characterising the inherent variability of textile...
TRANSCRIPT
GORDON KANYIKE - 0705970 Page 1
Characterising the Inherent Variability of
Textile Composites
Gordon Kanyike
0705970
Department of Mechanical Engineering
(BEng) Final Year Project
Supervisor: Dr Phil Harrison
Completed April 2011
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SUMMARY
This report consists of analysis on three different types of textile composite materials. The
first step involved using an image processing software to create the primary information
required to input for Matlab analysis.
Using several pre-written Matlab codes, re-generating mesh images for the materials as well
as obtaining vital information i.e. shear angles and standard deviations was carried out.
The main aim of this project was to develop a technique to reproduce the inherent variability
in 'off-the-roll' engineering fabrics for each material analysed. This was done by applying a
pre-written genetic algorithm code with Matlab. The code should automatically create textile
sheets suitable for post thermoforming analysis where the resulting behaviour of the material
can be pre-determined. Difficulties such as the code‟s mathematics for accurately predicting
exact variability became apparent.
Within the materials laboratory spring stiffness experimentation was carried out on the
springs used within the pre-designed blank holder. Using the existing set thermoforming
station experiments were conducted firstly to calibrate the time for the radiant heater to
reach a desired temperature. Forming tests were then conducted on a number of specimens
to create shell hemispheres. The tests were set at various specifications to discover how the
material responds under deformation.
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OBJECTIVES
● Cut-out and mark-out three large square samples each a different type of material then
divide each into 9 smaller squares (300x300mm)
● Analyse each sample using the program “ImageJ”
● Obtain shear angles, standard deviations and plot normal distributions for each specimen
using Matlab
● Predict the inherent variability for the large samples and thus the inherent variability in 'off-
the-roll' engineering fabrics.
● Run compression tests on springs
● Calibrate time to heat radiant heater
● Test specimens using thermoforming machine
ACKNOWLEDMENTS
I‟d like to give thanks to the help of the following people;
Dr. Phil Harrison for being my supervisor and giving his guidance throughout this project
Postgraduate Farag Abdiwi for his guidance throughout and providing me with Matlab codes
vital for this project
Technician John Davidson in aiding me with the various testing within the materials
laboratory
The technicians in the Electronics department for repairing the faulty apparatus required for
testing
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CONTENTS
INTRODUCTION .................................................................................................................. 9
MATERIALS ....................................................................................................................... 11
Self-reinforced Polypropylene (SrPP/Armordon) .............................................................. 11
Plain Glass Woven Fabric ............................................................................................... 12
Pre-consolidated Twintex Twill ........................................................................................ 12
LITERATURE REVIEW
Textile composites
Predicting variability ....................................................................................................... 13
Fibre behaviour ............................................................................................................... 13
Modelling strategies ......................................................................................................... 14
Thermoforming ................................................................................................................ 14
PROJECT ANALYSIS ......................................................................................................... 15
Cutting out/marking out ................................................................................................... 15
IMAGE J ............................................................................................................................. 16
MATLAB ............................................................................................................................. 18
Further Analysis. ............................................................................................................. 24
MODELLING THE VARIABILITY. ....................................................................................... 26
Varifab ............................................................................................................................. 28
VarifabGA. ....................................................................................................................... 28
Predicted mesh results .................................................................................................... 29
EXPERIMENTAL RESULTS
Compression tests. ......................................................................................................... 31
Calibrating the radiant heater. ......................................................................................... 31
CONCLUSION .................................................................................................................... 33
APPENDIX .......................................................................................................................... 34
REFERENCES ................................................................................................................... 70
BIBLIOGRAPHY ................................................................................................................. 71
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List of figures
Figure 1- Armordon material ............................................................................................... 11
Figure 2 - Glass fabric material . ........................................................................................ 12
Figure 3 - Twintex material .................................................................................................. 12
Figure 4 - SrPP sample and close-up of weave spacing ..................................................... 15
Figure 5 - Glass fabric sample and close-up of weave spacing ........................................... 15
Figure 6 - Twintex sample and close-up of weave spacing ................................................. 16
Figure 7 - ImageJ toolbar .................................................................................................... 17
Figure 8 - SrPP Sample with multi-point plot and close-up .................................................. 17
Figure 9 - SrPP mesh sample 1
Figure 10 - SrPP mesh sample 2 ........................................................................................ 18
Figure 11 - SrPP mesh sample 3 ........................................................................................ 18
Figure 12 - Glass fabric mesh sample 4
Figure 13 - Handled glass fabric mesh sample 4
Figure 14 - Glass fabric mesh sample 5
Figure 15 - Handled glass fabric mesh sample 5
Figure 16 - Glass fabric mesh sample 6
Figure 17 - Handled glass fabric mesh sample 6 ................................................................. 19
Figure 18 - Twintex mesh sample 7
Figure 19 - Twintex mesh sample 8
Figure 20 - Twintex mesh sample 9 .................................................................................... 20
Figure 21 - SrPP distribution
Figure 22 - Glass fabric distribution
Figure 23 - Handled glass fabric distribution
Figure 24 - Twintex distribution ........................................................................................... 22
Figure 25 - SrPP area divided distributions ......................................................................... 25
Figure 26 - Glass fabric area divided distributions ............................................................... 25
Figure 27 - Twintex area divided distributions ..................................................................... 26
Figure 28 - Genetic Algorithm plot of standard deviation vs. average shear angle .............. 28
Figure 29 - Predicted mesh of SrPP sample 1
Figure 30 - Actual mesh of SrPP sample 1 .......................................................................... 29
Figure 31 - Predicted mesh of Glass sample 6
Figure 32 - Actual mesh of Glass sample 6 ......................................................................... 30
