EFFECT OF REINFORCEMENT VOLUME FRACTION ON PHYSICAL

PROPERTIES OF GLASS/POLYESTER COMPOSITES

Prof. Dr. Nabeel K. Abid AL-sahib Dr. Louay S. Yousuf

AL-Khwarizmi College of Engineering College of Engineering

Mechatronics Eng. Dept. Mechanical Eng. Dept.

Baghdad University Baghdad University

dr_nabeelalsahab@hotmail.com louaysabah79@yahoo.com

ABSTRACT

The fiber volume fraction and their orientation have greater effect on the physical properties of the composite

specimens. The ability of the composite material to resist laminate tension or conduct laminate heating depends

on the quantities and qualities of the constituents. Very often composite materials results in anisotropic media and

their properties change along the axis because of the presence of reinforcing fibers embedded in the matrix. The

study was conducted in order to determine the thermal conductivity, coefficient of thermal expansion (for the side

of heating and cooling in another side), specific heat, tension and shear moduli of composite material [E-glass

fiber plies in thermosetting polyester matrix] for several fiber volume fraction ranges between (25%, 40%, 50%,

60%, 70%, 80%) with their effect on thermal and mechanical properties of composite specimen experimentally

and analytically. The temperature variation in two ranges between (25 C to 130C) for heating and (25 C to -

20C) for cooling effect on thermal expansion coefficient values aversely the thermal conductivity needs small

heating to reach the steady state case depends upon specimen thickness. The results show that both moduli and

thermal conductivity increase with the increasing of fiber volume fractions; but the coefficient of thermal expansion

Proceedings of the SEM Annual ConferenceJune 1-4, 2009 Albuquerque New Mexico USA

2009 Society for Experimental Mechanics Inc.

decrease with the increasing of fiber fractions along (x, y, z) directions. The properties in longitudinal direction are

larger than the properties in lateral direction for both thermal and mechanical analyses.

Key Words: Composite Materials, Volume Fractions, Physical Properties, Laminate Composite.

INTRODUCTION

Woven fabric/polymer matrix composites have been extensively studied because of the relative ease and the low

cost of their manufacturing. Generally used epoxy or polyester resins with glass or carbon fibers in many

industrial issues due to their very good specific mechanical and thermal properties. Most of the work was

concentrated on determining the thermal conductivity of the composite specimen in the form of Lee's disk, [1, 2, 3]

that the thermal conductivity is high along the fiber direction and low in a direction perpendicular to the fiber

direction. Polymer has been observed to have lower coefficient of thermal expansion at lower temperature than

at higher temperatures. Plots of strains vs. temperature are often bilinear, indicating a sharp change in the

coefficient of thermal expansion and specimen were test in the range between (-20 C to 60C). The reinforcement

of chopped glass fibers (1%) has no significant effect on thermal expansion of epoxy polymer while the inclusion

of carbon fibers (2%) has reducing effect on thermal expansion of this composite material, [4]. Analytical relations

are proposed to obtain an effective density, effective specific heat and effective thermal conductivity tensor of a

carbon woven fabric/phenolic matrix composite with fiber fraction (60%) with the aiding of Rayleigh and

Bruggeman models, [5]. The prediction of a model for calculating elastic moduli, coefficient of thermal expansion,

fiber volume and void contents of a unidirectional glass/epoxy composite laminate, [6]. The reduction of thermal

expansion coefficient of unsaturated polyester has been done by the addition of a cross linking agent which does

not interfere with the main polymerization process, [7]. In the other hand that the thermal conductivity increases

with increasing of fiber volume fractions with (10%,20%,30%,40%) of glass/epoxy and

carbon/polytetraflouroethylene composites by using an experimental work and finite element technique, [8]. The

aim of the present work is to investigate the physical properties and find the best fiber volume fraction were used

in aerospace industrial application of composite laminate plate with standard dimensions according to specimens

manufacturing process using a large number of fiber fractions.

EXPERIMENTAL SETUP AND PROCEDURE

Fiber reinforced like E-glass and Whisker composites is used in the fabrication of structural components due to

their excellent thermal performance. The resin matrix employed was a low viscosity thermosetting polyester resin

commonly used for hand lay-up at room temperature.

