Design and Manufacture of an Advanced

Composite

Meng in Mechanical Engineering with Aeronautics

Final Year Project 2010/11

Niall Morton - 0602279m

Supervisor: Dr P. Harrison

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Acknowledgements:

I would like to thank several people for their time and help during the progress of this project.

My project advisor Dr P Harrison for his help and guidance throughout the duration of this

project.

Mr J Kitching from the Department of Mechanical Engineering at The University of Glasgow

for his help in finishing the moulds and his valuable insights into composite lay-ups.

Mr J Davidson from the Department of Mechanical Engineering at The University of Glasgow

for all his help in performing the material tests and guidance when manufacturing the

composite

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Abstract:

This project investigates the suitability of several methods of manufacture for advanced composites

to be used to construct a complex, bicycle frame, geometry.

Samples of advanced composite are manufactured and physical tests are performed upon samples

of the material to obtain the composite’s response. These results are then used to compare the

validity of simulating the response of composite models. A finite element analysis program is used to

model the manufactured composite and the physical tests are simulated on these models, with the

future goal of modelling the complex composite frame geometry and obtaining accurate results for

the frames response.

An initial study of applying damage modelling to the simple composite FEA models is then

performed, so future work can start with a better knowledge base of how this damage modelling

procedure is obtained. This will hopefully lead to increased confidence in the results of damage

analysis for composite materials.

Finally the frame mould is to be prepared, so that an advanced composite frame can be

manufactured using the techniques ascertained earlier in the project. This will allow future work to

compare the results of a modelled composite frame with the physical frame’s response.

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Table of Contents:

Acknowledgements 1

Abstract 2

Table of contents 3

List of figures 5

List of tables 7

List of equations 8

List of notation 9

Introduction 10

List of objectives 12

Background 13

1.Testing Manufacturing Methods 15

o 1.1 Vacuum bagging 15

o 1.2 Vacuum infusion 19

o 1.3 Manufacturing methods discussion 21

2. Material testing 22

o 2.1 Tensile test method 24

o 2.2 3 Point bend test method 25

o 2.3 Results 26

2.3.1 Tensile results 26

2.3.2 3 Point bend results 27

o 2.4 Discussion 32

3. Calculation of ply mechanical properties 33

o 3.1 Method 33

o 3.2 Results 36

o 3.3 Discussion 37

4. Composite modelling using finite element analysis 39

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o 4.1 Modelling tensile test 39

4.1.1 Creating the part 39

4.1.2 Creating the material 40

4.1.3 Instancing the part 41

4.1.4 Meshing the part 41

4.1.5 Boundary conditions 42

4.1.6 Tensile results 44

o 4.2 Modelling 3 Point bend test 49

4.2.1 Modelling the supports 49

4.2.2 Instancing the part 50

4.2.3 Meshing the part 50

4.2.4 Boundary conditions 50

o 4.2.5 3 point bend simulation results 52

o 4.3 Discussion – Tensile and 3 point bend 56

5. Applying damage to the FEA model 60

o 5.1 Method 60

o 5.2 Results 64

o 5.3 Discussion 65

6. Finishing the frame mould 66

o 6.1 Method 66

o 6.2 Results 70

o 6.3 Discussion 71

Conclusions 72

References 73

Bibliography 75

Appendix A 76

Appendix B 78

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List of figures:

Figure 1 – Typical recumbent design

Figure 2 – Strength vs. Density diagram

Figure 3 – Berkle Bike + attachment

Figure 4 – PVA release agent + Acetone cleaner

Figure 5 – Twintex comingled woven fabric

Figure 6 – Epoxy resin and hardener

Figure 7 – Resin and hardener mix ratio

Figure 8 – Applying resin to lay-up + finished lay-up before vacuum bagging

Figure 9 – Bleeder cloth (White) + Peel Ply (Orange)

Figure 10 – Sealant tape and vacuum valve placement Figure 11 – Screwing on top of vacuum valve (left) + excess resin soaked in bleeder

cloth (right) cloth (right)

Figure 12 – Spiral wrap tube (Left) + T - junction (Right)

Figure 13 – During vacuum infusion (resin has fully infused part)

Figure 14 – Vacuum bagged Twintex sample

Figure 15 – Tensile samples

Figure 16 – 3 point bend samples

Figure 17 – Tensile test rig

Figure 18 – 3 point bend test rig

Figure 19 – Force vs. Displacement – Twintex Tensile Test

Figure 20 – Stress vs. Strain – Twintex Tensile Test

Figure 21 – Force vs. Displacement – Twintex 3 Point Bend Test

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Figure 22 – Flexural stress vs. Flexural Strain – Twintex 3 Point Bend Test

Figure 23 – Part sketch with dimensions (in metres)

Figure 24 – Input to create a lamina (left) + woven Twintex fabric (right)

Figure 25 – Different orientations for individual plies

Figure 26 – Deformed tensile model

Figure 27 – reaction force at corresponding contour colours

Figure 28 – Force vs. displacement comparison for FEA + physical tests

Figure 29 – Stress Strain curve comparison for FEA + physical tensile tests

Figure 30 – 3 point bend part + dimensions and set partitions

Figure 31 – Deformed 3 point bend model

Figure 32 – reaction force at corresponding contour colours

Figure 33 – Force vs. Displacement comparison for FEA + physical bend test

Figure 34 – Flexural stress vs. Strain comparison for FEA (both lay-ups) + physical bent test

Figure 35 – Force vs. Displacement for steel FEA model

Figure 36 – Inputs needed to apply Hashin damage

Figure 37 – Example outputs for Hashin damage initiation

Figure 38 – Bike frame mould with black coating

Figure 39 – Test lay-up stuck to mould surface

Figure 40 – Sample after removal, grey primer stuck to part

Figure 41 – Sanding of mould before application of primer

Figure 42 – Mould after application of primer

Figure 43 – Both frames fully finished

Figure 44 – Wax used on moulds

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Figure 45 – Test sample on cellulose finish

Figure 46 – Sample after removal, cellulose paint clearly shown to come off mould

List of tables:

Table 1 – Young’s Modulus found for the tensile samples

Table 2 – Calculation of the gradient for force displacement for each sample

Table 3 – Flexural modulus found for each 3 point bend sample

Table 4 – Material properties for composites fibres and the resin

Table 5 – Composite properties values needed to model the composite

Table 6 – Comparison of composite properties

Table 7 – Values for the different boundary conditions in tensile simulation

Table 8 – Results of mesh refinement study (a select range of data is shown)

Table 9 – Comparing orientations effect on resultant force

Table 10 – Comparison of modulus for physical and FEA simulation of tensile tests

Table 11 – Values for the different boundary conditions in 3 point bend simulation

Table 12 – Mesh convergence for the different ply orientations and a comparison

threeee between the reaction force at displacements during simulations.

Table 13 – Comparison of flexural modulus between physical samples and the two

threeeeisimulations

Table 14 – Comparison of Young’s modulus for FEA Analysis and physical tensile test

Table 15 – Comparison of flexural modulus between FEA Analysis and physical test

Table 16 – Example properties for Hashin damage of composite

Table 17 – Output variables for Hashin damage

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List of equations:

Equation 1. – Speed of 3 point bend test

Equation 2. – Axial stress equation

Equation 3. – Calculation of cross-sectional area

Equation 4. – Deformation strain equation

Equation 5. – Young’s modulus equation

Equation 6. – Flexural stress equation

Equation 7. – Flexural modulus equation

Equation 8. – Rule of mixtures to calculate E1

Equation 9. – semi-empirical Halpin-Tsai equation for transverse modulus

Equation 10. – adjustable parameter Xi for transverse modulus

Equation 11. – Equation 11 – Rule of mixtures for poisson’s ratio v12

Equation 12. – semi-empirical Halpin-Tsai equation for shear modulus G12

Equation 13. – Semi-empirical Halpin-Tsai equation for shear modulus G23 plus relevant

frerfrerfrerfrereriiequations to fully calculate this parameter

Equation 14. – Required span between supports

Equation 15. – Cross-sectional area

Equation 16. – Strain equation

Equation 17. – Re-arranged Young’s modulus equation

Equation 18. – Re-arranged axial stress equation

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Notation:

A = Area of cross section, mm2 v12 = Poisson ratio

E = Axial stiffness (Young’s modulus), Pa v21 = Poisson ratio

Ef = axial stiffness of fibres, Pa v23 = Poisson ratio

Em = axial stiffness of matrix resin, Pa σ = Stress, Pa

E1 = axial stiffness of composite ply, Pa ε = strain

E2 = transverse stiffness of composite ply, Pa

F = Force, N

Δ F = Chosen difference in force, N

Gf = Shear stiffness (modulus) of the fibre, Pa

Gm = Shear stiffness of the matrix resin, Pa

G12 = Shear stiffness of composite ply acting in 1 direction on a plane with normal in 2 direction, Pa

G13 = Shear stiffness of composite ply acting in 1 direction on a plane with normal in 3 direction, Pa

G23 = Shear stiffness of composite ply acting in 2 direction on a plane with normal in 3 direction, Pa

K = Bulk modulus

L = Original Length of specimen, mm (tensile test) / Length of span between supports (3 point bend

specimen)

V = Speed of test, mm/min (Note: in this equation K = 0.5 min-1 not bulk modulus)

b = Width of sample, mm

d =Displacement/ deflection, mm

Δ d = Resultant change in displacement for, Δ F

f = Volume fraction of fibres

h = Thickness of specimen, mm

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Introduction:

For people with disabilities or paralysis a wheelchair can be their only mode of transportation

around the house and outside. There are already manufacturers that produce a hand cranked

accessory for a wheelchair or a dedicated recumbent style bike, for the use of people with missing

limbs, paralysis or another disorder that affects leg strength and mobility[1]. The difference with this

project’s approach is the ability to go from an upright wheelchair to a recumbent wheelchair. It aims

to combine in one system the greater mobility and exercising efficiency, of the Berkle bike and

implement the greater stability and comfort of a recumbent with the convenience and compactness

of a regular wheelchair.