Figure 33 - Predicted mesh of Twintex sample 7
Figure 34 - Actual mesh of Twintex sample 7 . ................................................................... 30
Figure 35 - Image of single spring
Figure 36 - Image of 8 springs set-up on blankholder.......................................................... 31
Figure 37 - Radiant heater
Figure 38 - Graph of radiant heater calibration. ................................................................... 31
Figure 39 – Full set-up of blank holder with spring configuration ......................................... 32
Figure 40 – Image of Tracing attempt
Figure 41 - Large sample of SrPP
Figure 42 - Large sample of Glass fabric ............................................................................. 34
Figure 43 - Large sample of Twintex ................................................................................... 35
Figure 44 - Screenshot of ImageJ .................................................................................... 36
Figure 45 - Example excel file of ImageJ plot for SrPP sample 1 ........................................ 36
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Figure 46 - SrPP sample 4 mesh
Figure 47 - SrPP sample 5 mesh ........................................................................................ 42
Figure 48 - SrPP sample 6 mesh
Figure 49 - SrPP sample 7 mesh
Figure 50 - SrPP sample 8 mesh
Figure 51 - SrPP sample 9 mesh ........................................................................................ 42
Figure 52 - Glass fabric sample 1 mesh
Figure 53 - Glass fabric sample 2 mesh
Figure 54 - Glass fabric sample 3 mesh
Figure 55 - Glass fabric sample 7 mesh
Figure 56 - Glass fabric sample 8 mesh
Figure 57 - Glass fabric sample 9 mesh .............................................................................. 43
Figure 58 - Twintex sample 1 mesh
Figure 59 - Twintex sample 2 mesh
Figure 60 - Twintex sample 3 mesh
Figure 61 - Twintex sample 4 mesh .................................................................................... 44
Figure 62 - Twintex sample 5 mesh
Figure 63 - Twintex sample 6 mesh
Figure 64 - Handled Glass sample 1 mesh
Figure 65 - Handled Glass sample 3 mesh
Figure 66 - Handled Glass sample 2 mesh
Figure 67 - Handled Glass sample 7 mesh ......................................................................... 44
Figure 68 - Handled Glass sample 9 mesh
Figure 69 - Handled Glass sample 8 mesh ......................................................................... 45
Figure 70 - SrPP sample 2 predicted mesh
Figure 71 - SrPP sample 3 predicted mesh
Figure 72 - SrPP sample 4 predicted mesh
Figure 73 - SrPP sample 5 predicted mesh
Figure 74 - SrPP sample 6 predicted mesh
Figure 75 - SrPP sample 7 predicted mesh
Figure 76 - SrPP sample 8 predicted mesh
Figure 77 - SrPP sample 9 predicted mesh
Figure 78 - Glass sample 1 predicted mesh
Figure 79 - Glass sample 2 predicted mesh
Figure 80 - Glass sample 3 predicted mesh
Figure 81 - Glass sample 4 predicted mesh
Figure 82 - Glass sample 4 predicted mesh
Figure 83 - Glass sample 7 predicted mesh ........................................................................ 46
Figure 84 - Glass sample 8 predicted mesh
Figure 85 - Glass sample 9 predicted mesh
Figure 86 - Twintex sample 1 predicted mesh
Figure 87 - Twintex sample 2 predicted mesh ..................................................................... 48
Figure 88 - Twintex sample 3 predicted mesh
Figure 89 - Twintex sample 4 predicted mesh
Figure 90 - Twintex sample 5 predicted mesh
Figure 91 - Twintex sample 6 predicted mesh ..................................................................... 49
Figure 92 - Twintex sample 8 predicted mesh
Figure 93 - Twintex sample 9 predicted mesh ..................................................................... 49
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Figure 94 - Graph of SrPP standard deviation vs. area
Figure 95 - Graph of Glass fabric standard deviation vs. area
Figure 96 - Graph of Twintex standard deviation vs. area
Figure 97 - Graph of SrPP average standard deviation vs. area
Figure 98 - Graph of Glass fabric average standard deviation vs. area
Figure 99 - Graph of Twintex average standard deviation vs. area ..................................... 52
Figure 100 - Graph of spring test 1...................................................................................... 55
Figure 101 - Graph of spring test 2...................................................................................... 56
Figure 102 - Graph of spring test 3
Figure 103 - Set-up of testing under Zwick Roell machine
Figure 104 - Graph of thermoforming test 1
Figure 105 - Outer view of test 1
Figure 106 - Inner view of test 1 .......................................................................................... 58
Figure 107 - Outer view of test 2
Figure 108 - Inner view of test 2
Figure 109 - Graph of thermoforming test 3 ........................................................................ 60
Figure 110 - Outer view of test 3
Figure 111 - Inner view of test 3 .......................................................................................... 61
Figure 112 - Graph of thermoforming test 4
Figure 113 - Outer view of test 4
Figure 114 - Inner view of test 4
Figure 115 - Graph of thermoforming test 5
Figure 116 - Outer view of test 5
Figure 117 - Inner view of test 5 .......................................................................................... 63
Figure 118 - Graph of thermoforming test 6
Figure 119 - Outer view of test 6
Figure 120 - Inner view of test 6 .......................................................................................... 65
Figure 121 - Graph of thermoforming test 7
Figure 122 - Outer view of test 7
Figure 123 - Inner view of test 7 .......................................................................................... 66
Figure 124 - Graph of thermoforming test 8
Figure 125 - Outer view of test 8
Figure 126 - Inner view of test 8 .......................................................................................... 68
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List of tables
Table 1 - SrPP dimensions and stats
Table 2 - Glass fabric dimensions and stats
Table 3 - Twintex dimensions and stats .............................................................................. 50
Table 4 - Large sample stats ............................................................................................... 51
Table 5 - Input parameters for varifab program ................................................................... 51
Table 6 - Spring stiffness data ............................................................................................. 57
List of equations
Equation 1 - Probability Density Function Where: ............................................................. 22
Equation 2 - Standard deviation equation . ......................................................................... 24
Equation 3 - Ellipse equation
Equation 4 - Eccentricity equation ....................................................................................... 27
Equation 5 - Sine function ................................................................................................... 28
Equation 6 - Spring stiffness equation ................................................................................. 56
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INTRODUCTION
“Misalignment in textile composite‟s and dry fabrics‟ effects their material properties. Thus
understanding and predicting the effects of variability on the final part should allow variability
to be controlled.” 1
Textile Composites
“Textile composites can be defined as the combination of a resin system with a textile fibre,
yarn or fabric system. They can be flexible or quite rigid. The textile component provides
tensile strength and dimensional stability. Examples of inflexible or rigid textile composites
are found in a variety of products referred to as fibre reinforced plastic (FRP) systems.” 2
FRP products are now widely used as an alternative for metallic and wooden applications
such as; automotive/aircraft construction, hulls for boats, piping products, indoor/outdoor
containers and housing construction components.
The principal weaves are;
Plain for abrasion resistance and stability ideally suited to flat surfaces.
Twill for covering curved surfaces.
Satin more suitable for draping providing increased flexibility.
Available forms of reinforced plastics are:-
Glass fibre reinforced plastics (GFRP)
Carbon fibre reinforced plastics (CFRP)
Aramid fibre reinforced plastics (AFRP)
Natural fibre reinforced plastics (NFRP)
I have taken GFRP under consideration for this project.
