was developed for a wider range of uniform cross section 150 x
50mm (L x W) and the silicone/ fiber mixture was injected into the cavity. Figure 4.25 shows
the digitized image of the flow front and fiber motion with rotation for every second of filling the
cavity. The elliptical flow front profile in the wider area was reduced due to flow resistance from
the wall and the width of the cavity is higher compared to the thickness. The orientation angles
of fiber P1, P2, P3 are measured for every time interval and reported the experimental angle of
orientation. The orientation angles are measured in the XY plane because of wide area and flow
front is easily viewed than in the XZ plane.
Figure 4.25: Orientation angle of fiber particles P1, P2, P3 for Case-2
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Chapter 5 : Result and Discussion
5.1 Flow Behavior of Viscous Fluid and Orientation of Natural Fiber in the Cavity: Numerical analysis
5.1.1 Velocity distribution
The velocity distribution of silicone fluid in the mold cavity was numerically calculated and to
find the velocity at a specific position. The simulation was performed in Fluent software and
velocities in the domain were predicted for fluid flow inside the cavity. The Reynolds Average
Navier-Stokes (RANS) equation derived from the equation of motion in fluid dynamics was used
in simulation software to predict the velocities in the fluid domain. The flow velocity magnitude
of the silicone polymer at distance 20mm from inlet gate of the cavity is shown in Figure 5.1.
The velocity profile of silicone polymer was found to have minimum velocity near the wall of
the cavity and gradually rise to a maximum level in the center region of the cavity, forming an
elliptical profile. Oumer, A. N., et al., 2009 have reported the variation of velocity profiles for
natural fiber reinforced composites (Oumer, A. N., et al., 2009). It is clearly confirmed that a
non-uniform distribution of velocities is developed inside the cavity. The variation of the
velocity profile acting on the short rigid fiber particles was found minimum near the obstructed
area of the fiber particle.
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Figure 5.1: Velocity profile of fluid flow in domain
The 2D mold cavity was developed in CAD software, where the fiber particles of length 2mm
are fixed vertically at a position 20mm from the inlet gate and fluid flows radially inside the
cavity. Flow analysis was performed and observed a non-uniform distribution of velocities
magnitude at each position of the particle P1, P2, P3, P4, . The small flow front seen in
Figure 5.1 is the velocity distribution on the fiber particles fixed in vertical condition. It was
noted that the velocity distribution at each particle varies from a minimum to a maximum
velocity, which will rotate the fiber particle with respect to its center. The non-uniformity of the
velocity profile due to frictional resistance of the wall boundaries enables a local rotation in the
fluid element. The horizontal and vertical velocity profiles of the fluctuating flow acting on each
particle P1, P2, P3, P4, clearly emphasizing the non-uniform velocities are acting on the
particles. Figure 5.2(b) shows the orientation of rigid fiber particles rotates during filling the
cavity and Figure 5.2(a) shows the flow front profile of the silicone fluid obtained numerically.
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Figure 5.2: (a) Flow front profile from simulation software (b) Flow front profile from
experimental method.
5.1.2 Flow front comparison
The silicone fluid flow from the pin type gate has high shear near the narrow gate, causing non-
uniform velocities of the flow front. The numerical simulation of velocity distribution inside the
cavity and the flow front developed during a filling time of 8 secs is shown in Figure 5.2(a). The
flow inside the cavity was maintained at low laminar flow to study the rotation of the fiber
particle in the steady flow without turbulence. The flow front gradually changes at the fixed
position of rigid particles P1, P2, P3, P4 and the varying flow front along the varying section of
the cavity were observed. From the digitized images of the experiment shown in Figure 5.2(b), it
was observed that the flow front near the inlet gate of the cavity approximately match with the
numerical flow front. The rigid fiber fixed at position 20mm from inlet gate was found rotated
with respect to its geometric center and remained tangential to the flow front. The velocity
distribution of the flow front in the numerical simulation is approximately closeness with
experimental flow front shown in the Figure 5.3. Therefore, it is found that the shearing effect
on the flow front orients the short fiber particles. The higher shear pulls the one end of the fiber
from lower shear region in the XY plane by making uniform shear acting on the fiber surface to
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have translation. The direction of orientation depends on the tangential angle of the fiber relative
to the flow front and on the angular velocities of the fluid element carrying the fiber. (Zhang, D.,
et al., 2011).
Figure 5.3: Velocity distribution of flow front of numerical and experimental
5.1.3 Numerical result of orientation
The angular velocities of the fluid were calculated for each particle and were tabulated in
Table 4.1and Table 4.3. For the rigid particle P4, the angular velocity of 0.56 rad/sec was
predicted using equation 3.17. It was observed that the differences in velocity at the wall (2.88
mm/sec) and maximum velocity at the core (5.53 mm/sec), rotates the particle in an
anticlockwise direction. Similarly, angular velocities of 0.24 rad/sec, 0.32 rad/sec and
-0.52rad/sec were reported for particles P3, P2, and P1, respectively. The negative value of
angular velocity for P1 particle indicates that the rotation takes place in the clockwise direction.
These numerical techniques can be implemented in flow simulation software to predict the
angular velocity of the fluid elements for a specific unit of the aspect ratio. The orientation angle
of particles at P1, P2, P3, and P4 was numerically calculated to be 9.9°, 48.4°, 36.8° and 86.3°,
as shown in Table 5.1and Table 5.2.
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Figure 5.4: (a) Orientation angle of particle at 20 mm from inlet (b) Orientation angle of
particle at 20 mm from end
5.1.4 Experimental validation of orientation
The experimental results of orientation were digitized from video images through CAD software
and the orientation angles of the particles are tabulated in Table 5.1 and Table 5.2. The
orientation angle of rigid particles for P1, P2, P3 and P4 was measured to be 8°, 41°, 37°, and
81°, respectively. The experimental orientation angles were compared with the numerically
predicted angle from Table 5.1 and Figure 5.4(a). These method was already used in flow
simulation software and predicted the orientation of rigid fiber particles in the fluid domain
(McGrath, J. J., et al., 1995). From Table 5.2 and Figure 5.4(b), it was found that the measured
orientation angle of P5, P6, P7, and P8 were 82°, 132°, 129° and 135°, respectively. It was
observed that the orientation angles predicted numerically were different from experimental
angles, due to the flow of fluid in the reverse direction and the vorticity formed at the wall end of
the cavity. The cavity pressure generates an opposing force on the viscous fluid and changes the
direction of flow. The formation of vorticity and change in flow direction influence the
orientation of the fiber.
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Table 5.1: Numerical and experimental orientation angle of particles at 20
mm from inlet gate.
Particles Distance
(mm)
Numerical (°)
Experimental
(°)
P1 3 9.9 8
P2 7 48.4 41
P3 12 36.9 37
P4 17 86.4 81
Table 5.2 : Numerical and experimental orientation angle of particles
at 20 mm from end of the cavity.