This is a benefit to the user as it eliminates the need for owning two different wheelchairs, as an

upright does not provide the user with great mobility outdoors, especially for exercise or pleasure

riding. Similarly only owning a recumbent is not suitable as in general they have a much lower

seating position and longer wheelbase and so, it is not suitable for general mobility around the

house or in a shop, for example. The lower seating position can also put many users off as they do

not feel confident travelling outside as the visibility of the recumbent wheelchair is very limited for

drivers. Figure 1 shows a handcycle recumbent wheelchair and indicates clearly how low the riding

position is and the overall dimensions such as length and width indicate the problems, such as

doorframes being too narrow, using a normal recumbent in general use such as doorframes being

too narrow.

Figure 1 – Typical recumbent design [2]

The time constraints on this project means there will not be enough time to cover the whole design

procedure, so, this report will mainly focus on the manufacturing of the advanced composite

material, finishing a frame mould and applying a composite lay-up to this, physically testing the

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frame and comparing this with a Finite Element Analysis (FEA) model. The objective is to gain

confidence in modelling a composite material under loading and hence enable future project work

on how a different composite material would affect the response of the frame. This modelling

should allow quicker analysis of such materials rather than manufacturing a new frame and testing

it.

The aim was to manufacture and design a novel wheelchair that could convert into a recumbent like

design. The project examined the manufacturing of the advanced composite material and the

finishing of a frame mould. It is intended that the next stages of development of a computer aided

designed model of the wheelchair’s frame and transforming mechanism. It was decided that

modeling a wheelchair frame was beyond the scope of the projects timeframe, instead a bike frame

was chosen to be modeled as this is easier to manufacture and model, this will provide a good

starting point for the longer term goals of the project.

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List of objectives:

Study benefits of a recumbent wheelchair design

Complete the half-finished bike frame moulds from the previous project

Look into different manufacturing methods of composites

Manufacture of a composite

Physical testing of manufactured composites

Calculation of ply mechanical properties

Modelling and simulation using Finite Element Analysis (FEA)

Comparison of physical tests and FEA models

Modelling damage and failure in FEA models

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Background:

Composites:

Composites are materials that consist of two or more constituent materials, one a matrix / resin

material and the other a stiffer reinforcement material [3]. In this project the focus will be on aligned

continuous fibre reinforcement.

Manufactured composites are a relatively new type of material especially the manufacture of fibre

composites, with glass fibres first being produced commercially in the 1930’s and carbon fibres first

being commercially produced in the 1960’s [4].

Therefore while there are many uses of composites in modern engineering they are still being

examined and tested. Engineering is now moving to computer modelling to cut down design costs

and research time for new products, therefore it is easy to see how important investigating the

modelling of a composite using a Finite Element Analysis is to an engineer [5].

The challenge for producing low cost composite products is in devising less labour intensive

techniques. However this project is not concerned with mass production at this stage and

composites are ideal for developing high performance prototypes in low production volumes.

The difference between ordinary composites and advanced composites is to do with the type of

reinforcement that is present in the matrix. Advanced composites have aligned continuous fibre

reinforcements, the advantages of this being that; the longer the reinforcing fibres are the better the

mechanical properties of the composite will be. The processing however is slower and more difficult

using aligned continuous fibres as care is needed to align the fibres for the whole model.

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Figure 2 – Strength vs. Density diagram [6]

Composites are a very useful type of material and have been growing in importance in engineering

for some time and their main advantage is their weight savings.

As we can see from Figure 2, above, composites provide the high strength that metals and ceramics

offer while having a lower density and hence a lower weight for the same strength. This is why

composites had so much importance to high end engineering applications where weight is an

extremely important factor, such as in aircraft design, where any weight saving in the aircrafts

structure allows huge savings in fuel, and increased revenue gained from larger allowable capacity of

passengers and greater range. [7], [8]

Wheelchairs:

Traditionally there have been wheelchairs and recumbent but nothing that combined the two. There

have been some attempted solutions whereby a 3rd wheel, crank and gear mechanism is attached to

a traditional wheelchair but this does not introduce the benefits of a recumbent as the height of the

wheelchair is still the same. An example of this method is the Berkle Bike. Figure 3 shows the normal

styled wheelchair and the attachment end to turn this into a trike/handcycle.

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Figure 3 – Berkle Bike + attachment [9]

This, while helping with outdoor / sporty activity, still includes the disadvantage of the instability in

this set up. A standard wheelchair design which could be transformed into a more recumbent like

position, by lowering the seat and moving the wheels to a position further behind the chair would

increase the stability of the design for cornering and eliminate the need for two wheelchairs; instead

this flexible design would enable users to own one chair that fulfil the needs of users who desire the

ease of use in the home a wheelchair provide and greater mobility a recumbent provides. Having

only one wheelchair also eliminates the need to transfer to continually transfer from one chair to

another depending on what activity the user wants to do.

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1. Testing manufacturing methods:

There are many manufacturing methods that could be used to manufacture an advanced composite,

these include:

Pultrusion

RTM (Resin Transfer Moulding)

VARTM (Vacuum Assisted Resin Transfer Moulding) / also called Vacuum Infusion

Hand Lay-up

Compression Moulding

Filament winding

The decision was made to try making a composite using some of the methods mentioned previously.

Because of the limitations of the equipment available, vacuum infusion and vacuum bagging were

chosen to be examined.

1.1 Vacuum bagging:

The first stage in vacuum bagging is preparation of the mould; in this case a flat sheet of composite

is going to be produced, so a flat Perspex mould is used. The mould surface is cleaned with acetone

and then a release agent is applied to the mould surface. This will help the removal of the composite

part after curing.

Figure 4 - PVA release agent + Acetone cleaner

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Next the fibre reinforcement is cut out to the desired shape and fibre orientation from the roll.

Figure 5 – Twintex comingled woven fabric

If the material being used is not a comingled resin and fibre weave, now would be the time to mix

the resin with the relevant hardener in the desired ratio. (For our epoxy resin that will be used on

the final composite lay-up of the frame, this ratio is 100:26 by weight as shown in Figure 7). The

material used in this vacuum bagging process is a fabric called Twintex and has a commingled weave

consisting of E-glass fibres and Polypropylene resin fibres as, shown in Figures 5, and therefore there

is no need to add resin to the fibres.

Figure 6 – Epoxy resin and hardener

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Figure 7 – Resin and hardener mix ratio

Once this is done the ply layup can now be started, first resin is applied to the surface of the mould

(making sure to leave enough room for the vacuum bagging apparatus) and the first layer of the

fibres is laid down. Then more resin is applied and the next layer is put down in the correct

orientation, this continues until the desired composite lay-up is achieved as shown in Figure 8 and.

Note that Figure 8 does not show the Twintex lay-up as, for Twintex, it is simply a case of cutting the

desired orientation from the fabric weave and laying it down in the correct orientation as the resin is

comingled with the glass fibres and so no resin needs to be applied by hand. Figure 8 shows a test

lay-up on the mould that will be discussed later on in this report and consists of a glass fibre and

epoxy resin lay-up.

Figure 8 – Applying resin to lay-up + finished lay-up before vacuum bagging

The peel ply and bleeder cloth is then cut, making sure the size is sufficient, to cover the lay-up and

lie on top of the lay-up. The bleeder cloth’s purpose is to absorb excess resin and is shown in Figure

9, the peel ply, also shown in Figure 9, is designed so that the other layers do not stick to the

laminate, while the peel ply can be easily pulled of cured part. Enough room is left around the lay-

up, for the placement of the vacuum bag and sealant tape on the mould.

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Figure 9 – Bleeder cloth (White) + Peel Ply (Orange)

The sealant tape is put down around the lay-up, making sure the surface of the mould, where the

tape is to be placed, is cleaned with an acetone soaked cloth. This will ensure the removal of any

release agent that is present, which could cause poor adhesion of the tape. The strips of tape

overlap each other to ensure a better seal for the vacuum bag and the protective paper should be

left on the tape until the vacuum bag is ready to be applied. The paper should only be removed from

the areas where the tape overlaps so there is a good seal there as shown in Figure 10. Also, note the

placement of the lower part of the vacuum pump this will go under the vacuum bag and another

part of the vacuum valve will be screwed into this through the bag allowing the air to be extracted.

Figure 10 – Sealant tape and vacuum valve placement

The vacuum bag is then placed firmly onto the sealant tape. One side at a time ensuring that there

are the minimum number of ripples and kinks in the seal between the bag and the tape and that the

bag is pulled tight when sticking it down. A weight can also be run over the tape border to get rid of

the worst wrinkles. These ripples can allow air in during the vacuum process which is not desirable.

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Now the vacuum pump can be screwed into the base through the vacuum bag as shown in Figure 11

and the vacuum can be applied to the lay-up. The vacuum causes the excess resin to be drawn into

the bleeder cloth and gives the composite better consolidation than a normal wet lay-up technique.

The excess resin soaks into the bleeder cloth and is also shown, for the Twintex sample, in Figure 11.

Figure 11 – Screwing on top of vacuum valve (left) + excess resin soaked in bleeder cloth (right)

1.2 Vacuum infusion:

For vacuum infusion the mould is prepared in the same way as the vacuum bagging method, and the

individual plies are cut and laid down as before, but the resin is not directly applied to the plies at

this stage.

The lay-up is covered by the peel ply and bleeder cloth and the lower part of the vacuum pump is

put in place.

Now the breather mesh layer is cut and placed over the peel ply and bleeder cloth. This bleeder

mesh allows air to be removed even more easily from the vacuum bag. The layer of peel ply, bleeder

cloth and breather mesh can be taped down, over the lay-up. This is to prevent them moving when

we cover them with the vacuum bag.

