analytical and experimental evaluation of elastic properties of vacuum assisted resin infusion...

Analytical and Experimental Evaluation of ElasticProperties of Vacuum Assisted Resin InfusionMolded Polymer Composites with Eight-HarnessWoven Fiber Mats

Ahmed Khattab,1 A. Sherif El-Gizawy21Department of Industrial Technology, College of Engineering, University of Louisiana-Lafayette,Lafayette, Louisiana 70504

2Industrial and Technological Development Center, Mechanical and Aerospace Engineering,University of Missouri-Columbia, Columbia, Missouri 65211

An analytical and experimental evaluation of elasticproperties of composite materials under tensile load ispresented in this paper. The analysis focuses on com-posite materials molded by vacuum assisted resin infu-sion molding (VARIM). The molded composite structureconsists of AS4-8 harness carbon fiber mats and ahigh-temperature polymer (5250-4-RTM). The analyticalmodel presented is adapted and formulated using opti-cal microscopy observations of cross sections of sam-ples molded by VARIM. Effects of resin degree of cure,fiber undulation, and resin rich areas between fiber bun-dles are addressed in the model. An experimental casestudy is presented to evaluate the accuracy of theadapted analytical model. The evaluation shows a rea-sonable agreement between the experimental and ana-lytical results. POLYM. COMPOS., 29:63–71, 2008. ª 2007Society of Plastics Engineers

INTRODUCTION

Vacuum assisted resin infusion molding (VARIM) pro-

cess was recently found to be a viable process for fabrica-

tion of high-temperature polymer composites [1]. In this

process, the reinforcement, which is usually composed of

several layers of fiber mats, is placed in an open mold and

a plastic vacuum bag is placed on the top of the mold. The

mold is connected with a resin source and a vacuum pump.

As the vacuum is drawn through the mold, the liquid resin

infuses into the reinforcing fiber mats. Curing and de-

molding steps are followed to finish the product. VARIM

has been used primarily with resin systems that cure at

room temperature. Some important issues, such as elastic

properties prediction, remain to be explored before high-

temperature VARIM can be widely used for variety of

high performance applications. The analytical and experi-

mental evaluation in this study will highlight many of the

issues that need to be understood.

In an effort to simulate the entire VARIM process, a

three-dimensional model was developed by Loos et al. [2].

It constitutes modules for describing the resin flow, heat

transfer, preform compaction, cure kinetics, and residual

stresses during infiltration and cure. They addressed

VARIM process for resin that cures at room temperature

(vinyl ester). Tim et al. [3] performed an analysis on

shrinkage and warpage of compression-molded fiber-rein-

forced composite parts. Their research concentrated on nu-

merical simulation and experimental investigation of

shrinkage and warpage in thin compression molded parts.

Their numerical model incorporated cure-dependent me-

chanical properties of the composite. They considered the

composite at a macroscopic scale and did not differentiate

between the fiber- and resin-rich regions.

Chou and Ishikawa [4] presented three models for wo-

ven fiber composite analysis. These models are the Mosaic

model, the Crimp model, and the bridge model. The sim-

plest model is the mosaic model in which fiber continuity

and undulation have been excluded. Ito and Chou [5]) pre-

sented an analytical and experimental study to analyze the

strength and failure behavior of plain weave composites.

They developed a three-dimensional model to investigate

the geometrical characteristics of yarn shape, laminate

staking configuration, fiber volume fraction, and yarn pack-

ing fraction. The model predicts elastic properties, stress

distributions, and strengths under tensile loading. The

mathematical model was evaluated and also verified exper-

imentally using a composite material molded by resin

transfer molding (RTM) of a vinyl ester resin and plain

weave graphite fabrics.

Correspondence to: Ahmed Khattab; e-mail: [email protected]

DOI 10.1002/pc.20356

Published online in Wiley InterScience (www.interscience.wiley.com).