Particles Distance
mm
Numerical
(°)
Experimental
(°)
P5 3 59.0 82
P6 7 157.9 132
P7 12 146.1 129
P8 17 128.9 135
5.2 Flow Behavior of silicone fluid and orientation of Natural Fibers in a Cavity: An Experimental Method
5.2.1 Velocity distribution
The velocity distribution of fluid elements along the cross section of the mold cavity for case-1 is
shown in Figure 5.5. The velocity distribution was non-uniform and the shearing of the viscous
fluid led to the formation of a flow front. It was found from Figure 5.5 that the velocities were
changed during flow due to the varying cross section of the cavity. An increase in velocities also
took place in the core area relative to the boundary wall. The rotation of fibers in the core layer
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was slow because of uniform velocities acting on the boundary of fiber, which tended to move
fibers in a translation motion. The digital image of case-1 from Figure 5.5(a) shows shearing of
the fluid tilting the fiber tangentially to the flow front and causing a translation motion due to a
uniform distribution of velocities along the fiber.
5.2.2 Flow front comparison
The flow of fiber/silicone mixture inside the cavity causes high shear and deforms the fiber
through the tab type gate. The deformed fiber from inlet gate flows into the cavity with non-
uniform velocities orienting the fibers along the flow front. From Figure 5.5(a) and
Figure 5.5(b), the orientation of natural fibers in the XY plane shows the fibers in the center
region rotate along the flow front and move with low laminar flow. The flow front radius
gradually changes along the direction of flow due to the varying cross section and varying
velocities in the mold cavity. Figure 5.5(a) shows the fiber particles are randomly oriented in the
center region and the rotational effect is small with high velocity. The fiber swings and becomes
tangential to the flow front, until complete filling of the cavity. The relative velocity and
direction angle of fiber positioned in the flow-front, relative to the inlet gate was numerically
calculated and compared the velocity magnitudes of flow front in the numerical simulation
(Figure 5.4(a)) and experimental (Figure 5.4(b)). Folkes, M.J., et al., have reported about
deformation of a fluid element and the advancing flow front (Folkes.M.J., et al., 1980). Although
a similar flow front effect was observed for Case-2, Figure 5.6(a) and Figure 5.6(b), it was
different due to its larger cross section. The exit profile shows a negative velocity along the Y
axis causing the rotation of the fibers in an anticlockwise direction due to vorticity effect in a
corner of the cavity.
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Figure 5.5: (a) Flow front developed in experimental method for Case-1, (b) Flow front
developed in ANSYS Fluent for Case-1
Figure 5.6: (a) Flow front developed in ANSYS Fluent for Case-2, (b) Flow front developed
in experimental method for Case-2
5.2.3 Experimental validation of orientation
The orientation angle of fiber particles P1, P2, P3 were found at different times 2, 4, 6, and 8sec
of filling. The comparison was done for the case studies, case-1 and case-2. From Table 5.3, the
numerical orientations of P1 at 2 and 8 sec, P2 at 6 and 8sec, P3 at 4, 6, and 8 sec are closely in
agreement with experimental orientation angles of case-1. Whereas, P1 at 4 and 6sec, P2 at 2 and
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4 sec and P3 at 2 sec deviated from the experimental results because the fiber particle size was
less than 1.5mm and also because the formation of flow front differences in the thickness XZ
plane. In Table 5.3 the orientation angle θA (Teta A) was predicted from local velocity variation
during the complete filling period of the cavity, while θB (Teta B) represents the orientation
angle of the fiber particle due to the flow front motion relative to the inlet. From Table 5.3, the
column referred as the orientation angle was the summation of θA and θB, where the angles range
from negative values to positive values. The negative angles of orientation were converted to be
within the range 0° to 180° and are tabulated in the column (Table 5.3). The orientation angle
ranging from 0° to 180° is validated with the experimental orientation angle. Hine, P.J et al.,
have reported 180° ambiguity for θ° in 2D images has two angle θ° or θ°+180 and described that
the fiber is oriented with respect to X-axis(Hine, P. J. et al.1992). The orientation having duality
problems and are referred as a same angle of misalignment for both the alternative orientation
(Zak, G., et al., 2001).
Table 5.3 : Comparison of orientation angles obtained experimentally and
numerically for Case-1.
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From Table 5.4, for case-2, the numerical orientation angle of fibers in the cavity of the larger
cross section area was compared with the orientation angle obtained experimentally to validate
the result. It was found from Table 5.4 that the numerical orientation angle of P1 at 4, 6, and
8 sec, P3 at 2, 4, 6, and 8 sec is closely matched with the experimental orientation angle.
Whereas P2 at 6 and 8 sec are not in close agreement with the experimental orientation angle
because the velocity distribution in the Y-axis is negative. The formation of a flow front in the
XY plane was reduced due to a larger width of the cavity compared to its thickness in the XZ
plane.
Table 5.4 : Comparison of experimental orientation angle and numerical orientation angles
for Case-2.
5.3 Conclusions
The mathematical model for natural fiber composites was developed by incorporating a constant
curling factor in the angular velocity of the low laminar flow of silicone fluid. The studies were
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conducted and the orientation of fiber particles in silicone during filling of the cavity in 8secs
was predicted.
1. The orientation angle of particles obtained numerically for P1, P2, P3, and P4 were 9.9°,
48.4°, 36.9°, and 84.4° respectively, and the experimental angles 20mm from the inlet gate
were 8°, 41°, 37°, 81° respectively, validating the model.
2. The non-uniform distribution of the velocity profile obtained from FLUENT software was
visually compared and correlated well with the digitized image of velocity profile of the flow
front.
3. The digitized image of short fiber particles orientations confirms that particles were randomly
oriented in the center region of XY plane and aligned along the wall surface of the cavity.
4. The developed mathematical model for the low laminar flow was tested. It was found that the
angular velocity of the fluid element located at a distance of 20 mm from the inlet varied from
0.56 rad/s to -0.52 rad/s. At the terminal end of the cavity, the angular velocity of the fluid
varied from -3.20 rad/s to -2.74 rad/s due to circulation and air entrapment inside the cavity.
5. The two case studies were conducted in two transparent cavities with different cross sections
and the orientation of natural fibers was predicted for each time period. The angle of
orientation was numerically calculated for the Case-1 study and the fiber angle for P1, P2, and
P3, were 176°, 22°, and 6° respectively. These were validated with the experimental
orientation angles of 169°, 34°, and 7 ° for the corresponding fibers
6. The orientation angle for the Case-2 study was numerically calculated for a complete filling
time of 8sec and the angles of the fibers for P1, P2, and P3 were -1°, 180°, and 18°, which are
validated with experimental angles 0°, 103°, and 12°. The orientation in the natural fiber
composite in the center region of the cavity was found to be random.
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Chapter 6 : Mechanical Properties and morphological study of Sisal Fiber reinforced Silicone Composites
6.1 Introduction
Polymer composites are commonly used in engineering applications, where fibers are embedded
in a polymer to increase their mechanical properties (Thielemans, W., et al. 2004). Silicone
rubber is an ideal material to develop silicone mold and produce thermosetting parts in small
volumes at a reduced cost (Windecker 1977; Weber, M. E., et al.1992). Silicone is being used in
the application of structural joints, medical kit holding devices, rubber seals and water resisting
vibration pads. The use of silicone molds in rapid prototyping (RP) technology could produce a
newly designed product in quick time and allow the development of small volumes of parts for
functional testing. Rapid tooling (RT) is an extension of RP, where the silicone mold is
developed from RP parts and small volumes of products are produced(Rosochowski. A, et al
2000; Gebhardt.A, 2007). Moreover, no attempt has been made to reduce the cost of silicone
mold in RT and to offer attractive features such as tear strength, high modulus, hardness, etc.
