Förnamn Efternamn

Thermal conductivity in practical composite

laminates

Ram Babu Mishra

Degree Thesis

Plastics Technology

2012

ii

DEGREE THESIS

Arcada

Degree Programme: Plastics Technology

Identification number: 10325

Author: Ram Babu Mishra

Title: Thermal conductivity in practical composite laminates

Supervisor (Arcada): Rene Harrmann

Commissioned by: Arcada

This thesis investigates thermal resistance of composite materials containing fibre, resin

and voids. First, the mathematical model was derived based on statistics that describes the

thermal resistance of a composite made of three constituents, represented by equation

number (2.10). Secondly, the derived model was applied to study two distinct practical

cases. The derived equations in this thesis work that illustrate the change in relative ther-

mal resistance for:-

a) Constant volume equation (2.13)

b) Non-constant volume equation (2.16)

The results demonstrated that a vinyl ester, glass fibre laminate will increase its thermal

resistance by 2.13% for every 1% increase in void volume fraction. Within the frame

work of this thesis an experimental verification was done on foam specimen. The ex-

periment used a heat flux meter and the results differ with 14.77% of the expected value.

This means that the result can only be trusted with an error margin of 14.77%.

Keywords: Thermal conductivity, thermal resistivity, U-value, com-

posite laminate, open lamination, closed lamination

Number of pages: 42

Language: English

Date of acceptance: 24/04/2012

iii

Acknowledgements

It is my greatest pleasure to thank my supervisor Rene Harmann for all encouragement,

sound advice, excellent guidance and support during my thesis writing process. The way

he let me move with the project in my own pace have been extremely helpful in keeping

track of my course studies and the thesis at the same time. I would also like to thank my

examiner Mathew Vihtonen for his valuable knowledge and useful feedback for my the-

sis.

I would like to acknowledge Arcada University of Applied Sciences for providing ex-

cellent education and facilities.

I wish to thank my friends for their support, suggestions and comments.

Finally, and most importantly, I would like to thank my parents for nourishing me

physically and mentally. To them I dedicate this thesis. Without their support and wish,

I would not have come to this level.

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TABLE OF CONTENTS

1 Introduction .......................................................................................................... 1

1.1 Background ............................................................................................................... 1

1.2 Objectives .................................................................................................................. 3

2 Theory .................................................................................................................. 4

2.1 Probability Networking Model ..................................................................................... 4

2.2 Monolithic combinations in composites laminate ........................................................ 5

2.3 Visualization of total thermal resistance ...................................................................... 9

2.4 Manufacturing method ............................................................................................. 10

2.4.1 Open mould process ........................................................................................ 10

2.4.2 Closed mould process ...................................................................................... 12

2.5 Model characteristics ............................................................................................... 13

2.5.1 Closed lamination (constant volume) ................................................................ 14

2.5.2 Relative difference , V= constant .................................... 15

2.5.3 Open lamination (non-constant volume) ........................................................... 17

2.5.4 Relative difference (V≠ Constant) ..................................................................... 18

2.5.5 Comparison of relative change in thermal resistance of composite laminate

between constant volume and non-constant volume case ................................................ 21

3 Method ................................................................................................................ 23

3.1 Product design and test pieces ................................................................................ 23

3.2 Heat Flux meter ....................................................................................................... 23

3.3 Measurement set up ................................................................................................ 24

3.4 Measurement of the U-value of PET foams .............................................................. 25

3.5 Determination of thermal conductivity ....................................................................... 27

4 Results ............................................................................................................... 28

4.1 PET foam 1 ............................................................................................................. 28

4.2 PET foam 2 ............................................................................................................. 30

5 Discussion ......................................................................................................... 32

6 Conclusion ......................................................................................................... 33

7 References ......................................................................................................... 35

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LIST OF FIGURES

Figure 1Heat flow ......................................................................................................... 1

Figure 2 Parallel and Series combination ....................................................................... 4

Figure 3 Probability tube ............................................................................................... 5

Figure 4 Random order of composites blocks ................................................................ 6

Figure 5 Full view of composite laminate ...................................................................... 6

Figure 6 Individuals volume of fibers, resin and void .................................................... 7

Figure 7 Random and ordered order of fibre, resin, void ................................................ 8

Figure 8 Graphical view of amount of volume content of fibre, resin and void .............. 9

Figure 9 Hand lay-up [18] ........................................................................................... 11

Figure 10 Filament winding. [18] ................................................................................ 11

Figure 11 Resin Transfer Moulding (RTM) [17] ......................................................... 13

Figure 12 Vacuum infusion process [18] ..................................................................... 13

Figure 13 Real and Ideal laminate at constant volume (closed lamination) .................. 14

Figure 14 Graph between thermal resistance Vs void fraction ..................................... 17

Figure 15 Ideal and Real laminate at non constant volume (open lamination) .............. 18