VVC 2007 Society of Plastics Engineers

POLYMER COMPOSITES—-2008

An analysis on modeling the effect of cure on mechani-

cal properties in laminate composites was performed by

Golestanian and El-Gizawy [6]. They presented results on

cure-dependent properties of resin transfer molded thin

composites with woven fiber mats. In this study, resin

properties were assumed to change from viscoelastic liquid

to properties of the solid, as the part cures. This work was

aimed at modeling the cure-dependent mechanical proper-

ties of molded composites with woven fiber mats produced

by RTM. Chen and Chou [7] proposed a three-dimensional

model of the unit cell for multilayer fabrics to predict the

compressive behavior of yarns. Their analytical study pre-

sented results for the nesting and elastic deformation dur-

ing the compaction of multilayer woven fabric preforms.

The authors did not however experimentally verify their

analytical model.

Kwon and Altekin [8] developed an approach to analyze

woven-fabric composite structure based on microlevel

properties of fiber and matrix materials. This approach can

predict the stiffness, strength, and progressive failure of

woven-fabric composites. The predicted properties by this

approach were in good agreement with some other pub-

lished data. Recently, also Naik and Kuchibhotla [9] pre-

sented a two-dimensional analytical model for the failure

behavior of plain weave fabric composites made of

twisted yarns under tensile loading. The model was used

to predict mechanical properties as functions of yarn angle

of twist. The model however again was not confirmed

experimentally.

A literature review shows that a large portion of the pub-

lished work on modeling for woven fiber/high-temperature

polymer composites deals primarily with the conventional

RTM process. Nevertheless, these findings and results could

also help in the development of the science-base for

VARIM processes using high-temperature polymers.

The present paper introduces an analytical-experimental

evaluation of elastic properties of molded polymer compo-

sites with eight-harness woven fiber mats produced by

VARIM. The analytical study aims at modeling the elastic

properties of vacuum assisted resin infusion molded

composites. The adapted model for VARIM composites is

based on a previous model presented by one of the authors

[6] for resin transfer molded composites. This investigation

provides the capability for prediction and characterization

of elastic properties of high-temperature polymer compo-

sites produced by VARIM. The effect of resin degree of

cure on the properties is also addressed in the adapted

model.

ANALYTICAL INVESTIGATION

The current analytical model assumes the applicability

of the Classical Laminate Theory (CLT) to the infinitesi-

mal regions of the composite unit cell. Cure-dependent me-

chanical properties of composite parts with eight-harness

fiber are determined. Resin properties are assumed to

change from that of a liquid to properties of a solid, as the

part cures. The shape function used in the mathematical

model is formulated based on the observation of cross sec-

tions of samples molded by VARIM under an optical

microscope. This model takes into account the fiber conti-

nuity and undulation. Resin degree of cure, resin-rich areas

between fiber bundles, and the fraction of resin within the

fiber bundles are also taken into account.

FIG. 1. Schematic of a top view of eight-harness carbon fiber mat.

FIG. 2. Geometry of a cross section of eight-harness carbon fiber mat.

(a) a CAD drawing and (b) a picture obtained by an optical microscope, at

70�, for a sample produced by VARIM.

FIG. 3. Geometry of eight-harness carbon fiber mat; each section repre-

sents a cross section of the mat along the y-direction.

64 POLYMER COMPOSITES—-2008 DOI 10.1002/pc

FIBER MAT STRUCTURE

To model mechanical properties of carbon fiber mat

composites, the geometry of the mat was first analyzed on

the microscopic level. Figure 1 shows a schematic of a top

view of eight-harness (8H) weave. This number (8H) refers

to the number of yarns that are passed over by one yarn. In

an eight-harness satin weave, yarns are weaved by passing

over seven and under one yarn before the pattern repeats

itself. The fiber yarns which run in x-direction are called

the fill yarns, and those running in the y-direction are

called the warp yarns, with the same fibers count in both

directions.

