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lUST-International Journal of Engineering Science, Vol. 15, No. 3, 2004, pp. 141-149Iran University of Science and Technology.

THERMAL AND FLOW ANALYSES OF A RESIN TRANSFERMOLDED COMPOSITE CYLINDER

H. GolestanianI, s. Ziaei-Rad2

1 University of Shahr-E-KordShahr-E-Kord, Iran

2Isfahan University of TechnologyIsfahan, Iran

E-mail:golestanian@eng.sku.ac.irszrad@cc.iut.ac.ir

Abstract: This paper presents the results of mold filling and cures analyses of a Resin TransferMolding (RTM) process. Three dimensional mold filling and cure analyses have beenperformed to model resin transfer molding of a hollow composite cylinder. Fiberglass andcarbon fiber mats with EPON826 epoxy resin composites are considered. Numerical models aredeveloped in commercial finite element software to simulate resin flow into a mold ofcylindrical shape. The cylindrical part has inner and outer diameters of 9 and 10 centimeters,respectively while its length is 100 centimeters. Resin flow through fiber mats is modeled asflow through porous media with Darcy's law. The effects of reinforcement type on mold fillingtimes are investigated. In modeling the composite cure cycle, three-dimensional energy and sp-ecies equations are solved in the mold domain using a finite difference method. Thermal andcure histories of the composite part are determined in the cure cycle. Based on the results of thisinvestigation the injection cycle of the process is the most time consuming part in themanufacturing of these composite parts. This information can help in the design of the mold,selection of injection pressure, and the cure cycle parameters prior to part manufacture.

Keywords: Resin Transfer Molding, Mold Filling, Flow Through Porous Media, Thermal andCure analyses

1. INTRODUCTION

Resin Transfer Molding (RTM) is a processwhich involves transfer of resin into an enclosedmold containing previously positioned reinforc-ement preforms. This process can be employed tomanufacture large and complicated parts. Typi-cal examples of products that are produced withRTM include fiberglass boats, swimming pools,bathtubs, and parts in automotive and aircraftindustries [1,2]. The reinforcement is composedof several layers of woven fiber mats laid inside atwo-piece mold. The mold is closed and resin isinjected into the mold through one or multipleinjection ports and impregnates the fibers of thepreform. The injection is continued until themold is completely filled. The mold fillingprocess is carried out under low pressure, thusreducing the restrictions on the toolingequipment. Once the mold is filled, injection isstopped and the part is cured inside the mold byincreasing the mold wall temperature. The

integrity of the finished part in RTM processdepends on the selection of the preform, surfacetreatment of fibers, design of the mold, the choiceof resin type, filling parameters, and the resincure conditions.

Mold design is a highly labor intensive andcomplex operation [1]. Proper mold fillingrequires proper positioning of the inlets andoutlets, close monitoring of mold temperatureand injection pressure, and selection of optimumresin flow rate into the mold. If the inlet pressureor resin flow rate is set too high, fiber wash outcould occur [2]. Fill time must be long enough toensure complete fiber impregnation. Also, byproper positioning of the injection ports, one canreduce the possibility of void formation. Moldwall temperature should be set at proper levels toassure complete cure of the part in a reasonabletime. If the mold wall temperature is set too lowthe part might not cure at all or cure timebecomes too long. This increases production timeand cost. If the mold wall temperature is set too

142

high, resin could char and damage the part. Thus,before any attempt is made in manufacturing, theoptimum injection and cure cycle parametersmust be determined for each part geometry andresin/fiber combination.

Due to the interaction of different variablesand the complexity of the process, mold and pro-cess design and optimization is currently perfor-med using the trial and error practice. Experime-ntal methods for optimization of mold and proce-ss design can be too time consuming and econo-mically prohibitive. A computer model capableof simulating the process can help manufacturingengineers and mold designers in optimizing vari-ous parameters involved before a new mold orpart is manufactured.