COMPOSITE LAMINATE FABRICATION AND TREATMENT

Fabrication of composite laminates was conducted in a mold consisting of (24 cm * 24 cm) aluminum with two X-

ray photo sheets to avoid abrasive and insure flattening of specimen surface. The X-ray photo sheet, which was

first placed on the bottom of aluminum mold, was wet with the catalyzed polyester resin before the first ply was

placed on it. More catalyzed resin was applied to this first ply with brush until it was thoroughly wet. Following this,

the remaining plies were placed in the mold following the same sequence. The mold left for one day with sufficient

pressure (2604.1667 N

m2 brass blocks) to get rid of the excess resin and entrapped air bubbles, remove the

composite plate from the mold, and the assembly was heated to (70 C) in an oven at (3 hours) curing time to

complete cross-linking. The fiber volume fraction was determined for the glass fiber composites from the following

relationship, [9]:

f =1

1+1

fm

(1)

=m f

mc (2)

Where:

is the fiber weight fraction.

mf , mc are the mass density for both fiber and composite material respectively.

The samples were cut into the required dimensions using a steel saw and then finished by abrasive grinding of

the edges.

EXPERIMENTAL MODEL FOR THERMAL CONDUCTIVITY

The test apparatus (Lee's disk apparatus) of type (Griffin and George) with tested composite specimen and some

accessories are presented in Figure (1) to measure the temperature of both sides of the composite specimen in

the direction x, y, z. The heater is switch on with (V = 6 Volts and I = 0.2 Amp.) to heat the brass disks (2, 3). And

the temperatures were recorded every (5 minutes) until reach to the equilibrium temperature of all disks. The

fibers were arranged in the lateral (perpendicular) and longitudinal (parallel) directions to the heat source. The

Lee's disk method is in the form of a disk whose thickness (d1 = d2 = d3 = 1.3 cm) is small relative to its radius (r

= 2.1cm). The thin samples of thickness (ds = 4 mm) means that the system will reach thermal equilibrium more

quickly. The thermal conductivity can be calculated experimentally by using the following equation, [10]:

K (T2T1)

ds= e [T1 +

2

r d1 +

ds

2 T1 +

ds T2

r] (3)

And the term (e) can be evaluated from, [10]:

I V = r2 e T1 + T3 + 2 r e [d1 T1 +ds T1+T2

2+ d2 T2 + d3 T3] (4)

Figure (1) Lee's disk apparatus

EXPERIMENTAL MODEL FOR THERMAL EXPANSION COEFFICIENT

The test method described in (ASTM C531) covers the determination of linear thermal expansion of polyester

materials over the two ranges (25 C to 130C) for heating and (25 C to -20C) for cooling by using strain gauge

and plot the curve between strain and temperature; then the slop of this curve represents the linear thermal

expansion. The specimens have the dimensions (20 * 50 * 4) mm.

EXPERIMENTAL MODEL FOR TENSION AND SHEAR MODULI

The tension moduli, for the E-glass and polyester matrix were determined by taking the average Young's Modulus

of three specimens with loading (10 KN). The machine that made a tensile and compression testing device, type

INSTRON, model 1195, at a speed of (1mm/min).The test specimens of composites were prepared according to

the (ASTM E 8M) standard. The INSTRON'S plotter was drawn the load-deflection curves and the stress can be

calculated from the equation ( =

), where (P) and (A) represent the load taken from the curve, and the

instantaneous cross sectional area respectively. The shear modulus for composite plate can be found from the

following formula, [11]:

G12 =1

(4

Ex

1

E1

1

E2+

212E1

) (5)

Where:

E1, E2 are the modulus of elasticity in 1, 2 directions respectively.

Ex is the modulus of elasticity at 45 to the 1-direction.

12 is the Poisson's ratio in 1-2 plane.

The specimen geometry used for both tension and shear moduli test can be shown in Figure (2).

Figure (2) Dimensions of tensile test specimen

ANALYTICAL PROCEDURE

The thermal and mechanical properties for both E-glass fiber and polyester matrix can be taken from, [12]. In

analytical formulation the rule of mixture accurately predicts the physical properties of composite laminate plate as

below:

ANALYTICAL FORMULATION FOR THERMAL CONDUCTIVITY

When the fibers arranged in the longitudinal direction, [11]:

KxC = Ky

C = Kf f + Km m (6)

When the fibers arranged in the lateral direction:

KzC =

KfKm

Kfm +Km f (7)