Figure 16 Graphical analysis of non-constant volume.................................................. 20

Figure 17 Constant and non-constant volume .............................................................. 21

Figure 18 Measurement set up..................................................................................... 24

Figure 19 Thermal circuit ............................................................................................ 24

Figure 20 PET foam with round holes ......................................................................... 26

Figure 21 PET foam with cross channels ..................................................................... 27

Figure 22 Calculation of volume percentage ............................................................... 29

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LIST OF TABLES

Table 1 Thermal conductivities ................................................................................... 16

Table 2 Comparison of relative change in thermal resistance ....................................... 22

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ACRONYMS AND ABBREVIATIONS

E Young’s modulus of composite

Em Young’s modulus of matrix

Ef Young’s modulus of fibre

A Area

T Temperature

Q Power

K Thermal conductivity

R Thermal resistance

U Thermal transmittance

ζa Volume fraction of fibre

ζb Volume fraction of resin

ζc Volume fraction of voids

k Kelvin

m Meter

w Watt

wt% Weight percentage

PET Polyethylene Terephthalate

1

1 INTRODUCTION

1.1 Background

Composites are engineered or naturally occurring materials made out of two or more

components. To obtain the better properties of composites material its individual con-

stituents are modified. Generally in composites, there are two phases; continual phase is

called matrix and the reinforcing phase is called fibre. Mirmira [1]. The function of ma-

trix is to transfer external load, to hold the fibre and to protect fibre from external envi-

ronment. In addition, it also carries transverse load and inter-laminar shear stress. Bar-

bero [2]. Similarly, the role of fibre is to increase Young’s modulus of composites.

McMahon [16]. i.e.

(E=Em*f+Ef*(1-f) (1.1)

Where, Em is young’s modulus of matrix i.e. resin

Ef is young’s modulus of fibre

E is young’s modulus of composite

f is volume fraction

Thermal conductivity is the ability of material to conduct heat through it. On the other

hand, thermal resistivity is reciprocal of thermal conductivity. Each material has its own

thermal behaviour. The key aim of this thesis is to model the thermal conductivity of

practical composite laminates with respect to lamination imperfections as measured by

volume fraction of voids and interfaces of resin in sandwich structure. Similarly, the

other aims are to analyze the thermal resistivity in the composites structure as parallel

and series or combination of both and to do the detail study of thermal behaviour.

Figure 1Heat flow

2

The theory of thermal conductivity was proposed by Fourier in 1822. According to Fou-

rier, the fundamental heat conduction equation can be stated as “For a homogeneous

solid, the local heat flux is proportional to the negative local temperature gradient”. Thi-

rumaleshwar [3]. For one dimensional steady state heat transfer, this statement can be

represented by Equation

Q´´= -k*(dT/dx) (1.2)

And heat flow

Q= -K*(dT/dx)*A (1.3)

Where Q´´ is the heat flux, K is the thermal conductivity of the material, which is a

positive 2nd

order tensor quantity, dT/dx represents change in temperature across the

thickness and negative sign indicates the temperature reduction from hotter surface to

cooler surface.

And from above definition, thermal conductivity can be written as

K= (Q/A)/(ΔT/ ΔX) (1.4)

Where; Q is heat flow, K is thermal conductivity, A is cross-section area, ΔT is

temperature difference (T1-T2) and ΔX is length of heat flow. The unit of thermal

conductivity is (W/mK).

However, Q = ΔT/R , R = ΔX/(K*A) (1.5)

Where, R is thermal resistance.

Similar research was done by the Bhyrav (2006). The thesis title was “Thermal Conduc-

tivity Characterization of Composite Materials”. The key findings were E-glass/vinyl

ester samples exhibited in-plane and through-the-thickness thermal conductivity of

0.35±0.05 W/m K. Thermal conductivity of carbon/vinyl ester composite is almost

twice the conductivity in transverse and four times greater than through-the-thickness

direction. Addition of 10 wt%, 12.5 wt% of graphite powder additive in neat vinyl ester

resin increased the conductivity by nearly 88% and 170% respectively. During the the-

sis work, the research was done by using Guarded heat flow meter, Super probe method,

Transient Plot method, Flash plus measurement system. Bhyrav [4].

3

1.2 Objectives

The objective of the thesis is to find out effects of voids on the thermal conductivity of

composite laminate. Composite laminate never can be perfect because generally it con-

tains at least some amount of voids. Voids present in composite material are not good in

terms of mechanical properties. However, they can be very beneficial to increase the

thermal resistance of composite laminates. So this thesis study also explains how the

void contains affects the thermal resistance of composite laminate. The main objectives

of thesis are to model the thermal conductivity of practical composite laminates with

respect to

1. Lamination imperfections as measured by ζc (Volume fraction of voids).

2. Interfaces of resin in sandwich structures.

3. Verify the models experimentally by measuring the U-value.

4

2 THEORY

In composite material, heat transfer depends mainly on how the constitutes materials are

structured. The structure is created according to the volume fraction of matrix, volume

fraction of reinforcement material and volume fraction of the voids. Therefore, the heat

transfer depends on volume fraction of individual components. In actual fact, these in-

dividuals act as heat resistances. Heat resistance can be in series, parallel and combina-

tion of both. The overall heat resistance is a function of parallel resistances. Each of

these resistances is series resistances and their probability to exist is proportional to

their volume fraction.