The cross section of some samples produced by VARIM

were prepared, polished, and analyzed under an optical

microscope. Figure 2b shows the shape of a cross section

through the thickness of the molded sample. All the dimen-

sions of the fill and warp yarn were obtained from the ob-

servation under the microscope and then the cross section

was redrawn in CAD system as shown in Fig. 2a. These

observations showed that the warp yarn, which crosses

over the fill yarn, resemble an ellipse. Because of the high

compression in VARIM process, the following seven

yarns, which cross under the fill yarn, regroup together to

act as one bundle. Measurements were made (under the

microscope) of the wavelength of a yarn, yarn thickness,

elliptical shape of the warp yarn, and some other necessary

dimensions to draw the cross section in CAD system. The

area of the elliptical shape of the warp yarn and the total

fiber bundle cross section area were used to calculate the

bundle fiber volume fraction.

The analysis is performed on a unit cell which repre-

sents the building block of the entire mat. The geometry of

eight-harness mat repeats itself every eight yarns in both

x- and y-directions. The unit cell chosen for the analysis

should contain all the patterns present in the mat. So, the

complete unit cell for eight-harness mat consists of eight

rows. Figure 3 shows the geometry of eight-harness carbon

fiber mat as was seen under the microscope. Each section

represents a cross section of the mat along the y-direction,as shown in Fig. 1. The section length (L) in Fig. 3 repre-

sents the length of a unit cell.

SHAPE FUNCTION FORMULATION

The shape function is formulated using optical micros-

copy observations of samples cross sections. On the basis

of these observations, the fill yarn is modeled as a sinusoi-

dal wave. Figure 4 shows the CAD drawing for a cross

section of an eight-harness fiber mat. The figure shows

also a picture obtained by an optical microscope for a sam-

ple produced by VARIM. The geometrical relation be-

tween the fill yarn and the warp yarn of eight-harness fiber

mat, as shown in Fig. 5, is used to define the shape func-

tion based on the shape characterization performed by Ito

and Chou [5] and Golestanian and El-Gizawy [6].

The center line of the fill yarn z0 is defined as:

z0ðxÞ ¼ � hz2sin

2pax

� �where � a

4� x � 3a

4

� �(1)

The fill yarn thickness hz is assumed to be constant. The

upper boundary of the fill yarn is defined as:

zuðxÞ ¼ z0ðxÞ þ hz2

(2)

And the lower boundary of the fill yarn is defined as:

ztðxÞ ¼ z0ðxÞ � hz2

(3)

FIG. 4. Geometry of a cross section of eight-harness carbon fiber mat.

(a) CAD drawing and (b) a picture obtained by an optical microscope, at

40�, for a sample produced by VARIM.

FIG. 5. Geometrical relation between the fill yarn and the warp yarn of

8H fiber mat.

FIG. 6. Variation of resin elastic modulus and Poisson’s ratio with

cure [6].

TABLE 1. Elastic properties of the carbon fiber AS4 and 5250-4-RTM

resin.

Materials

EL

(GPa)

ET

(GPa)

GLT

(GPa)

GTT

(GPa) nLT

Carbon fiber (AS4) 228 40 24 14.3 0.26

Resin 5250-4-RTM 4.6 4.6 1.7 1.7 0.36

DOI 10.1002/pc POLYMER COMPOSITES—-2008 65

The shape of the warp yarn cross section, based on the

observation under the microscope, is assumed to be ellipti-

cal and given as:

ztðxÞ ¼ 2h2a� 4xg

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið2x� 2xgÞða� 2xg � 2xÞ

qþ hz � h0 where xg � x � a

2� xg

� �� ð4Þ

Based on the geometrical shape the variable, hc in the

previous equation is defined as:

h0 ¼ hz2

sin2xgpa

þ 1

� �� (5)

The local angle between fiber direction and x-axis is:

yðxÞ ¼ tan�1 dz0ðxÞdx

� �(6)

where, in the previous equations z0 is the center line of fill

yarn, zu is the upper boundary of the fill yarn, zl is the

lower boundary of the fill yarn, hz is the yarn thickness, ais the wavelength of a yarn, zt is the boundary of elliptical

shape of warp yarn, xg is the offset distance of the warp

yarn from zero coordinate, and y is the angle between fiber

direction and x-axis.