Natural fibers are being used in polymer composites to increase the strength and make eco-
friendly products (Arumugam, et al., 1989). Cellulose fibers are abundantly available at a lower
cost and are combined with rubber to enhance the mechanical properties of rubber composites
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(Boustany, K, et al. 1976). Varghese et al., have reported the increase of mechanical and
viscoelastic properties of short sisal fiber reinforced natural rubber composites and studied the
effect of chemical treatment on fiber loading (Varghese, S., et al., 1994; John, M. J., et al., 2008).
However, limited literature research attention has been devoted to silicone composites to
evaluate the use of sisal fiber as reinforcement.
The physical structure of natural fibers consists of hemicelluloses, lignin, and waxes which
establish a poor interface due to the hydrophilic nature of the fibers, which decreases the strength
of the composites. Therefore, chemical treatment is necessary to enhance the compatibility of
fiber /matrix adhesion and increase the hydrophobic nature of the fiber (Li, X., et al., 2007). In
studies of the effect of alkali treatment on sisal fiber, 4% NaOH treatment resulted in maximum
tensile strength (Geethamma, V. G., et al. 1995; Jacob, M., et al., 2004). The silane treatments
were implemented to reduce the hydroxyl group and establish a covalent bond with the cell wall
of sisal fiber (Herrera‐Franco, P. J., et al., 1997). The formation of hydrocarbon chains during
silane treatment may cause resistance to the swelling of fibers and establish covalent bond in the
form of a cross-link network between fiber and matrix (Varghese, S., et al., 1994;
Herrera‐Franco, P. J., et al., 1997).
Cross-linking is an entanglement of the polymer chain network and is evaluated by the degree of
swelling in solvent through the Flory-Rehner equation (Barlkani, M., et al.1992). The modulus of
elastomeric materials is related to the degree of cross-linking, where the lower degree of cross-
linking results in higher degree of swelling and tends to cause low modulus and flexibility
(Keshavaraj, R., et al., 1994; Da Costa et al., 2001). Many researchers have studied the swelling
behavior of short fiber reinforced elastomeric composites. George.S.C., et al. (1999) studied the
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effect of cross-linking density on swelling and on the mechanical properties of styrene-butadiene
rubber. Varghese. S, et al. (1994) investigated the adhesion between sisal fiber and rubber using
an equilibrium swelling method. There is little information available on the effect of cross-
linking density for different fiber loadings in silicone composites.
There is a limited research on the low cost manufacturing of silicone composite molds for Rapid
Tooling application. There are a few studies documenting fiber reinforced natural rubber
composites, but there is no significant work on the effect of fiber loading in silicone composites.
Furthermore, the cross-linking density of silicone composites has not been predicted using the
Flory-Rehner equation and the swelling method. The defects, fiber dimension, microstructure,
and interfacial adhesion between the fiber/matrix composite have not been analyzed using non-
destructive methods.
In this study, sisal fiber was treated with 3-amino propyl triethoxysilane and reinforced a silicone
sealant. The composite was produced using the compression molding process, and its mechanical
and morphological characteristics were studied. The properties of tensile, hardness, and tear
strength were compared for both treated and untreated sisal fiber composites. The swelling test
was performed to predict the cross-linking density of composites using the Flory-Rehner
equation. The microstructure was examined using X-Ray tomography and SEM analysis, and the
fiber/matrix interaction and defects in silane treated fiber composites were studied.
6.2 Experimental
6.2.1 Materials
The commercial resin silicone-methyl tri (ethyl methyl ketoxime) silane was used as the viscous
fluid and was obtained from Dow Corning from DAP, Inc. (Scarborough, Canada). The viscous
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resin is a single component moisture cured polymer and has low intermolecular forces. The
physical properties of silicone resin were as follows: density, 0.982 gm/cc; specific gravity, 1.03;
and service temperature, 0 °C to 200 °C. The sisal fiber was obtained from M/s Vibrant Nature
(Chennai, India). The sisal fiber had a density of 1.45 gm /cm3 and strength of 450 to 700 M Pa.
6.2.2 Fiber treatment
All the sisal fibers were pretreated with 1% NaOH solution for the partial removal of lignin, wax
content, and undesirable material. The treatment was carried out at room temperature for 2 h, and
the fiber was washed with distilled water until neutral pH was attained. The whole process was
carried out two times to remove the wax content and to generate roughness on the surface of the
fiber. The fibers were then chopped to an average length of 3 mm and sieved to maintain uniform
size. The short fibers were further treated with silane to reduce the proportion of cellulose
hydroxyl groups at the fiber surface; the possible chemical reaction is shown in Figure 6.1. The
presences of alkoxy groups in silane are hydrolyzed to form silanol. The hydroxyl group present
in the fiber reacts with silanol to form stable covalent bonds to cell wall of the fiber. The silane
(3-amino propyl triethoxy silane) (2% by weight) was dissolved in distilled water for 5 min, and
the sisal fibers were immersed in this solution for 2 h at room temperature for silane hydrolysis.
Therefore it is anticipated that the reaction of the silane with the water took place rapidly, giving
rise to colloidal matter, which might not be sufficiently active to react with the cellulosic
surfaces. Fibers were washed with distilled water for removal of acid until they reached a pH of
4.5 to 5.5. Then the fiber was dried in air for 2 h and subsequently oven-dried for 12 h at 75 °C,
and stored in polythene bags to prevent moisture (Li, X., et al., 2007).
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Figure 6.1: Schemes of interaction of silane with natural fiber
6.2.3 Compounding process and specimen preparation
The fiber was chopped to a length of 3mm for short fiber and 10mm for long fiber, with diameter
less than 0.4mm. Chopped fibers were mixed with silicone uniformly in a Brabender, Plasti-
Corder® Lab-Station (Duisburg, Germany). The mixer was driven at a rotor speed of 50 rpm
with a maximum torque of 150 Nm for 10 min for uniform mixing at room temperature. The
sisal/silicone composition was prepared for both treated and untreated sisal fiber. The
experimental setup was developed based on the principle of the injection molding process and
prepared the tensile specimen for 15% composition. The specimens were developed for 5%,
10%, 15%, and 20%, of sisal fiber reinforced silicone composite. The tensile specimen was
developed in compression moulding at room temperature, as per standard test method of tensile
test ASTM D412-15a (2015). The tear specimen was developed in compression moulding as per
standard test method of tear test ASTM D624-00 (2012). The thermosetting silicone composites
were moisture cured over the air for 96 h to form cross-linked molecular bonds in all composites.