The sealant tape is laid down around lay-up leaving enough room for the spiral wrap which permits

the flow of resin. The area that the sealant tape is to be put on should be cleaned with acetone to

remove any release agent present, as the release agent could stop the tape from adhering properly.

Now the spiral wrap, shown in Figure 12, is laid down, when placing this, careful consideration needs

to be given to the flow of the resin. If the resin does not infuse the whole lay-up and leaves it with

dry patches, no matter what size they are, the whole part will need to be scrapped.

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The spiral wrap tubing should be in contact with the bleeder cloth and breather fabric so the resin

and air have an easy route to travel, to the lay-up.

Figure 12 – Spiral wrap tube (Left) + T - junction (Right)

The resin enters the spiral wrap through a T- junction, also shown in fig 12, and this can be placed

wherever it is desired.

The outlet tube removes the air and excess resin and air out of the lay-up and should pass through a

catch tank before entering the pump; this is to stop resin entering the pump. If this happens the

pump will become unusable and must be replaced.

The tubes are stuck down with sealant tape and the vacuum bag is placed on in the same fashion as

the vacuum bagging method and the vacuum is then turned on. Leaving it on until all the part has

been fully infused as shown in Figure 13.

Figure 13 – During vacuum infusion (resin has fully infused part)

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1.3 Manufacturing methods discussion:

Both methods were relatively straightforward to complete but the decision was made that the

vacuum bagging method would be used to manufacture the composite bike frame. This was decided

primarily on the fact that because of the frames complex geometry the vacuum infusion process

would end up being very laborious as the infusion path that would be needed would be very tricky to

implement. For example the areas of double curvature on the mould and protruding brackets, are

extremely difficult areas to ensure total resin infusion takes place. This would be a problem as if the

part is not fully infused in one sitting then the whole part is rendered worthless through only one un-

infused area, no matter what the size.

Whereas with the hand lay-up vac infusion method it is relatively straightforward to ensure every

layer of the lay-up has got resin applied to it and so the risk of un-infused parts is decreased

dramatically in this method.

Another factor is the relative importance of the vacuum applied to both methods, in vacuum

infusion the vacuum takes a higher importance than vacuum bagging; the loss of the vacuum during

the vacuum infusion process is much more damaging to the part than any loss of vacuum on a

vacuum bagged part. This is because the vacuum is needed, in the infusion process, to draw the

resin into and through the lay-up, whereas the vacuum in the bagging method simply helps

withdraw excess resin out of the lay-up.

Taking these factors into account it is clear that the vacuum bagging method is a more appropriate

method to use for the manufacture of the bike frame.

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2. Material testing:

The Twintex composite made during vacuum infusion was chosen to be tested, shown in Figure 14;

samples were cut out of the Twintex and tested in a 3 point bend test and a tensile test.

Figure 14 – Vacuum bagged Twintex sample

The standards that were followed for the 3 point bend test and tensile test were British Standards

and are as follows:

BS EN 2747:1998 : Glass fibre reinforced plastics – Tensile test

BS EN 2746:1998 : Glass fibre reinforced plastics – Flexural test – Three point bend method

One of the main objectives is to model the response of a bicycle frame, however a bicycle frame,

when in use, undergoes complex loading and it was decided the main objective here was to at least

obtain the correct response, under simple conditions, for the composite before attempting to model

the full bike frame.

Each test was carried out for four samples of the Twintex composite. These samples were cut to the

sizes specified in the standards which are as follows:

For the tensile test, dog bone shaped samples are required and the dimensions of the samples are:

free length of 60 mm, an average free length thickness of 3 mm and an average free length width of

15 mm. The free length being the rectangular shaped area of the sample in-between the two wider

curved ends. The dog bone shapes were only roughly cut out of the Twintex, hence the non-uniform

curvatures of the samples, as seen in Figure 15, and the rough edges simply filed down. For the 3

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point bend test rectangular samples of length 60 mm, width 15 mm and thickness 3 mm as shown in

Figure 16. Again the samples sides were roughly filed down.

Figure 15 – Tensile samples

Figure 16 – 3 point bend samples

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2.1 Tensile test method:

The four samples were tested using a 50 kN load cell and the speed of the test machine was set,

according to the standard, at 2 mm/min. The samples were clamped in the machine and then pulled

to failure. The data that was output on computer, using the program Labview, was the force and the

displacement of the specimen corresponding to the force. This data was then made into a force vs.

displacement curve for each sample. The test rig is shown in Figure 17. It should be noted that in this

tensile method no strain gauge was used.

Figure 17 – Tensile test rig

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2.2 3 point bend test method:

The test was going to follow the standards, but the supports and the loading struts radius, r1 and r2

respectively, were not able to be matched to the standards. The standards indicate, r1 = (5 ± 0.1) mm

and r2 = (2 ± 0.2) mm, unfortunately the equipment available did not have the correct size of

supports and punch. The machine’s support radius r2 and punch radius r1, were both 9 mm.

However it was decided to continue with the test as it would still be possible to compare the results

to the results obtained from Finite Element Analysis simulation. The speed of the test was obtained

from Equation 1.

Equation 1 – Speed of 3 point bend test

The test rig is shown in Figure 18.

Figure 18 – 3 point bend test rig

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2.3 Results:

Both the tensile and 3 point bend tests, provided displacement data and force applied to obtain this

displacement / deflection of the sample. Thus Force vs. Displacement graphs are obtained for all of

the samples.

From the data in the graphs and using the standards, this data was converted into stress and strain

graphs.

2.3.1 Tensile results:

For the tensile test, we can calculate the stress and strains present on the material using known

relationships.

Calculating stress from the force data:

The stress is calculated according to Equation 2.

Equation 2 – Axial stress equation

F = force at any point in the test, A = cross sectional area at the start of the test in mm2.

With this equation the stress at each data point gathered can be calculated. The cross-sectional area

for each sample is the same:

Equation 3 – Calculation of cross-sectional area

With; b = width of sample and h = thickness of sample.

Therefore by dividing all the force data points by 45 mm2, the stress in megapascals, present under

the applied forces is obtained.

Calculating strain from the displacement data:

The strain is calculated from Equation 4.

Equation 4 – Deformation strain equation

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L = original sample length, l = new length.

The original length, L, is the same for all four samples: 60 mm

Therefore by dividing all the deflection data points by 60 mm, the strains present at each deflection

is obtained. For this tensile test the deflection data is the difference in the new length to the original

length (i.e. l – L).

The modulus of elasticity for the composite can also be calculated using Equation 5.

Equation 5 – Young’s modulus equation

It can also be derived from the gradient of the linear elastic region of the stress strain curve.

The Stress vs. Strain graphs can then be plotted using the data obtained shown in Figure 19 and the

Stress vs. Strain curves are plotted in Figure 20.

The Young’s modulus for the four tensile samples is recorded in Table 1.

Table 1 – Young’s Modulus found for the tensile samples

Modulus:

Sample 1 2058.448106 MPa → 2.06 GPa

Sample 2 1654.985627 MPa → 1.65 GPa

Sample 3 1640.22701 MPa → 1.64 GPa

Sample 4 1991.948951 MPa → 1.99 GPa

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Figure 19 – Force vs. Displacement – Twintex Tensile Test

Figure 20 – Stress vs. Strain – Twintex Tensile Test

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2.3.2 3 Point bend results:

Calculating stress vs. strain graphs for 3 point bend test:

For the bend test the previous calculations are not relevant, instead the standards direct the

calculation of the flexural stress and flexural strain in the sample.

The flexural stress is defined as the stress present at the surface of the material in the middle of the

span of the specimen between the supports at any time during the test and is calculated from

Equation 6.

Note: Equation 6 and 7 are from the British Standard BS EN 2746: 1998 : Glass fibre reinforced

plastics – Flexural test – Three point bend method

Flexural stress:

Equation 6 – Flexural stress equation

σf is the flexural stress in megapascals, F is the force applied in newtons, L is the span in millimetres,

b is the width of the specimen in millimetres, h is the thickness of the specimen in millimetres and d

is the deflection in millimetres.

From this the flexural stress corresponding to the each force data point can be obtained with the aid

of the samples dimensions.

There is no expression for flexural strain but a method for calculating the flexural modulus is given.

This is the ratio of flexural stress to flexural strain in the material and is found from Equation 7.

The flexural modulus:

Equation 7 – Flexural modulus equation

Where; Ef is the modulus in megapascals, L is the span between the supports in millimetres, b is the

width of the specimen in millimetres, h is the thickness of the specimen, in millimetres, ΔF is a

chosen difference in force, in newtons and Δd is the difference in deflection

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The flexural modulus is dependent on the force vs. displacement diagram shown in Figure 21,

specifically the initial rectilinear region. It was advised, in the standard, to use at least 5 points on

the rectilinear part, if the initial region was not linear then a straight line would be drawn between

25% and 10% of the force and the gradient (essentially, ) to be taken from this. See Table 2.

Table 2 – Calculation of the gradient for force displacement for each sample

Sample 1 Sample 2 Sample 3 Sample 4

(mm) (N) mm (N) (mm) (N) (mm) (N)

Max 2.93487 422.475 2.81576 380.083 2.64084 364.226 2.6646 344.758

10% 0.293487 42.2475 0.281576 38.0083 0.264084 36.4226 0.26646 34.4758

25% 0.733718 105.6188 0.70394 95.02075 0.66021 91.0565 0.66615 86.1895

Sample 1 Sample 2 Sample 3 Sample 4

∆F/∆d ∆F/∆d ∆F/∆d ∆F/∆d

143.9502 134.9842 137.9205 129.3845

Because the flexural modulus is the relationship between the flexural stress and flexural strain in the

elastic region we can calculate the strain and hence plot the samples flexural Stress vs. Strain for the

initial linear elastic region of the diagram as shown in Figure 22.