MODELING OF COMPOSITEMECHANICAL PROPERTIES

As mentioned earlier, the CLT is assumed to be applica-

ble to the infinitesimal regions of the composite unit cell.

FIG. 7. Distribution of Young’s modulus for section A-A at the end of

cure cycle.

FIG. 8. Distribution of Young’s modulus at an area with fiber undulation.

FIG. 9. Average of Young’s modulus through the thickness and along

the length for one section.


the length for 8 sections.


The stiffness of the fill, warp, and the matrix are evaluated

based on the properties of each constituent. The fiber vol-

ume fraction of the fill and warp was calculated based on

the dimension obtained under the microscope for the shape

of the yarn and the total cross section area of the fiber in

the bundle. The bundle fiber volume fraction was found to

be 62%. The properties of the fill and warp yarn are deter-

mined based on the rule of mixtures as follows:

The longitudinal Young’s modulus of the yarn is given

by:

E1 ¼ VfEf þ ð1� VfÞEm (7)

The transverse Young’s modulus of the yarn, using

Halpin and Tsai semi-empirical models [10], is given by:

E2 ¼ Em

1þ xZVf

1� ZVf

� �(8)

Z ¼ ðEf=EmÞ � 1

ðEf=EmÞ þ x(9)

The reinforcing factor, x, is given by the empirical for-

mula [11]:

x ¼ 1þ 40V10f (10)

The shear modulus is given by:

G12 ¼ Gm

1þ xZVf

1� ZVf

� �(11)

Z ¼ ðGf=GmÞ � 1

ðGf=GmÞ þ x(12)

G23 ¼ Gm=ð1� V1=2f ð1� Gm=G23fÞÞ (13)

The Poisson’s ratios are given by:

u12 ¼ u13 ¼ Vfnf þ ð1� VfÞnm (14)

u21 ¼ n12E2=E11 (15)

u23 ¼ Vfu23f þ Vmð2nm � n21Þ (16)

where Em and Ef are the tensile moduli for the matrix and

the fiber respectively. Vf is the fiber volume fraction. Gm

and Gf are the shear moduli for the matrix and the fiber

respectively. nm and nf are the Poisson’s ratios for the ma-

trix and the fiber respectively. The changes in fiber orienta-

tion due to yarn undulation must be taken into account.

The effective elastic constants for the fill and warp yarns

are given as follows:

1

Ex¼cos4 y

E1

þ sin4 yE1

þ 1

G12

� 2n12E1

� �sin2 y cos2 y (17)

Ey ¼ E2 (18)

nxy ¼ Ex

"n12E1

ðsin4 yþ cos4 yÞ � 1

E1

þ 1

E2

� 1

G12

� �

� sin2 y cos2 y

#ð19Þ

1

Gxy¼ 2

2

E1

þ 2

E2

þ 4n12E1

� 1

G12

� �sin2 y cos2 y

þ 1

G12

ðsin4 yþ cos4 yÞ ð20Þ

CURE-DEPENDANT MECHANICAL PROPERTIES

While the molded composite material is considered to

be orthotropic, the matrix, i.e., the resin, is considered to

be isotropic. At the early stages of curing, before gelation,

resin acts as a liquid. As the degree of cure increases, more

cross linking occurs, and the resin acts as a solid media.

The mechanical properties of resin change as a function of

degree of cure. Figure 6 shows a linear relation between

the degree of cure and the mechanical properties of the

resin. This relation was presented in the early 90s and used

after that successfully in different studies [6]. In this paper,


the length for the eight sections of the unit cell of a one-layer laminate.

