an analysis of the three-dimensional resin-transfer mold filling process

An analysis of the three-dimensional resin-transfermold ®lling process

Seong Taek Lim, Woo Il Lee *

Department of Mechanical Engineering, Seoul National University, Seoul 151-742, South Korea

Received 13 April 1999; received in revised form 26 July 1999; accepted 21 October 1999

Abstract

Resin-transfer molding (RTM) is a process in which thermosetting resin is injected into a mold cavity pre-loaded with a porous

®brous preform. For parts with small thickness, the mold-®lling process can be modeled as two-dimensional by neglecting theresin ¯ow in the thickness direction. However thicker parts require extensive resin ¯ow through the thickness and thus the three-dimensional e�ect in the resin ¯ow must be considered. In this study, numerical simulations of three-dimensional mold ®lling during

RTM were performed. The governing di�erential equations were discretized by using the control volume ®nite element method(CVFEM). The CVFEM technique was employed bacause of its simplicity in handling the moving boundary problems. The tem-perature and the degree of cure were also calculated. In order to evaluate the validity of the numerical results, they were compared

with exact solutions for simple geometries, and close agreement was observed. Experiments were also performed. To check thethree-dimensional resin front location as a function of time inside the preform, an optical ®ber was used as a sensing element. Theagreements between the experimental data and the numerical results were found to be satisfactory. Numerical calculations forcomplicated geometries were also performed to illustrate the e�ectiveness of the computer code developed in this study. # 2000

Elsevier Science Ltd. All rights reserved.

Keywords: Resin-transfer molding (RTM); Finite-element analysis (FEA); Permeability

1. Introduction

Resin-transfer molding (RTM) is a process in whichthermosetting resin is injected into a preheated mold.After the ®ber preform is completely wetted out by theresin, the curing process follows (Fig. 1).In RTM, the injection pressure, temperature of the

mold, permeability of the ®ber mat and resin viscosityare the major processing variables. In general, higherinjection pressure and mold temperature and lower resinviscosity shortens the manufacturing cycle time. How-ever, excessive injection pressure may cause deformationof the mold and wash-out of the ®ber preform. Anexcessively high mold temperature may induce pre-mature resin gelation and cause short shot. All of theprocess variables are interrelated and have e�ects on themechanical properties of the products. It is thereforeessential to predict the e�ect of the process variables inorder to optimize the conditions.

In simulating the RTM process, the prediction of themoving boundary is a major concern. Coulter andGuÈ cË eri [1] have performed numerical simulations usingthe ®nite-di�erence method and boundary ®tted coor-dinates, while Chan and Hwang [2] used the ®nite-ele-ment method. Um and Lee [3] and Yoo et al. [4]adopted the boundary-element method for mold-®llingsimulation. In solving moving boundary problems usingthe FDM or FEM, as the resin-¯ow front advances, thecalculation domain should be rede®ned and the numer-ical mesh regenerated. The regeneration of the meshrequires large calculation time as the calculation domainbecomes complicated. Among numerical techniques, thecontrol volume ®nite element method (CVFEM) is thata set of equations is formed for nodal control volumesand solved as if they are ®nite elements. As a ®xed gridsystem is employed in CVFEM, there is no need for theregeneration of the mesh and the simulation for com-plex geometry can be done rapidly and e�ectively.Bruschke and Advani [5] obtained reasonable results forisothermal resin ¯ow by FE/CV method to predict ®ll-ing patterns for complex shell-like molds. Lin et al. [6]

0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved.

PI I : S0266-3538(99 )00160-8

Composites Science and Technology 60 (2000) 961±975

* Corresponding author. Tel.: +82-2-880-7122; fax: 82-2-883-0179.

E-mail address: [email protected] (W.I. Lee).

used CVFEM in considering heat transfer and chemicalreaction problems. Kang [7] simulated the mold-®llingprocess including the temperature and the curing e�ect.Most of the previous works were done for thin parts,where the resin ¯ow is two-dimensional. However,thicker products with more complex geometry requireextensive ¯ow in the thickness direction. Temperatureand degree of cure also vary signi®cantly through thethickness. Young [8] simulated RTM process three-dimensionally using CVFEM to predict the ¯ow-frontlocations during the ®lling process and Phelan [9]adopted FEM to solve the governing equation set andsimulated RTM mold-®lling process including runnerdistribution systems, shell geometries and fully three-dimensional ¯ows. Also Varma et al. [10] and Lam et al.[11] suggested the governing equations and the numer-ical methods for RTM analysis which were applicable tofull three-dimensional analysis.In this study, an attempt was made to develop a com-

puter code which can simulate the three-dimensionalRTM mold-®lling process, including the temperatureand the curing e�ects. In order to validate the developedcomputer code experimentally, the ¯ow-front locationinside the thick preform should be monitored during the®lling process. The resin-front locations were observedusing optical-®ber sensors. In order to perform numer-ical simulation, three-dimensional permeability must beknown. The permeability of the ®ber preform was mea-sured also using optical-®ber sensors.