ANALYTICAL FORMULATION FOR THERMAL EXPANSION COEFFICIENT

When the fibers arranged in the longitudinal direction, [13]:

xC = y

C =m Em m +fEff

Em m +Eff (8)

When the fiber arranged in the lateral direction:

zC = m m 1 m + f f 1 f 12 x

C (9)

And;

12 = f f + m m

ANALYTICAL FORMULATION FOR SPECIFIC HEAT

CPC =

CPf ff +CP

m m m

C , [14] (10)

And;

C

= f f + m m

ANALYTICAL FORMULATION FOR TENSION AND SHEAR MODULI

When the fibers arranged in the longitudinal direction, [11]:

ExC = Ey

C = Ef f + Em m (11)

When the fibers arranged in the lateral direction:

1

EzC =

f

Ef+

m

Em (12)

; But the shear modulus from the following equation, [15]:

1

G12=

f

G f+

m

Gm (13)

RESULTS AND DISCUSSIONS

Tables (1,2) show the thermal conductivity and specific heat values of the composite specimen when the fibers

are arranged in the lateral (perpendicular) and longitudinal (parallel) directions to the heat source using different

fiber volume fractions with the aiding of analytical procedure (equations 6, 7, 10). The thermal conductivity and

specific heat in (x ,y ,z) directions increase with the increasing of fiber volume fractions because the increasing of

fiber fractions lead to increasing the number of layers which reduce the temperature difference cross the sample,

since that is causing increase in thermal conductivity and specific heat.

Table (1) Thermal conductivity and specific heat properties of the composite specimen when the fibers are

arranged in the lateral (perpendicular) direction to the heat source

f % 25.076% 40% 50% 60% 70% 80%

Kxc

W

m . K

0.4533 0.622 0.735 0.848 0.961 1.074

Kyc

W

m . K

0.4533 0.622 0.735 0.848 0.961 1.074

Kzc

W

m . K

0.2174 0.2626 0.30068 0.3553 0.43418 0.55808

Cpc 768.139 780.894 787.7133 793.5087 798.495 802.8304

Table (2) Thermal conductivity and specific heat properties of the composite specimen when the fibers are

arranged in the longitudinal (parallel) direction to the heat source

f % 25.076% 40% 50% 60% 70% 80%

Kxc

W

m . K

0.2174 0.2626 0.30068 0.3553 0.43418 0.55808

Kyc

W

m . K

0.2174 0.2626 0.30068 0.3553 0.43418 0.55808

Kzc

W

m . K

0.4533 0.622 0.735 0.848 0.961 1.074

Cpc 768.139 780.89 787.7133 793.5087 798.495 802.8304

Table s (3, 4, 5, 6) give the thermal expansion coefficient of composite specimen when the fiber arranged in the

lateral (perpendicular) and longitudinal (parallel) directions to the heat source for both heating and cooling using

different fiber volume fractions with the aiding of analytical procedure (equations 8, 9). The thermal expansion in

(x ,y ,z) directions decrease with the increasing of fiber fractions because the increasing of fiber fractions do not

allow the atoms to move and give more strength for composite laminate plate that leads to decrease the thermal

expansion coefficient for both heating and cooling.

Table (3) Coefficient of thermal expansion of the composite specimen when the fibers are arranged in the lateral

(perpendicular) direction to the heat source for heating from (25Cto 130C )

f % 25.076% 40% 50% 60% 70% 80%

xC

1

C

41.6248 E-6 35.0226 E-6 29.988 E-6 24.7344 E-6 19.3511 E-6 13.8849 E-6

yC

1

C

41.6248 E-6 35.0226 E-6 29.988 E-6 24.7344 E-6 19.3511 E-6 13.8849 E-6

zC

1

C

14.1919 E-6 9.8262 E-6 8.2677 E-6 7.2014 E-6 6.426 E-6 5.8365 E-6

Table (4) Coefficient of thermal expansion of the composite specimen when the fibers are arranged in the

longitudinal (parallel) direction to the heat source for heating from (25C to 130C )

f % 25.076% 40% 50% 60% 70% 80%

xC

1

C

14.1919 E-6 9.8262 E-6 8.2677 E-6 7.2014 E-6 6.426 E-6 5.8365 E-6

yC

1

C

14.1919 E-6 9.8262 E-6 8.2677 E-6 7.2014 E-6 6.426 E-6 5.8365 E-6

zC

1

C

41.6248 E-6 35.0226 E-6 29.988 E-6 24.7344 E-6 19.3511 E-6 13.8849 E-6

Table (5) Coefficient of thermal expansion of the composite specimen when the fibers are arranged in the lateral

