JOURNAL OFCOMPOSITE
M AT E R I A L S

ArticleGate optimization for resin transfer
molding in dual-scale porous media:
Numerical simulation and experimentmeasurement

Journal of Composite Materials
2020, Vol. 54(16) 2131–2145! The Author(s) 2019
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DOI: 10.1177/0021998319890122
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Yutaka Oya1 , Tsubasa Matsumiya1, Akira Ito1,
Ryosuke Matsuzaki2,3 and Tomonaga Okabe1,4

Abstract
For resin transfer molding in a woven fabric, this study developed a novel framework for optimization by combining a multiobjective genetic algorithm and mold-filling simulation including a void-formation model, which gives us not only the spatial
distribution of the mesoscopic and microscopic voids but also the correlations between molding characteristics such as filltime, total amount of void, weld line, and wasted resin. Our experiment observation of one-point radial injection successfully
captured the anisotropic distribution of mesoscopic voids, which qualitatively validates the simulated result. As a result ofmulti-objective optimization for an arrangement of two injection positions, we found the trade-off relations of weld line withthe other characteristics, which also have positive correlation with each other. Furthermore, visualization techniques such as
self-organizing maps and parallel coordinate maps extracted the design rule of the arrangement. For example, a diagonal gate
arrangement with an appropriate distance is required for reducing the both total amount of voids, fill time, and wasted resin;
however, the total area of the weld line becomes relatively large. Our framework and the knowledge obtained from thisstudy will enable us to determine the appropriate mold design for resin transfer molding.

Keywords
Finite element analysis, resin transfer molding, multi-objective optimization

Introduction
In the past few decades, fiber-reinforced plastic (FRP)
has been widely used for structural parts in the aerospace
and automobile fields, due to their high specific strengthand stiﬀness.1 Resin transfer molding (RTM) has become
an attractive process for manufacturing a large number
of FRPs because of its high eﬃciency and low cost compared to conventional autoclave molding. In RTM, lowviscosity resin is usually injected into preplaced reinforcement material where a random fiber mat and a woven
fabric are commonly used as the reinforcement.
Although a random mat is an isotropic media for fluid,
woven fabric has a microscopic flow path inside the fiber
bundle in addition to an inter-bundle region; thus, it is
known as dual-scale porous medium.2–7 The velocity difference between the intra-bundle and inter-bundle paths
causes air entrapment (void), which degrades the mechanical properties of the FRP.8,9 If the velocity of theintra-bundle (inter-bundle) region exceeds that of theinter-bundle (intra-bundle) region, a void is generated
in the inter-bundle (intra-bundle) region. A void
formed in the inter-bundle region is known as a mesoscopic void, whereas air entrapment inside the fiber
bundle10–13 is known as a microscopic void. It should
be noted that a macroscopic void (also called a dry
spot10,14) is a dry region where the fabric is not
1

Department of Aerospace Engineering, Tohoku University, Japan
Department of Mechanical Engineering, Tokyo University of Science,Japan
3
Institute of Fluid Science, Tohoku University, Japan
4
Department of Materials Science and Engineering, University ofWashington, USA
2

Corresponding author:
Yutaka Oya, Tohoku University, 6-6-01 Aramaki-Aza-Aoba, Aoba-ku,
Sendai, Miyagi 980-8579, Japan.
Email: oya@plum.mech.tohoku.ac.jp

2132

Journal of Composite Materials 54(16)impregnated by resin in either the inter- or intra-bundle
regions. This velocity diﬀerence comes from a diﬀerent
dominant force in each flow path. Flow in the interbundle region is driven mainly by viscous force, whereas
capillary force is dominant in the intra-bundle region.
Therefore, the flow in each path should be considered
independently.
Several researchers have investigated resin flow in theintra-bundle flow path.15–18 Foley et al.15 conducted a
numerical simulation inside the fiber bundle and demonstrated that surface tension, contact angle, and fiber
diameter strongly aﬀect the rate of impregnation into
the fiber bundle. These parameters are not usually considered in the macroscopic governing equation (Darcy’slaw). In an eﬀort to reproduce advancement of resin in
the intra-bundle region, Kang et al.11 modified Darcy’s
law by considering the capillary eﬀect. They developed amathematical model based on the experiment result toanalyze void formation. Their experiment result confirmed that the void content was related to the modified
capillary number Ca! , which is expressed as
Ca! ¼