2. Problem statements

Consider an RTM mold with an arbitrary three-dimensional geometry. The mold is loaded with ®berpreform with anisotropic permeability. The mold isthick so that the resin ¯ow through the thickness mustbe considered. Resin is injected at speci®ed locations on themold surface. Either the injection pressure or the injection¯ow rate is given as a function of time. The mold maybe preheated to facilitate the resin ¯ow. The pre-loaded®ber mat, therefore, can be assumed to be heated at thesame temperature. The temperature and degree of cure

of the resin are considered to be maintained constant atthe injection gates. Air vents are ventilated to theatmosphere. They are assumed to be closed when theresin front reaches. The resin-front location and thepressure ®eld during the ®lling process are to be pre-dicted. Also, the temperature distribution and thedegree of resin curing are to be estimated.

3. Mathematical modeling and governing equations

In the RTM mold-®lling process, thermosetting resin¯ows through the porous ®ber preform. Therefore, the¯ow can be assumed to follow Darcy's law [12]

V!� ÿ 1

�K� �rP �1�

where V!

is the velocity of the resin ¯ow, � is the visc-osity of the resin, K� � is the permeability tensor of the®ber preform and P is the pressure.As the resin is incompressible, mass conservation can

be stated as

r�V!� 0 �2�

The energy equation for the resin can be written asfollows [6]:

��rcpr@Tr

@t� �rcpr V

!�rTr � �r�krrTr

� �hv Tf ÿ Tr

ÿ �� G:�3�

where �; cp; k are the density, the speci®c heat and thethermal conductivity of the resin, respectively. hv is theconvection heat transfer coe�cient between the ®berand the resin, T is the temperature, and � is the porosityof the ®ber preform. The subscripts r and f representresin and ®ber, respectively. � is the viscous dissipationrates which comes from the heat generated by the resin¯ow through the pore. G

:is the heat generated by the

resin curing reaction and is expressed as [13]

G: � �H k1 � k2�

m1� � 1ÿ �� m2 �4�

The energy equation for the ®ber preform can bewritten as follows [6]:

1ÿ �� fcpf @Tf

@t� 1ÿ �� r�kfrTf � �hv Tr ÿ Tf

ÿ � �5�

Mass conservation of chemical species represents theconversion between monomer and polymer [6]

@�

@t� V:

��r� � m

: �6�

Fig. 1. Resin transfer modeling process.

962 S.T. Lim, W.I. Lee /Composites Science and Technology 60 (2000) 961±975

where � is the degree of cure and m:is the chemical

reaction rate of the resin, which can be related to thedegree of cure as [13]

m: � k1 � k2�

m1� � 1ÿ �� m2 �7�

Constitutive equations can be obtained in the formsto be used in the CVFEM technique, if the controlvolume method is applied to the governing equations[14]. First, the mass conservation equation [Eq. (2)] isintegrated for control volume and the divergence theo-rem is applied,�

C:V:

r�V!

d� ��

C:S:

V!� n! dS � 0 �8�

Eqs. (1) and (8) are combined to yield the followingexpression:�

C:S:

ÿ 1

�K� �rP� n! dS � 0 �9�

The energy equations of resin and ®ber [Eqs. (3)±(5)]can be joined into a single equation [Eq. (10)] by theassumption that the temperature of the resin and the®ber become identical as the resin impregnates the dry®ber [6].

�cp@T

@t� �rcpr V

!�rT � r�krT� �G: �10�

where �cp and k are expressed as

�cp � ��rcpr � 1ÿ �� fcpfk � �kr � 1ÿ �� kf �11�

Integration of the combined energy equation [Eq.(10)] for control volume with the aid of Green's theoremyields

@

@t

�C:V:

�cpTd��

C:S:

�rcprTV!� n! dS �

�C:S:

krT� n! dS

��

C:V:

��H k1 � k2�m1� � 1ÿ �� m2d�

�12�Likewise, the chemical species mass conservation

[Eqs. (6) and (7)] can be expressed as

@

@t

�C:V:

�d��

C:S:

�

�V!� n! dS

��

C:V:

k1 � k2�m2� � 1ÿ �� m2d�

�13�

The boundary conditions can be stated as follows.At the injection gate:

Pinlet � P0 or uinlet � u0

Tinlet � T0

�inlet � �0 �14�

At the mold wall:

@P

@nwall� 0

Tmold � Tm �15�

On the ¯ow front region:

Pfront � 0

k@T

@n front� 1ÿ �� fcpfun Tf0 ÿ T

ÿ � �16�

Solutions to Eqs. (12) and (13) along with the boundaryconditions [Eqs. (14)±(16)] yield the resin front locationas well as pressure, temperature and degree of cure dis-tributions as functions of time.