FIG. 12. A laminate with six layers of carbon fiber randomly distributed.


the relation is used to determine resin mechanical proper-

ties as functions of degree of cure.

The modulus, Ex, for each section of the fiber mat unit

cell is determined by integration of the modulus of each

constituent through the thickness for each infinitesimal

length (dx). Thus in the region where (0 � x � xg), shownin Fig. 5, for section A-A, shown in Fig. 3, is given as

follows:

ExðxÞ ¼ 1

H

"Z h1

0

Emx dzþ

Z h2

h1

Ewx dz

þZ h3

h2

Efxdzþ

Z h4

h3

Emx dz

#ð21Þ

where Emx , E

wx , and Ef

x are the moduli in x-direction for the

matrix, the warp, and the fill yarn respectively. H is the

total thickness of the laminate. From 0 to h1 is the thick-

ness of the matrix bottom layer, from h1 to h2 is warp yarn

thickness, from h2 to h3 is the thickness of the fill yarn,

and from h3 to h4 is the thickness of the matrix top layer.

Similar relations apply to other region within section A-A

of the unit cell. Then the effective modulus for this section

is obtained by integration of Ex(x) along the length of the

section.

Ex ¼ 1

Lx

Z Lx

0

ExðxÞdx (22)

Similar steps apply to the other sections, from section

B-B to section H-H, to find the Ex(x) along the length of

each section. The effective Young’s modulus, Ex, for the

whole laminate is obtained by taking the average of Ex for

all of the sections.

All other properties (e.g., nxy and Gxy) are obtained in a

similar manner.

MODELING RESULTS

The elastic properties were determined for every 5% of

resin cure and up to the end of the cure cycle. A series of

MATLAB codes were written for this model using Eqs. 1–22.The elastic properties of the fill and warp yarn are calcu-

lated based on the fiber bundle volume fraction and the

elastic properties of fiber and matrix using mechanical

properties of each constituent. Table 1 shows the elastic

mechanical properties of the materials used in this study,

which are eight-harness carbon fiber mats weaved by AS4

and 5250-4-RTM BMI resin. The properties of AS4 carbon

fiber were obtained from Ref. [12], while the properties for

5250-4-RTM were obtained from Ref. [13].

The first step in the model was to determine the elastic

properties in each infinitesimal region for each section, of

the eight sections, of the unit cell, shown in Fig. 3. The

fiber bundle volume fraction was calculated, based on the

dimensions obtained under the microscope for several

cross sections of the molded composite, and was found to

be 62%. The cure-dependant properties were determined

for the resin in the fiber bundle and resin-rich regions. The

composite tensile moduli were determined for every 5% of

resin degree of cure from zero and up to the end of curing

cycle, 100% for every section of the eight sections using

Eqs. 17 and 18. Figure 7 shows the distribution of Young’s

modulus for section A-A at the end of cure cycle. Figure 8

shows the change in the modulus due to fiber undulation

for the same section. Then, the average of the modulus

through the thickness and along the section length was

determined by Eq. 21 for each section of the unit cell. A

curve that represents this average is shown in Fig. 9.

Figure 10 shows the average for every section of the eight

sections, of the unit cell, along x-direction.The distribution of the effective modulus of the unit

cell, as shown in Fig. 11, was determined by taking the av-

erage for the eight sections along the y-direction for a one-

layer laminate of carbon fiber mat. A laminate with several

layers of carbon fiber randomly distributed, as shown in

Fig. 12, reduced the wavy distribution of the effective

modulus. Figure 13 shows this distribution for a six-layer

laminate.


the length for the eight sections of the unit cell of a six-layer laminate.

FIG. 14. Variation of Young’s modulus with resin degree of cure.

TABLE 2. Cure-dependent properties for carbon fiber/5250-4-RTM

resin.