The power in terms of heat resistance can be written as Thirumaleshwar [3]

(2.1)

Figure 2 Parallel and Series combination

In series,

(2.2)

Similarly in parallel,

(2.3)

2.1 Probability Networking Model

For example, a water pipe which has large diameter and it contains 9 small pipes with

equal diameter. Probability of water flow through the large diameter pipe is P (Pl) = 1.

Then, the probability of amount of water flow through each of small pipe is P (Ps) = 1/9.

5

Now, if 9 pipes have same diameter and one pipe has doubled the cross section area of

smaller one. Then the probability of amount of water flow through the one pipe is P

(P2s) = 2/10 = 1/5.

Figure 3 Probability tube

Similarly, in composite laminate, where the probability of heat flow Q = 1 through

cross-section area A. In probability network Q is ∑Qi probabilities according to ∑Qi =

1, with Qk proportional with respect to cross section A which in turn is proportional to

the volume fraction of constituents.

2.2 Monolithic combinations in composites laminate

Although the orientations of matrix, reinforcement materials and voids are random, here

it is considered them as a solid block. Therefore, their combinations can be in series,

parallel or combination of series and parallel. There are different probabilities for each

resistance to occur. The following paragraphs include explanation on how to derive a

model for the thermal resistance of a monolithic laminate.

6

Figure 4 Random order of composites blocks

Figure 4 shows that a monolithic composite laminate which contains infinitely small

pieces with completely random ordered blocks of fibre (a), resin (b) and void (c). The

temperature difference between two faces is ΔT(x) . Although the order of a, b and c are

random, we assume that it has same cross section area A and with differing thickness

dxi . Therefore, individual volume (Vi) can be written as Vi=Ai*dxi and i goes from a to

c.

Again, it is supposed that the laminate contains many rectangular rod with length X and

cross-section area Aj.

Figure 5 Full view of composite laminate

7

If it is considered that one rectangular rod of length X and with number of small length

dx0, dx1, dx2 … and dxn and these small lengths represent the thickness of a , b , c , b ,a , c

and so on respectively. The sequence of a, b and c are random.

Figure 6 Individuals volume of fibers, resin and void

In figure 6, ∑dxi = X and Vi = Ai*dxi is volume of individual. Therefore the volume of

resin ∑Vai= Va, for fiber ∑Vbi= Vb and for void ∑Vci= Vc

Now, volume fraction in laminate can be written as

(2.4)

During the heat transfer, the individual dx0, dx1, dx2 and so on act as resistors in series.

Then the total resistance can be written as sum of the individual i.e.

8

Figure 7 Random and ordered order of fibre, resin, void

Rtot = ∑Ri = R0 + R1 + R2 ………… Rn. In figure 7, both random and ordered are

equivalent to each other and there in no difference in total thermal conductivity.

Now, heat resistance in terms of thermal conductivity of this laminate can be written as

(2.5)

The total volume of resin Va= Aj*Xa and which implies that

(2.6)

Therefore, the total heat resistance of single rectangular tube is represented by

As shown in the equation R= R0+ R1 + R2 +R3 ………… Rn can be written as

R= Ra + Rb + Rc

R= Xa/(ka*Aj) + Xb/(kb*Aj) + Xc/(kc*Aj) and for whole laminate if the area is A then the

total heat resistance is given by

Rtot= Xa/(ka*A) + Xb/(kb*A) + Xc/(kc*A)

Rtot= (1/A)*{(Xa/ka) + (Xb/kb) + (Xc/kc)} (2.7)

We know that, Vtot = A*X and Va = A*Xa which implies that

Xa = X*(Va/ Vtot) (2.8)

From equations (2.4) and (2.8)

9

Xa = X*ζa

Xb = X*ζb (2.9)

Xc = X*ζc

Substituting values of equation (2.7) in equation (2.9)

Rtot= (X/A)*(ζa/ ka + ζb/ kb + ζc/ kc )

Rtot*(A/X) = (ζa/ ka + ζb/ kb + ζc/ kc ) (2.10)

This equation (2.10) can be compared to the equation of plane equation Ax + By + Cz

=D, where ζa , ζb and ζc are volume fraction of the constituents and Rtot*(A/X) is D ( i.e.

perpendicular distance from the origin). In this equation (2.10), ka, kb, kc are known

physical thermal conductivities, ζa, ζb, ζc are measured and Rtot*(A/X) is calculated.