4. Numerical simulation

The RTM mold ®lling process is a moving boundaryproblem, which means that the computation domainchanges continuously with time. Therefore, those con-ventional methods such as FEM and FDM requiremesh regeneration at every time step to describe thechange of the calculation domain. The control volumemethod saves much trouble in mesh regeneration whencombined with the volume of ¯uid (VOF) [15] which issuggested by Tadmor and Broyer [16±18]. In order tosolve the governing equations, the CVFEM was used.Discretization of the three-dimensional domain wasdone with a tetrahedron ®nite element (see Fig. 3). Atetrahedron element consists of four sub-volumes divi-ded by four control surfaces. Each control volume iscomposed of sub-volumes surrounding a node. Forexample, as shown in Fig. 3, the control volume i ismade up of sub-volumes of every element which sur-rounds the node i. In the CVFEM, the net ¯ux of mass,momentum, energy and chemical species through thecontrol surfaces is conserved rigorously within the cor-responding control volume. In this method, the wholedomain is divided into a ®xed grid system and a scalarparameter f is introduced for each cell to represent theratio of occupied volume to the total volume. As the¯ow front advances, all of the control volumes can beclassi®ed into three categories as (see Fig. 2):

f � 1: main ¯ow region0 < f < 1: ¯ow front regionf � 0: empty region

S.T. Lim, W.I. Lee /Composites Science and Technology 60 (2000) 961±975 963

The ¯ow front lies over the control volumes of whichthe ®lled fraction is between 0 and 1. If f reaches a cer-tain value, say 0.5, the ®ll time at the moment is recor-ded as the ®ll time of the control volume. After theentire mold is ®lled, the ®lling patterns of the ¯ow frontcan be obtained by interpolating the recorded ®ll timesof the respective control volume [19]. This methodenables us e�cient advancement of the ¯ow front whichsatis®es the mass conservation more strictly.In the energy equation [Eq. (10)] and the chemical

species equation [Eq. (6)], the transient terms are inclu-ded. For time integration of these equations, an explicitmethod was used [20]. The necessary condition for sta-bility can be expressed as Eq. (17) based upon the VonNeuman stability analysis [20].

�t42�x�x2� 2�y

�y2� 2�z

�z2� u!

�x� v!

�y� w!

�z

" #ÿ1�17�

where ai, represents the di�usion coe�cient, u!; v!; w!

represent the velocities of the resin ¯ows, �t is the timeincrement and �x;�y;�z are the characteristic ®nite-element lengths.On the ¯ow-front region, the ®lled fraction f is upda-

ted at each time step as the ¯ow front advances. There-fore, the ®lled fraction f is included in the di�erentialterm of time. On that region, Eq. (12) can be written inmatrix form as

Cd fT t� ��

dt� ÿDT t� � � f ES t� � � df

dtEF �18�

where T�t� represents the temperature, ÿDT t� � is theenergy convection by resin ¯ow, and f ES t� � is the heatreleased by resin curing. df

dtEF is the energy absorbedfrom the pre-heated ®ber mat. The energy convectionÿDT t� � into the newly added calculation domain is tobe calculated using the information from the previoustime step (explicit scheme) and the upstream (upwindscheme). Therefore, the energy convection by resin ¯ow,the exothermal heat by resin curing and the energy ofthe pre-heated ®ber mat are to be added to the energy ofthe newly de®ned ¯ow-front domain one time step later.This can be written as

Cnf n�1Tn�1 � f nCn ÿ�tDn� �Tn ��tf nEnS

��t f n�1 ÿ f nÿ �

EF �19�

where the superscript n represents the nth time step.The numerical simulation procedure is illustrated in

the ¯ow chart (Fig. 4). Eqs. (12) and (13) include thegeneration term which is a function of the temperatureand degree of cure. Therefore, Eqs. (9), (l2) and (13) areall coupled and must be satis®ed simultaneously. First,the viscosity calculated based upon the temperature andthe degree of cure at the previous time step is used tosolve Eq. (9). Then the volumetric mass ¯ux througheach control surface can be obtained. Eqs. (12) and (13)are solved using this volumetric mass ¯ux alreadyobtained and the resin viscosity is updated for the next

Fig. 3. The shape of the element used in numerical simulation. An

element is divided into four sub-volumes by the control surfaces.

Control volume i consists of sub-volumes from every element which

surrounds node i.

Fig. 2. Illustration of the ¯ow front advancing technique. According

to the ®lled fraction f, the entire calculation domain can be divided

into three categories. In this ®gure, solid and dashed lines represent

element and control volume boundaries, respectively (see Fig. 3).