Table 3 – Flexural modulus found for each 3 point bend sample

Flexural Modulus

Sample 1 9826.997448 MPa → 9.83 GPa

Sample 2 9214.918696 MPa → 9.21 GPa

Sample 3 9415.373492 MPa → 9.42 GPa

Sample 4 8832.650104 MPa → 8.83 GPa

32

Figure 21 – Force vs. Displacement – Twintex 3 Point Bend Test

Figure 22 – Flexural stress vs. Flexural Strain – Twintex 3 Point Bend Test

33

2.4 Discussion:

Using the Stress vs. Strain curves, Figures 20 and 22 above for both the tensile and 3 point bend

tests, allows a comparison to be made with the stress and strain curves that will be derived from the

FEA analysis that will be completed later on. The main focus of the analysis will take the initial linear

region of the stress strain curves the reason for this will be discussed in section 4.1.5 later on.

The results for the tensile test are unusual as in the tensile direction the fibre reinforcement is

expected to dominate the composite response and looking at the modulus of the samples, which is

basically the gradient of the initial linear region of the graph, the modulus found is to be between

1.64 GPa and 2.06 GPa but it would be expected that the composites axial modulus would be around

half of the E1 value of the Twintex composite, it will be shown later in Section 4.1.6 that this would

be expected to be around 12 GPa. This is because Twintex’s woven fabric makes it a biaxial

composite with half the reinforcement pointing in a perpendicular direction.

The flexural modulus is quite harder to estimate and the samples are found to have a modulus in

between 8.83 – 9.83 GPa. As seen in Table 3.

These results will be compared with results obtained by modelling the composite in finite element

analysis, which will be discussed later in this report in section.

34

3. Calculation of Ply Mechanical Properties:

To model a composite material in the Abaqus FEA package the individual ply’s mechanical properties

need to be calculated. These will determine how the material behaves in the simulations. To fully

model a composite in the FEA program used six composite properties are required: E1, E2, V12, G12,

G13, and G23

E1 – axial stiffness of the composite, E2- transverse stiffness of the composite, V12 poisson’s ratio of

the composite, G12 – axial shear stiffness, G13 - shear stiffness (stress) acting in the 1 direction on a

plane with a normal in the 3 direction, G23 - shear stiffness (stress) acting in the 2 direction on a

plane with a normal in the 3 direction.

As a composite is essentially a mix of two macroscopic materials and the overall composites

properties will be influenced by the mechanical properties of each of these materials.

3.1 Method:

The axial stiffness E1 is derived from the well-known Rule of Mixtures:

Equation 8 – Rule of mixtures to calculate E1

Hull and Clyde [10] expect this value to be valid to a high degree of precision, providing the fibres are

long enough for the equal strain (Voigt model) assumption to apply.

For the transverse stiffness, E2:

Equation 9 – semi-empirical Halpin-Tsai equation for transverse modulus

ξ, is an adjustable parameter and for E2 is: [10]

Equation 10 – adjustable parameter Xi for transverse modulus

35

Equation 9 is not based on rigorous elastic theory, but it does try to take the enhanced fibre load

bearing, relative to the equal stress assumption, that using a more basic rule of mixtures style

equation does not. [10]

Poisson’s ratio in ν12:

ν12 describes the contraction in the 2 direction when a stress is applied in the 1 direction, the 12

poisson’s ratio can be found from a rule of mixtures.

Equation 11 – Rule of mixtures for poisson’s ratio v12

The shear modulus, G12, indicates the ratio of a shear stress (acting in the 1 direction on the plane

with a normal in the 2 direction) and shear strain (is a rotation towards the 1 direction of the 2 axis)

It should be noted that since the composite body isn’t rotating, therefore Gij = Gji and since in for

aligned fibre composites, the 2- and 3-directions are equivalent, there are only 2 shear moduli as,

G12=G21=G13=G31≠G23=G32. [10]

Again for this property the semi-empirical Halpin-Tsai expression has been found to be a decent

approximation of the axial shear modulus G12.

Equation 12 – semi-empirical Halpin-Tsai equation for shear modulus G12

For the shear modulus G13:

G12 = G13

36

Lastly the shear modulus G23 needs to be calculated: [10]

Equation 13 – Semi-empirical Halpin-Tsai equation for shear modulus G23 plus relevant equations to fully

calculate this parameter

Using these relationships the composite’s ply’s mechanical properties can be calculated.

Before this process can be started the fibre’s and matrixes mechanical properties are needed. The

properties needed are the fibre and matrices Young’s modulus, their respective Poisson’s ratios, the

shear modulus of both and finally the fibre volume fraction in the finished composite material.

For the Twintex composite samples, made with the vacuum bagging method, the material used for

the fibre was E-glass and the matrix resin was polypropylene. Data for these are found from relevant

literature and relevant material databases.

37

3.2 Results:

The data for the material properties are from various sources and are tabulated in Table 4.

Table 4 – Material properties for composites fibres and the resin

Material Property Value Unit Source

Fibre : E-Glass

Young’s modulus, E 76 GPa [10]

Poisson’s ratio, v 0.22 [10]

Shear modulus, G 30 GPa [11]

Matrix – Polypropylene

Young’s modulus, E 1.2

(average of range 1-1.4)

GPa [12]

Poisson’s ratio, v 0.3 [10]

Shear modulus, G 0.538 GPa [13]

Glass Fibre content 35 % in volume [14]

Using the properties in Table 4 and equations 8 -13, the properties needed to model a composite in

the FEA program Abaqus are found. These values are shown in Table 5. The calculations are provided

in Appendix A

Table 5 – Composite properties values needed to model the composite

Property: Value: Units

E1 27.38 GPa

E2 3.005 GPa

V12 0.272

G12 1.09 GPa

G13 1.09 GPa

G23 1.141 GPa

38

3.3 Discussion:

The material that properties are being calculated for is Twintex and properties are supplied by the

manufacturer of Twintex, OVC Reinforcements. [15]

Table 6 – Comparison of composite properties

Comparison: Calculated: OVC Reinforcements:

E1 27.38 GPa 14 GPa

E2 3.005 GPa 13 GPa

v12 0.272 0.1

G12 1.09 GPa 1.7 GPa

G13 1.09 GPa 1.8 GPa

G23 1.141 GPa 1.7 GPa

At first viewing our calculated properties seem out by around 50% but this is because the OVC

Reinforcement data is taken for a woven, biaxial, ply. The calculated data is simply for a uniaxial ply

thus we would expect the data for a uniaxial ply to be about double for the axial, E1, property which

matches up reasonably well.

For E2 it is not so straightforward, because the supplier’s sample would have half the axial properties

in the transverse direction it would be expected that their transverse result would be quite close to

the axial result E1. Whereas in the calculated ply there is a significantly lower value and hence

strength in the transverse direction as it is dominated by the resin not the fibres.

This can be explained by considering that the calculated ply has all the fibres in one direction only,

whereas the supplier’s ply data is taken from a ply with only half the fibres in the calculated samples

direction and the other half in a perpendicular direction.

The material data in Table 4 which is used to obtain the composite properties are prone to error.

There is no unified agreement for the values of E-glass or polypropylene and so for every value in

Table 4 a different value might be obtained from a different material database.

It is also worth noting that even though the relationships and equations used in section 3.1 are

widely used they do carry errors. In these processes the assumption is made that the composite has

perfect bonding between the matrix and the reinforcement fibres and perfect bonding between

39

each ply. This means that these techniques do not allow for interface debonding, cracking or sliding.

These processes tend to initiate and promote plastic deformation and can also be failure initiators.

40

4. Composite Modelling Using FEA:

The FEA (Finite Element Analysis) program that is used is Abaqus. To model the tests in Abaqus the

following steps had to be taken:

A part needs to be created

A material needs to be created

A composite lay-up needs to be created

Meshing the part

Boundary conditions need to be imposed

4.1 Modelling Tensile Test:

4.1.1 Creating the part:

The part created needs to match the test specimen. Therefore a 3D deformable shell planar part is

created, the part is drawn as a 2D shape and then a conventional shell section is applied to indicate

the thickness of the part. The initial 2D face is dimensioned the same as the samples, 15 mm wide

and 60 mm long.

Figure 23 – Part sketch with dimensions (in metres)

41

4.1.2 Creating the material:

To model the composite material we create the composite material. By defining the mechanical

properties as Elastic and setting the type to Lamina, the individual ply material properties can be

input from what was calculated before. E1, E2, V12, G12, G13, G23.The Input window is shown in Figure

24 below.

Figure 24 – Input to create a lamina (left) + woven Twintex fabric (right) [14]

Since the composite material only models the mechanical properties of one individual ply, a ply lay-

up needs to be created and applied to the part. This needs to match the lay-up from the vacuum

bagged specimens. This meant a lay-up of 6 plies with an orientation of [0, 90,-45, 45, 90, 0] °, as

shown in Figure 24, there is a potential discrepancy here, as the Twintex roving used to manufacture

the composite was a weave. This means that there were three layers of material laid down to form

the total ply lay-up and each layer of the Twintex is concerned with two plies in simulated lay-up,

therefore, it is not known if the model should be created with the top two and bottom two plies

oriented at [90/0] ° or [0/90] ° and it is also not known whether the middle two plies should oriented

at [-45/45] ° or [45/-45] ° It was found that for the tensile simulation this change in orientation did

not affect the results as shown in section 4.1.6 Table 8. This is important as the change in orientation

lay-up can affects the composites stiffness and response to the modelled tests. The woven Twintex

fabric, also shown in Figure 24, shows how one layer of the material contains two different

orientations.

42

For the ply thickness, it is known that the thickness of the manufactured specimens is three

millimetres and for this specimen 3 layers each of 2 plies is used therefore there are six plies for a

three millimetre thickness, hence each ply has a thickness of 0.5 millimetres which needs to be input

in meters i.e. it is entered as a value of 0.0005.

4.1.3 Instancing the part:

Before creating any boundary conditions or meshes the part is instanced, to be a dependant (mesh

on part instance.