6.3 Mechanical Characterization
6.3.1 Tensile test
The tensile test was performed using Instron 3367 tensile testing machine (Norwood, US)
equipped with 30 KN. The testing process was carried out at a crosshead speed of 50 mm/min
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and a gauge length of 33 mm, and the average values of tensile strength and modulus were
recorded for 10 samples of treated and untreated sisal fiber silicone composites. The tear test was
performed as per ISO 34-1 and B for 6 samples in the Instron tensile testing machine with a
gauge length of 50 mm for both treated and untreated sisal fiber composites.
6.3.2 Hardness
The hardness was measured using Shore A type durometer (Zwick, Germany) and followed
ASTM D2240. The depth of indentation on flat, cured specimens was measured for a given
period of 10 s at 10 different locations on the composites. The average value of Shore A hardness
number was tabulated.
6.3.3 Swelling test
The cross-link density of sisal fiber reinforced silicone composites was determined by a swelling
test, performed in xylene solvent at room temperature. The specimen was cut to 20 mm × 20 mm
x 3 mm and weighed before being immersed in the solvent. Composites were immersed in a jar
containing xylene solvent for 72 hrs and the swollen composites were weighed for calculating
cross-link density (Da Costa, et al., 2001; Marzocca, A. J., et al., 2007). From the experimental
data, the molar volume of solvent and volume fraction of swollen composites were calculated to
obtain the cross-link density in moles/g using the Flory-Rehner equation (Barlkani, M., et al.,
1992; Gan, T. F., et al., 2008). The average molecular weight between cross – link is given as
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Where the volume fraction of polymer in swollen condition; is the Polymer –Solvent
interaction parameter; is the molar volume of solvent; is the density of the polymer. The
volume fraction of polymer was calculated from equation
Where is the weight of the polymer before swelling; is the density of solvent; is the
weight of the polymer after swelling; is the density of polymer.
6.3.4 Morphological Study
6.3.4.1 Scanning electron microscopy
Scanning electron microscopy (SEM) (S-3400 SEM, Hitachi Ltd., Ibaraki, Japan) was used to
analyze fracture surfaces of the composites and to visualize the differences between treated and
untreated natural fiber. The micropores, voids, microstructures, and interfacial interaction of
fiber and matrix were investigated with the scanning electron microscope with a magnification
factor (500 X) and an accelerating voltage of 5.00 kV. The fracture surfaces of tensile
composites were mounted on stubs and gold-sputtered to establish effective conductivity for
examination. The images were processed using software to measure the cross-section, fibers, and
voids.
6.3.4.2 X-Ray tomography
The internal structures of the fiber arrangement in the matrix were examined using a non-
destructive technique by X-ray computed tomography (CT) (Nanotom-m, GE, Phoenix, AZ).
The specimen size of 10X10X3mm was examined in the X-ray tomography and the pattern of
natural fiber orientation was studied. The scanning was performed using nano-focus tube at
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8.56µ voxel resolutions of 23.35X magnifications and investigated voids, uncured matrix, and
improper adhesion in the composites.
6.3.4.3 Optical Microscopy
The composites specimen was produced in the experimental setup by the injection process and
studied the pattern of orientation in the skin and core layer. The composite specimen was
prepared for both short fiber (< 3mm) and long fiber (>10mm) in a non-standard dimension of
size 130X30X7mm. The sample size of 10X10X7mm was cut from the specimen and the sample
was examined under the optical microscope. The orientations of fiber were visualized at a
thickness of 1 mm (the skin layer) and 5mm (the core layer). Also, the dimension of the fibers
was measured using USB Digital microscope at 10X to 150X magnification. The composite
defects, orientation pattern, and fiber deformations on the surface were examined using an
optical microscope.
6.4 Results and Discussion
6.4.1 Tensile strength and tensile modulus of the composites by injection molding process
The composite specimens were prepared for 15% composition in the developed experimental
setup of the injection process. The experimental method was discussed in section 4.3 and the
composite specimens were produced in the lab scale model as per ASTM D412. The test result
of tensile strength and tensile modulus of 15% composites for both untreated and silane treated
sisal fiber composites are shown in Figure 6.2(a).The tensile strength and tensile modulus of
silane treated sisal fiber composites were 0.48MPa and 1.48MPa respectively. It was found that
the tensile strength and tensile modulus were improved after the silane treatment. This is
attributed to better interfacial interaction between the fiber surface and the matrix, which
111
enhances the strength of the composites. The composite samples prepared from the experimental
setup of injection process were not consistent with the thickness and having an uneven surface.
Hence, we used a more consistent process, compression molding to validate the effect of
interface modifier on the mechanical properties of the composites.
Figure 6.2: (a) Tensile strength and Tensile modulus of 15% Silicone/ Sisal fiber composites
by Injection molding process. (b) Tensile strength and Tensile modulus of 15% Silicone /
Sisal fiber composites by Compression molding Process
6.4.2 Comparison of the composite strength by injection and compression process
The composite specimens were produced in the compression molding process for the same
composition of 15% for both treated and untreated composites. The tensile strength and tensile
modulus of silane treated composites were 0.50MPa and 1.76MPa, respectively (Figure 6.2(b)).
The tensile strength of composites prepared in the experimental setup of injection process and
the compression molding process was 0.48MPa and 0.50MPa, respectively. Although
mechanical properties of manufactured composite through both techniques are compatible,
however, ease of operation and improved surface finish warrants the compression molding as
112
more feasible method in this case. Prior art has also demonstrated similar observations while
extruding rubber formulations through compression and injection molding process (Skrobak, et
al. 2013,). Henceforth we adopt to develop the composites in compression molding process for
different fiber loading.
6.4.3 Tensile Strength of Composites by compression molding process
The tensile strength of the sisal fiber composites depends on the interfacial interaction between
the fiber and matrix, fiber orientation, and fiber length. The tensile strength for various
compositions of untreated and treated fibers is graphically represented in Figure 6.3. The tensile
properties for various compositions for both untreated and treated fiber are presented in
Table 6.1.
Figure 6.3: Tensile strength of untreated and treated sisal fiber
reinforced silicone composites
An improvement in tensile strength was observed for silane treated short fibers, which
established a better interfacial bonding between the fiber surface and matrix. The increase in
fiber / matrix interaction is attributed to enhanced roughness on the surface of the fibers (Yao, Y.
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(2012)). It was noted that the strength of the composites was decreasing for the composition
containing 5%, 10%, and 15% of untreated fibers. The decrease in strength was due to the
presence of wax and other contamination on the smooth surface of natural fiber. This leads to
poor adhesion at the interface with a silicone polymer. Therefore, the stress transfer is poor at the
interface of fiber and matrix because of the stress concentration acts on the fiber (Jacob, M., et
al., 2004).