Fig. 4. Flow chart of the numerical simulation procedure.


time step. Then, the ¯ow front advances until any con-trol volume on the ¯ow-front region is completely ®lledusing the volumetric mass ¯ux and the calculationdomain is rede®ned. In solving Eqs. (12) and (13), alarge truncation error might appear because the con-vection term is dominant compared to the di�usionterm. Also, because the Eqs. (12) and (13) are coupled,some iteration is required to solve these two equations.In order to settle this situation, the time step used forthe integration of Eqs. (12) and (13) should be smallerthan that for the ¯ow-front advancement (see Fig. 4)and hence Eqs. (12) and (13) could be linearized by anexplicit scheme. After the temperature and the degree ofcure at the current time step is calculated, the resinviscosity is updated. This procedure is repeated until theentire cavity is completely ®lled.Resin viscosity depends on the temperature and the

degree of cure as [21]:

� � �1 exp�E

RT� ��

� ��20�

The cure model adopted in this study is as follows[22]:

d�

dt� k1 � k2�

m1� � 1ÿ �� m2 �21�

where � represents the isothermal degree of cure and k1,k2 are expressed as

k1 � A1 exp ÿ E1

RT

� �; k2 � A2 exp ÿ E2

RT

� ��22�

From the isothermal degree of cure �, the degree ofcure � can be obtained.

� � HT

HU�

HT

HU� C1 � T� C2 T < TC� �;HU � HT T5TC� � �23�

where HT is the isothermal heat of reaction which isde®ned as the total amount of heat generated from timet � 0 until no evidence is found of further reactions at aconstant temperature and can be obtained from iso-thermal scanning measurement. The ultimate heat ofreaction HU is the amount of heat generated duringdynamic scanning till the completion of the chemicalreactions. The material properties used in this numericalsimulation were taken from the experimental results ofKang et al. [7]. The resin was vinylester (825 and 280 byNational Korea, Inc. with the mixing ratio of 7:3). Thevalues of the parameters required for Eqs. (20)±(23) areshown in Table 1. Other properties of the resin and ®berreinforcement used in this study are listed in Table 2.

5. Veri®cation of the numerical results

The validity of the numerical code was veri®ed withsimple problems for which the exact solutions were known.In order to verify the pressure ®eld, a steady resin ¯ow

through a cube where resin was injected from the frontsurface at constant pressure Po � 1� � is considered. Onthe other ®ve surfaces, the pressure was maintained atzero. In this case, the momentum equation [Eq. (1)] andthe continuity equation [Eq. (2)] can be combined toyield

Table 1

Curve ®t variables for the viscosity and cure model [see Eqs. (20)±(23)]

[7]

Viscosity model Cure model

�1 5.419�10ÿ5 Pa s A1 1.2483�1010 minÿ1�ER 3636.45 K A2 2.0433�1011 minÿ1

� 26.89 E1

R ÿ100048.4 KE2

R ÿ9505.58 K

m1 0.693

m2 1.327

TC 100�CC1 0.02639

C2 8.8466

Table 2

Properties of resin and ®ber mat used in RTM simulation [7]

Resin Fiber

�r 1030 kg/m3 �f 2540 kg/m3

cpr 1900 J/kg K cpf 835 J/kg K

kr 0.193 W/m K kf 0.76 W/m K

Kxx 1�10ÿ9 m2

Kyy 1�10ÿ9 m2

Kzz 1�10ÿ9 m2

Fig. 5. Three-dimensional pressure distribution along the centre line for

a cube. Comparison between the analytical solution and the numerical

results for three-dimensional steady ¯ow. Pressure of unity is applied

on one surface while the pressure is kept zero on other surfaces.


r� ÿ K� ��rP

� �� 0 �24�

If the permeability is isotropic and the viscosity isconstants Eq. (24) can be simpli®ed as

r2P � 0 �25�

Eq. (25) can be solved for a cube of unit size and thesolution can be found elsewhere as [23]:

P � 16

�2

X1i�0

X1j�0

sinh 1ÿ x� � sin 2i� 1� ��y� � sin 2j� 1� ��z� �2i� 1� � 2j� 1� � sinh 1� �

� ��26�

The exact solution was compared with the numericalsolution in Fig. 5 along the center line. Both solutionsagreed well, as shown in the ®gure.In order to validate the ¯ow front advancement

scheme, a one-dimensional advancement of the resinfront was considered. The resin was injected at one sur-face of the cube and air was ventilated at the oppositesurface. In this case, the resin ¯ow becomes one-dimen-sional. The exact solution for the ¯ow front location canbe obtained as [24]

x ��2KP0

�t

s�27�

Fig. 6. Veri®cation of the ¯ow front advancement scheme. One-

dimensional ¯ow in the cartesian coordinate system.

Fig. 7. Principle of the optical ®ber sensor. Before the resin reaches

the sensing spot, light can be transmitted through the optical ®ber but

leaks as soon as the resin reaches the spot.