4.1.4 Meshing the part:

The mesh controls are set for structured meshing with quad only elements and the element used is a

S4R Quad shell element. For the tensile test it is desirable to have an even number of elements along

the top and bottom edges of the sample as this provides a node in the middle of the part, this is

useful when it comes to applying boundary conditions later on. To create the correct number of

elements (i.e. an even number) along the top and bottom edges these edges should be seeded by

the “edge by number” process. This involves selecting the top and bottom edges and inputting the

desired even number of elements.

Usually the more refined the mesh is the more accurate the result but with this simplistic

rectangular shape it has been found that the factor of refinement and hence number of elements in

the mesh does not affect output and hence a largely refined mesh is not needed in this case. This is

Figure 25 – Different orientations for individual plies

43

advantageous as the higher the mesh refinement, the more computing power is needed to complete

the simulation and hence time and cost to a project.

4.1.5 Creating Boundary Conditions:

The boundary conditions (BC’s) allow for accurate modelling of the physical test. Here we can specify

constraints and displacements onto our created part, trying to match the physical test as closely as

possible.

For the tensile test, the physical test stretches the part in the Y(2) direction which in-turn causes the

sample to contract in the X(1) direction. There is no movement in the Z(3) direction and the bottom

edge is clamped in place.

To simulate the clamped rigid bottom surface, a boundary condition is made in Abaqus. This BC is

only used on the nodes along the bottom of the sample; hence a node set of the bottom nodes

needs to be created (not including the middle node). This node set is used to create a

displacement/rotation BC on the region corresponding to the bottom node set created previously.

They nodes do not move in any direction but are allowed to contract in the X(1) direction, so, the

fields U2, U3,UR1, UR2 and UR3 in the BC options box are selected and set to zero, leaving U1

unselected and blank. This ensures that this set of nodes will not move in any direction, apart from

the x direction, or rotate about any axis.

Using the middle node, on the bottom of the part a node set is created consisting of this node. A

boundary condition is then created, that fully constrains this node. This BC acts as an anchor point in

the simulation so that the part is stretched during the simulation, not simply displaced from the

original position.

The next boundary condition that needs to be made is for all the nodes in the body except those on

the top and bottom sides. Because the material lay-up used for the physical test is not symmetrical,

(because of the -45/45° plies), this results in a un-balanced stress acting in the lay-up which causes

the model to buckle and warp very slightly and it will not cause a huge discrepancy to simplify the

reaction forces by constraining the model in the Z(3) direction.

The final boundary condition that needs to be made is concerned with the displacement of the

nodes at the top of the part. For this a node set is made consisting of the nodes along the top edge

and a displacement/rotation boundary system is created using this set. This boundary condition

needs to let the nodes move in the Y(2) and X(1) direction with no rotations and no movement in the

Z(3) direction, thus, all the rotations and the z(3) direction are set to 0 (i.e. U3, UR1, UR2, UR3 = 0)

44

and the X(1) direction is left unchecked. However the Y(2) direction is not left unchecked as a

specific displacement of three millimetre, therefore Y(2) is set at three millimetre displacement (i.e.

U2 = 0.003) as it is in meters.

The displacement of 3 millimetres is chosen as the model does not take into account any failure

modes and so can only model the linear elastic response of the composite and so to compare with

the physical tests a displacement is needed that matches a displacement in the linear region of the

physical test. Thus we can compare the values of this linear elastic region. Three millimetres

displacements fit in this region for all the samples and it’s quite late on in the region so it allows a

greater range of data to be analysed.

The desired output for field and history outputs are the reaction forces and displacements that occur

on the specimen as a whole and more specifically the set that is to do with the top nodes.

Table 7 – Values for the different boundary conditions in tensile simulation

Tensile Sets U1 U2 U3 UR1 UR2 UR3

Top - 0.003 0 0 0 0

Bottom - 0 0 0 0 0

Encastre 0 0 0 0 0 0

Body - - 0 - - -

45

4.1.6 Tensile Results:

Figure 26 – Deformed tensile model

The contour plot of the reaction force along the specimen is shown in

Figure 26. To calculate the total reaction force, in the Y direction, the

reaction force, at each node, along the top of the specimen needs to

be summed.

Doing this obtains a total reaction force, for this simulated composite

material stretching by three millimetres, of 50628.5 N. A mesh

refinement was performed on this specimen, this would indicate

whether a larger number of elements and hence a more refined mesh

would alter the accuracy of the resultant force measured. It was

found that the number of nodes and hence elements in the model did

not affect the total resultant force measured as is shown in Table 8

with the resultant forces being the same for every number of elements.

Figure 27 – reaction force at

corresponding contour colours

46

Table 8 – Results of mesh refinement study (a select range of data is shown)

4 Elements

along the top set

10 elements

along the top set

16 elements

along the top set

Total resultant

Force (N)

Total resultant

Force (N)

Total resultant

Force (N)

0 0 0

562.539 562.539 562.539

1125.08 1125.08 1125.08

1687.62 1687.62 1687.62

2250.16 2250.15 2250.16

↓

Jump in data

↓

Jump in data

↓

Jump in data

48940.9 48940.9 48940.9

49503.4 49503.4 49503.4

50066 50065.9 50066

50628.5 50628.5 50628.5

Figure 27 shows the value of reaction force, in the Y(2) direction, the coloured contours represent in

Figure 26, at each node that is present in the model.

To check on the uncertainty of orientation, as described in section 4.1.2 The resultant force at the

top nodes of the model were compared for the two lay ups, the original lay-up orientation [0, 90,-45,

45, 90, 0] ° and the possible new orientation [90, 0,-45, 45, 0, 90] °. It was found that both

orientations of lay-up produced identical results, so for the tensile simulation the lay-up orientation

is not an affection factor for the Twintex composite. This result is shown in Table 9.

47

Table 9 – Comparing orientations effect on resultant force

Old lay-up orientation

[90, 0, -45, 45, 0, 90] °

New lay-up orientation

[90, 0, -45, 45, 0, 90] °

Total resultant Force (N) Total resultant Force (N)

0 0

562.539 562.539

1125.08 1125.08

1687.62 1687.62

↓ ↓

48940.9 48940.9

49503.4 49503.4

50066 50066

50628.5 50628.5

A force displacement diagram is obtained from the reaction force data, for the nodes, along the Top

set of the model and relevant displacement data. This displacement data is obtained from the spatial

displacement values for any node along the top of the specimen (any node can be used as they are

all displaced equally).

Comparing this force displacement data with the data obtained from our physical results can be

done by plotting the FEA analysis data onto the force vs. displacement graph that was obtained for

the physical tensile test and is shown in Figure 28.

48

Figure 28 – Force vs. displacement comparison for FEA + physical tensile tests

This data can be converted to a stress vs. strain diagram in the same way as the physical test data

was. The combined stress vs. strain graph of the FEA analysis and the physical tensile data is graphed

in Figure 29. It shows how the simulated test has an increased modulus to that of the physical tests.

Figure 29 – Stress Strain curve comparison for FEA + physical tensile tests

49

Table 10 shows a comparison of the modulus calculated for the physical tests and the modulus

calculated for the FEA simulation. It is shown that the modulus is around six times higher than the

physical samples modulus.

Table 10 – Comparison of modulus for physical and FEA simulation of tensile tests

Modulus:

Sample 1 2058.448106 MPa → 2.06 GPa

Sample 2 1654.985627 MPa → 1.65 GPa

Sample 3 1640.22701 MPa → 1.64 GPa

Sample 4 1991.948951 MPa → 1.99 GPa

FEA analysis 12618.01262 MPa → 12.62 GPa

50

4.2 Modelling 3 point bend test:

The method taken for modelling a 3 point bend test is similar to, and has many of the same steps as,

the tensile test model. There are some differences in the modelling process.

The part is created as before as a 3D deformable shell planar part, with dimensions corresponding to

the physical specimen (60 mm long, 15 mm wide). The composite material is created with the same

procedure and the same properties as before and is applied to the created part.

Before the part can be meshed, the supports need to be modelled. The composite sample rests upon

them during the test and is not fixed onto them, so a first attempt was made to model the supports

as analytically rigid bodies that were positioned under the part. This process did not work out as it

would not allow the desired part to be used. Instead of a 3D deformable part, this process needs to

have a 2D deformable part. Difficulties were encountered in positioning the parts and modelling the

bar that applied the bending force along with frictional components and contact modelling.

It was decided that a simpler approach would be used instead. So a 3D deformable part was created

with the correct part geometry as shown in Figure 30.

Figure 30 – 3 point bend part + dimensions and set partitions

4.2.1 Modelling the supports:

Instead of modelling the supports as analytically rigid parts, it was decided to use constraints to try

and model the effect of the supports on the sample. This means boundary conditions will need to be

51

applied to the areas where the composite sample rests on the supports. This is found using the

standard BS 2476 used in the previous section 2.3.2; it describes the span length, the distance

between the supports, to be:

Equation 14 – Required span between supports

So the distance from the middle of the specimen to the supports is 24 millimetres with the supports

situated 6 millimetres from the ends of the specimen. To model the nodes situated at the supports

the specimen is partitioned 6 millimetres from each end, as shown in Figure 30. A partition is also

created at the middle of the support, again shown in Figure 30; this ensures there will be nodes

along the middle of the specimen which is desired, as this is where the specimen will have a

displacement applied.

4.2.2 Instancing the model:

The model is instanced in the same way as the tensile model, as a dependant mesh on part instance.

4.2.3 Meshing the model:

Because the model has been partitioned three times and hence split into four sections, all the

sections need to be selected when applying the final mesh to the part.

As before all sections of the model will have structured quad element only controls applied to them

and the type of meshing element to be used will be the same as in the tensile test, a S4R Quad shell

element.

4.2.4 Boundary Conditions:

Three node sets need to be created, these will be used to apply three boundary conditions to the

model. The sets should comprise of one middle set for the nodes along the partition created at the

middle of the sample, and the other two are for the nodes along the two partitions that model the

supports, near each end of the sample.