“The characteristics, in addition to the choice of fibre and matrix material, are largely
determined by the orientation of the fibres in the textile fabric.” 3
1Long (2005)
2 Ko (1989)
3 http://www.zwick.co.uk/en/applications/composites/fiber-composites.html
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Why choose GFRP?
● GFRP has a very high strength to weight ratio
● Low weights per square metre means faster installation, less structural framing,
and lower shipping costs
● Resistant to salt water, chemicals, and the environment - unaffected by acid rain,
salts, and most chemicals
● A seamless construction as domes and cupolas are resigned together to form a
one-piece, air/watertight structure
● Virtually any shape or form can be moulded
● Research shows no loss of laminate properties after 30 years so low maintenance
required
● Very durable, Stromberg GFRP stood up to category 5 hurricane Floyd with no
damage, while nearby structures were destroyed
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MATERIALS
Self-reinforced Polypropylene (SrPP/Armordon)
Figure 1- Armordon material
The woven fabric is produced with Co-extruded tapes. Each individual co-extruded tape has
a high melting point polymer core, surrounded by a lower melting point copolymer “cap” coat.
Armordon is a composite material with unique properties. High impact strength and low
density makes Armordon the preferred choice where strength and weight saving priorities
are key. It offers important environmental benefits as it is 100% recyclable and with no glass
reinforcement, there are considerable advantages in both processing and machining. 4
Summary of properties:-
● High impact strength and abrasion resistant
● Low density
● 100% recyclable
● No glass fibre
● Non-toxic and inert
● Price
● Machineability
With prospects in ballistics and blast protection, passenger luggage, construction and
automotive and medical applications, Armordon can be developed to suit an extensive range
of product markets.
4 http://www.armordon.com/
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Plain Glass Woven Fabric
Figure 2 - Glass fabric material
The plain woven glass fibre fabric is used for anticorrosion, corrosion resistance and
insulation of pipes and storage tank in power stations, oil fields, chemical plant, paper mill
and environment protection projection where highly corrosive mediums are present. Along
with high heat resistance qualities it can also be used in the construction work involving
reinforced plastics.
Pre-consolidated Twintex Twill
Figure 3 - Twintex material
“Made from commingled E-glass and polypropylene filaments, Twintex has a fast processing
cycle time. The dry prepreg is made by commingling the continuous glass and
Polypropylene (PP) filaments. Consolidation process is done by heating material above
melting temperature of PP matrix 180 C – 230 C) and applying a low pressure (1-30 bars)
before cooling under pressure.” 5
5 http://www.twintex.com/
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LITERATURE REVIEW
Textile composites
“Textile composites have three structural levels:
1. The macro (M)-level defines the 3D geometry of the composite part and the distribution of
local reinforcements.
2. The meso (m)-level defines the internal structure of the reinforcement and variations of
the fibre direction and the fibre volume fraction inside the yarns and the fibrous plies.
3. The micro ( )-level defines the arrangement of the fibres in the representative volume
element (RVE) of the impregnated yarn or fibrous ply.” 6
Predicting variability
Dependable prediction of mechanical behaviour of composite materials is a primary
importance within textile composites. A study involving thermoforming experiments and
Finite Element ( FE) simulations of a commingled glass-Polypropylene(PP) woven
composite on a double dome was undertaken with the aim of assessing the comparison
between predicted and experimental shear angle data “The constitutive model is constituted
of a dedicated non orthogonal hypo-elastic shear resistance mode… It was concluded that
the shear angles were fairly well predicted for this particular case study, which could be
expected in view of the fact that no wrinkles had formed during the thermoforming
experiment.” 7
Fibre behaviour
The mechanisms of how a composite‟s inter-ply/in-plane shear is formed is an important
factor to how the fibres are aligned “The formed fibre pattern is governed mainly by the trellis
effect, i.e., local intra-ply shearing between initially orthogonal fibres” 8 Under biaxial testing
“a significant rise in shear resistance with an increase in tension was measured, but due to
the non-uniform shear distribution the measured shear force may be affected by the
variations in) yarn tensile load during the shear deformation” 9
6 Lomov, et al., 2006
7 Willems L. V. 8 Lin, Wang, Long, Clifford, & P.Harrison, 2007
9 Willems, Lomov, Verpoest, & D.Vandepitte, 2008
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Modelling strategies
Creating accurate modelling and design tools for textile composites was conducted at the
University of Leuven in Belgium. They were able to construct numerous 2-Dimensional and
3-Dimensional weave structures using manufacturer‟s fabric and yarn data as a starting
point for modelling. It was concluded “the structures were easily constructed within TGP
tools, providing great flexibility of input data. WiseTex allows easy manipulation of fabric and
yarn data and visualisation tools.” 10
Another challenge undertaken at the same university was to use a technique to characterize
textile composites using Digital Image Correlation (DIC). Using a digital charge-coupled
device (CCD) camera tangential displacement and strains to the surface are calculated
bases on the comparison between subsequent images of an object during loading. The
loading is present due to biaxial/shear testing using picture frames. “It is concluded that
optical measurements are mandatory for reliable assessment of the textile deformation” 9
Thermoforming
After a study involving forming shell hemispheres it was deduced that “wrinkling is a result of
the interaction between shear deformation and compressive force.” 8
“Process parameters like the membrane stresses introduced by a blankholder, the mold and
preheating temperature, the blank shape and punch force can affect the drape behaviour,
the occurrence of wrinkling, and the consolidation and impregnation quality.” 7
10
Lomov, et al., 2001
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PROJECT ANALYSIS
Cutting out/marking out
● For each of the materials a large square sample of roughly 900x900mm was cut-out
(Appendix A)
● The large samples were then divided up into nine smaller squares (3 rows of 3) of
approximately 300x300mm
● With a permanent marker horizontal and vertical lines were marked on every specimen to
create cells and nodes
● For the Armordon and Glass fabric the cell lines were spaced eight weaves apart shown
below
Figure 4 - SrPP sample and close-up of weave spacing
Figure 5 - Glass fabric sample and close-up of weave spacing
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As the weaves for twintex are larger, the cell lines were drawn on 4 weaves apart
Figure 6 - Twintex sample and close-up of weave spacing
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IMAGE J
“ImageJ is a public domain, Java-based image processing program developed at the
National Institutes of Health. User-written plug-ins makes it possible to solve many image
processing and analysis problems, from three-dimensional live-cell imaging to radiological
image processing multiple imaging system data comparisons to automated haematology
systems.” 11 Screenshot of imageJ is shown in Appendix B
With ImageJ‟s multi-point selection tool (Figure 7) points on every crossover point (nodes)
were plotted for each specimen (Figure 8).