Degree of Cure (%) Ex (GPa) Ey (GPa) Gxy (GPa) nxy

20 61.5 61.5 1.4 0.215

40 66.9 66.9 2.7 0.207

60 70.7 70.7 3.8 0.201

80 73.9 73.9 5.0 0.195

100 74.0 74.0 5.1 0.194


The previous steps were repeated to determine the mod-

ulus of the laminate at every 5% of resin degree of cure.

The rest of the elastic properties were determined in a sim-

ilar manner. Figure 14 shows the variation of Young’s

modulus with resin degree of cure. The modulus showed

an exponential increase with resin degree of cure till it

reaches 80%, and then it levels off. All other properties

(e.g., vxy and Gxy) are obtained in a similar manner. Table 2

shows cure-dependant mechanical properties at every 20%

of resin degree of cure.

CASE STUDY

A case study was investigated analytically, using the

presented model, to determine the tensile modulus, Ex, for

a laminate of two layers of carbon fiber mats. Figure 15

shows a schematic of a laminate with two layers of fiber

mats randomly distributed. The distance (S) in the figure

represents an offset distance in x-direction between the two

layers. The average distribution of Young’s modulus

through the thickness and along the length for the eight

sections of the unit cell of a two-layer laminate with an

offset distance (S) of 2.54 mm (0.1 in.) is shown in Fig. 16.

Since the distribution is wavy, the minimum value within

the unit cell is considered as the laminate Young’s modulus

of elasticity.

A parametric study of the effect the offset distance (S)shows that the lowest modulus can be obtained at no offset

between the two layers. As the offset distance increases the

modulus increases till it reaches a maximum point and

then decreases once again. So the modulus changes up and

down between these two points as a function of the offset

distance. Figure 17 shows the effect of the offset distance

(S) on the modulus of the two-layer laminate of eight-har-

ness carbon fiber mats. The figure shows that the maxi-

mum, minimum, and average values for the modulus are

73.4, 70.9, and 71.8 GPa. As mentioned before the mini-

mum value of 70.9 GPa is used as the effective value

for Young’s modulus of elasticity for the two-layer

laminate.

The presented analytical case study of a laminate with

two-layer mats was also investigated experimentally to

determine the tensile modulus, Ex. The two-layer laminate

was molded by VARIM process. The materials used are

AS4-8H carbon fiber mats and a high-temperature polymer

called 5250-4RTM. Molding process parameters were set

at a maximum cure temperature of 1888C (3708F) and a

heating rate of 1.678C/min (38F/min). Full description of

the experimental setup was reported in a previous publica-

tion by the authors [14].

Room temperature tension tests were performed using

ASTM (D3039/D3039M-00) standard test method for ten-

sile properties of polymer matrix composite materials.

Specimens used in the test are 200 mm (8.0 in.) long, 25

mm (1.0 in.) wide, and on average 0.79 mm (0.031 in.)

thick. The machine which was used in the evaluation is Se-

ries 812 Materials Test System from MTS Systems Corpo-

ration. Hydraulic grips were used with a gripping pressure

of 10 MPa. The tension test was performed using a con-

stant head speed of 1.27 mm/min (0.05 in/min).

A data acquisition system based on LABVEIW software

was used to collect the test data. The tensile modulus was

calculated using chord modulus calculation as recommended

by ASTM standards, Fig. 18 shows a typical stress–strain

curve obtained from one of the test. The two strain points

used in the calculations are 1000 micro-strain and 3000

micro-strain. If the data was not available at the exact

strain end points, the closest available data was used. The

data collected was load in pounds, ram displacement in

inches, and strain. According to ASTM standards the per-

FIG. 15. A laminate with two layers of carbon fiber randomly distributed.