The boundary conditions are, again, important to get right as this will allow the physical test to be

modelled with a greater accuracy. For the boundary condition at the nodes which correspond to the

tests supports, we want the material to rotate around the Y(2) axis. We want this as, in the physical

test, when the load is applied the specimen is pushed down against the supports. As the force

52

applied increases the middle of the specimen is displaced further down but at the supports it is

constrained, and cannot move further down, instead it bends against the supports. This rotation in

the Y(2) axis allows this behaviour to be realised.

In the physical test the specimen is not clamped down during the application of the load and during

the subsequent bending, the specimen is free to slip down the support. The only thing stopping it is

the friction of the sample being pressed onto the support. To try and model this accurately it was

decided that the nodes at the line of the supports should be constrained to be fixed in the Y(2)

direction this allows the sample to be able to model the pulling down and pulling in of the specimen

around the support. Unlike the physical model which allows the sample to move in the X(1) and Z(3)

direction as well, if only minutely, as it slides against the support. The simulated model cannot be

freely allowed to move in these directions as well, because, if the two support sets are not

constrained in the Z(3) direction then the whole model will be moved down this axis by the

displacement applied to the middle nodes. Therefore the support boundary conditions also have to

include Z(3) direction constrained (U3 = 0)

Now a boundary condition is applied to the nodes, along the partition, in the middle of the

specimen. In the physical test this part of the specimen is where the load is applied and so is where a

displacement is applied for the simulation. Like the tensile test simulation, this simulation of the 3

point bend test does not take into account any modes of failure and so can only be used to model

the linear elastic response of the specimen. Thus a displacement is applied that corresponds to a

displacement that is in the physical tests linear elastic region, so the two tests are comparable. In

this case a displacement is applied in the Z(3) direction of -0.0025, this indicates 0.0025 meters as

Abaqus requires a consistent set of units and meters has been used throughout.

Table 11 - Values for the different boundary conditions in 3 point bend simulation

3 point bend Sets U1 U2 U3 UR1 UR2 UR3

Middle - 0 0.0025 0 0 0

Support (1 and 2) - 0 0 0 - 0

53

4.2.5 3 point bend simulation results:

Figure 31 – Deformed 3 point bend model

Figure 31 shows the reaction forces at the nodes on the middle

partition, which is the area that the displacement is applied to. Figure

32 shows the legend that appears in Figure 31.This indicates which

area on the model has what value of nodal reaction force in the Z(3)

direction.

Figure 32 - reaction force at

corresponding contour

colours

54

Figure 33 – Force vs. Displacement comparison for FEA (both lay-ups) + physical bend test

Figure 34 – Flexural stress vs. Strain comparison for FEA (both lay-ups) + physical bent test

55

It was desired to understand the uncertainty regarding the orientation of the lay-up in modelling,

whether it be [0, 90, -45, 45, 90, 0] ° or [90, 0, -45, 45, 90, 0] ° as described in section 4.1.2. Unlike

the tensile result, the different orientations of plies affect the results of the 3 point bend test

simulation extensively as shown in table 10. The force vs. displacement data for this new orientation

of the lay-up is also shown in Figure 33, above. Note that the four physical samples in Figure 33 have

been greyed out to improve the visibility of the FEA result for the [90, 0, -45, 45, 90, 0] ° orientation

shown in orange, while the original oriented lay-up is shown in blue and the corresponding Stress vs.

Strain curve for the two lay-up orientations and the physical samples for the 3 point bend test is

shown in Figure 34.

Table 12 – Mesh convergence for the different ply orientations and a comparison between the reaction

force at displacements during simulations.

Ply orientation: [90, 0, -45, 45, 0, 90] °

(New orientation)

[0, 90, -45, 45, 90, 0] °

(Original orientation)

4

elements

6

elements

15

elements

4

elements

6

elements

15

elements

Displacement

(mm) Force (N) Force (N) Force (N) Force (N) Force (N) Force (N)

0 0 0 0 0 0 0

0.025 3.32493 3.31086 3.30433 6.9526 6.92405 6.91085

0.05 6.64985 6.62172 6.60866 13.9052 13.8481 13.8217

0.075 9.97478 9.93259 9.91299 20.8578 20.7722 20.7325

(Jump in data) ↓ ↓ ↓ ↓ ↓ ↓

2.45 325.843 324.464 323.824 681.355 678.557 677.263

2.475 329.168 327.775 327.129 688.307 685.481 684.174

2.5 332.493 331.086 330.433 695.26 692.405 691.085

Table 11 shows the reaction force in the model at displacements that were obtained for the two

potential ply orientations simulations. It also indicates if a more refined mesh obtains significant

changes in results. Taking the two ply lay-ups on their own it can be seen that there is only an

insignificant change between the flexural stress values at a displacement of 2.5 mm so it will not be

that significant, when running the simulation, to use a highly refined mesh. Table 11 also indicates

56

how important it is to run the model with the orientation that is physically manufactured, as the

change in ply orientation halves the total reaction force and also decreases the flexural modulus

found for the simulation as shown in Table 12.

Table 13 – Comparison of flexural modulus between physical samples and the two simulations

Flexural Modulus

Sample 1 9826.997448 MPa → 9.83 GPa

Sample 2 9214.918696 MPa → 9.21 GPa

Sample 3 9415.373492 MPa → 9.42 GPa

Sample 4 8832.650104 MPa → 8.83 GPa

FEA original lay-up orientation 18871.36427 MPa → 18.87 GPa

FEA altered lay-up orientation 9022.941867 MPa → 9.02 GPa

57

4.3 Discussion - Tensile and 3 point bend:

This modelling has errors associated with it and it is important to understand them. For both

simulations there will be errors in modelling the actual composite. The physical material is a woven

fabric and thus has, for each layer of material, two plies associated with it. This does cause

uncertainty when applying the composite lay-up in the simulation as it is unknown which orientation

of the reinforcement fibres has to be taken as the “top” layer in the simulation this is also the case

with the subsequent layers and so we cannot be sure our lay-up matches the physical one.

Tensile Discussion:

As can be seen from the data curves obtained, the modulus for our FEA analysis is of a much higher

magnitude than that calculated from the physical testing of the composite.

Because of the large difference in results for the simulation and physical results, the validity of the

model is put into question.

The decision was made to model a steel sample and apply a certain displacement to this and

compare the resultant force on this to the calculated force that would be present using simply

elastic mechanics. For the calculation of the expected force please refer to Appendix B.

Figure 35 – Force vs. Displacement for steel FEA model

58

Comparing this calculated force with an Abaqus FEA model with the same dimensions and an elastic

isotropic material defined by Young’s modulus E = 200x109 and Poisson’s ratio, v = 0.3 and a

displacement of 3 mm applied to the steel model, which produces the same strain as our calculation,

the reaction force output for the nodes that the displacement was applied to is measured at 45000

N as shown in Figure 35. And the reaction force calculated for the steel sample was also found to be

45000 N. As found in Appendix B.

This model results in the same force that was calculated before, in equation 18, and so it can be safe

to assume the model for the composite is reasonably reliable. Since this is the case we must look at

the physical results as being erroneous.

Indeed when examining Figure 34 and comparing the modulus of each physical test and the FEA

analysis:

Table 14 – Comparison of Young’s modulus for FEA Analysis and physical tensile test

Data: Modulus: Modulus at initial steeper gradient

FEA Analysis 12.62 GPa

Physical Test 1 2.02 GPa 4.5 GPa

Physical Test 2 1.614 GPa 3.11 GPa

Physical Test 3 1.628 GPa 3.48 GPa

Physical Test 4 1.987 GPa 4.06 GPa

The FEA analysis model indicates a modulus of 12.62GPa for the simulated composite, this is what

we would expect, as, in tension the fibres oriented in the direction of the force dominates the

behaviour of the composite in testing and since we would expect and want the fibres to fail before

our matrix we would expect the modulus measured from our tensile test to be essentially much

higher than the matrix materials modulus, which is true for the FEA analysis.

However, the modulus found from the physical test is very low an order of ten lower than the FEA

result as seen in Table 8. This is not what is expected and this is why the test method is under

question.

The initial gradient for the physical tensile stress vs. Strain graph is studied, possibly the initial

steeper gradient might produce the correct modulus before the sample perhaps slipping in the

59

clamps. The findings are presented in table 8 above. However it was found that while this did

produce a higher modulus than later on in the tensile test, it only doubled the modulus to around

3.5 GPa on average which is still almost an order of 10 out from the FEA Analysis.

It is thought that redoing the tensile tests with strain gauges, directly attached to the samples, would

produce better strain data than the previous method described in section 2.1. As the strain reading

would be measured directly on the sample and so slippage in the clamps would not affect the

readings, while in the previous test the strain is calculated from the ratio in displacement to original

length as shown in Equation 15. This means slippage in the test machine causes false displacement

readings and hence erroneous strain readings.

3 Point bend discussion:

This weaved fabric causes the reinforcement fibres to buckle, underneath and over the other fibres

as has been shown previously in Figure 24. This buckled nature causes the reinforcements to be

weaker than unbuckled straight fibres especially in compression, [16], West and Adams have shown

a braided composite can have a decrease in axial compressive strength of 30% [17] and so this

affects the total mechanical properties of the final composite. This buckling is complex to model and

is beyond the scope of this project; however there are programs being created, such as texgen that

will allow for this process in the future allowing for better representation of simulations. [18, 19]

Table 15 – Comparison of flexural modulus between FEA Analysis and physical test

Flexural Modulus

Sample 1 9826.997448 MPa 9.83 GPa

Sample 2 9214.918696 MPa 9.21 GPa

Sample 3 9415.373492 MPa 9.42 GPa

Sample 4 8832.650104 MPa 8.83 GPa

FEA original lay-up 18871.36427 MPa 18.87 GPa

FEA altered lay-up 9022.941867 MPa 9.02 GPa

Comparing the flexural modulus it is clear for the first simulation with our unaltered [0, 90, -45, 45,

90, 0] ° the simulated modulus is found to be double that of the physical 3 point bend test results,

60

this initially seems a decent result as from our model it would be expected that the modulus for the

simulation would be higher than the physical tests. Due to the simulation not taking into account the

weave of the fabric and the voids present in the physical test, both of which decrease the

composites strength.