2.3 Visualization of total thermal resistance

Figure 8 Graphical view of amount of volume content of fibre, resin and void

Equation (2.10) is representing a plane equation in three dimensional spaces

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d= ax + by + cz. Where d = Rtot*(A/X), a = 1/ka, b= 1/kb and c=1/kc. The slope of the

plane in direction of one constituent’s amount depends on its thermal resistivity of its

constituent. Graphically, d = Rtot*(A/X) is the distance of the plane to origin.

2.4 Manufacturing method

There are many different lamination techniques available. Several automated and semi

automated fabrication techniques have been developed to eliminate variability in hand

lamination and to prolong production runs. The semi-automated methods are based on

matched die moulding which permits critical control of thickness and glass content and

produces am moulding with two good surfaces. Based on mould is used to laminate the

composite material, there are two kinds of lamination process. They are open mould

process and closed mould process.

2.4.1 Open mould process

Open mould process is one of the types of lamination process which is also known as

hand lamination process. The reinforcement materials (glass fibres, carbon fibres, ara-

mid fibres and etc.) are placed in the mould and wet resin is poured into the mould si-

multaneously one after another layer of fibres with resin until the desired thickness is

reached. CTS-composites [8]. Later on the reinforcement is wet out with resin. Some-

time the laminate further takes more resin to improve wet out. This method is com-

monly used in the manufacturing of composite material. The thickness is varied depend-

ing on how the lamination proceeds. The main advantage of hand lamination is its ver-

satility. There is no size limitation and the additional glass reinforcement can be added

when they are needed. This type of mould is inexpensive and suitable for small produc-

tion. On the other hand, the main disadvantage of this type of mould is only one have

good surface finish. In addition, it is more laborious and quality depends on laminator.

Anthony [15]. Hand lay-up, Spray-up and Filament winding are the examples of open

moulding process.

Hand lay-up is open moulding method to manufacturing the composites product which

has a wide variety of products including: boats, tanks, housing for auto components and

many other products. First of all gel coat is applied in the moulding surface. Then after

11

roll stock glass fibre are placed when the gel coat has cured. The laminating resin is ap-

plied by pouring, brushing, spraying, or using a paint roller. Paint rollers or squeegees

are used to consolidate the laminate, thoroughly wetting the reinforcement, and remov-

ing entrapped air. Low density core materials are also added sometime when it is neces-

sary. Boy Scouts [18].

Figure 9 Hand lay-up [18]

Filament winding is also the open moulding process to manufacturing the composite

products. It is the process of winding fibre material and resin simultaneously around the

shape of product, know as a mandrel, to create composite product. This process is typi-

cally used to produce circular composites products with hollow core. The filament

winding process can utilize many different fibres and resins to achieve desired charac-

teristics for the finished component. The end result is an extremely efficient process to

create low cost, lightweight, and strong composite materials. Bicycle components tubes,

Transmission poles, Sail boat masts and tank for water and gas are the example of prod-

ucts made from filament winding process. Boy Scouts [18].

Figure 10 Filament winding. [18]

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2.4.2 Closed mould process

This method is also commonly used process in the manufacturing of composite laminate

especially for better geometric design and for the mass production of same product. In

this method, the mould has two parts; one is top half and another is bottom half. The

mould itself contains resin inlet and vacuum outlet. In one half, the reinforcement mate-

rial is placed and covered with another half. After that the resin is passed into the mould

from the resin inlet and reinforcement material sucks the resin. Excess resin is sucked

with the help of vacuum outlet. There are different types of closed mould process like

Infusion, RTM (resin transfer mould), RTM light. They are in opposition to Hand Lay-

Up and Spray-Up (open mould) processes; because resin is not in direct contact with the

workshop air but is processed only when mould is tightly closed, so that no volatile or-

ganic compound or styrene is released in the air. Wet compression, which is not really a

closed mould process, is also taken into account here because it has the same product

requirements as RTM, RTM-Light and Infusion. Composites [9].

RTM is the short foam of Resin Transfer moulding. It is commonly referred to a

"Closed Mould Process" in which reinforcement material is placed between two match-

ing mould surfaces. One is called male mould and another one is called female mould.

The matching mould set is then closed and clamped and a low-viscosity thermoset resin

is injected under moderate pressures (50-100 PSI typically) into the mould cavity

through a port or series of ports within the mould. The resin is injected to fill all voids

within the mould set and thus penetrates and wets out all surfaces of the reinforcing ma-

terials. The reinforcement’s materials may include a variety of fibre types, in various

forms such as continuous fibres, mat, or more than one fibre type. Vacuum is sometimes

used to enhance the resin flow and reduce void formation. The part is typically cured

with heat. In some applications, the exothermic reaction of the resin may be sufficient

for proper cure. RTM as a process, is multi-compatible with a variety of resin systems

including polyester, vinyl ester, epoxy and hybrid resins such as polyester and urethane.