2. LITERATURE SURVEY

Large amount of research has been carried out onmodeling RTM processes using finite elementmethods in recent years. Golestanian et. al. havemodeled resin flow in rectangular and irregularmold geometries [3,4]. First, they have determin-ed fiber mat permeabilities for woven fiberglassand carbon mats experimentally. Next, a numer-ical simulation was performed and the resultswere verified with experimental measurements.Their results showed the importance of edge effe-cts on resin flow behavior in small cavities. In aseparate research, they also performed thermaland cure analyses of rectangular composite par-ts. Finally, using these results, they determinedcuredependent mechanical properties of both co-mposite systems [5]. Trochu, Gauvin, and Gao[6] developed a finite element model capable ofpredicting pressure distributions and resin frontpositions within the mold. They considered mo-Id configurations with one or two injection ports.They also studied molds with inserts and the caseof anisotropic preforms. They presented experi-mental verifications of their models. Chan andHwang [7] employed a two-dimensional finiteelement method to model resin transfer moldingprocess of thin composite parts. They investiga-ted the effects of inlet resin temperature and resininjection pressure on the mold filling time. Noexperimental verification is presented for theirmodels. Gauvin and Trochu [8] simulated twodimensional flows through molds to obtain resinfront and pressure distributions. They presentedcomparisons between experimental and numeri-

H. Golestanian, S. Ziaei-Rad

cal results for three cases. Parnas and Phelan [9]considered one-dimensional flow through themold to study the effects of preform heterogenei-ties in RTM. In their work, consideration wasgiven to the macroscopic flow of resin throughthe preform and the impregnation of the fiberbundles. Boundary inhomogeneities were invest-igated by solving the problem of parallel flowthrough porous media bounded by an openchannel next to the mold wall. The results of theirwork illustrated the importance of edge effectsand deviation of experimental results from thoseobtained from Darcy's law. Perry et al. [10] alsoperformed flow analysis of an RTM process.They conducted permeability measurements onwoven graphite fibers. A two-dimensional moldfilling was modeled by these researchers. Inanother study, Urn and Lee [11] simulated themold filling stage of resin transfer molding usingboundary element method. They also presentedexperimental verification of their results. Theyconsidered resin flow in two and threedimensions. Isothermal mold filling of two- andthree-dimensional cases were modeled by Younget al. [12]. They presented experimental verific-ation of their model. Broschke and Advani [13]considered mold filling stage for an anisotropicpreform. They used finite element method tomodel three-dimensional shell geometry. Theiranalysis concentrated on variation of fiber matpermeability. They also presented experimentalverification of their models. Lam et. al. used fin-ite element method to simulate mold filling inrectangular and semi-cylindrical compo-site parts[14]. They considered one dimensional resin flowand did not model composite cure. Lim and Lee[15] simulated mold filling of thick rectangularcomposite parts. They also performed thermaland cure analysis of the composite part. Theydetermined three-dimensional permeability tensorfor glass fiber mats. These investigators compa-red their flow analysis results with experimentalmeasurements and found up to 32% error in resinfront positions. This error was observed in somelocations, but was much lower in most placesinside the mold cavity. These researchers alsoperformed flow analysis in centrifugal pumpcover geometry. They did not perform any ther-mal and cure analyses. Han et. al. performed per-meability measurements of anisotropic fiber pref-orms with high fiber contents [16]. These inves-tigators performed pressure measurements at fourlocations in the flow field to determine the per-

Thennal and Flow Analyses of a Resin Transfer Molded ...

meabilities for several types of fiber preform.Choi et. al. [17] used a finite element softwarepackage to determine permeability at a microsc-opic level. They then developed a flow model topredict resin flow in real fiber preforms. Theirmodel predicts the interrelation-ship between pre-form properties such as permeability, fiber pack-ing, fiber radius, and fiber volume fraction.Sawley et al. used smoothed particle hydrodyna-mics in finite element models to predict flowthrough porous media [18]. They modeled theporous media as a network of particles betweenwhich fluid flows. They performed experimentalmeasurements and compared the results withtheir numerical results. They demonstrated thatDarcy's law predicts flow accurately when thedrift velocity is low. Kay investigated the possib-ility of manufacturing the front part of a helicop-ter by an RTM process [19]. He showed that thispart which consists of many different pieces cou-ld be manufactured as one single piece, thusreducing labor and manufacturing costs. He usedan electron beam curing resin for this part. He didnot, however, present any results on ther-mal andcure analyses.