However it also became apparent that modelling the correct orientation is an important factor to

consider. When the lay-up is changed to [90, 0, -45, 45, 90, 0] ° it is found that the modulus of the

simulation is changed such that it matches the physical tests results. It is not known which

orientation best models the physical lay-up however, it would be expected that the simulated lay-up

should be higher than the physical specimens modulus because of the perfect modelling between

layer, lack of voids and the lack of crimp that occurs in the FEA simulation.

It is advised that future work, implements, or at least looks into modelling the woven fabric

reinforcement structure using packages mentioned previously in this discussion to try and eliminate

this uncertainty due to ply orientation and crimp in the fibres.

61

5. Applying damage to the FEA model:

In the previous simulations the model has only been able to simulate the elastic behaviour of the

composite material; this means no matter how much force is applied or how far the model is

displaced the resultant force acting at the chosen nodes will only ever increase.

5.1 Method:

The Abaqus software allows the implementation of composite damage initiation and evolution. The

damage initiation criteria for fibre reinforced composites in Abaqus are based on Hashin’s theory

(19) and it requires that the behaviour of the undamaged material is linearly elastic, which is what

has been modelled up to this point in the previous Abaqus models. Damage is characterised by the

degradation of material stiffness [20] and many fibre-reinforced composite materials exhibit elastic-

brittle behaviour. Thus hardly any plastic behaviour is seen and after initially deforming elastically

the composite then fails in a brittle manner, usually in the fibres, depending on the orientation of

the loading. So, in the simulations there is no need to try and model plastic behaviour. [20]

Hashin’s theory takes into account four different modes of failure which are:

Fibre ruption in tension Fibre buckling and kinking in

compression

Matrix cracking under transverse

tension and shearing

Matrix crushing under transverse

compression and shearing

The data that is requested for input when applying the Hashin damage model is shown in Figure 36

and is:

Longitudinal Tensile

Strength

Transverse Tensile

Strength

Longitudinal Shear

Strength

Longitudinal

Compressive Strength

Transverse Compressive

Strength

Transverse Shear

Strength

62

These values are input with the data:

Fibre Tensile Strength Matrix Tensile Strength Longitudinal Shear

Strength

Fibre Compressive

Strength

Matrix Compressive

Strength

Transverse Shear

Strength

There is also the coefficient alpha, α, this coefficient determines the contribution of the shear stress

to the fibre tensile initiation criterion.

To use this damage model for composites it must be used with elements that have a plane stress

formulation these include plane stress, shell, continuum shell and membrane elements. [20]

Figure 36 – Inputs needed to apply Hashin damage

63

Table 16 – Example properties for Hashin damage of composite

Property: Data:

Fibre tensile strength 3448000000 Pa

Fibre compressive strength 3448000000 Pa

Matrix tensile strength 30300000 Pa

Matrix compressive strength 40710000 Pa

Matrix longitudinal shear strength 30532500 Pa

Matrix compressive shear strength 20355000 Pa

For fibre tensile strength a value of a generic e-glass fibre was obtained from the material database,

see the reference for more information.

The compressive strength is taken as the same as the fibres tensile strength because, for glass fibres

reinforced composites the strength is approximately equal in strength and compression

For the matrix tensile strength a tensile strength found from literature [10]. The average of the range

of values is taken here.

Data for the compressive strength was hard to come by and meaningful values could not be found

in timeframe of the project.

Instead of trying to model any meaningful damage criterion data, it was decided that the

compressive strength for the matrix would be taken as half the tensile strength, while the

longitudinal shear strength of the matrix was taken as a value in between the compressive shear

strength and the compressive strength of the matrix.

The matrix compressive shear strength is taken as half the matrix compressive strength as this is a

specific model and the alpha value is known to be 0 for this model. [20], [21]

The process is tested by applying this damage model to the tensile simulation that was simulated

previously. After applying the Hashin damage model to the part, field variables, relating to the

damage initiation criteria, need to be selected for the part; these allow the damage initiation results

to be shown.

64

Table 17 – Output variables for Hashin damage

Output Variables: Description:

DMICRT All damage initiation criteria components.

HSNFTCRT Maximum value of the fibre tensile initiation criterion experienced during the analysis.

HSNFCCRT Maximum value of the fibre compressive initiation criterion experienced during the analysis.

HSNMTCRT Maximum value of the matrix tensile initiation criterion experienced during the analysis.

HSNMCCRT Maximum value of the matrix compressive initiation criterion experienced during the analysis.

These output variables indicate whether an initiation criterion in a damage mode has been satisfied

or not. This is shown a numerical value. If the value is less than 1.0 this indicates the criterion has

not been satisfied, if the value is over 1.0 then the criterion has been satisfied. Because no damage

evolution model has been applied the values can go past 1.0, the further past 1.0 and hence the

larger number indicates how much the criterion has been exceeded, if, however, a damage evolution

model has been applied then the value would reach 1.0 and no more. [20]

It should be noted that these results are not expected to be correct, and are not expected to

accurately model the damage initiation for this FEA model. The aim of running the model with these

values was to give an example of the output method that the Hashin damage model uses.

65

5.2 Results:

Figure 37 – Example outputs for Hashin damage initiation

66

5.3 Discussion:

Using the properties in Table 13, a damage model was simulated as is shown in Figure 37; an output

is produced for the four damage initiation criterion. From the data used here it is shown that for the

fibre tensile initiation criterion (HSNFTCRT – top right Figure 37) there is an output of 0, since this is

below 1 then for this simulation the fibre tensile failure has not been initiated.

For fibre compressive initiation criterion (HSNFCCRT – Top left Figure 37) the output is 1.489x10-2

this is again less than 1 so the fibre compressive failure has not been initiated.

For matrix tensile initiation criterion (HSNMTCRT – Bottom right Figure 37) the output is 9.078x103

this is greater than 1 so the matrix tensile failure has been initiated.

For matrix compressive initiation criterion (HSNMCCRT – Bottom left Figure 37) the output is 0 which

is below 1 and hence the matrix compressive failure has not been initiated.

It should be noted that these results are not expected to be correct, and are not expected to

accurately model the damage initiation for this FEA model. The aim of running the model with these

values was to give an example of the output method that the Hashin damage model uses.

To find actual results for the Twintex composite would require testing the materials specific to the

composite, for Twintex this would involve the testing of E-glass fibres and polypropylene, to relevant

standards, designed to accurately calculate the properties needed to be input when apply Hashin

damage. [21]

However it is useful to look over the damage initiation method and examine how it is output as this

will allow further work to be done more efficiently and allow progress to applying damage evolution

which involves modelling the damage so that the simulation models element removal [22].This has

not been studied in this project due to the time constraints.

67

6. Finishing the frame mould:

6.1 Method:

The frame mould used in this project was inherited from a previous project and is a bicycle frame,

not a wheelchair frame, it would not be possible to manufacture a wheelchair frame within the

timeframe of this project and the bicycle frame is suitable as it has quite complex, full-suspension

geometry allowing the opportunity to make a simpler frame while retaining some of the

complexities of a wheelchair frame.

The mould itself came in two separate parts, one for each half of the frame. As can be seen in

Figures 38 and 41 the moulds were found with two different finishes; one had a glossy black coating

and the other had no coating at all. The black glossy coating was found to be a layer of black

cellulose paint and it was also found that there were layers of cellulose primer that was sprayed

onto the bare mould to provide a smooth base for this paint. Before being able to manufacture

composite frame the second, unfinished, mould needs to be finished.

Figure 38 – Bike frame mould with black coating

The cellulose finish aids in the release of the composite lay-up which is important as a small sample

lay-up was tested on a piece of foam, which was the same as the mould; this, was sanded down then

sprayed with the cellulose primer. This process of sanding and priming was repeated until a smooth

coating was achieved. Next a wet lay-up was made using the vacuum bagging technique. After the

part was fully consolidated in an oven, the lay-up and the vacuum pump valve seemed stuck to the

foam base as shown in Figure 39.

68

Note: pictures of the wet lay-up have already been shown in the report in section 1.1 in Figures 8,10

and 11

Figure 39 – Test lay-up stuck to mould surface

Figure 40 – Sample after removal, grey primer stuck to part

After some considerable effort the vacuum valve and composite was finally removed from the

mould surface but, as is shown in Figure 40, the grey primer was ripped off of the mould base and

stuck to the surface of the lay-up.

The unfinished half of the mould was prepared for the cellulose paint by sanding down the mould

with 800/600 grade sandpaper, shown in Figure 41, then spraying a primer onto it. The only primer

available was a grey acrylic primer but after contacting the Mr J. Kitching, a model maker and

technician of Glasgow University’s Mechanical Engineering Department, who actually made the

69

moulds, this acrylic based primer was deemed suitable for use as it was able to be used with

cellulose paint. After a few more cycles of sanding and coating with the primer until a smooth grey

finish was achieved, shown in Figure 42, the mould was then sent to Mr Kitching to get the black

cellulose paint sprayed onto it. This had to be done at Acre Road laboratory as they had suitable

extraction fan facilities and they also had access to the thinner needed to use the paint.

Figure 41 – Sanding of mould before application of primer

Figure 42 – Mould after application of primer

Once the mould was coated with the black cellulose paint, as shown in Figure 43, they were then

thought to be ready to have a lay-up applied to them. A small change needs to be made from the

vacuum bagged method described earlier on though. Instead of cleaning the surface of the mould

with acetone, as described before, they need to be run over with a very fine grade sandpaper and

then a PVA/silicone wax coating, as shown in Figure 44, is applied then the release agent is put on

top of this.