Typically, it requires a resin viscosity of 200-600 centipoises to penetrate all surfaces of

the mould cavity. Acma [17].

13

Figure 11 Resin Transfer Moulding (RTM) [17]

Vacuum infusion is also one type of closed mould process, it is a variation of vacuum

bagging, where the resin is introduced into the mould after the vacuum has pulled the

bag down and compacted the laminate. The method is defined as having lower than at-

mospheric pressure in the mould cavity. The reinforcement and core material are laid-up

dry in the mould. This is generally done by hand and provides the opportunity to pre-

cisely position the reinforcement. When the resin is pulled into the mould the laminate

is already compacted; therefore, there is no room for excess resin. Very high resin to

glass ratios is possible with vacuum infusion and the mechanical properties of the lami-

nate are superior. Vacuum infusion is suitable to mould very large structures and is con-

sidered a low volume moulding process. Boy Scouts [18].

Figure 12 Vacuum infusion process [18]

2.5 Model characteristics

There are two kinds of laminates in composite. One is a perfect laminate that is called

ideal (laminate without voids) laminate. Similarly, the other one is non-perfect laminate

and is called real laminate (laminate content with voids). In practical composites lami-

nation, there are two possible relationships between a real and ideal lamination. One is

constant volume and another is non constant volume. Generally the case of constant

14

volume appears in closed mould lamination and non constant volume case appears in

open mould lamination case. In case of constant volume (closed mould), there is same

amount of fibre in real and ideal lamination but has less volume fraction of resin due to

the presence of voids in the laminate. In case of non constant volume (open mould),

there is same amount of fibre and resin but overall volume fraction of both are changed

along with presence of voids.

V=Vfibre+ Vresin+ Vvoid

2.5.1 Closed lamination (constant volume)

It is assumed that in real and ideal lamination, there is constant thickness(X), area (A)

and volume fraction of fibres is same. Overall the volume of both laminate ideal and

real is same (A0=A1 and X0 =X1).

Figure 13 Real and Ideal laminate at constant volume (closed lamination)

Then, the total resistance in real and ideal lamination can be written as

(2.11)

(2.12)

Here, , ,and (since the decrease amount of the volume of

resin is replaced by presence of voids which means total volume of resin in ideal lami-

nate is equal to the sum of volume of resin and volume of void in real laminate)

15

2.5.2 Relative difference

, V= constant

Absolute difference computers the difference between the two numbers where result is

always in positive value. It is assumed that in real and ideal lamination there is constant

thickness(X), area (A) and volume fraction of fibres is same. Then absolute difference is

written as

Now,

16

This equation can be compare as Y= mX and

This equation depicts how the relative thermal resistance is changed in terms of differ-

ent fibre volume fraction ( ) and void volume fraction ( ) in composite laminate. A

term

is constant in here since has different values. This shows that

relative thermal resistance is directly proportional to the void volume fraction in com-

posite laminate (i.e. means the relative thermal resistance increases when void volume

fraction increases). In the below table, there is the value of constant terms Ka, Kb and Kc.

Table 1 Thermal conductivities

Materials Value Source

Glass fibre(Ka) 0.04W/m.K Comparison [5]

Vinyl

ester resin(Kb) 0.24W/m.k Comp and Polycon [6]

Void(Kc) 0.024W/m.K Ther. Conductivity [7]

Since the equation (2.13) is linear equation and its slope can be calculated as

If there is 0.6 volume fraction of fibre and using above values, we found that

17

Figure 14 Graph between thermal resistance Vs void fraction

The graph presented above shows the effect of voids fraction on the heat resistance of

composite laminate at constant volume fraction of fibres at 40%, 45%, 50%, 55%, 60%

and 65%.

It is taken another example from this graph with laminate content 60% fibres. In this

case, 5 % (0.05) voids change thermal resistivity of composite laminate by 10 % (0.1)

while 10% voids change the thermal conductivity of the composite laminate by 20 %.

This shows that the overall change in thermal resistivity is linearly proportional to the

change in void content. In other words, it is considered as a slope of straight line in case

of 60% fibre content laminate. From the graph, it is obtained a slope (m)

=

. This value tells us that every one unit (i.e. 1%) increase in vol-

ume of void increase the relative change in thermal resistance by 2.13.

2.5.3 Open lamination (non-constant volume)

In the case of non-constant volume case, the overall volume of the laminate is changed

and increase in volume is due to the presence of voids. In this case, the thickness of

laminate varies accordingly in different composite laminates. There is same amount of

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 0.02 0.04 0.06 0.08 0.1 0.12

ΔR

/R0

voids volume fraction(ζc)

constant volume

ΔR/R0(40% fiber)

ΔR/R0(45% fiber)

ΔR/R0(50% fiber)

ΔR/R0(55% fiber)

ΔR/R0(60% fiber)

ΔR/R0(65% fiber)

18

fibres and resin but different thickness in real laminate. The overall volume of both real

and ideal laminate is different (A0=A1 and X0+ΔX = X1) due to the increase in thickness

of real laminate.