Fig. 8. Typical signal from the optical ®ber sensor. The intensity of

the infrared light decreases sharply as the resin front reaches the sen-

sing bare spots on an optical ®ber.

Table 3

Refractive indices of air, resin and glass for l � 632:8 nm

Material Refractive

index

Mismatch with

glass ®ber (%)

Air 1.000293 ÿ35.6Water 1.3307 ÿ14.4Polyester resin 1.5556 0.13

Glass ®ber (silica core) 1.55365 0

Fig. 9. Experimental setup for the three-dimensional RTM mold ®ll-

ing process.


where P0 is the injection pressure, � is the viscosity,K is thepermeability, x is the location of the ¯ow front and t is time.In Fig. 6, the exact solution was compared with the numer-ical result. As can be seen, the agreement is very close.

6. Experiments

In order to further verify the numerical results, experi-ments were performed. There are several experimental

techniques to ®nd out the resin front location duringthe ®lling process such as ¯ow visualization techni-ques [25±27], the dielectric method [29], and amethod using thermocouples [30]. In these techniques,sensors are mainly installed on the mold surface. As aconsequence, resin ¯ow only along the mold wall can bemonitored and hence these methods are inappropriateto ®nd out the ¯ow front location inside the ®ber pre-form. In this study, the optical ®ber was used to moni-tor the ¯ow of the resin inside the thick ®ber preform[28].

6.1. Principle of the ®ber-optic sensor

Optical ®ber consists of core and cladding. The core isthe path of light and the cladding is the mechanicalprotection from outside impact. In this study, optical®bers with silica core and polymer cladding were used.First, a very shod section of polymer cladding wasremoved from the optical ®ber by burning or chemicaletching. The length of the bare spot is as short as 1 mm.Three or four bare spots were made consecutively alonga single ®ber, each bare spot serving as a sensor. Theoptical ®ber thus prepared was positioned inside the®ber preform. An infrared light signal was transmittedthrough the optical ®ber from one end and the intensityof the light signal was monitored on the other end. Beforethe resin reaches the bare spots along the optical-®bersensor, a relatively large light signal can be transmittedthrough the optical ®ber (see Fig. 7). However, as theresin reaches the bare spots, the light leaks throughthese bare spots because the refractive indices of theresin and the silica are close (Table 3) [31]. Therefore,the intensity of the transmitted light signal drops sig-ni®cantly and the arrival of the resin front can bedetected. A typical signal from the sensor is demon-strated in Fig. 8.

Fig. 10. The locations of sensing planes where optical ®ber sensors

were installed, between stacked ®ber preform inside the mold. The

inlet gate was placed at the centre of the bottom surface and the posi-

tions of the sensing spots are given in Table 4.

Fig. 11. Installation of the optical ®ber sensors on each plane shown

in Fig. 10. The positions of the sensing spots are given in Table 4.

Table 4

The locations of the optical ®ber sensors embedded inside the ®ber preform for the measurement of the three-dimensional ¯ow front location (see

Figs. 9±11)

Sensor 1 Sensor 2 Sensor 3 Sensor 4

x (mm) y (mm) x (mm) y (mm) x (mm) y (mm) x (mm) y (mm)

1st plane (z � 0:0 mm) 23.3 0.0 0.0 23.3 ÿ23.3 0.0 0.0 ÿ23.346.6 0.0 0.0 46.6 ÿ46.6 0.0 0.0 ÿ46.670.0 0.0 0.0 70.0 ÿ70.0 0.0 0.0 ÿ70.0

2nd plane (z � 10:2 mm) 0.0 0.0 0.0 0.0

23.3 0.0 0.0 23.3

46.6 0.0 0.0 46.6

3rd plane (z � 19:6 mm) 0.0 0.0 0.0 0.0

23.3 0.0 0.0 23.3

46.6 0.0 0.0 46.6

4th plane (z � 29:0 mm) 0.0 0.0


6.2. Three-dimensional permeability measurement

The three-dimensional permeability must be knownfor the three-dimensional RTM mold-®lling analysis.The three-dimensional permeability was measured usingthe optical-®ber sensors described above.First, the optical-®ber sensors were embedded in the

®ber preform at designated locations (see Figs. 10 and11). The optical ®ber used in this experiment was amultimode ®ber (CeramOptec, HWF 200/230/500T)which can transmit the light of a wavelength between0.4 and 2.4 mm. The cubic mold cavity was closed andthen resin was injected from the inlet gate at the centerof the bottom surface. As the permeability is aniso-tropic, the shape of the resin front is known to be ellip-soidal [28]. As the resin reached the sensor point, thesignal from the photo detector changed sharply and thetime to the sensing point was recorded. Once the times forthe resin front to reach the speci®c locations are measured,the three-dimensional permeability can be estimatedfrom curve-®tting to the following equation [28,29].