Table 6.1:Tensile Properties of Untreated and Treated Fiber Reinforced Composites
S No. Silicone Sisal Composite
Untreated Sisal fiber Treated Sisal fiber
Tensile strength Automated Modulus
Tensile strength
Automated Modulus
% MPa MPa MPa MPa
1 100 0.57 ± 0.04 0.48 ± 0.04 0.57 ± 0.04 0.48 ± 0.04
2 95/5 0.47 ± 0.02 0.76 ± 0.11 0.46 ± 0.04 0.57 ± 0.10
3 90/10 0.43 ± 0.08 1.13 ± 0.11 0.46 ± 0.05 1.04 ± 0.26
4 85/15 0.42 ± 0.06 1.67 ± 0.38 0.5 ± 0.06 1.76 ± 0.62
5 80/20 0.37 ± 0.04 2.44 ± 0.33 0.72 ± 0.08 2.98 ± 0.7
From Table 6.1, the silane treatment of natural fiber has given a considerable increase in tensile
strength of 5%, 10%, 15%, and 20% sisal fiber composites. The incorporation of 20% treated
sisal fiber in a silicone matrix allows an enhancement of 25% of the tensile strength of
composites compared to virgin silicone. When fiber is treated with functional chemical such as
silane (3 – Aminopropyltriethoxysilane), the interface adhesion between silicone polymer and
fiber improves, therefore stress transfer through fiber is enhanced. This increase in the properties
of composites by (0.72 ±0.08 MPa ) is higher than silicone polymer without reinforcement
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(0.57±0.04 MPa ). This ensures a good mechanical interlocking of rough fibers with the matrix
(Yao, Y. (2012)).
6.4.4 Tensile Modulus of the composite by compression molding process
The modulus of composites depends on the volume fraction of fibers and the distribution of
fibers in the composites. The tensile modulus of treated and untreated fibers reinforced with
silicone composites is presented in Figure 6.4. The incorporation of fibers in the matrix
increases the modulus of the composites for both treated and untreated fibers. This result
indicated that modulus depended on the fiber volume fraction and did not depend as much on the
length of the fiber. The tensile modulus of 20% fiber composites was 2.44 MPa, which was
higher than virgin silicone (0.48 MPa) because of reinforcement effect of short fibers in
composites. A similar effect was observed in treated fiber reinforced composites, and the
modulus value for 20% fiber composition was 2.98 MPa, which was 22% higher than untreated
fiber composites. Composite strength largely depends on the mean aspect ratio and mean fiber
length, but composite modulus correlates through fiber volume fraction and distribution.
Figure 6.4: Tensile modulus of untreated and treated sisal
fiber reinforced silicone composites
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6.4.5 Hardness of Composites
The hardness of short fiber reinforced elastomers depends on fiber concentration and fiber
distribution. However, increased hardness results from better interaction between matrix and
short fibers. Figure 6.5 shows the Shore A hardness of silane treated and untreated sisal fiber
reinforced silicone composites. The hardness of the silicone fiber composites increased for fiber
composition of 5%, 10%, 15%, and 20%. The incorporation of fiber enhanced the composites,
making them harder and stiffer. The increases in fiber volume fraction improved the modulus
and hardness due to enhancement of the cross link density. Figure 6.5 shows that the Shore A
hardness of silane treated silicone composites was improved for each fiber composition
compared with untreated silicone composites. The hardness of treated sisal fiber composites for
20% composition was 10% higher than the untreated fiber composites; this result was attributed
to better adhesion between fiber-silicone matrix and enhanced network structures within the
cross-linked system.
Figure 6.5: Hardness of untreated and treated sisal fiber reinforced
silicone composites
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6.4.6 Tear Strength
Tear resistance describes the material strength of elastomers under the action of static force and
kinetic forces on tearing. The right angles tear strength of the silicone material was 2.72 N/mm,
as measured by a tensile testing machine. Figure 6.6 shows the tear strength of various
percentages of fiber composition for both treated and untreated sisal fibers. The incorporation of
short fibers in silicone material increased the tear strength. The tear strength of the composite for
20% fiber loading was 5.08 N/mm, which was increased by 80% compared with virgin silicone.
This result is due to the short fibers aligned along the direction of loading, which is
perpendicular to the direction of tear propagation. Therefore, the short fibers transfer stress
around and prevent crack growth. The concentration of short fibers increases tear strength by
obstructing the tear path (Figure 6.6) shows that treated fiber enhanced the tear strength. The
tear strength of 20% composites was increased by 13% compared with untreated composites.
Also, there was a 23% increase in tear strength for the composition of 15% compared with
treated and untreated sisal fiber silicone composites. The increase in concentration and fiber-
matrix adhesion results in an improved stiffness and modulus of short fiber composites. Also, the
load acting on the matrix was transfers to fiber and reduces the crack growth rate.
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Figure 6.6: Tear strength of silane treated and untreated sisal reinforced
composites
6.4.7 Cross-Linking Density
The cross-linking density of polymer composite is a major factor influencing the mechanical
behavior of fiber filled and unfilled elastomers. The degree of cross-linking in the elastomeric
material was determined by swelling method. The Flory-Rehner equation was used to calculate
the network cross-linking density, where molecular weight Mc between the cross-link networks
is inversely proportional to cross-link density. Figure 6.7(a) shows the cross-linking density for
various percentages of fiber loading composites. The cross-linking density for 20% of fiber
loading was 5.19 × 107 moles/m
3, which may resist swelling due to the presence of fibers and
reduce the penetration of xylene into silicone composites. There were fewer moles in a low
volume fraction of fiber composites, which increased the gap of neighboring molecules to enable
flexibility in the swollen specimen. The increase of fiber loading might decrease the uptake of
solvent in cured composites and resist swelling, which may be attributed to better interfacial
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adhesion. Therefore, the increase in cross-link density might increase material stiffness,
modulus, and hardness of silicone composites.
Figure 6.7: (a) Cross-linking density, (b) Swelling coefficient of silicone composites
The swelling coefficient is a measure of swelling resistance of silicone composites. There was a
gradual decrease in swelling coefficient as seen in Figure 6.7(b), for an increase in fiber loading.
This indicates resistance in the uptake of the solvent by composites due to rigid bonding
established between fiber and matrix. There was variation in swelling coefficient at specific fiber
loading due to the effect of fiber orientation in composites. There was a maximum swelling
capacity in the composites that were extended in a direction normal to the fiber orientation. This
is due to the fact that the penetration of solvent in the matrix was prevented by fibers, when the
fibers are arranged in the perpendicular direction to the sample surface. Higher values of
swelling coefficient have a low number of moles in unit volume; this gives a weak Si-O bonding
and enhanced flexibility in the low volume fraction of fiber loading.
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6.4.8 Effect of Fiber Length on Mechanical Property
Certain parameters affect the performance of fiber reinforced silicone composites such as fiber
concentration, fiber aspect ratio, the degree of fiber dispersion, fiber/rubber matrix adhesion, and
voids. The interaction between matrix and fiber enables resistance to elongation. Thus, the
tensile strength of short fiber and long fiber composites were compared for 5%, 10%, and 15% of
fiber loading (Figure 6.8). As shown in Figure 6.8(a), the incorporation of short fibers in
silicone composites remarkably decreases its strength, thereby causing a low interfacial bonding
between fiber and matrix. The composite with a fiber length greater than 10 mm showed
improved mechanical properties due to the large area of long fiber surface bonded to the rubber
matrix. Therefore, the tensile strength was increased for various compositions of long fiber
composites, as seen in Figure 6.8(a).