All of the above investigators modeled resinflow inside the mold as flow through porous me-dia and employed Darcy's law in their analyses.Most of these researchers have considered two-dimensional rectangular molds. None have mod-eled resin flow in three-dimensional cylindricalmolds. No one has performed thermal and cureanalyses of cylindrical composite parts manufact-ured with an RTM process. The current researchis intended to cover areas not addressed by otherresearches. Three dimensional mold filling andcure analyses have been performed to modelresin transfer molding of a hollow compositecylinder. Details of these models and the resultsof these analyses are presented in the followingsections.

3. THEORY AND IMPLEMENT A TION

In order to simulate resin transfer molding of ahollow composite cylinder two main tasks havebeen performed: 1- Three dimensional mold filli-ng and 2- Cure and thermal analysis. The firsttask was carried out by a commercial finite elem-ent software while for the second task a finitedifference program was developed and used by

143

the authors. These two tasks will be explained inthe following sections.

3.1 Resin flow analysis

Numerical models are developed in ANSYSfinite element software to simulate the moldfilling stage of an RTM process. In this study theflow of a polymer resin in woven preform mats isconsidered. The axis of the mold is considered tobe horizontal throughout the injection cycle.Flow of the resin in the woven fiber mats wasmodeled as flow through porous media andDarcy's law was used in the analyses.

For the flow of a fluid through a porous medi-um the equations of continuity and motion arereplaced by [3, 21];Modified equation of continuity:

t:dp + V. (pv) =0dt

(1)

Darcy's law:

Kv = - - (VP - pg)

f.L(2)

In equation (1) Eis porosity of the fiber bed, pis fluid density, t is time, and v is fluid velocity.In equation (2) K is the permeability tensor, !l isthe fluid viscosity, and Y'Pis pressure gradient.

In case of an RTM process the resin is consid-ered to be incompressible, then the continuity eq-uation reduces to:

V.v=O (3)

In addition, the gravitational forces in the mo-mentum equation are negligible, then equation 2reduces to:

Kv=--VP

f.L(4)

Then, from equation 3, for the flow of anincompressible fluid through a porous mediumwith negligible gravitational forces Darcy's lawreduces to [21];

I11'1

,.

..

144

v(-:vp)=o(5)

Jq~ q~!,

Boundary conditions for equation 5 are:- P = Po at the injection port, Where Po is theinjection pressure.- P =0 at the resin front, and- Along the impermeable mold boundary the deri-vative of the pressure in the outward normal dire-ction is zero.

Proper modeling of resin flow inside the moldrequires the knowledge of the fiber mat permea-bility and resin properties. This mat property wasdetermined experimentally by the first author forboth types of fIber mats (glass and carbon) consi-dered in this research. The details of this analysisare presented in reference [3]. The resulting per-meability values are listed in Table 1. Resin andfIber mat physical properties were also taken fro-m reference [3] and are listed in Table 2.

In the present investigation mold filling simul-ations of the cylindrical mold geometry are carri-ed out for both glass and carbon. Epoxy resin isused as the fluid. The mold geometry and inject-ion port position are shown in Figure 1. Resin isinjected from one end of the mold at a constantinjection pressure of 500 kPa. in each case. AN-SYS finite element software is used in the analy-sis. Due to symmetry a quarter of the mold hasbeen modeled in ANSYS. The time-dependentresin flow is analyzed as a quasi steady-state pro-blem. This approximation is valid if a proper timestepping is selected [3]. The analysis procedureinvolves taking a small region at the injection po-rt at the beginning of the injection cycle as thefirst saturated region. This region is modeled inANSYS and the boundary conditions are applied.By solving the model, the pressure distribution isdetermined in this small region. Then the resinfront velocity is determined using Equation 1. Aproper time step is selected and the resin is adva-nced into the mold according to the resin frontvelocity and the selected time step. Finally thenew resin saturated region is modeled. These ste-ps are repeated until the mold is completelyfilled.