Fig. 12. Typical signals from the optical ®ber sensors. The voltage

outputs are obtained from photo-detector sensors after proper signal

conditioning.

Fig. 13. Dimensionless front locations along x, y and z direction versus the modi®ed time. Experimental data are curve-®tted to a line to yield the

permeability values [see Eq. (27)].


1

3�3fi ÿ

1

2�2fi �

1

6� �i i � x; y; z �28�

where �fi � rir0i

and �i � KiP0t�"r2

0i

. ri is the resin-front loca-

tion and r0i is the radius of the inlet gate. P0 is the inletpressure and t is the time for the resin front to reach aspeci®c sensor location. � is the resin viscosity and " isthe porosity of the ®ber preform.The experimental setup is shown in Fig. 9. A halogen

lamp was used for the infrared light source. A photo-transistor (Opto Electronics, ST-1KLA) was used forthe detection of the intensity of the infrared light. Thevoltage signal from the photo transistor was ampli®edand then recorded by a data acquisition system(Advantech, PCL-812PG). In this study, three barespots per optical ®ber were prepared. Fig. 10 illustrateshow the optical ®bers were placed inside the preform.

Ten glass-®ber mats were stacked between each sensingplane. A total of 54 chopped-strand mats were laid up.In the ®rst sensing plane, four optical ®bers were placedin the x and y directions. Thus, there were 12 sensingpoints in the ®rst plane. In the second and third planes,two optical ®bers were installed and, in the fourth plane,only one optical ®ber was used with one bare spot.Therefore, the number of sensing points was 25 in oneexperiment. The sensing point locations are shown inTable 4 and Figs. 10 and 11.In order to measure the pressure at the inlet gate, a

pressure transducer (Sea Systems, Model C208) wasused. The box-shape mold cavity was constructed of 30mm thick aluminum plates. The mold was designed tochange the cavity height so that the ®ber-volume frac-tion can be changed. The resin was pressurized bycompressed nitrogen and the inlet-gate pressure wascontrolled by a pressure regulator.Automobile engine oil (LG Caltex, SAE 7.5W/30,

viscosity=0.29 Pa s at 25�C) was used for the perme-ability measurement. The pressure at the inlet gate was0.142 MPa. The ®ber reinforcement used in this studywas a glass-®ber chopped-strand mat (LG Owens-Corning, CM450-723, 450 g/m2). The ®ber-volumefraction was 20.9%. The inlet-gate diameter was 1.70mm. In the chopped-strand mat, the ®bers are randomlyoriented, but all in the same plane. Thus the in-planepermeability can be assumed to be isotropic and theout-of-plane principal permeability is perpendicular tothe plane of the ®bers [28].

Fig. 14. Locations of the sensor points. At these locations, results of

numerical simulation and the experimental data are compared in Table 5.

Fig. 15. Three-dimensional RTM mold ®lling pattern at di�erent

times. Result of numerical simulation to be used for the comparison

with the experimental data (see Table 5).

Table 5

Comparison between numerical simulation and experimental results

by the optical ®ber sensora

Sensing points

number

Experiment

(s)

Simulation

(s)

Error

(s)

Error

(%)

Sensor 1 Sensor 2

1 2.5 2.5 2.6 0.1 4

2 21.9 23.5 23.3 0.2±1.4 0.9±6.4

3 76.1 83.3 79.8 3.5±3.7 4.2±4.9

4 3.8 4.7 3.3 0.5±1.4 13.2±29.8

5 31.3 32.6 29.3 2.0±3.3 6.4±10.1

6 96.1 93.6 100.6 4.5±7.0 4.7±7.5

7 1.6 1.6 0.7 0.9 56.3

8 6.9 5.9 1 14.5

9 33.5 29.7 3.8 11.3

10 10.3 7 3.3 32

11 45.1 36.4 8.7 19.3

12 10.3 9.7 9.5 0.2±0.8 2.1±7.8

13 18.8 18.6 0.2 1.1

14 45.1 47.7 2.6 5.8

15 20.1 20 0.1 0.5

16 64.8 55.4 9.4 14.5

17 34.4 35.1 0.7 2

a The locations of the sensing points are shown in Fig. 14.


Fig. 16. Results of mold ®lling simulation for a cubic shape. The inlet gate was located at the centre of the front surface. Pressure distributions (b),

temperature distributions (c), degree of cure distributions (d) and ®lling time (e) are shown at three di�erent cross-sectional planes along the thick-

ness as described in (a).


Fig. 17. Results of mold ®lling simulation for the thick slab with a pit and a projection. The inlet gate was located at the centre of the hollow pit.

Pressure distributions (b), temperature distributions (c), degree of cure distributions (d) and ®lling time (e) are shown at di�erent cross-sectional

planes along the y and z directions as described in (a).