Figure 6.8: (a) Tensile strength for long fiber and short fiber; (b) tensile modulus for long
fiber and short
The increase in fiber concentration remarkably improves the modulus of composites, and the
length of fibers also affects the modulus. Thus, there was a remarkable increase in modulus for
5%, 10%, and 15% fiber loading in the elongated fiber composites (Figure 6.8(b)). There was an
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increase in modulus for 15% loading of long fiber composites enabled by the entanglement of
fibers and uniform dispersion of fibers. The long fibers took on an increased amount of stress,
which enhanced the modulus.
6.4.9 Morphological Analysis
6.4.9.1 Fiber orientation
The microstructure of composites such as fiber distribution, fiber-fiber interaction, fiber
orientation, fiber/matrix interaction, voids, and air bubbles was investigated using X-ray
tomography and optical microscopy. Sisal / silicone composite were developed using the
injection molding process and the orthographical views of the specimen are shown in Figure 6.9.
The sample was cut near the inlet gate as shown in Figure 6.9 where the XY plane represents the
front view, and the thickness of the specimen was considered to be the YZ Plane. The sample
was viewed in X-Ray tomography and the parameters were as follows: voltage: 40-50Kv,
Current: 300-400 µA. The duration of the scanning was increased based on the resolution and
magnification of fiber size. Since both silicone and natural fiber have low absorbing capacity, the
images were contrasted in gray scale, to differentiate matrix and fiber.
Figure 6.9: Composites specimen from injection process
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The fiber arrangements in the composites were visualized using the non-destructive method and
are shown in Figure 6.10. Composites specimen of size 10x10x3mm were viewed in X-ray
tomography. It was observed that the natural fiber and silicon images absorb a low range of X-
radiation. The images are shown in gray scales in Figure 6.10(b). The natural fibers in the
composites were separately visualized using phoenix datosx software to hide the matrix in order
to show the fiber arrangement and fiber distribution in the composite (Figure 6.10(a)). The
shapes of the natural fiber in the composites included curls; the fibers were also agglomerated, as
shown in Figure 6.10(a). The non-uniform distributions of natural fibers in the composites
produced non-homogeneous strength and were responsible for the failure of the composites in
loading.
Figure 6.10: (a) Sisal fiber arrangement in 3D space of composite, (b) Cut Sample of
Sisal/Silicone composites in X-Ray tomography.
Figure 6.11 shows the cut sample of silicone composites from the inlet gate; the coordinate axes
are indicated in the sample. The XZ plane shows the thickness and the XY plane shows the top
surface of the composites. Figure 6.11(b) shows the top view representing the XY plane and it
can be seen that orientation of the fibers is random. The natural fiber and silicone have a low
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range of X-ray absorption; the scanning was performed at voltage 45Kv, Current 220µA,
exposure time of 1000ms with a resolution of 9.9µm, to differentiate natural fibers and the
polymer. The 3D orientation of fibers is shown in the Figure 6.11(c) it was observed that there
were entrapped air holes in the composites. The natural fibers were randomly oriented in the XY
plane and the fibers were deformed with curl. The same fibers were oriented horizontally in the
XZ plane, representing planar orientation in the Figure 6.11(d).
Figure 6.11: a) 3D sample near inlet gate, (b) Front view of Sisal/Silicone composites, (c)
Fiber orientation in 3D space, (d) Fiber orientation in XZ plane
The sliced images of X-ray tomography reveal the fiber arrangement and the poor adhesion
along the thickness of composites. The Figure 6.12 shows the successive sliced images of
composites focussing on the defects such as poor adhesion, uncured matrix, entrapped air
bubbles, micro pores at end of fiber, and voids. Also, found the internal structure of natural
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fiber composites such as fiber orientation, fiber dimension, fiber shape, and fiber intersection.
The sliced images along the thickness XZ plane are shown in Figure 6.12(a) and the uncured
state of polymer and poor adhesion between fiber and matrix caused a decrease in strength. In
the skin layer, the shape of the fibers was observed to be curled fibers with horizontal
orientation; fibers in the core layer were curved and transversely oriented (Figure 6.12(b)). The
curve in fiber is induced by bending stresses due to shear forces of fluids along the cavityand the
change of fiber curl depended on the flow speed. The fiber debonding was observed at end of
fiber and matrix, as shown in Figure 6.12(d), the entrapped air bubbles (Figure 6.12(c))
resulted in failure of the composites.
Figure 6.12: X-Ray Tomography - Sliced images of the composites
6.4.9.2 Long fiber orientation
The fibers are differentiated into long fibers (> 10mm) and short fibers (<3mm). The high
magnification of 10-40X, 150X, with 2mega pixel USB optical digital microscopy was focused
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on the surface of the specimen to view the orientation of fibers in the composites. The
Figure 6.13(a) shows the XY plane of the composites and Figure 6.13(b) shows the XZ plane,
where long fiber orientations are illustrated. The fibers were observed to be horizontally
deformed in the narrow area of the inlet gate. Fibers moved along the direction of fluid orienting
the long fiber tangentially to the flow front. The wide area of the composites in XY plane shows
the dense fibers were arranged along the flow front and that fibers were curled with orientation
angle ranges from 30° to 150° in the center region. The long fibers near the wall were aligned
parallel to the direction of flow as described in the Figure 6.13(a). The long fibers in XZ plane
of the specimen shown in the Figure 6.13(b) have planar orientation in the skin layer and fiber
oriented an angle in the core layer. It was observed that the long fibers are deformed in curl and
tangential to the flow front in the core layer.
Figure 6.13: (a) Long fiber orientation in composites XY plane, (b) Curl fiber orientation in
XZ plane.
6.4.9.3 Long fiber orientation in thin section
The long fibers are oriented in a random manner and the fibers have a kinked and curled shape.
The cavity was designed with a tab gate of 2mm thickness; the long fibers were not
agglomerated near the inlet gate. The Figure 6.14 shows shows the random orientation of long
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fibers in XY plane of the composites and the long fibers of length greater than 10mm were
oriented in planar along the thickness XZ plane. The curled fibers were aligned along the frontal
flow shown in the Figure 6.14, remained transverse to the direction of flow. It was observed that
the long fiber orientation in the injection-molded composites has planar orientation in XZ plane
and random orientation in XY plane. The flow of fluid oriented the long fibers along the flow
front and the velocities were uniformly distributed on the surface of the fiber causing
translational motion during filling of the cavity.
Figure 6.14: Long fiber planar orientation in 2mm thick specimen
6.4.9.4 Short fiber orientation
Short fibers of length 3mm were oriented randomly. The flexibility of short fibers was decreased
compared to long fibers. The orientation of short fibers in the silicone composites is
demonstrated in the Figure 6.15. The dispersion of short fibers in the mold cavity is non-uniform
because of inconsistent curled lengths and because of the shape of the natural fibers. The
Figure 6.15 shows the short fibers are horizontally oriented near the wall where the high shear
rate of the silicone fluid tends to orient the fiber parallel to the wall. The orientations of fiber in
the center region are transverse to the direction of flow and the fibers were oriented tangentially
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to the flow front. The concentration of short fibers caused fiber interaction and fibers were not
uniformly distributed in the mold cavity, as shown in the Figure 6.15(a). This fiber interaction
results in random orientation in the center region of the cavity and creates a concentration in
composite that reduces the strength. Figure 6.15(b) shows the orientation of short fibers in the
XZ plane in the skin, shell, and core layers. The short fibers were oriented horizontally in the
skin layer of the XZ plane and randomly oriented in the XZ plane in a planar orientation. Next to
the skin layer was the shell layer, where the fibers were oriented in angular relative to the flow
front. The fibers in the core layer are transverse to the direction of the flow and the short fibers
remain tangential to flow front. The velocities of a fluid element are minimum near the wall and
tend to move in a layer with successively higher velocities to maximum in the core layer.