The time step selection is based on the Coura-nt number restriction. This means that the resin isadvanced one element length at each time step.At the early stages of the modeling smaller meshand consequently smaller time steps are used.This is because pressure gradients and thus resin

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H. Golestanian, S. Ziaei-Rad

velocity is high at the beginning of the injectioncycle. Time steps as small as 0.01 seconds areused at the early stages of the mold filling. As theresin front reached the end of the mold time stepsas large as 500 seconds could be used. A sampleof the meshed geometry in ANSYS software isshown in Figure 2. This figure shows a model atthe last stage of the mold filling when the resinhas advanced all the way into the mold. Note thatsmaller elements are used at the resin frontposition (near the end of the cylinder).

This provides higher precision in the determi-nation of resin front velocity and direction. Theresin front profiles at various stages of mold fill-ing process are presented in Figures 3 and 4 forboth composites.

Results of flow analysis on carbon/epoxycomposite are presented in Figure 3. Thenumbers given near each profile are time inseconds. Note that resin advances very quicklyinto the mold at the early stages of the injectioncycle. As the resin front advances further into themold, pressure gradient drops and resin velocitydecreases. In fact it takes about 2900 seconds forthe resin to fill the last 10 centimeters of themold. It takes 17770 seconds for this compositeto fill completely.

Resin front positions for the fiberglass/epoxycomposite are shown in Figure 4. Fill time forthis composite is about 2800 seconds. This is al-most one-sixth of the fill time obtained for thecarbon/epoxy composite. The reason for higherfill time for carbon/epoxy composite is lower per-meability of carbon fibers compared to fiberglassfIbers. See Table 1.

Fig. 1. The cylindrical mold geometry and the endinjection port position.

"I " " , )0 20 40 60 80 100

Axi0l Dist0nce (CM)

iiJ)() 00

'~ N"1 N

Thermal and Flow Analyses of a Resin Transfer Molded ...

Fig. 2. Meshed geometry of the cylindrical mold. Notethat smaller elements are used at the resin front (end

of the cylinder).

0 100

0 20

AxioJ40 60 80 100

DisTOXiCe (CM)

Fig. 4. Resin front positions for fiberglass/epoxycomposite. The given times are in seconds.

Table 1.Experimental Permeability results for thefiber mats.

3.2 Cure and Thermal analyses

After the injection cycle of the process was anal-yzed, the cure cycle was modeled. The goal inthis stage of the analysis was to determine therm-al and cure histories for both composite systems.The energy equation in cylindrical coordinateswith no convective heat transfer is given by:

145

aT 1 a aT 1 a ke aT a aT .pC -=--(rk -)+--(--)+-(k -)+S

P at r ar r ar r ae r ae az Zaz(6)

where; p is the density, Cpis the specific heat,T is temperature, kr are thermal conductivities, r,e, and z are coordinates. s is the source term dueto resin cure given by;

. -ES =C[ko exp(-)(l-'Jf)n (Mf)

RT

In equation 7: Cr is the initial concentration ofuncured resin, ko is the pre exponential constant,E is the activation energy, R is the gas constant,and ~H is the heat of reaction. Finally, 'V is resindegree of cure given by;

(7)

Cl -CAIj/=-

Cl(8)

where CA is the local concentration of uncuredreSlll.

The species equation for this case, when theresin is stationary in the mold, is given by:

all( -E n~=k exp(-)(I-'Jf)at 0 RT

(9)

The energy and species equations are coupledthrough the source term. Thus these equations sh-ould be solved simultaneously in the compositedomain. A finite difference method based on Pat-ankar's formulations was used to solve theseequations. A total of 1500 nodes were used in themodel for both types of composite systems. Init-ial composite temperature was assumed to be 60degrees centigrade at the beginning of the curecycle. The mold wall temperature was kept const-ant at 130 degrees centigrade throughout the curecycle. Fiber volume fraction of 0.45 was conside-red for both composite systems. A 5-second timestep is used in the analyses. The required thermaland kinetic properties of the fiber mats and epoxyresin were taken from reference 3 and are listedin Tables 2 and 3.