FIG. 17. Effect of the offset distance (S) on the modulus of the two-layer

laminate of eight-harness carbon fiber mats.


the length for the eight sections of the unit cell of a one-layer laminate.


centage of coefficient of variation of the tensile modulus is

calculated as follows:

x ¼Xni¼1

xi

!=n (23)

Sn�1 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

i¼1

x2i � nx2

!=ðn� 1Þ

vuut (24)

CV ¼ 100Sn�1=x (25)

where x is the sample mean (average), Sn�1 is the sample

standard deviation, CV is the sample coefficient of varia-

tion, in percentage, n is the number of specimens, and xi isthe measured property.

The results of the test for tensile modulus are shown in

Table 3. The test was repeated several times to count for

error and mistakes. The tensile test was performed for 13

samples from six different batches of the molded compo-

sites. The statistical analysis of the results shows an aver-

age tensile modulus of 66.9 GPa, a standard deviation of 3,

and a coefficient of variation of 5.7%, as shown in Table 4.

Histogram was used to examine the shape and spread of

sample data as shown in Fig. 19. The figure shows that the

majority of results falls close to the average. Figure 20

shows probability plot for tensile modulus where all results

are inside the confidence interval curves of 95%.

The value of Young’s modulus obtained experimentally

(66.9 GPa) in this study is 5.6% less than the value obtained

by the mathematical model (70.9 GPa). This difference may

be due to the assumptions that no interfacial sliding occurs

between fiber/matrix or between the layers of the fiber mats

and no voids exist in the molded composite. Experimental

observations showed 0.25% average void contents [1]. The

difficulty in laying up carbon fiber mats parallel to each

other is one of the reasons behind the differences. More-

over, difficulties in machining the specimens with their

sides parallel to the direction of fibers inside the molded

panels also contribute to a lower experimental value.

CONCLUSIONS

This paper presents an analytical and experimental eval-

uation of elastic properties of carbon-reinforced polymer

composites molded by VARIM. The investigated compos-

ite structure composed of high-temperature polymer (5250-

4-RTM) and eight-harness woven fiber mats. The follow-

ing conclusions can be drawn from the generated results:

1. The present study provides the capability for prediction

and characterization of elastic properties of high-tem-

perature polymer composites produced by VARIM.

2. The adapted analytical model is a simple and effective

tool in determining elastic properties of vacuum assisted

resin infusion molded composites.

3. The model predicts the elastic properties as functions of

resin degree of cure and takes into account the fiber conti-

FIG. 18. Stress–strain curve of tensile test for one of the specimen.

TABLE 3. Tensile modulus of carbon fiber/5250-4-RT-molded

composites.

Specimen no. Batch no. Tensile modulus, Ex (GPa)

1 1 66

2 1 68

3 2 71

4 2 62

5 3 68

6 3 60

7 4 65

8 4 69

9 5 75

10 5 68

11 6 64

12 6 67

13 6 67FIG. 19. Histogram of tensile modulus with normal distribution curve.

TABLE 4. Statistical analysis of tensile test results.

No. of

samples

tested

No. of

batches

Tensile modulus

Average

tensile

modulus (GPa)

Standard

deviation

(GPa)

Coefficient

of variation

(%)

13 6 66.9 3.8 5.7


nuity and undulation, resin-rich areas between fiber bun-

dles, and the fraction of resin within the fiber bundles.

4. The investigated case studies in the present work reveal

very small differences (average 5%) between experi-

mental and analytical results.

ACKNOWLEDGMENTS

The authors acknowledge the support of the Boeing

Company and Cytec Engineered Materials for the present

research. They also acknowledge Mr. Barton Moenster,

Director Advanced Manufacturing R&D, Mr. Gregg Bogucki,

and Mr. John Griffith of the Boeing Company for their valu-

able discussions and encouragements.

REFERENCES

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3. T.A. Osswald, M. Esther, and S.-C. Tseng, Polym. Polym.Compos., 2, 3 (1994).

4. T.-W. Chou and T. Ishikawa, Textile Structural Composites,Elsevier, New York (1989).

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FIG. 20. Probability plot of tensile modulus with 95% confidence

interval.


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