Typical output from the sensor during the experimentsis shown in Fig. 12. From the voltage-output data, thetime of resin-front arrival at each sensing point can bemonitored. Based on Eq. (23), the three-dimensionalpermeability was obtained (see Fig. 13). As was expec-ted, kxx is identical to kyy, assuring that the in-planepermeability is isotropic.

6.3. Comparison between experimental and numericalresults

It is noted that once the resin front reaches the moldboundary, the exact solution as used in the permeabilitymeasurement is not valid. Using the measured perme-ability, numerical simulation was performed for thesame geometry described above. Sensor location areshown in Fig. 14. Only a quarter is displayed in this®gure because of the symmetry of the geometry. Thesensing points 1±6, 7, 12 have extra experimental resultsbecause there were two sensors at the same location.The numerical results are displayed in Fig. 15. Com-parisons between the two results are shown in Table 5.

The absolute error in ®lling time was within 9.4 s wherethe time to ®ll the entire cavity was 100.6 s. Compara-tively close agreements are found.

7. Practical applications of the computer code

Numerical calculations were done for four di�erentgeometries to demonstrate the e�ectiveness of the com-puter code developed in this study. First, a simple cubic-shaped preform (10 cm�10 cm�10 cm) was ®lled withan injection gate at the center of the front surface. Thetotal numbers of nodes and elements were 1331 and5000, respectively. The injection pressure was 1.0 MPaand the injection temperature was 25�C. The preformwas preheated to 70�C. The locations of the air ventswere expected to be at the four vertices of the oppositesurface as these were the farthest points from the gate.However, the results showed that the vent hole wasrequired at the center of the opposite surface. This wasbecause the heat transferred from the heated moldlowered the resin viscosity near the wall and thus made

Fig. 18. Results of mold ®lling simulation for automobile head lamp bezel. Resin was injected at two points. Pressure distribution (a) and ®lling time

(b) are shown along the boundary surface.


the ¯ow along the wall easier [see Fig. 16(e)]. The tem-perature distribution is illustrated in Fig. 16(c). As canbe seen, the temperature near the wall is higher.The second geometry considered was a thick slab (20

cm�10 cm�4 cm) with a pit (6 cm�4 cm�2 cm) and aprojection (6 cm�6 cm�2 cm) as illustrated in Fig. 17a.The number of discretized cubic ®nite elements was4120. Numerical results are shown in Fig. 17(b)±(e). Theresin was injected at the location where the thicknessis the least and the inlet pressure was 0.7 MPa. Thetemperature of the injected resin was 25�C and roseimmediately to the mold temperature 70�C afterinjection, as injection was done at the thinnest part ofthe cavity and the heat from the hot mold wall wastransferred well to the resin [see Figure 17(c)]. Thismeans that the resin viscosity was lowered and the ®ll-ing time was shortened.To check the e�ectiveness of this computer code fur-

ther, an automobile headlamp bezel was considered. Inthis example, resin was injected at two points. As shown

in Fig. 18(b), the locations of the ``weld lines'' as well asthe air vents could be predicted using the code devel-oped in this study. Next, the insert was replaced with athin hollow cavity without ®ber preform to allow easyresin ¯ow. Therefore, in place of a hole at the insert, athin resin membrane was formed after the molding. Thethin cavity allowed the ¯ow resistance to be lowered,resulting in a faster ®lling time compared with the casewith a hole [see Fig. 19(b)]. In the two example cases,the inlet gate pressure was 0.7 MPa, the inlet tempera-ture was also 25�C and the wall temperature was 70�C.The last numerical example was molding of a

centrifugal-pump casing (Fig. 20). This complicatedgeometry was discretized into 2035 nodes and 7874 ele-ments. The resin was injected from the inlet surface(surface gating) at 0.6 MPa. The temperature of theresin and mold was 70�C. The marks in Fig. 20(b) indi-cate the expected air-vent locations where two ¯owfronts met each other. These simulation results can beused for the design of the RTM mold.

Fig. 19. Results of mold ®lling simulation for automobile headlamp bezel with membrane. Resin was injected at the centre of the hollow membrane.

Pressure distribution (a) and ®lling time (b) are shown along the boundary surface.


8. Conclusions

A numerical code for the RTM process was developed.Three-dimensional analyses of resin ¯ow were performedincluding the non-isothermal e�ect and conversion dis-tribution. In the simulation of the RTMprocess for thickerparts, the necessity of three-dimensional analysis was illu-strated by sample runs. Using optical-®ber sensors, the¯ow-front location was monitored and the three-dimen-sional permeability was measured. Numerical and experi-mental results were also compared. Close agreements werefound.Numerical simulationswere done for some practicalcases to illustrate the e�ectiveness of the numerical code.

Acknowledgements

This work was supported by the Turbo and PowerMachinery Research Center and the Ministry of Scienceand Technology.