Figure 7 - ImageJ toolbar
Using the analyze tool the program then automatically produces a table of coordinates for
every node in terms of pixels, which were converted to millimetres by multiplying each pixel
value by a scale. Using Microsoft excel the minimum x and y values were found. Each
column was then multiplied by their respective minimum values to create a node matrix table
to input into Matlab. Another table required for the Matlab program was a table of elements
to create the cell squares. This four column table represents each valid square cell in every
specimen, each column depicting the nodes that make up that cell. (Appendix B)
Figure 8 - SrPP Sample with multi-point plot and close-up
11
http://en.wikipedia.org/wiki/Image_J
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MATLAB
A Matlab code created by Farag Abdiwi was devised to regenerate a mesh images for each
of the specimens. For each mesh the code named “ExpMesh1” Appendix C) was
programmed to find the shear angle for each node as well as the average shear angles and
standard deviations. The following figures show resulting mesh images generated from the
three types of textiles, with Farag‟s handled glass fabric samples also added for comparison.
SrPP meshes for bottom row:-
Figure 9 - SrPP mesh sample 1 Figure 10 - SrPP mesh sample 2
Figure 11 - SrPP mesh sample 3
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Glass fabric and Handled Glass fabric meshes for middle row:-
Figure 12 - Glass fabric mesh sample 4 Figure 13 - Handled glass fabric mesh sample 4
Figure 14 - Glass fabric mesh sample 5 Figure 15 - Handled glass fabric mesh sample 5
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Figure 16 - Glass fabric mesh sample 6 Figure 17 - Handled glass fabric mesh sample 6
Twintex meshes for top row:-
Figure 18 - Twintex mesh sample 7 Figure 19 - Twintex mesh sample 8
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Figure 20 - Twintex mesh sample 9
Ideally the cell lines (elements) should be perfectly parallel and perpendicular to each other
when it comes off the roll. This is somewhat accurate for the SrPP samples, but due to
minute handling for the Glass fabric there is slight variability in the angle between the
elements. Farag‟s glass fabric samples display increased variability due to frequent handling
of the material. As for the Twintex, specimen results show the variability is largely significant
with shear angles on the right side of the large sample dropping to well below 80˚ and shear
angles on the left side reaching above 100˚. Obvious reasons for this will be traced back to
the pre-consolidating process done during manufacturing of the roll. The results for a column
from each large sample material i.e. (samples1, 4 and 7) were similar. The rest of the
meshes are shown in Appendix D.
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Histograms:-
Using a 2nd code developed by Farag named “histfit” Appendix C) a histogram for each
specimen was produced. The bell shaped graph portrays the normal distribution of
probability density versus shear angles which incorporates the probability density function
(PDF) (Equation 1)
Equation 1 - Probability Density Function 12
Where:
▪ μ is the mean
▪ σ 2 is the variance
▪ ɣ is the shear angle
The graphs below compares each material type‟s individual sample‟s distribution blue) with
the distribution for all samples collectively (red).
Figure 21 - SrPP distribution
12
Modern Engineering mathematics 4th edition
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Figure 22 - Glass fabric distribution
Figure 23 - Handled glass fabric distribution
Figure 24 - Twintex distribution
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It is clearly seen that these graphs correspond to their respective mesh results from earlier in
terms of the level of variability.
Further Analysis
The areas for each specimen were then divided to study the textile‟s fibre orientation over
several regions, firstly by half, then by a quarter and an eighth. The standard deviations for
these areas were plotted against their areas in graphs presented in Appendix F. Also within
this appendix lie graphs for average standard deviations against area. Results show
standard deviation increases with decreasing area.
Equation 2 - Standard deviation equation
The mesh generation process was repeated again for these new areas using the same
ExpMesh1 code as before. Again distributions of probability against shear angles for these
various areas were produced. By reconfiguring the “histfit” code from earlier to apply for
multiple average shear angles and standard deviations the code was renamed “histfit2” A
brief sample of the code is shown Appendix C.
The following graphs are the resulting distributions for histfit2 showing the different divisional
areas‟ probability density against the shear angle. A colour code is also supplied.
Single samples – Red
1/2 samples – Cyan
1/4 samples – Black
1/8 samples - Magenta
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Figure 25 - SrPP area divided distributions
Figure 26 - Glass fabric area divided distributions
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Figure 27 - Twintex area divided distributions
Once again these divisional distributions adopt the same characteristics as the predeceding
“hisfit” results, which show that the material acts similarly in terms of variability no matter the
size of the area.
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MODELLING THE VARIABILITY
“Meshgen” a Matlab program written by Ikuo Koyama for his project on „Development of a
mesh generator including directional variability‟. 13 Based on ellipse and eccentricity
equations 3 and 4. Meshgen generates a „semi-discrete‟ or „meso-scale‟ element which is a
combination of truss and membrane elements.
Equation 3 - Ellipse equation
Equation 4 - Eccentricity equation
Where A is the major x-axis, C is the major y-axis, e is eccentricity, x and y are horizontal
and vertical displacements.
The program operates by the concept of; if there is progression of diagonals in every cell
then the positional relation between all the nodes can be found. In reality the variability that
takes place in the textile composites can look like curved lines, which is what limits Meshgen
as it can‟t re-represent the exact variability i.e. the formation of the curved weave. It can only
just model straight lines.
13
http://www.mech.gla.ac.uk/~pharriso/Teaching/index.html
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Varifab
Equation 5 - Sine function
To be able to account for curved lines Farag included a sine function to the code (equation
5), which was thus named “Varifab” which is short for Variable fabric.
VarifabGA
Genetic algorithms GA‟s) are based on Charles Darwin‟s evolutionary theory „survival of the
fittest‟. The origin of species: “Preservation of favourable variations and rejection of
unfavourable variations.” 14 GA‟s are a technique for solving problems which need optimizing
(Choosing the best element from a set of available alternatives).
0 20 40 60 80 100 120 140 160 1800
1
2
3
4
5
6
7
8
9
Mean (Degree)
Sta
ndard
Devia
tion
Figure 28 - Genetic Algorithm plot of standard deviation vs. average shear angle
14
http://en.wikipedia.org/wiki/Survival_of_the_fittest
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The code used to generate the following meshes is named “GARan4mfun25”, which was
created by Farag Abdiwi. There are a number of input variables that control the structure of
the generated mesh shown in Appendix E. The basis of the program can be explained from
Figure 28. There is a search space from which a target standard deviation is set for the
program to search for (the red circle). The program then selects a random number of
standard deviations (green circles) from the search space then plots a population these
possible solutions. In GA‟s programming these possible solutions are called chromosomes
and a group of chromosomes is called a population with every stage called a generation.