Figure 6.15: (a) Short fiber orientation in composites XY plane, (b) Short fiber orientation
in XZ plane.
6.4.10 SEM Analysis
6.4.10.1 Fiber surface analysis
Surface impurities and physical irregularities were observed on the fiber surface and are
examined by SEM (Figure 6.16). Node-like material representing lignin appeared on the surface
of fibers (Figure 6.16(a)). Untreated sisal fibers were smooth on their surfaces due to the
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presence of wax and lignin, which hinder interfacial interaction with the matrix. Figure 6.16(b)
shows the surface of treated fiber, which contained rough irregularities. This was assumed to
allow better mechanical interlocking between fiber and matrix due to the removal of wax and
node-like material. While physical changes in the fiber and surface texture were observed by the
SEM analysis. It was found that the adsorption of silane on the surface of fiber might
significantly improve the adhesion (Belgacem, M. N., et al., 2005).
Figure 6.16: (a) Untreated fiber, (b) silane treated fiber
6.4.10.2 Fractography
Fractographic techniques were used to find the cause of failure in fiber reinforced composites
(Figure 6.17). The distribution of sisal fiber in the silicone matrix was random, and fiber pull-out
holes confirmed the poor adhesion with silicone. This debonding was due to tensile forces at the
fiber ends exceeding the tolerance of silicone, causing the elastomer to shear at the interface and
allow pull out. There are microspores on the fiber surface that also contribute to interfacial
failure. Micro-pores result from the removal of lignin and hemicelluloses during fiber treatment
(Shi, J., et al., 2011). Figure 6.17(c) shows the poor adhesion of fiber matrix interaction and
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pull-out holes in composites, resulting in bonding failure. Figure 6.17(d) shows good adhesion
with fiber tearing and fracture of fibers. This results in increased tensile strength. Also, poor
adhesion at the fiber-matrix interface, air holes, and debonding was observed, which may initiate
cracks causing failure of the composite during tensile modes.
Figure 6.17: SEM micrographs (a) after tensile fracture; (b) fiber micro-pores and good
adhesion; (c) fiber fracture and poor adhesion; and (d) pullout hole and fiber tear
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6.5 Conclusions
The incorporation of silane treated sisal fiber in silicone improved the tensile strength of
composites for 10%, 15%, and 20% fiber loading. There was an increase in tensile strength
by 25% for 20% of fiber loading compared with silicone material.
The tensile modulus for various fiber loading was increased for both treated and untreated
fiber composites, where treated composite for 20% fiber loading was higher than untreated
composites by 22%.
The tensile modulus of treated sisal silicone composites with 15% and 20% fiber loading was
increased compared with virgin silicone and untreated sisal silicone composites.
The incorporation of short fibers in silicone increased hardness and tear strength of
composites for both treated and untreated fiber. Treated fiber composites were superior to
untreated composites, and a maximum increase of 23 % in tear strength for composites with
15% fiber loading was observed.
The cross-link density was predicted using the swelling method, and the hardness of fiber
composites was higher for 15% and 20% of fiber loading. It was found that the uptake of
solvent was higher in Si-O bonding, resulting in higher flexibility in the siloxane chain.
The microstructure of composites was analyzed using SEM and X-ray tomography, and the
following defects were observed: debonding, poor adhesion, micro-air bubbles, fiber fracture,
and micropores on fiber surfaces.
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Chapter 7 : Conclusions and Recommendation
7.1 Conclusion
This dissertation describes the orientation of short natural fibers in polymer composites and its
influence on the mechanical properties of the polymer composite. In this study, the shape factor
of natural fibers was considered and an equation for predicting the orientation of natural fibers in
a polymer composite was derived. The orientation angle of fibers predicted numerically was
validated with experimental results. Two case studies were conducted and the orientation of
fibers in a silicone composite was predicted numerically and experimentally. In this research, an
integration of computational fluid dynamics and a dynamics study of fluid flow was
implemented to characterize the velocity profiles of viscous fluid flow in a 2D model of the mold
cavity. The digitized images of fluid flow and fiber orientation confirmed the random orientation
of fibers in the center region of the cavity in the XY Plane. The micro-computed tomography
results authenticated the fiber orientation as well as the internal structure of the composite which
included voids, cracks, and the interfacial interaction of sisal fiber/silicone composites. Based on
the observations and experiments, the following conclusions were drawn and the results were
discussed in this thesis.
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The mathematical model for natural fiber composites was developed by incorporating a
constant curling factor in the angular velocity of the viscous fluid for a complete filling time
of 8 seconds.
The orientation angle of particles positioned at 20mm from the inlet gate was
numerically predicted for P1, P2, P3, and P4 to be 9.9°, 48.4°, 36.9°, and 84.4°
respectively. The numerically predicted orientation angles were compared and
correlated with the experimental orientation angle of fiber particles P1, P2, P3, and P4
and were found to be 8°, 41°, 37°, 81° respectively.
The orientation angle of fiber particles positioned at 20 mm from the terminal end of
the cavity was calculated using the derived equation. Also, the orientation angles of
short particles obtained numerically for P5, P6, P7, and P8, were 59°, 157.9°, 146.1°,
and 128.9° respectively. The digitized angles of particle orientation obtained from the
experimental method for particles P5, P6, P7 and P8 were 82°, 132°, 129° and 135°
respectively. It was observed that there exists a considerable deviation with the model
results because of the circulation of fluid at the end of the cavity.
The non-uniform distribution of the velocity profile obtained from FLUENT software
was compared to the experimental data, and correlated well with the digitized images
of the velocity profile of the flow front.
The digitized images of short fiber particles orientations confirm that particles were
randomly oriented in the center region of XY plane and aligned along the wall surface
of the cavity.
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The developed mathematical model for the low laminar flow was tested. It was found
that the angular velocity of the fluid element located at a distance of 20 mm from the
inlet varied from 0.56 rad/s to -0.52 rad/s. At the terminal end of the cavity, the
angular velocity of the fluid varied from -3.20 rad/s to -2.74 rad/s because of turbulent
and circulation effect developed during cavity filling.
The two case studies were conducted in two transparent cavities with different cross sections
and the orientation of natural fiber was predicted for each interval of time. It was
authenticated that the fibers are randomly oriented in the center region of the XY plane and
aligned along the wall of the cavity.
The derived equation was modified by incorporating a tangential angle of flow front,
at a specific position, relative to the inlet gate, which further improved the predicted
orientation angle of the fiber. The angle of orientation was numerically calculated for
the Case-1 study and the fiber angles for P1, P2, and P3 are 176°, 22°, and 6°
respectively. These were validated with the experimental orientation angles 169°, 34°,
and 7 ° of the corresponding fibers.