Figure 15 Ideal and Real laminate at non constant volume (open lamination)

(2.14)

(2.15)

Here, but Va=Va´ and Vb=Vb´

2.5.4 Relative difference (V≠ Constant)

Now, the equation below shows the relative difference in thermal resistivity of the open

laminate by comparing it to the ideal and the real laminate. So that,

Here,

19

Again

.

Now,

20

In this equation

is constant term and is only variable. Since, this

equation is second degree polynomial equation; the slope of this equation varies accord-

ing to different values of void volume fraction. The slope is

By substituting the values of table 1 in the equation (2.16), the following graph is seen.

Figure 16 Graphical analysis of non-constant volume

The graph shows that there is parabolic changed in relative thermal resistance of lami-

nate when volume of voids increase gradually. But relative change is very small in

thermal resistance between the ideal and real laminate.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0 0.02 0.04 0.06 0.08 0.1 0.12

ΔR

/R0

(voids volumefraction)ζc

Non-constant volume

ΔR/R0(40% fiber)

ΔR/R0(45% fiber)

ΔR/R0(50% fiber)

ΔR/R0(55% fiber)

ΔR/R0(60% fiber)

ΔR/R0(65% fiber)

21

2.5.5 Comparison of relative change in thermal resistance of composite

laminate between constant volume and non-constant volume case

Figure 17 Constant and non-constant volume

In above graph, the straight line represents a constant volume of laminate and the curve

line represents the non-constant volume of laminate. It is assumed that each graph is

divided into different regions according to the void content. First region with less than

0%- 5% of void, second region with 5%-10% of voids and third region with more than

10% of voids. In each region of first graph the relative change in thermal resistance is

constant which means there is relative change with constant ratio. But in case of second

graph relative change in thermal resistance is not constant and which varies in every

points of line.

These graph shows that the relative change in thermal resistance in case of constant vol-

ume case is higher than the one in case of non-constant volume. Although there is high

change in relative thermal conductivity when the void is increased from 5% to 10% but

still that is quite less compared to relative change where the volume constant. That

means for better thermal resistance properties of the laminate, closed mould system of

composite laminate is better and suitable

22

Table 2 Comparison of relative change in thermal resistance

60% fibre volume fraction in laminate

ζc(void fraction)

Constant volume Non-constant volume

ΔR/R0 relative change in % ΔR/R0 relative change in %

0 0 0 0 0

0.01 0.0226 2.26 0.00025 0.025

0.02 0.0453 4.53 0.00102 0.102

0.03 0.068 6.8 0.00232 0.232

0.04 0.0907 9.07 0.00418 0.418

0.05 0.1134 11.34 0.0066 0.66

0.06 0.1361 13.61 0.00961 0.961

0.07 0.1588 15.88 0.01322 1.322

0.08 0.1815 18.15 0.01746 1.746

0.09 0.2042 20.42 0.02234 2.234

0.1 0.226 22.6 0.02788 2.788

Table 2 shows that the relative change in thermal resistance in constant volume case is

almost 10 times higher than the non-constant volume case when volume percentage of

void goes from 1% to 10 %. Now it makes sense that the close mould process to make

composite laminate is better to have much better thermal resistance properties. On the

other hand, in closed mould process, the laminate takes less resin and has less overall

weight.

23

3 METHOD

The method section describes the fundamental aspect for the thesis work which deals

with the many experimental works to prove the derived theory. It comes with how the

product is designed, how the product is tested and how the product verified. For this

thesis work, heat flux heater (U-value) measurement device was used. Composite mate-

rials have non homogeneous nature. So it is difficult to measure the thermal characteris-

tic of composite laminate at once. Therefore, in order to find the thermal behaviour of

composite laminate, at first it needs to analyze the thermal characteristics of individual

components. In case of monolithic composite laminate, there are only fibres, resin and

voids.

3.1 Product design and test pieces

The resulting product does not have difficult structure so the product can be rectangular

enough. The reason is that a test piece has same thermal properties as final product, it

has more or less even thickness and it is not necessary have to be complex shapes even

though the final products have different shapes and sizes. As the test piece, PET (Poly-

ethylene Terephthalate) foam was used.

3.2 Heat Flux meter

This device is quite useful to measure the u-value of any kind of material. This device

was used to measure the thermal conductivity of the composite laminates in this thesis

work. It records amount of heat lost through the given surface area of the material wall.