The best solution (The chromosome closest to our target standard deviation) is chosen and
the rest are discarded. The following are some of the resulting meshes from the program.
Predicted mesh results
Figure 29 - Predicted mesh of SrPP sample 1 Figure 30 - Actual mesh of SrPP sample 1
GORDON KANYIKE - 0705970 Page 30
Figure 31 - Predicted mesh of Glass sample 6 Figure 32 - Actual mesh of Glass sample 6
Figure 33 - Predicted mesh of Twintex sample 7 Figure 34 - Actual mesh of Twintex sample 7
Although the predicted meshes don‟t exactly match their real-life equivalents, the results are
still fairly accurate and also give a good quality account of how the textile material could be
formed. The rest of the predicted meshes are presented in Appendix D.
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EXPERIMENTAL RESULTS
Compression tests
Method and results for compression tests on blank holder springs are shown in Appendix G.
Figure 35 - Image of single spring Figure 36 - Image of 8 springs set-up on blankholder
Calibrating the radiant heater
A single test was carried out to determine the time required for the radiant heater (bought by
Laurent Maurel )15 to settle at a specific temperature.
With a set temperature of 180 ˚C, the set-up for the experiment was similar to that done by
Gordon Pettigrew in his report.16 Figure 38 shows the resulting graph.
Figure 37 - Radiant heater 17
15
Maurel, 2007 16
Pettigrew, 2007 17
Richards, 2009
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Figure 38 - Graph of radiant heater calibration
Thermoforming tests
Using the current blank holder set-up with stainless steel springs, thermoforming of the
specimens was completed under the same method done in related projects by previous
undergraduate students i.e. Alana Richard 17 and Gail Gemmel 18
Results for the tests are presented in Appendix H.
Figure 39 – Full set-up of blank holder with spring configuration
18
Gemmel, 2008
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CONCLUSION
ImageJ
Although the ImageJ software was very useful for processing and analysing images, the
stage using the multi-point plotting tool was time consuming. Improving the method for
solving this led me to briefly look into finding and/or modifying a Matlab code that can
automatically traces the images taken of the specimens, locate the coordinates of their
nodes and measure shear angles from the image files.
Figure 40 – Image of Tracing attempt
Figure 38 shows the best attempt achieved. The program uses greyscale values to trace the
lines, but configuring the code to identify the nodes, shear angles etc would take time and is
something that should be further looked into as the end result would be greatly beneficial for
the user.
Predicting Variability
The Genetic Algorithm code appears to be an optimum method for predicting the variability
in textile composites. It‟s accuracy although very close to what is desired isn‟t perfect.
Reasons for this could be down to human error from; initial marking/ cutting out of the
materials, plotting using ImageJ or perhaps the code itself may need slight reconfiguration.
Modelling a predicted mesh for the large square samples was also an objective for this
project but the program reported errors when inputting larger dimensions for the code to re-
model.
Thermoforming Testing
The forming of desired hemispherical shapes resulted in slight wrinkling for the SrPP
samples and increased wrinkling for the Twintex samples factors that affected this most
likely will have been the temperature of the blank holder o- ring at time of forming. The
edges of the specimen will not have been properly heated to the desired temperatures
causing buckling for the material and also for the blank holder itself.
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APPENDIX
APPENDIX A - LARGE SAMPLES
Figure 41 - Large sample of SrPP
Figure 42 - Large sample of Glass fabric
GORDON KANYIKE - 0705970 Page 35
Figure 43 - Large sample of Twintex
GORDON KANYIKE - 0705970 Page 36
APPENDIX B - IMAGEJ
Figure 44 - Screenshot of ImageJ 19
Figure 45 - Example excel file of ImageJ plot for SrPP sample 1
19
http://en.wikipedia.org/wiki/File:ImageJScreenshot.png
GORDON KANYIKE - 0705970 Page 37
APPENDIX C - MATLAB CODES
EXPMESH1
clear all
clf
clc
load ('InElementTable.txt');
load ('NodeMatrix.txt');
TrussElementTable = [];
for num1 = 1:size(InElementTable,1)
TrussElementTable =[TrussElementTable;[InElementTable(num1,2)
InElementTable(num1,3);InElementTable(num1,3) InElementTable(num1,4);InElementTable(num1,4)
InElementTable(num1,5);InElementTable(num1,5) InElementTable(num1,2)]];
end
TElementMatrix = [[1:size(TrussElementTable,1)]' TrussElementTable];
MElementMatrix = InElementTable;
for i=1:size(NodeMatrix,1)
NodeMatrixXX(i,1)=NodeMatrix(i,2);
end
for i=1:size(NodeMatrix,1)
NodeMatrixYY(i,1)=NodeMatrix(i,3);
end
Elementvaluexx=[];
num=1;
for i=1:size(MElementMatrix,1)
Elementvaluexx=[Elementvaluexx; num NodeMatrixXX(MElementMatrix(i,2),1)
NodeMatrixXX(MElementMatrix(i,3),1) NodeMatrixXX(MElementMatrix(i,4),1)