The orientation angle for the Case-2 study numerically calculated for the fibers P1, P2,
and P3 were -1°, 180°, and 18°, which are validated with experimental angles 0°, 103°,
and 12°. This kinematic approach of the developed mathematical model is able to
predict the orientation of short fibers inside the composite and also confirms the
random orientation in the center region of the natural fiber composite.
133
The experiment was conducted for different fiber loadings of sisal fiber in reinforced
silicone composites produced by compression molding process and the mechanical
characteristics and morphological behaviour of the composites were characterized.
The incorporation of silane treated sisal fiber in silicone improved the tensile strength
of the composites for 10%, 15%, and 20% fiber loading. There was an increase in
tensile strength by 25% for 20% of fiber loading compared with pure silicone material.
The tensile modulus for various fiber loadings was increased for both treated and
untreated fiber composites, where treated composite for 20% fiber loading was higher
than untreated composites by 22%.
The tensile modulus of treated sisal silicone composites of 15% and 20% fiber loading
was increased compared with virgin silicone and untreated sisal silicone composites.
The incorporation of short fibers in silicone increased hardness and the tear strength of
composites for both treated and untreated fiber. Treated fiber composites were
superior to untreated composites, and a maximum increase in tear strength for 15%
fiber loading of the composite by 23% was observed.
The cross-link density was predicted using the swelling method, and the hardness of
fiber composites was higher for 15% and 20% of fiber loading. It was found that the
uptake of solvent was higher in Si-O bonding, resulting in higher flexibility in the
siloxane chain.
The microstructure of composites was analyzed using SEM and Vision measuring
machine, and the following defects were observed: debonding, poor adhesion, micro-
air bubbles, fiber fracture, and micropores on fiber surfaces.
134
The orientation of natural fibers in the silicone composite was investigated using Xray
Tomography and optical microscopy. It was found that natural fibers were deformed and
curled due to shear, causing the fiber to orient tangentially to the flow front, authenticating
planar orientation along the XZ plane and random orientation in the XY plane of the
composite.
7.2 Study Limitations and recommendations
The lack of fiber flexibility parameter and deformational terms of the fluid element could be
corrected to improve the accuracy of the fiber orientation prediction. Furthermore, the
mathematical model can be further developed by coupling a nonlinear function of the
flexibility shape factor with rotational, translation, deformation terms of the fluid element to
improve the accuracy of orientation prediction.
The volumetric velocimetry method could be used to digitize images and to measure the
three components of velocity to track the 3D orientation of particles. The algorithm could be
developed to remove the distortions of the images on the order of microseconds during the
transient state of flow.
The developed mathematical model can be further applied into programming software or can
be applied in a user defined function of analysis software to predict the fiber orientation.
Hence an algorithm can be developed for simulation of fiber orientation to benefit the
industrial application.
The developed mathematical model has laid a platform for other researchers to develop new
models that incorporate other resisting factors such as process parameters, fiber anatomy,
and fluidity constant in order to improve the accuracy of the anticipated orientation of the
fiber.
135
The mathematical model can be developed for the 3D domain by incorporating the process
parameter and predict the orientation of the fiber in the injection molding process.
The chopping system is designed to maintain uniformity in size of chopped natural fiber and
is recommended for the injection molding process
7.3 Scientific and engineering contributions of the work
The kinematic mechanisms in the dynamics of fluids enable us to predict the rotational and
translation motions of fluid elements. Further, the model is used to predict the angular
velocity of the viscous fluid. Based on this, the orientation of the fibers could be predicted in
the composite product at specific positions.
The derived equation could be implemented in CFD application software to customize a
user-defined function that can find the angular velocity at any position of the fluid domain.
The developed experimental setup could contribute to the understanding and visualization
of fiber behaviour in the viscous fluid during filling of the cavity. This provides evidence to
show that random orientation exists in the composite product.
136
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Appendices
Appendix A: Velocity Distribution on each particle P1, P2, P3, P4 located at distance 20
mm from inlet for a complete filling time of 8 sec.
Tab
le B
1 C
ase1
sam
ple
s 1:
Vel
oci
ty D
istr
ibuti
on o
n e
ach p
arti
cle
P1,
P2,
P3,
P4 l
oca
ted a
t dis
tance
20 m
m
from
inle
t fo
r a
com
ple
te f
illi
ng t
ime
of
8 s
ec.
159
Appendix C: Velocity Distribution on each particle P5, P6, P7, P8 located at
distance 20 mm from end of cavity for a complete filling time of 8 sec.
Tab
le C
.1 C
ase1
sam
ple
s 1:
Vel
oci
ty D
istr
ibuti
on o
n e
ach
par
ticl
e P
5,
P6,
P7,
P8 l
oca
ted a
t dis
tan
ce 2
0 m
m
from
end of
cavit
y f
or
a co
mple
te f
illi
ng t
ime
of
8 s
ec.
160
Appendix D: Flow front distribution of viscous fluid for complete filling of cavity in
8 second
161
Appendix E: Experimental validation of particle orientation with numerical
prediction of fiber orientation for complete filling of 8 seconds.
Table E.1: Predicted orientation angle of particles and experimental angle of particle for
complete filling of 8 second at position 20 mm from inlet gate
Table E.2: Predicted orientation angle of rigid particles and experimental angle of rigid
particles for complete filing of 8 second at position 20 mm from end of cavity
162
Table E.3 Velocity distribution of each particle at 20 mm from Inlet gate of cavity
163
Table E4 Velocity distribution of each particle at 20 mm from end of cavity
164
Table E.5: Case1 sample 2 - Predicted orientation angle of particles and experimental
angle of particle for complete filling of 8 second at position 20 mm from inlet gate.
Table E.6: Case1 sample 2 - Predicted orientation angle of rigid particles and
experimental angle of rigid particles for complete filing of 8 second at position 20 mm
from end of cavity
165
Tab
le E
7 :
Cas
e1 s
ample
2 :
Num
eric
al p
redic
tion o
f ri
gid
par
ticl
e ori
enta
tion a
t 20 m
m f
rom
inle
t
Tab
le E
8 :
Cas
e1 s
ample
2:
Num
eric
al p
redic
tion o
f ri
gid
par
ticl
e ori
enta
tion a
t 20 m
m f
rom
end o
f ca
vit
y
Tab
le
E7 C
ase
2 s
ample
s 1:
Vel
oci
ty D
istr
ibuti
on o
n e
ach p
arti
cle
P1,
P2,
P3,
P4 l
oca
ted a
t dis
tance
20 m
m f
rom
inle
t
for
a co
mple
te f
illi
ng t
ime
of
8 s
ec.
Tab
le E
8 C
ase2
sam
ple
s 1:
Vel
oci
ty D
istr
ibuti
on o
n e
ach p
arti
cle
P5,
P6,
P7,
P8 l
oca
ted a
t dis
tance
20 m
m f
rom
end
of
cavit
y f
or
a co
mple
te f
illi
ng t
ime
of
8 s
ec.
166
Appendix F: X-Ray tomography images of fiber orientation in Sisal /silicone composites
Sliced images of the sisal/ silicone composites in non destructive method – X-Ray
Tomography