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Fiber Mat Permeability (m2)Glass 2.18e-8

Carbon 3.56e-9

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146 H. Golestanian, S. Ziaei-Rad

Table 2. Properties of Fiber Mats and Epoxy Resin

Table 3. Kinetic Parameters for Epoxy Resin (EPON 826)

A careful review of the results revealed minorthermal and degree of cure gradients through thepart thickness. There were no differences in ther-mal and cure results of nodes along the cylinder(z-direction). This was expected since all bounda-ry nodes along the cylinder were kept at the cons-tant cure temperature. Nodes at different locatio-ns through the composite thickness showed betw-een 2 degrees difference in thermal results. Thisdifference is more pronounced at the early stagesof the cure cycle and diminishes as thermal ener-gy is conducted to the inner sections of the partfrom the wall. Largest difference in degree ofcure through the thickness of the part was about 2percent. Based on these observations, four nodesin thickness direction of the composite part wereselected for the presentation of the results. Thesenodes will be referred to as nodes 1 through 4.Nodes 1 through 4 are located at 0.2, 004,0.6, and0.8 of cylinder thickness measured from the outercomposite diameter respectively. The results forevery other data point is plotted in the figures toreduce the number of symbols in each curve. Thiswas done to make the curves more clearly in eachplot.

Figure 5 presents thermal history of the refer-ence nodes for the carbon/epoxy composite. Notethat the composite is initially at 60 degrees centi-grade. Temperature increases due to higher moldwall temperature and resin exotherm as the partcures. In fact resin exotherm is responsible for apeak temperature of 2.2 degrees above the moldwall temperature for this composite. Once the po-lymerization reaction is nearly complete no moreexotherm is present and the composite temperatu-

re decreases and approaches the mold wall temp-erature. Cure history for the same nodes for thiscomposite is shown in figure 6. At the beginningof the cure cycle the degree of cure increases slo-wly. Once the polymerization reaction starts thedegree of cure increases sharply. As polymeriza-tion reaction ends and the part reaches a 100%cure, the slope decreases. This composite systemreaches 85% cure at 1400 seconds. This is thetime to remove the part from the mold and startpreparing for the manufacture of the next part.

140

6' 1200>(I)e.!!! 100~~E 80~

--- Node 1

Node2

~ Node3-- Node4

600 730 1230 1730 2230 2730

Time (sec.)

Figure 5. Thermal history for carbon/epoxycomposite.

- 0.8.:.

--- Node1Node2

-><-- Node 3

Node 4

~ 0.6()15lE 0.40,(I)

Cl 0.2

0

0 400 800 1200 1600 2000 2490

Time (sec.)

Fig. 6. Cure history for carbon/epoxy composite.

Material Density Specific Heat Thermal Conductivity(k!Z/m3) (J/kg K) (W/m K)

Fiberl!lass 2560 670 1.04Carbon 1760 870 8.50

Epoxy Resin 1160 1255 0.2

Parameter Symbol ValuePre-exponential Constant K -1

0 7.88E7 secActivation Energy Ek 83.2 kJ/moleHeat of Reaction H 401 kJ/kl!Order of Reaction N 1.0

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Thermal and Flow Analyses of a Resin Transfer Molded ...

Thermal history for reference nodes of fiberg-lass/epoxy composite is shown in figure 7. Thiscurve has the same trend as the thermal historyfor carbon/epoxy system. The temperature peakis 2.2 degrees above the mold wall temperaturefor this composite system as well. Cure historyfor this composite system is shown in figure 8.The trend is the same as that of carbon/epoxy sy-stem. This composite reaches 85% cure at 1400seconds as well. The reason for equal cure timesfor both composites is the part small thicknessand equal fiber volume fraction of both composi-te systems.