70

Figure 43 – Both frames fully finished

Figure 44 – Wax used on moulds

It was decided to test this technique on a sample of the foam that the bike frames are made from.

This was done primarily to investigate whether the lay-up would damage the mould and to test

whether the paint finish is suitable for use.

Before a lay-up was applied some more release agent was applied and then a basic composite lay-up

was produced using basic hand lay-up methods. The part was then left to infuse in an oven at 85° for

around 6 hours. If there was time the composite would ideally be left at a lower temperature for a

longer time but the timeframe of the project did not allow this.

71

6.2 Results:

The results of this lay-up are shown in Figure 45.

Figure 45 – Test sample on cellulose finish

It is clear to see that the cellulose paint coating does not perform as was hoped. After peeling the

infused lay-up off of the mould it can clearly be seen that the paint is ripped up off the mould along

with the composite shown in Figure 46.

Studying the lay-up it does seem like the cellulose layer has melted and then, when the part is

cooled, it seems to have solidified to the composite lay-up. This clearly is an unintended occurrence.

Figure 46 – sample after removal, cellulose paint clearly shown to come off mould

72

6.3 Discussion:

While this result is not what is wanted, there are some points that are worthy of note. It could be

that the cellulose paint was not suitable for high temperature operation and it may be that leaving

that part to infuse in a lower temper for longer; it may be found that the composite does not rip the

cellulose paint layer off the mould. Unfortunately this was unable to be confirmed due to the time

frame of the project and so any future work could apply a lay-up to a part coated with the same

cellulose paint finish and infuse it at a lower temperature (lower than 85°C) then check to see if the

lay-up comes off without damaging the cellulose finish.

One important point to note is that even though some of the grey primer that was laid down

underneath the cellulose paint layer has come off, it is clear the actual base of the mould has not

been damaged. This means that if it was desired, the bike moulds could be used to manufacture one

piece. The mould would then simply have to be cleaned with acetone and it would be ready to use

again, whether or not it would need a new coating is unclear. Unfortunately this would involve the

manufactured part to have the black cellulose paint stuck to the underside of the part.

73

Conclusions:

In the introduction to this project the ambition of manufacturing a composite frame was expressed.

Unfortunately due to time constraints and the ambition of the project this was unable to be

achieved.

A decision has been made on the suitability of a manufacturing process for the advanced composite

frame taking into account the difficulties of the geometry and the ease of manufacture for the

desired bike frame. There is still the question of whether the finish of the mould is suitable for use

with the composite manufacturing process, though this can be explored in future work by testing a

lay-up on the finish and consolidating at a lower temperature than the previously used 85°C.

The process of calculating mechanical ply properties was investigated thoroughly and while it would

be beneficial to obtain exact constituent material properties, before, starting this process it was

found that for, the most part, using constituent material values obtained from material databases

provided suitable in obtaining values for a composites overall ply properties.

An extensive review of modelling simple composite parts using Abaqus software has been given for

the two specific tests performed on the manufactured samples. This allowed a comparison between

the physical and FEA simulation results. It was found that there is, for modelling a 3 point bend test,

an issue regarding the chosen orientation of the simulated plies. This problem arose due to the

woven nature of the reinforcement fabric. The tensile simulation highlighted a problem with the

physical tensile test and a suggested course of action was proposed. Re-running the physical test

with strain gauges to directly monitor the strain present on the surface of the sample, this would

eliminate the suspected errors due to the sample slipping in the machine and thereby outputting

false readings. Future work could be undertaken to enhance the models accuracy by investigating

programs available that allow the modelling of a woven fabric composite in finite element analysis.

The time frame limited what work could be carried out when investigating damage modelling in

Abaqus. The modelling was held up by the lack of available data on the compressive and shear

properties of polypropylene and there was not enough time to obtain the relevant data through

material testing. However a damage model was ran using very rough values; this allowed

information to be gathered on how the outputs are presented during the process and what the

output values represent. This knowledge would allow future work, in modelling damage initiation

and damage evolution, to be completed with greater confidence.

74

References:

[1] http://www.berkelbike.com/

[2] http://www.bicycle-riding-for-boomers.com/recumbent-hand-cycle.html

[3] http://composite.about.com/od/aboutcompositesplastics/l/aa060297.htm

[4] A.R. Bunsell, 1997,” Fibre reinforcements for composite materials”, 4th international conference

on deformation and fracture of composites, Introduction, The Manchester Conference Centre,

UMIST, UK, 24-26 March 1997

[5] http://www.simulia.com/products/unified_fea.html

[6] http://www-materials.eng.cam.ac.uk/mpsite/interactive_charts/strength-density/composites.jpg

- strength and density data for different materials

[7] http://www.boeing.com/commercial/787family/background.html - composite use in Boeing

aircraft

[8] http://www.environmentalgraffiti.com/sciencetech/boeing-dreamliner-composites-trial-part-

ii/13303 - composite use in Boeing aircraft

[9] http://www.berkelbike.com/models_en

[10] D. Hull and T.W. Clyne, 1996, An Introduction to composite Materials, second edition,

Cambridge University Press, Cambridge

chapter 4 – Elastic deformation of long-fibre composites

chapter 2 – Fibres and matrices

[11] http://www.mse.mtu.edu/~drjohn/my4150/ht/ht.html - Halpin- Tsai equations

[12]

http://www.matweb.com/search/DataSheet.aspx?MatGUID=d9c18047c49147a2a7c0b0bb1743e812

– constituent material data

[13]

http://www.matweb.com/search/DataSheet.aspx?MatGUID=1202140c34e8443bbf273862e24c5f0e

– constituent material data

75

[14] http://www.ocvreinforcements.com/solutions/Twintex.asp – (T PP material)

[15] http://www.ocvreinforcements.com/Pages/Physical_Properties_for_FEA_Modeling.asp -

Twintex properties

[16] M.R. Piggot, 1995, “The Effect of fibre waviness on the mechanical properties of unidirectional

fibre composites: A Review”

(Electronic copy –

http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6TWT-3YYT6C9-V-

1&_cdi=5571&_user=121723&_pii=0266353895000194&_origin=search&_coverDate=12%2F31%2F

1995&_sk=999469997&view=c&wchp=dGLbVlz-

zSkWb&_valck=1&md5=700a1223d14712e13d184f4ca85b4e31&ie=/sdarticle.pdf )

[17] A.C. West and D.O Adams, 1999, “ Axial Yarn Crimping Effects in Braided Composite Materials,

vol. 33, Journal of Composite materials, Sage publications

[18] http://texgen.sourceforge.net/index.php/Main_Page - modelling woven fibre

[19] http://sirius.mtm.kuleuven.be/Research/C2/poly/software.html - modelling woven fibres

[20]

http://www.mech.gla.ac.uk/v6.7/books/usb/default.htm?startat=pt05ch19s03abm41.html#usb-

mat-cdamageinitfibercomposite / section 19.3.2 of the Abaqus CAE User’s Manual – damage

initiation criterion using Abaqus

[21] Hashin, Z., and A. Rotem, “A Fatigue Criterion for Fibre-Reinforced Materials,” Journal of

Composite Materials, vol. 7, pp. 448–464, 1973

[22]

http://www.mech.gla.ac.uk/v6.7/books/usb/default.htm?startat=pt05ch19s03abm41.html#usb-

mat-cdamageinitfibercomposite / section 19.3.3 of the Abaqus CAE User’s Manual

76

Bibliography:

C.J.Spragg and L.T. Drzal “Fibre, Matrix and Interface Properties”, ASTM, U.S.A

Various, “Fibre Composite Materials”, Seminar of the American society for metals, October

17-18, 1964, Chapman & Hall Ltd

J.W. Bull ed. “Numerical Analysis and Modelling of Composite Materials”, 1996, Chapman

and Hall

N.D. Critescu, E. Craciun, E. Soós, “Mechanics of Elastic Composites”, 2004, Chapman and

Hall

http://www.bis.gov.uk/~/media/BISCore/corporate/docs/C/Composites-Strategy

http://www.mdacomposites.org/mda/psgbridge_cb_mfg_process.html

http://composite.about.com/od/howto/How_To_Instructions_for_Composites_Manufacturi

ng.htm

http://www.empa.ch/plugin/template/empa/*/54293/---/l=2

http://www.simulia.com/

Hashin, Z., “Failure Criteria for Unidirectional Fibre Composites,” Journal of Applied

Mechanics, vol. 47, pp. 329–334, 1980.

77

Appendix A: Detailed calculation of ply properties:

Data: f, volume fraction of fibres: 0.35

Ef, fibres young’s modulus: 76000000000

Em, matrix young’s modulus: 1200000000

Vf, poisson’s ratio of fibre: 0.22

Gm, shear modulus of matrix: 538000000

Gf, shear modulus of the fibre: 3000000000

Vm, poisson’s ratio of matrix: 0.3

From Equation 8:

From Equation 9 and 10:

From Equation 11:

78

From Equation 12:

Noting G12=G13

From Equation 13, Equation 10 and Equation 8:

Therefore:

79

Appendix B: Validating the tensile FEA model with a steel

sample:

Say the steel sample is the same dimensions as the composite sample and we stretch it by 3 mm and

has a cross-sectional area as defined in Equation 15:

Equation 15 – Cross-sectional area

A = 15 x 3 = 45 mm2 = 45x10-5 m2.

Steel has approximate isotropic properties of Young’s modulus, E = 200 GPa and Poisson’s ratio, v =

0.3 (ref) and by stretching the sample by a length, lo = 3 mm, with an initial length, L = 60 mm the

strain present is found from equation 16:

Equation 16 – Strain equation

Therefore the stress present in the steel sample is found using Equation 17.

Equation 14 – Re-arranged Young’s modulus equation

The force this produces is found from Equation 18.

Equation 15 – Re-arranged axial stress equation