(perpendicular) direction to the heat source for cooling from (25Cto 20C)

f % 25.076% 40% 50% 60% 70% 80%

xC

1

C

25.746 E-6 21.6044 E-6 18.5098 E-6 15.3005 E-6 12.0234 E-6 8.70307 E-6

yC

1

C

25.746 E-6 21.6044 E-6 18.5098 E-6 15.3005 E-6 12.0234 E-6 8.70307 E-6

zC

1

C

10.5844 E-6 7.932 E-6 6.9852 E-6 6.3374 E-6 5.8663 E-6 5.5082 E-6

Table (6) Coefficient of thermal expansion of the composite specimen when the fibers are arranged in the

longitudinal (parallel) direction to the heat source for cooling from (25C to 20C)

f % 25.076% 40% 50% 60% 70% 80%

xC

1

C

10.5844 E-6 7.932 E-6 6.9852 E-6 6.3374 E-6 5.8663 E-6 5.5082 E-6

yC

1

C

10.5844 E-6 7.932 E-6 6.9852 E-6 6.3374 E-6 5.8663 E-6 5.5082 E-6

zC

1

C

25.746 E-6 21.6044 E-6 18.5098 E-6 15.3005 E-6 12.0234 E-6 8.70307 E-6

Table (7) estimates the increasing of different fiber volume fractions on mechanical properties with the aiding of

analytical procedure (equations 11, 12, 13). All mechanical properties except Poisson's ratio increase with the

increasing of fiber fractions because that leads to increasing the number of layers and gives the composite

laminate more strength; but the decreasing of Poisson's ratio because the longitudinal strain in x-direction has

been increased. Table (8) gives the comparison analysis between analytical and experimental works for different

physical properties.

Table (7) Mechanical properties of the woven roving E-glass fibers / polyester composite laminate

f % 25.076% 40% 50% 60% 70% 80%

Exc (GPa.) 19.933 30.4038 37.41988 44.435 51.452 58.468

Eyc (GPa. ) 19.933 30.4038 37.41988 44.435 51.452 58.468

Ezc(GPa. ) 3.0896 3.81746 4.53322 5.5793 7.25302 10.3612

12 0.3835 0.35098 0.32915 0.30732 0.2855 0.26366

G12(GPa. ) 1.07675 1.33379 1.5878 1.9614 2.5648 3.70468

C

kg

m3

1464.18 1686.48 1835.4 1984.32 2133.24 2282.16

Table (8) Verification test between analytical formulation and experimental work for composite plate

Physical Properties Analytical

Formulation

Experimental

Work

Percentage Error (%)

Kzc

W

m . K

0.2174 0.23085 5.826%

Exc(GPa. ) 19.933 19.16933 3.831%

Eyc (GPa. ) 19.933 19.16933 3.831%

G12(GPa. ) 1.07675 1.06558 1.037%

Figure (3) shows the experimental temperature history of brass disks cross composite specimen during thermal

conductivity test. It is clear that the wall surface temperature increase in nonlinear relationship with time required

reaching equilibrium temperature. The temperatures on points (2, 3) is higher than on point (1) as given in Figure

(1) because insulation which can be taken the readings of temperature from thermometer in a hole dragged in the

brass disks.

Figure (3) Temperature history of brass disks during thermal conductivity test

Figure (4) illustrate the thermal expansion vary with temperature for heating experimentally from (25Cto 130C ). It

can be noticed that the relationship between thermal expansion and temperature is approximately linear and that

the same reason of ignoring thermal expansion for cooling in this figure.

Figure (4) Dependence of thermal expansion on temperature for polyester matrix

CONCLUSIONS

The thermal conductivity in (x, y) directions is the same because the distance between fiber yarns are the

same in (x, y) directions.

The thermal expansion coefficient follows the bilinear law because the slop between strain and

temperature is linear.

The best fiber volume fractions is (80%) because this gives small difference in thermal expansion

coefficient of glass fiber and polyester matrix and that leads to reduce the thermal cycling effect on

composite laminate in aerospace application.

The tension and shear moduli increased with the increasing of fiber volume fraction because the previous

increased the number of layers and the specimen resist the fracture by INSTRON apparatus.