24

3.3 Measurement set up

Figure 18 Measurement set up

The measurement set up was done as shown in figure 18. Now, in the thermal circuit

form, the above diagram looks like below

Figure 19 Thermal circuit

In the figure 19, by Fourier’s law, Q´= ΔT/Rt= ΔT/ (R1+ R2+ R3). And the U-value of com-

posite element can also write

U*A= 1/Rt = 1/ {(X1/K1A) + (X2/K2A) + (X3/K3A)}

U=1/ {(X1/K1) + (X2/K2) + (X3/K3)}

Here, it is assumed that the term X1/K1 tends to zero since glass has high thermal con-

ductivity (i.e. 1.05 W/mK) as compare to the thickness of glass is very small (i.e. 5*10-3

25

m). Similarly the term (X3/K3) also tends to zero since there is very low volume per-

centage of air. So it can be assumed that if the terms having less thickness compare to

high thermal conductivity can be eliminated. Then the remaining term can be written as

U=1/ {0 + (X2/K2) + 0}

K2= U*X2

Where, X2 is known thickness of PET foam, U-value is measured by heat flux meter and the

thermal conductivity of PET foam is determined.

3.4 Measurement of the U-value of PET foams

Measurement was carried out in the Arcada Laboratory. The measurement set up con-

sists of a glass container filled with running cold water (below 6 oC). The reason behind

running cold water was to adjust the temperature difference between inside and outside

surface (room temperature) of glass container wall. During the measurement period, the

running water temperature was 5.6oC and outside room temperature was 18.68

oC. The

sheet of PET foam was attached on the wall of the glass container along with the heat

flux meter. There should be air tight between contract area of the wall of glass plate and

the PET sheet otherwise the air gap play the role of another material and the result will

not be correct. It took about half an hour to do an experiment depending upon varies of

surrounding temperature. After half an hour, the experimental U-value was recorded

from the Heat flux meter.

26

Figure 20 PET foam with round holes

The above figure is recycled PET (Polyethylene Terephthalate) foam which has certain

thickness 15.3 mm with numbers of holes. The foam contains a 2 mm radius hole in

every 389 mm2. Here, the holes represent void volume fraction.

27

Figure 21 PET foam with cross channels

The above figure 21 is also recycled PET (polyethylene terephthalate) foam of having

thickness 15.3 mm with both sides cross channels. There is one cross channel in every

396 mm2 area. The width and depth of channel is 2 mm. Here, the channels represent

void volume fraction.

3.5 Determination of thermal conductivity

Experimentally, U-value of PET foam was obtained by using the heat flux meter. Then

the relation between the U-value and the thermal conductivity is written as

Since, there is known value of thickness of PET foam X and U- value is measured then

thermal conductivity K is determined.

28

4 RESULTS

4.1 PET foam 1

The experiment shows that the U-value of the PET foam with circular holes of thickness

15.3mm is 1.67 W/m2K. Thermal resistance is the reciprocal of the U-value. Therefore

the experimental thermal resistance (Rexp) of the foam is 0.589 m2K/W.

The PET foam contains a hole of diameter 2mm in per 389 mm2 of area of foam which

is about 0.81% of holes area and rest of 99.19% of foam surface area. Therefore the

volume of hole

Π*d2*thickness of PET foam

=3.14*22*15.3

=48.04 mm3

And total volume of foam which contains only one hole is

=19.652*15.3

=5907.67 mm3

Now, the voids volume fraction in PET foam is 48.04/5907.67= 0.818%

So from the theoretical calculation, the thermal resistance of the PET foam without

holes is

Rf=thickness/thermal conductivity of foam.

=15.176*10-3

/0.03

=0.508 m2K/W

And the thermal resistance of hole which contains air in the foam is

Ra= thickness/thermal conductivity of air.

= 0.124*10-3

/0.024

= 0.00516 m2K/W

29

It is considered that both PET foam and voids are in series connection then the total

thermal resistance (i.e. theoretical) of the foam (total thickness 15.3mm) with the hole is

Figure 22 Calculation of volume percentage

Rtheo= Rf + Ra

= 0.508+0.00516

= 0.51316 m2K/W

Then, the error percentage between theoretical and experimental thermal resistance of

the void is

dR/Rtheo= (Rtheo-Rexp)/Rtheo

= (0.51316-0.589)/0.51316

= 14.77%

When comparing experimental results to theoretical model we find a relative error of

14.77%. The experiment was done on a sample in which the change in thermal resis-

tance should be of magnitude 1.74% (2.13*0.818). It was found that the change in ther-

mal resistivity (1.74%) can only be trusted with an error margin of 14.77%.

30

Similarly, to calculate the thermal conductivity of PET foam of having thickness

15.17*10-3

m and the measured U-value 1.67 W/m2K then the relation between thermal

conductivity and U-value is

K=U*X

K = 1.67 W/m2K* 15.17*10

-3 m

K = 0.0253 W/mK

And theoretical K value of PET foam is 0.03 W/mK. Then error percentage is

(0.03-0.0253)/0.03

= 15.6%

Also this way the result can only trusted with the error margin of 15.6%.