References

[1] Coulter JP, GuÈ cË eri SI. Resin impregnation during the manu-

facturing of composite materials. CCM report no. 88-07, Uni-

versity of Delaware, 1988.

[2] Chan AW, Hwang ST. Modeling of impregnation process during

resin transfer molding. Polym Eng Sci 1991;31:1149±56.

[3] Um MK, Lee WI. A study on mold ®lling process in resin trans-

fer molding. Polym Eng Sci 1991;31:765±71.

[4] Yoo YE, Lee WI. Numerical simulation of the resin transfer

mold ®lling process using the boundary element method. Polym

Compos 1996;17:368±74.

[5] Bruschke MV, Advani SG. Filling simulation of complex three

dimensional shell-like structures. SAMPE Quart 1991; October;

2±11.

[6] Lin R, Lee LJ, Liou M. Non-isothermal mold ®lling and curing

simulation in thin cavities with preplaced ®ber mats. Intern

Polymer Processing VI 1991;4:356±69.

[7] Kang MK. Mold ®lling and curing simulation in non-isothermal

resin transfer molding. Master's thesis of mechanical engineering,

Seoul National University, 1993.

[8] Young WB. 3-Dimensional nonisothermal mold ®lling simula-

tions in resin transfer molding. Polym Compos 1994;15:118±

27.

Fig. 20. Filling time distribution for a centrifugal pump casing. The resin was injected at the rear surface. The dot marks represent the expected vent

locations.


[9] Phelan FR. Simulation of the injection process in resin transfer

molding. Polym Compos 1997;18:460±76.

[10] Varma RR, Advani SG. Three-dimensional simulations of ®lling

in resin transfer molding. Advances in ®nite element analysis in

¯uid dynamics (ASME), 1994;200:21±7.

[11] Lam YC, Joshi SC, Liu XL. Application of a general-purpose

®nite element package for numerical modelling of resin ¯ow

through ®brous media. International Conference on Advances in

Materials and Processing Technologies (AMPT-4) Proceedings,

August 1998. p. 926±33.

[12] Dullien FAL. Porous media ¯uid transport and pore structure.

Academic Press, 1979. p. 157±9.

[13] Kamal MR, Sourour S. Kinetics and thermal characterization of

thermoset resin. Polym Eng Sci 1973;13:59.

[14] Baliga BR, Patankar SV. Handbook of numerical heat transfer.

John Wiley & Sons, Inc., 1988. p. 421±61.

[15] Hirt CW, Nicholas BD. Volume of ¯uid (VOF) method for the

dynamics of free boundaries. J Computational Physics,

1981;39:201±25.

[16] Broyer E, Tadmor Z, Gut®nger C. Israel J Technology

1973;11:189.

[17] Tadmor Z, Broyer E, Gut®nger C. Polym Eng Sci 1974;14:660.

[18] Broyer E, Gut®nger C, Tadmor Z. Trans Soc Rheol 1975;19:423.

[19] Tucker CL. Fundamentals of computer modeling for polymer

processing. New York: Hanser Publishers, Oxford University

Press, 1989.

[20] Ferziger JH. Numerical methods for engineering application.

Wiley-Interscience, 1981.

[21] Lee WI, Loos AC, Springer GS. Heat of reaction, degree of cure

and viscosity of Hercules 3501-6 resin. J Compos Mater

1982;16:510±20.

[22] Dusi MR, Lee WI, Ciriscioli PR, Springer GS. Cure kinetics and

viscosity of Fiberite 976 resin. J Compos Mater 1987;21:243±61.

[23] Carslaw HS, Jaeger JC. Conduction of heat in solids. Oxford

University Press, 1959.

[24] Cai Z. Analysis of mold ®lling in RTM process. J Compos Mater

1992;26:1310±38.

[25] Adams KL, Miller B, Rebenfeld L. Forced in-plane ¯ow of epoxy

resin in ®brous networks. Polym Eng Sci 1986;26:1434±41.

[26] Adams KL, Rebenfeld L. Permeability characteristics of multi-

layer ®ber reinforcements. Part I: experimental observations.

Polym Compos 1991;12:179±85.

[27] Chan AW, Hwang ST. Anisotropic in-plane permeability of fab-

ric media. Polym Eng Sci 1991;31:1223±39.

[28] Ahn SH, Lee WI, Springer GS. Measurements of the three

dimensional permeability of ®ber preforms using embedded ®ber

optic sensors. J Compos Mater 1995;29:714±33.

[29] Aklonis JJ, MacKnight WJ. Introduction to polymer viscoelas-

tieity. John Wiley & Sons, Inc., 1983.

[30] Beckwith TG, Marangoni RD, Lienhard VJH. Mechanical mea-

surements. Addison-Wesley Publishing Company, 1995.

[31] Hecht E. Optics. Addison-Wesley Publishing Company, 1987.


an analysis of the three-dimensional resin-transfer mold filling process

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