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--- Node 1Node2

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600 360 760 1160 1560 1760 1960

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Fig. 7. Thermal history for fiberglass/epoxycomposite.

;ctions calcu--- Node1

Node2--*- Node3--- Node4

- 0.8~

n1 theoretiC?* 0.6()"0iB 0.4e,~ 0.2

00 400 800 1200 1600 2000 2390 3200

lime (sec.)

Fig. 8. Cure history for fiberglass/epoxy composite.

3.3Evaluation of Results

It was necessary to verify the results of this work.This is done by comparing the trends of the curr-ent research results to published data. As wasmentioned in the literature survey, no one hasmodeled resin flow and cure in a cylindrical part.Therefore there is no possibility of verifying theresults directly. Performing experimental measur-ements to verify the results is another approach,but this requires rather expensive equipment andthat is not available at this time. Therefore it was

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147

decided to check the trends of the results withavailable references. For verifying the results ofthe flow analysis part previous published workfrom the first author was selected. In a journalpaper from the author's PhD thesis he determinedresin flow positions in a rectangular mold [4].The results of that study also indicated fill timesin carbon fibers to be about six times that of glassfibers. This is also what is seen in the results ofmold filling analysis in this study. Chachad et al.performed numerical thermal and cure analysesof a pultrusion process [21]. They also performedexperimental measurements of temperature andDSC scans to measure the degree of cure forround pultruded parts. The trends of thermal andcure results in their work is very similar to thetrends of the results of the current study.

Therefore some degrees of confidence can beput on the results of proposed model for the resintransfer molded composite cylinder.

4. CONCLUSIONS

Resin flow inside the mold was modeled as flowthrough porous media in ANSYS finite elementsoftware. Numerical models were developed whi-ch simulate resin flow in fiberglass and carbonfiber mats. Fill times for composites with carbonfibers were much higher than fiberglass composi-tes. The flow analysis results on this compositesuggest the need for multiple injection ports forlong composite parts. Lower permeability of car-bon fibers is the reason for this increased injec-tion time.

In the second part of this study, models weredeveloped to simulate the cure cycle for both co-mposite systems. Resin exotherm resulted in apeak composite temperature of 2.2 degrees higherthan the mold wall temperature. Fiberglass/ epo-xy composite reached 85% cure in 1400 seconds.Total production time (injection and cure) for thiscomposite system was determined to be 4200seconds (about 70 minutes). Carbon/epoxy comp-osite reached 85% cure also in 1400 seconds aswell. Total production time for this composite is19170 seconds (about 320 minutes). Productiontime for carbon/epoxy composite is about 4.5times that of fiberglass/epoxy composite. Moldfilling stage was found to be the most time cons-uming part of the production in the manufacturi-ng process.

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REFERENCES

[1] Richardson, Terry, "Composites, A Desig-n Guide," Industrial Press Inc., New York,NY,1987.

H. Golestanian, S. Ziaei-Rad

fer Molding Preforms on Mold Filling,"International SAMPE Symposium andExhibition, Vo1.36, No. 1, 1991, pp. 506-520.

'10] Perry, Mark J., Wang, T. James, Ma, Y.,and Lee, L. James, "Resin Transfer Mold-ing of Epoxy/Graphite Composites," 24thJr.ternational SAMPE Technical Conferen-ce, '1ctober 20-22,1992, pp. T421-T435.

[2] Cai, Zhong, "Simplified Mold FillingSimulation in Resin Transfer Molding,"Journal of Composite Materials, V01. 26No. 17, 1992, pp. 2606-2630.

[11] Urn, Moon-Kwang and Lee, Woo n, "AStudy on the Mold Filling Process inResin Transfer Molding," Polymer Engin-eering and Science, Vo1.31, No. 11, Mid-June 1991, pp. 765-771.

[3] Golestanian, H., "Modeling of ProcessInduced Residual Stresses and Resin FlowBehavior in Resin Transfer Molded Com-posites with Woven Fiber Mats", Ph-DDissertation, Mechanical and AerospaceEngineering, University of Missouri-Colu-mbia, 1997. [12] Young, W., B., Han, K., Fong, L., H., Lee,

L., James, and Liou, Ming, J., " FlowSimulation in Molds With Preplaced FiberMats," Polymer Composites, Vo1. 12, No.6, 1991, pp. 391-403.