!U
" cos #

ð1Þ

where ! is resin viscosity, U is global resin velocity, " isthe surface tension of the resin, and # is the contact angle
between the resin and the fiber fabric. Garcia et al.19
simulated distribution of microscopic and mesoscopic
voids by two phase flow models of air and resin. Parket al.12 proposed the void formation model in consideration of woven fabric structure of reinforced mat. Theyevaluated void content based on the time diﬀerence inresin impregnation between the inter-bundle and intrabundle regions and agreed well with experiment data.
This model also enables us to evaluate void contents
depending on tow orientations. Matsuzaki et al.20 also
conducted a unidirectional experiment to obtain themesoscopic void contents of woven fabric on the basisof a diﬀerent concept from Park et al.
In order to extract optimum molding conditions, it isimportant to predict distribution of microscopic andmesoscopic void depending on structure of woven
fabric. For predicting the distribution of voids, flow-filling simulation combined with void formation model proposed by Park et al.12 is an eﬀective way. In this study, we
combined this void-formation model with resin filling
simulation based on finite element method (FEM). This
study also conducted experiments of one-point radial
injection to compare simulated distributions of mesoscopic voids. Furthermore, to obtain appropriate molding conditions establishing both productivity and quality,
the framework of multi-objective optimization (MOO) is
newly developed as the combination of this filling simulation and the gene algorithm (GA) to search global

optimum solutions (Pareto solutions) for multi-disciplinary characteristics.21–23 This study considers the twodimensional square system and an arrangement of twoinjection positions of resin as a design variable. For
industrial application, the multi-injection location has
been considered an eﬃcient way to increase the productivity of RTM; however, conjunction of resin flows from
diﬀerent injection locations induces another defectknown as weld line. Therefore, total voids (sum of mesoscopic and microscopic voids), filling time, wasted resin,
and weld line are adopted as objective functions to beminimized for optimization. The correlation among
objective functions and design rule of gate location are
extracted using a clustering approach known as a selforganizing map (SOM).24 This manuscript is organized
as follows. Section Numerical Procedure describes thedetails of the numerical method of the void-formation
model, resin filling simulation, and MOO. Section
Experiment Method discusses the experimental procedure for extracting the inherent characteristics of the filling
simulation and validating the void-formation model as aradial injection. Section Result and Discussion presents
the results and a discussion, demonstrating the eﬃciencyof our developed framework, and extracting the correlations among objective functions and the design rule of
the arrangement of injection positions.

Numerical procedure
We combined a numerical simulation with an existingvoid-formation model proposed by Park et al.12 The
finite-element/control-volume (FE/CV) method is used
to simulate flow advancement, and it is combined withthe void-formation model. We used four node isoparametric quadrilateral elements for FEM model. In thefollowing, we describe the procedure for the filling
simulation
andthevoid-formation
model.
Additionally, this section introduces the optimization
procedure. We used our original in-house codes forboth flow advancing simulation and MOO.

RTM filling simulation
In RTM, resin impregnates fabric at low speed (theReynolds number is usually much less than 1).
Therefore, resin flow can be described by Darcy’s law.
Since woven fabrics have dual-scale pores (inter- andintra-bundle), we considered two flow paths in a unit
cell model, which is illustrated in Figure 1. The red line
indicates the inter-bundle flow path, and the blue line
indicates the intra-bundle flow path. As mentioned in
the previous section, inter-bundle flow can be expressed
as usual by Darcy’s law; however, in intra-bundle flow
the capillary eﬀect should be considered, because of thesmall gap between fiber filaments. Therefore, resin flow

Oya et al.

2133

Figure 1. (a) Simulation unit cell of woven fabric. (b) Schematic diagrams of void formation models.

velocity for each flow path can be expressed as the following equations19,21
U ¼ %!

Kn" rPn
1 % Vf, c !

#
$
KT
Pcap
"
u ¼ %!
rPT %l
1 % Vf,t !

ð2Þ
ð3Þ

where U is the resin velocity in the resin impregnation
direction, Vf, c is the fiber volume fraction, Kn is the permeability of fabric in the resin impregnation direction,rPn is the pressure gradient of the impregnation direction, u is the resin velocity inside the fiber bundle, KT isthe permeability of the fiber bundle as defined by eachfiber direction, Vf,t is the fiber volume fraction of thefiber bundle, rPT is the pressure gradient decomposed
into each fiber direction, and Pcap is the capillary pressure. l is the length of the fiber bundle, and we used
constant values for l with weft and warp directions.12
These values are listed as ‘‘L’’ and ‘‘W’’ in Table 2. To
obtain the pressure and velocity distributions in the analytical model, equation (2) was coupled with the continuity equation for an incompressible fluid (i.e. thedivergence of the velocity is zero). The coupled equation
was solved under the following boundary conditions
P ¼ P0 at the resin inlet

P ¼ 0 at the flow front@P¼ 0 at the mold wall@nperpendicular to the mold wall. Details of the numerical procedure are given in our previous paper.25 The
impregnation direction of the resin flow can be determined using equation (5)$ ¼ tan%1ð5Þ

where $ is the impregnation angle of the resin, Uy is they-axis velocity, and Ux is the x-axis velocity. This angle
is used to determine the decomposed pressure gradientused in equation (3), and rPT can be calculated fromthe pressure gradient of the impregnation direction
using equation (6)rPT ¼ rPn cos $ ðfor warp directionÞ
rPT ¼ rPn sin $ ðfor weft directionÞ

ð6Þ

The capillary pressure that appears in equation (3) isexpressed as12
Pcap ¼# $FVf,t" cos #
df 1 % Vf,t