NodeMatrixXX(MElementMatrix(i,5),1)];
num=num+1;
end
Elementvalueyy=[];
num=1;
for i=1:size(MElementMatrix,1)
Elementvalueyy=[Elementvalueyy; num NodeMatrixYY(MElementMatrix(i,2),1)
NodeMatrixYY(MElementMatrix(i,3),1) NodeMatrixYY(MElementMatrix(i,4),1)
NodeMatrixYY(MElementMatrix(i,5),1)];
num=num+1;
end
aone=[];
atwo=[];
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bone=[];
btwo=[];
num=1;
for i=1:size(MElementMatrix,1)
aone=[aone; num abs(Elementvaluexx(i,4)-Elementvaluexx(i,5))];
atwo=[atwo; num abs(Elementvalueyy(i,4)-Elementvalueyy(i,5))];
bone=[bone; num abs(Elementvaluexx(i,2)-Elementvaluexx(i,5))];
btwo=[btwo; num abs(Elementvalueyy(i,2)-Elementvalueyy(i,5))];
num=num+1;
end
P1=[];
P2=[];
P3=[];
P1=[P1; (Elementvaluexx(:,2)-Elementvaluexx(:,2)) (Elementvalueyy(:,2)-Elementvalueyy(:,2))]; %%
if theta=0 otherwise for example theta=45 P1=[P1; Elementvaluexx(:,2) Elementvalueyy(:,2)];
P2=[P2; (Elementvaluexx(:,5)-Elementvaluexx(:,2)) (Elementvalueyy(:,5)-Elementvalueyy(:,2))]; %%
P2=[P2; Elementvaluexx(:,5) Elementvalueyy(:,5)];
P3=[P3; (Elementvaluexx(:,3)-Elementvaluexx(:,2)) (Elementvalueyy(:,3)-Elementvalueyy(:,2))]; %%
P3=[P3; Elementvaluexx(:,3) Elementvalueyy(:,3)];
InitialShearAng=[];
i=[];
for i=1:size(P1,1)
InitialShearAng=[InitialShearAng; triangle_angles([P1(i,:);P2(i,:);P3(i,:)],'d')];
end
InitialShearAng=abs(InitialShearAng(:,:));
InitialShearAngmin=min (InitialShearAng (:,1));
InitialShearAngmax=max (InitialShearAng (:,1));
InitialShearAngminmax=[];
InitialShearAngminmax=[InitialShearAngminmax; InitialShearAngmin; InitialShearAngmax];
mu=mean (InitialShearAng (:,1));
stdiv=std (InitialShearAng (:,1));
figure (1)
hist(InitialShearAng(:,1),(1:size(InitialShearAng,1)))
hold on
xlabel('Shear Angle (Degrees)');
ylabel('Number of Cells');
h = findobj(gca,'Type','patch');
set(h,'FaceColor','b','EdgeColor','w');
hold off
GORDON KANYIKE - 0705970 Page 39
figure (2)
hold on
HISTFIT
load 'xd.txt'
mu=mean(xd);
sigma=std(xd);
xdmin=min(xd);
xdmax=max(xd);
p1 = pdf ('Normal',xdmin:xdmax,mu,sigma);
figure (1)
plot (xdmin:xdmax,p1,'LineWidth',2,'Color','b');
hold on plot
title(' Sample 1 ')
xlabel( 'Shear Angle(Degrees)' ), ylabel( 'Probabilty Density (%)');
HISTFIT2
load 'xd.txt'
mu=mean(xd);
sigma=std(xd);
xdmin=min(xd);
xdmax=max(xd);
p1 = pdf ('Normal',xdmin:xdmax,mu,sigma);
figure (1)
plot (xdmin:xdmax,p1,'LineWidth',2,'Color','blue');
hold on plot
load 'xd1.txt'
mu1=mean(xd1);
sigma=std(xd1);
xd1min=min(xd1);
xd1max=max(xd1);
p1 = pdf ('Normal',xd1min:xd1max,mu,sigma);
figure (1)
plot (xd1min:xd1max,p1,'LineWidth',2,'Color','red');
hold on plot
load 'xd2.txt'
mu2=mean(xd2);
sigma=std(xd2);
xd2min=min(xd2);
xd2max=max(xd2);
GORDON KANYIKE - 0705970 Page 40
p1 = pdf ('Normal',xd2min:xd2max,mu,sigma);
figure (1)
plot (xd2min:xd2max,p1,'LineWidth',2,'Color','red');
hold on plot
load 'xd3.txt'
mu3=mean(xd3);
sigma=std(xd3);
xd3min=min(xd3);
xd3max=max(xd3);
p1 = pdf ('Normal',xd3min:xd3max,mu,sigma);
figure (1)
plot (xd3min:xd3max,p1,'LineWidth',2,'Color','red');
hold on plot
load 'xd4.txt'
mu4=mean(xd4);
sigma=std(xd4);
xd4min=min(xd4);
xd4max=max(xd4);
p1 = pdf ('Normal',xd4min:xd4max,mu,sigma);
figure (1)
plot (xd4min:xd4max,p1,'LineWidth',2,'Color','red');
hold on plot
load 'xd5.txt'
mu5=mean(xd5);
sigma=std(xd5);
xd5min=min(xd5);
xd5max=max(xd5);
p1 = pdf ('Normal',xd5min:xd5max,mu,sigma);
figure (1)
plot (xd5min:xd5max,p1,'LineWidth',2,'Color','red');
hold on plot
load 'xd6.txt'
mu6=mean(xd6);
sigma=std(xd6);
xd6min=min(xd6);
xd6max=max(xd6);
p1 = pdf ('Normal',xd6min:xd6max,mu,sigma);
figure (1)
plot (xd6min:xd6max,p1,'LineWidth',2,'Color','red');
hold on plot
GORDON KANYIKE - 0705970 Page 41
load 'xd7.txt'
mu=mean(xd7);
sigma=std(xd7);
xd7min=min(xd7);
xd7max=max(xd7);
p1 = pdf ('Normal',xd7min:xd7max,mu,sigma);
figure (1)
plot (xd7min:xd7max,p1,'LineWidth',2,'Color','red');
hold on plot
load 'xd8.txt'
mu=mean(xd8);
sigma=std(xd8);
xd8min=min(xd8);
xd8max=max(xd8);
p1 = pdf ('Normal',xd8min:xd8max,mu,sigma);
figure (1)
plot (xd8min:xd8max,p1,'LineWidth',2,'Color','red');
hold on plot
load 'xd9.txt'
mu=mean(xd9);
sigma=std(xd9);
xd9min=min(xd9);
xd9max=max(xd9);
p1 = pdf ('Normal',xd9min:xd9max,mu,sigma);
figure (1)
plot (xd9min:xd9max,p1,'LineWidth',2,'Color','red');
hold on plot
GORDON KANYIKE - 0705970 Page 42
APPENDIX D – MESHES
Armordon
Figure 46 - SrPP sample 4 mesh Figure 47 - SrPP sample 5 mesh
Figure 48 - SrPP sample 6 mesh Figure 49 - SrPP sample 7 mesh
Figure 50 - SrPP sample 8 mesh Figure 51 - SrPP sample 9 mesh
GORDON KANYIKE - 0705970 Page 43
Glass Fabric
Figure 52 - Glass fabric sample 1 mesh Figure 53 - Glass fabric sample 2 mesh
Figure 54 - Glass fabric sample 3 mesh Figure 55 - Glass fabric sample 7 mesh
Figure 56 - Glass fabric sample 8 mesh Figure 57 - Glass fabric sample 9 mesh
GORDON KANYIKE - 0705970 Page 44
Twintex
Figure 58 - Twintex sample 1 mesh Figure 59 - Twintex sample 2 mesh
Figure 60 - Twintex sample 3 mesh Figure 61 - Twintex sample 4 mesh
Figure 62 - Twintex sample 5 mesh Figure 63 - Twintex sample 6 mesh
GORDON KANYIKE - 0705970 Page 45