4.2 PET foam 2

The experiment shows that the U-value of the PET foam with having both sides cross

channel of thickness 15.3mm is 1.44 W/m2K. That means the experimental thermal re-

sistance (Rexp) of the foam is 0.694 m2K/W (which is reciprocal of U-value).

Total area of foam for one cross channel is 19.9*19.9 mm2 and

Total length of channel = (19.9+19.9-2 =37.8 mm)

Depth and wide of channel = 2 mm

Total volume of one side channel = 37.8*2*2 mm3=151.2 mm

3

Total volume of with two sides channel=2*151.2 mm3=302.2 mm

3

Volume of foam = (19.9*19.9)*15.3(thickness of foam) – volume of channel

= (6058.95-302.2) mm3=5756.73mm

3=5756.73/6058.95 =95%

Now, the voids (channels) volume fraction in PET foam is 302.2/6058.95= 4.9%

So from the theoretical calculation the thermal resistance of the PET foam without

channels is

Rf=thickness/thermal conductivity of foam.

= (15.3*95/100)*10-3

/0.03

= 0.484 m2K/W

31

And the thermal resistance of channel which contains air in the foam is

Ra=thickness/thermal conductivity of air.

= (15.3*4.9/100)*10-3

/0.024

= 0.0312 m2K/W

Now total thermal resistance (i.e. theoretical) of the foam (total thickness 15.3mm) with

the channel is

Rtheo= Rf + Ra

= 0.484+0.0312

= 0.5152 m2K/W

Then, the error percentage between theoretical and experimental thermal resistance of

the void is

dR/Rtheo= (Rtheo-Rexp)/Rtheo

= (0.5152-0.694)/0.5152

= 34.7%

That is quite high error percentage which shows that the measurement result couldn’t be

correct due the air flowing in the contact surface of Heat flux meter and the PET foam.

32

5 DISCUSSION

This thesis work can assist to determine the possible thermal resistance of the composite

laminate before the actual lamination happens. It helps to planning and developing the

composite laminate. The hypothesis of this thesis work is thermal resistivity of compos-

ite laminate increases with increase in volume fraction of voids. The theoretical model

that gives the statistical value of increasing of thermal resistance by 2.13% in every 1%

increase in void volume fraction in the composite laminate (glass fibre and vinyl ester

laminate) is different from the experimental results. The different might be due to mis-

takes in measurement, measurement device itself and uneven sample piece.

The theoretical value of increase in thermal resistance by 2.13% is for such condition

that the sample must be perfect. This mean there must be even distribution of fibre,

resin and void throughout the surface area. But the obtained data from the experimental

result, the distribution of all constituent’s elements in the sample are not perfect (uneven

distribution of fibre, resin and void) and the measurement environment is not good as

considered as in theoretical assumptions. Other factors that also affects are what type of

resin is used in the lamination. If the vinyl ester resin is used then it shrinks with 1%, if

polyester resin is used then it shrinks about 3% and epoxy resin shrinks about 0.1%. If

these considerations are accounted in the derivation of theoretical model then the result

from the experimental method will be similar to the theoretical value.

33

6 CONCLUSION

From this thesis work it can be concluded that voids volume fraction play major role in

the thermal resistance of the composite laminate if the lamination process is done

through the closed mould process and contains only fibre, resin and voids. By adopting

the closed mould process the thermal resistivity is increased by magnitude of 2.13 in

every 1 % increased in volume fraction of voids. However, in case of closed mould

process, the change in thermal resistivity is very little and it does not show almost any

effect until the volume fraction of void reach 6%. In addition, to have voids percentage

of more than 6% in composite laminate is not good in terms of mechanical properties.

The results show that the composite laminate contains core materials (any types of

foams) which have thermal conductivity less than air and thus, have high thermal resis-

tivity capacity. This is quite opposite to the composite laminate which contains only

fibre, resin and voids where thermal resistivity increases with increase in voids volume

fraction. It also shows from the result that in case of use of composite laminate for insu-

lation purpose, it is good to have holes or gaps in the core material if the core material

has the thermal conductivity less than air. On the other hand, if the core material has the

thermal resistivity higher than air then it is not considered good to have hole and gaps in

the core material.

The derived theory in this thesis is valid on any kind of composite materials which con-

tains three components only. The model require the constituents to be

Small as compared to the overall structure (i.e. small grain).

The small grains are randomly distributed over the entire structure.

The model can be extended as there are series combinations of heat resistances in the

constituent’s elements in the composite structure.

Where, , and the terms with less volume fraction compare to high thermal con-

ductivity can be eliminated.

34

Therefore this model can be extended in series connection of multiple structural compo-

nents: Rtot = R1 + R2 + R3 + …….. + R3 + R2+R1 and it follow also a model for sand-

wich structure of composite laminate.

35

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