[4] Golestanian, H. and EI-Gizawy Sherif, A.,"Physical and Numerical Modeling ofMold Filling in Resin Transfer Molding",Journal of Polymer Composites, August1998, Vo1.19, No. 4, pp.395-407. [13] Bruschke, M. V., and Advani, S. G., "A

Finite Element/Control Volume Approachto Mold Filling in Anisotropic PorousMedia," Polymer Composites, Vo1. 11,No. 6, 1990, pp. 398-405.

[5] Golestanian, H. and EI-Gizawy Sherif, A.,"Cure Dependent Lamina Stiffness Matri-ces of Resin Transfer Molded CompositeParts with Woven Fiber Mats", Journal ofComposite Materials, Vo1. 31, No. 23,1997, pp. 2402-2423.

[14] Lam, Y. c., Joshi, Sunil C., and Liu, X.L., "Numerical simulation of the mould-filling process in resin-transfer molding,"Composites Science and Technology, Vo1.60, 2000, pp. 845-855.

[6] Trochu, F., Gauvin, R., and Gao, D.-M.,"Numerical Analysis of the Resin TransferMolding Process by the Finite ElementMethod," Advances in Polymer Technolo-gy, Vo1.12, No. 4, 1993, pp. 329-342.

[15] Lim, Seong Taek and Lee, Woo n, "Ananalysis of the three-dimensional resin-transfer mold filling process," CompositesScience and Technology, Vo1. 60, 2000,pp. 961-975.

[7] Chan, A. W., Hwang, Sun-Tak, "ModelingResin Transfer Molding of Polyimide (P-MR-15)/Fiber Composites," Polymer Co-mposites, Vo1. 14, No. 6, 1993, pp. 524-528.

[16] Han, K. Ken, Lee, C. William, and Rice,Brian P., "Measurements of the permeabil-ity of fiber preforms and applications,"Composites Science and Technology, Vo1.60, 2000, pp. 2435-2441.

[8] Gauvin, R., and Trochu, F., "ComparisonBetween Numerical and ExperimentalResults for Mold Filling in Resin TransferMolding," Plastics, Rubber and Composi-tes Processing and Applications, Vo1. 19,No. 3, 1993, pp. 151-157.

[17] Choi, Mi Ae, Lee, Mi Hye, Chang, Jaeeon,and Lee, Seung Jong, "Permeability mode-ling of fibrous media in composite proces-sing," J. Non-Newtonian Fluid Mech.,Vo1.79, 1998, pp. 585-598.[9] Parnas, R. S., Phelan, F. R. Jr., "The

Effects of Heterogeneities in Resin Trans-

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Thermal and Flow Analyses of a Resin Transfer Molded ... 149

[18] Sawley, Mark L., Cleary, Paul W, andHA, Joseph, "Modeling of flow throughporous media and resin transfer moldingusing smoothed particle hydrodynamics.CSIRO Melbourne, Australia, 6-8 Decem-ber 1999.

[19] Kay, Bruce F., "RWSTD Airframe Techn-ology-Foundation for the 21stCentury," 57th Annual Forum of the American

Helicopter Society, Washington D.e.,May 9-11,2001.

[20] Bird, R. B., Stewart, W. E., and Lightfoot,E. N., " Transport Phenomena", JohnWiley & Sons INe., New York 1960, pp.149-151, and 311-320.

[21] Chachad, Y. R., Golestanian, H., Valliap-pan, M., Roux, J. A., and Vaughan, J. G.,"Temperature and Cure Characterization ofPultruded Composites and Kinetic Analys-is of Epoxy Resin Systems Using a Differ-ential Scanning Calorimeter," 38thInterna-tional SAMPE Symposium, April 6-9,1987, pp. 1288-1298.

Received: 3/912003

Accepted: 8/25/2003

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