Figure 64 - Handled Glass sample 1 mesh Figure 65 - Handled Glass sample 3 mesh
Figure 66 - Handled Glass sample 2 mesh Figure 67 - Handled Glass sample 7 mesh
Figure 68 - Handled Glass sample 9 mesh Figure 69 - Handled Glass sample 8 mesh
GORDON KANYIKE - 0705970 Page 46
Predicted Meshes
Figure 70 - SrPP sample 2 predicted mesh Figure 71 - SrPP sample 3 predicted mesh
Figure 72 - SrPP sample 4 predicted mesh Figure 73 - SrPP sample 5 predicted mesh
Figure 74 - SrPP sample 6 predicted mesh Figure 75 - SrPP sample 7 predicted mesh
GORDON KANYIKE - 0705970 Page 47
Figure 76 - SrPP sample 8 predicted mesh Figure 77 - SrPP sample 9 predicted mesh
Figure 78 - Glass sample 1 predicted mesh Figure 79 - Glass sample 2 predicted mesh
Figure 80 - Glass sample 3 predicted mesh Figure 81 - Glass sample 4 predicted mesh
GORDON KANYIKE - 0705970 Page 48
Figure 82 - Glass sample 4 predicted mesh Figure 83 - Glass sample 7 predicted mesh
Figure 84 - Glass sample 8 predicted mesh Figure 85 - Glass sample 9 predicted mesh
Figure 86 - Twintex sample 1 predicted mesh Figure 87 - Twintex sample 2 predicted mesh
GORDON KANYIKE - 0705970 Page 49
Figure 88 - Twintex sample 3 predicted mesh Figure 89 - Twintex sample 4 predicted mesh
Figure 90 - Twintex sample 5 predicted mesh Figure 91 - Twintex sample 6 predicted mesh
Figure 92 - Twintex sample 8 predicted mesh Figure 93 - Twintex sample 9 predicted mesh
GORDON KANYIKE - 0705970 Page 50
APPENDIX E - TABLES
Table 1 - SrPP dimensions and stats
Table 2 - Glass fabric dimensions and stats
Table 3 - Twintex dimensions and stats
GORDON KANYIKE - 0705970 Page 51
Table 4 - Large sample stats
Table 5 - Input parameters for varifab program
GORDON KANYIKE - 0705970 Page 52
APPENDIX F - STANDARD DEVIATION VS AREA GRAPHS
Figure 94 - Graph of SrPP standard deviation vs. area
Figure 95 - Graph of Glass fabric standard deviation vs. area
GORDON KANYIKE - 0705970 Page 53
Figure 96 - Graph of Twintex standard deviation vs. area
Figure 97 - Graph of SrPP average standard deviation vs. area
GORDON KANYIKE - 0705970 Page 54
Figure 98 - Graph of Glass fabric average standard deviation vs. area
Figure 99 - Graph of Twintex average standard deviation vs. area
GORDON KANYIKE - 0705970 Page 55
APPENDIX G - COMPRESSION TESTING
John and I ran three seperate compression tests on a single stainless steel spring used
within the current blankholder set-up modified by Farag Abdiwi consisting of eight springs.
Using the computer-aided Zwick Roell machine the top tool was lowered applying a force to
the spring at a designated speed compressing the spring to a desired distance.
At maximum compression the spring length was 17mm.
At full size(uncompressed) the spring length is 55mm.
Outer diameter: 11mm
Inner diameter: 9mm
Wire thickness: 1mm
Force limit of Zwick Roell machine: 2kN
Test 1:
No. of cycles = 3
Speed of Zwick Roell machine = 10mm/m
Desired spring distance = 27.5mm (50% compression)
Max Load = 22N
Figure 100 - Graph of spring test 1
GORDON KANYIKE - 0705970 Page 56
Test 2:
No. of cycles = 3
Speed of Zwick Roell machine = 20mm/m
Desired spring distance = 38mm (69.1% compression)*MAXIMUM*
Max Load = 30.2N
Figure 101 - Graph of spring test 2
Test 3:
No. of cycles = 3
Speed of Zwick Roell machine = 500mm/m
Desired spring distance = 13.75mm (25% compression)
Max Load = 10.31N
GORDON KANYIKE - 0705970 Page 57
Figure 102 - Graph of spring test 3
Overall the graphs show ideal results of force being directly proportional to travel distance
(displacement).
The spring stiffness was found using equation 5
Equation 6 - Spring stiffness equation
X = displacement of spring‟s length
K = spring‟s stiffness
F = The force applied by the single spring on the pressure distribution plate.
Ftotal = The force applied by all eight springs on the pressure distribution plate.
Test No.
Free length
(mm) x (mm) k (Nmm) F(N) Ftotal(N)
1 55 27.5 0.8 22 176
2 55 38 0.794736842 30.2 241.6
3 55 13.75 0.750058182 10.3133 82.5064
Table 6 - Spring stiffness data
GORDON KANYIKE - 0705970 Page 58
APPENDIX H - THERMOFORMING TESTS
Figure 103 - Set-up of testing under Zwick Roell machine
All springs where set to maximum compression for the following testing.
Test 1
1-layer using Armordon sample 1
No. of springs = 8
Total spring force = 241.6N
Set temperatures:-
Blankholder = 140˚C
Radiant heater = 140˚C
Top tool = 140˚C
Botom tool = 140˚C
Actual forming temperatures:-
Blankholder = 135˚C
Radiant heater = 136˚C
Top tool = 135˚C
Botom tool = 138˚C
GORDON KANYIKE - 0705970 Page 59
Figure 104 - Graph of thermoforming test 1
Figure 105 - Outer view of test 1 Figure 106 - Inner view of test 1
Test 2
1-layer using Twintex sample 2
No. of springs = 8
Total spring force = 241.6N
Set temperatures:-
Blankholder = 190˚C
Radiant heater = 200˚C
Top tool = 185˚C
Botom tool = 185˚C
GORDON KANYIKE - 0705970 Page 60
Actual forming temperatures:-
Blankholder = 180˚C
Radiant heater = 195˚C
Top tool = 184˚C
Botom tool = 179˚C
Figure 107 - Outer view of test 2 Figure 108 - Inner view of test 2
Due to issues with the program, graphical results for test 2 couldnt be shown.