REFERENCES

[1] Gaglord M.W.," Reinforced Plastic Theory and Practice", Second Edition, Chahnenrs Put. Co. Inc., 1974.

[2] Pilling M.W., Yates B., and Black M.A.," The Thermal Conductivity of Carbon Fiber-Reinforced Composites",

Journal of Material Science, Vol. 14, 1979.

[3] Price Duncan M., and Jarratt Mark," Thermal Conductivity of PTFE and PTFE Composites", Twenty-Eight

Conference of the North American Thermal Analysis, p.p.579-584, 4-6 October, 2000.

[4] Ribeiro M.C.S., Reis J.M.L., Ferreira A.J.M., and Marques A.T.," Thermal Expansion of Epoxy and Polyester

Polymer Mortars-Plain Mortars and Fiber-Reinforced Mortars", Journal of Polymer Testing, Science Direct, 22,

p.p. 849-857, 13 February, 2003.

[5] Goyheneche J.M., and Cosculluela A.," A Multiscale Model for the Effective Thermal Conductivity Tensor of a

Standard Composite Material", Fifteen Symposium on Thermophysical Properties, 22-27 June, 2003.

[6] Raghava R. S.," Prediction of Thermal and Mechanical Properties of Glass-Epoxy Composite Laminates",

Journal of Polymer Composites, Vol. 5, Iss. 3, p.p. 173-178, 30 August, 2004.

[7] Aldrighetti Claudia, Tassone Pierpaolo, Ciardelli Francesco, and Ruggeri Giacomo," Reduction of the Thermal

Expansion of Unsaturated Polyesters by Chain-End Modification", Journal of Polymer Degradation and Stability,

Science Direct, 90, p.p. 346-353, 20 January 2005.

[8] Dr. Jawad Kadhim Uleiwi, and Sura Salem," Study of Thermal Characteristics of a Composite Specimen by

Using Experimental Method and Finite Element Method", Engineering and Technology Journal, Vol. 26, No. 4,

2008.

[9] Kleinholz R., and Molinier G.," Aramid Carbon and Glass Fiber Specialized Reinforcement Materials for

Composites", Vetrotex Fiber World, No. 22, p.p. 13, 1986.

[10] Murthy BSR, Dr. Krishna A. Rama, and Krishna B.V Rama," Thermal Analysis of Epoxy Based Fiber-

Reinforced", IE(I) Journal-MC, Vol. 84, April, 2004.

[11] Jones Robert M.," Mechanics of Composite Materials", McGraw-Hill Book Company, 1975.

[12] Callister William D.," Materials Science and Engineering An Introduction", Sixth Edition, John Wiley and

Sons, Inc., 2003.

[13] Hashin Z.," Analysis of Properties of Fiber Composite with Anisotropic Constituents", Journal of Applied

Mechanics, Vol. 46, 1979.

[14] Lua James, O'Brien Jeff, Key Christopher T., Wu Yongshu, and Lattimer Brian Y.," A Temperature and Mass

Dependent Thermal Model for Fire Response Prediction of Marine Composites", Journal of Applied Science and

Manufacturing, p.p. 1024-1039, 2006.

[15] Vasiliev Valery V., and Morozov Evgeny V.," Mechanics and Analysis of Composite Materials", Book

Company, Elsevier Applied Mechanics, p.p. 86, 2001.

NOMENECLATURES

Symbols Definitions

T1 , T2 , T3 Temperature across the sample sides.

K Thermal conductivity in both longitudinal and lateral direction.

G12 Modulus rigidity in 1-2 plane.

KxC , Ky

C , KzC Thermal conductivity for composite in x, y, z directions respectively.

Kf , Km Thermal conductivity of fiber and matrix respectively.

f ,m Volume fraction for fiber and matrix respectively.

xC ,y

C ,zC Thermal expansion coefficient for composite in x, y, z directions respectively.

f ,m Thermal expansion coefficient for fiber and matrix respectively.

Ef , Em Modulus of elasticity for fiber and matrix respectively.

f , m Poisson's ratio for fiber and matrix respectively.

CPC Specific heat for composite.

CPf , CP

m Specific heat for fiber and matrix respectively.

f

,m

Density of fiber and matrix respectively.

C Density for composite plate.

ExC , Ey

C , EzC Modulus of elasticity for composite in x, y, z directions respectively.

Gf , Gm Modulus of rigidity for fiber and matrix respectively.

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