Test 3
1-layer using Armordon sample 2
No. of springs = 4
Total spring force = 120.8N
Set temperatures:-
Blankholder = 140˚C
Radiant heater = 140˚C
Top tool = 140˚C
Botom tool = 140˚C
Actual forming temperatures:-
Blankholder = 133˚C
Radiant heater = 143˚C
Top tool = 138˚C
Botom tool = 133˚C
GORDON KANYIKE - 0705970 Page 61
Figure 109 - Graph of thermoforming test 3
Figure 110 - Outer view of test 3 Figure 111 - Inner view of test 3
GORDON KANYIKE - 0705970 Page 62
Test 4
1-layerUsing Twintex sample#3
No. of springs = 4
Total spring force = 120.8N
Set temperatures:-
Blankholder = 190˚C
Radiant heater = 200˚C
Top tool = 190˚C
Botom tool = 190˚C
Actual forming temperatures:-
Blankholder = 181˚C
Radiant heater = 194˚C
Top tool = 187˚C
Botom tool = 182˚C
Figure 112 - Graph of thermoforming test 4
GORDON KANYIKE - 0705970 Page 63
Figure 113 - Outer view of test 4 Figure 114 - Inner view of test 4
Test 5
1-layer using Armordon sample 3
No. of springs = 4
Total spring force = 120.8N
Set temperatures:-
Blankholder = 140˚C
Radiant heater = 140˚C
Top tool = 140˚C
Botom tool = 140˚C
Actual forming temperatures:-
Blankholder = 137˚C
Radiant heater = 137˚C
Top tool = 131˚C
Botom tool = 138˚C
GORDON KANYIKE - 0705970 Page 64
Figure 115 - Graph of thermoforming test 5
Figure 116 - Outer view of test 5 Figure 117 - Inner view of test 5
GORDON KANYIKE - 0705970 Page 65
Test 6
1-layer Using Twintex sample 4
No. of springs = 4
Total spring force = 120.8N
Set temperatures:-
Blankholder = 190˚C
Radiant heater = 200˚C
Top tool = 190˚C
Botom tool = 190˚C
Actual forming temperatures:-
Blankholder = 180˚C
Radiant heater = 194˚C
Top tool = 187˚C
Botom tool = 181˚C
Figure 118 - Graph of thermoforming test 6
GORDON KANYIKE - 0705970 Page 66
Figure 119 - Outer view of test 6 Figure 120 - Inner view of test 6
Test 7
2-layers using Armordon samples 6 and 7
Orientation of samples at 0˚/90˚
No. of springs = 8
Total spring force = 241.6N
Set temperatures:-
Blankholder = 125˚C
Radiant heater = 120˚C
Top tool = 120˚C
Botom tool = 120˚C
Actual forming temperatures:-
Blankholder = 120˚C
Radiant heater = 117˚C
Top tool = 123˚C
Botom tool = 117˚C
GORDON KANYIKE - 0705970 Page 67
Figure 121 - Graph of thermoforming test 7
Figure 122 - Outer view of test 7 Figure 123 - Inner view of test 7
GORDON KANYIKE - 0705970 Page 68
Test 8
2-layers using samples 8 and 9
Orientation of samples at ± 45˚
No. of springs = 8
Total spring force = 241.6N
Set temperatures:-
Blankholder = 125˚C
Radiant heater = 124˚C
Top tool = 120˚C
Botom tool = 124˚C
Actual forming temperatures:-
Blankholder = 123˚C
Radiant heater = 118˚C
Top tool = 120˚C
Botom tool = 119˚C
Figure 124 - Graph of thermoforming test 8
GORDON KANYIKE - 0705970 Page 69
Figure 125 - Outer view of test 8 Figure 126 - Inner view of test 8
GORDON KANYIKE - 0705970 Page 70
REFERENCES
(Ko, 1989)
(Morozov, 2001)
(Hollaway, 1993)
(James, 2008)
(Long, 2005)
(Zwick UK)
(OCV Reinforcements)
(Wikipedia)
(Glasgow University )
(Richards, 2009)
(Wikipedia)
(McCrum, Buckley, & Bucknall, 1997)
(Powell, 1994)
(Willems, Lomov, Verpoest, & D.Vandepitte, 2008)
(Armordon Company)
(Lomov, et al., 2001)
(Lin, Wang, Long, Clifford, & P.Harrison, 2007)
(Lomov, et al., 2006)
(Willems L. V.)
(Wikipedia)
(Maurel, 2007)
(Pettigrew, 2007)
(Gemmel, 2008)
GORDON KANYIKE - 0705970 Page 71
BIBLIOGRAPHY
Armordon Company. (n.d.). Armordon Home page. Retrieved from Armordon Web site:
http://www.armordon.com/
Gemmel, G. (2008). Design of a heated blank holder for a thermoforming station. Glasgow.
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http://www.mech.gla.ac.uk/~pharriso/Teaching/index.html
Hollaway, L. (1993). Polymer Composites for Civil and Structural Engineering. Blackie
Academic & Professional.
James, G. (2008). Modern Engineering Mathematics. Pearson .
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Lin, H., Wang, J., Long, A., Clifford, M., & P.Harrison. (2007). Predictive modelling for
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Maurel, L. (2007). Thermoforming station project. Glasgow.
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OCV Reinforcements. (n.d.). Twintex: OCV Reinforcements. Retrieved from OCV
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Pettigrew, G. (2007). Thermoforming station project. Glasgow.
Powell, P. C. (1994). Engineering with Fibre-Polymer Laminates. Chapman & Hall.
Richards, A. (2009). Design and Manufacture of a Thermoforming Station.
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Wikipedia. (n.d.). Retrieved from http://en.wikipedia.org/wiki/File:ImageJScreenshot.png
Wikipedia. (n.d.). Image J: Wikipedia. Retrieved from Wikipedia Web site:
http://en.wikipedia.org/wiki/Image_J
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Wikipedia. (n.d.). Survival of the fittest: Wikipedia Web site. Retrieved from
http://en.wikipedia.org/wiki/Survival_of_the_fittest
Willems, A., Lomov, S., Verpoest, I., & D.Vandepitte. (2008). Drape-abilitiy characterization
of textile composite reinforcements using digital image correlation. Leuven: Elsevier.
Willems, L. V. Forming simulation of a thermoplastic commingled woven textile on a double
dome.
Zwick UK. (n.d.). Fibre-composites: Zwick UK. Retrieved from Zwick UK Web site:
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