ð7Þ

where F is a shape factor determined by the experimentand df is the fiber filament diameter. The impregnation
times for both flow paths can be obtained by integrating equations (2) and (3) over time, as expressed below

ð4ÞHere, P is the resin pressure, P0 is the prescribedinjection pressure, and @P@n is the pressure gradient

# $
Uy
Ux

!T ¼
!t ¼

%
#
$&
Pcap
l & rPT1þln
1%l & rPT
Pcap& K!T & rPT
l

1
1%Vf, T

L
Kn
1
1%Vf, c & ! & rPn

ð8Þ
ð9Þ

2134

Journal of Composite Materials 54(16)Here, !T is the travel time for the inter-bundle path,
L is the length of the inter-bundle path, and !t is thetravel time for the intra-bundle path. The presence ofvoids is determined from the time diﬀerence between
the two flow paths and will be discussed in detail in
the next section.

Void-formation modelThis section presents a brief overview of the void-formation model proposed by Park et al.12. The diﬀerencein travel times of the flow between inter- and intrabundle regions determines the volume fraction of mesoscopic or microscopic voids. Figure 1(b) presents aschematic diagram of these formations for mesoscopic
and microscopic voids. When the travel time of theinter-bundle flow calculated by equation (8) is shorter
than that in the fiber bundle calculated by equation (9),voids form in the fiber bundle (microscopic voids). In
contrast, voids between fiber bundles (mesoscopic
voids) form in the opposite case. The unimpregnatedarea is considered to be proportional to these time differences. If the total flow does not coincide with theorientation of the fiber bundle, the pressure gradientmust be decomposed in the longitudinal and transverse
directions with respect to the fiber bundle. Based onthese assumptions, mathematical formulations for thevoid-formation model are given below.
'(!tT, wp ¼ min !tx, T, wp , !ty, T, wp'(!tC, wp ¼ min !tx, C, wp , !ty, C, wp

ð10Þ

Here, the void fractions for the warp are formulated.
The impregnation time in the warp and the flow time inthe channel region along the warp are determined asfollows
When !tT, wp 4 !tC, wp , microscopic voids form andthe portion of unimpregnated region is estimated by#$ #$!tC, wp!tC, wp
jT, wp ¼ hv, T, wp & 1 %& 1%!tx, T, wp!ty, T, wp
ð11Þ
where hv, T, wp is a structure factor of microscopic voids,
which is determined by observation of voids. For!tT, wp 5 !tC, wp , microscopic voids form, and the portion of unimpregnated region is estimated by#$ #$!tT, wp!tT, wp
jC, wp ¼ hv, C, wp & 1 %& 1%!tx, C, wp!ty, C, wp
ð12Þ
where hv, C, wp is a structure factor. Equations (11) and (12)give the volume fraction of voids, which is proportional tothe diﬀerence between impregnation times in the inter- andintra-bundle regions. Using almost the same formulations,the portion for the weft can also be estimated.
Finally, the void fractions for mesoscopic and microscopic voids are estimated by considering the volume
fraction of a tow for a unit cell and that of a fiber for atow. The mesoscopic void fraction emerging in theinter-bundle region is obtained as
Va, C ¼"
jC, wp & vwp þ jC, wt & vwt !
1 % vwp % vwt
vwp þ vwt

ð13Þ

where vwp is the volume fraction for warp and vwt is thatfor weft. In contrast, the microscopic voids inside tow
regions are represented by!
"Va, wp ¼ jT, wp & vwp & 1 % Vf, wp!
"
Va, wt ¼ jT, wt & vwt & 1 % Vf, wt

ð14Þ

where Vf, wp is the fiber volume fraction for warp andVf, wt for weft. Our study investigated void fractions
calculated using equations (13) and (14). However,some additional considerations are necessary to reproduce the actual void formation process in RTM.
Compression of voids is an especially important phenomenon. In this study, the compression phenomenon
during void formation is also implemented, and thevoid fractions obtained by equations (13) and (14) are
improved to better values. The formulation of the compression phenomenon is described below.
The compression phenomena of voids occur under
the influence of the resin pressure around them. They
are considered for both mesoscopic and microscopic
voids and are calculated in diﬀerent procedures. Once
formed at the flow front of the resin, mesoscopic voids
continue to be compressed over time, due to the resinpressure around them. When the temperature of theresin is constant, the mesoscopic void fraction can be
updated by considering the law of ideal gas as follows
Va, C ðx, y, t þ !tÞ ¼

Pðx, y, tÞ
Va, C ðx, y, tÞPðx, y, t þ !tÞ

ð15Þ

where !t is a time step.
After microscopic voids form in the fiber bundle,
they are compressed not only by the surrounding
resin but also by the capillary pressure generated in
the fiber bundle. The capillary pressure has a considerable eﬀect on the surrounding resin flow and causes
resin flow into the fiber bundle when the microscopic
voids are compressed. Since the actual cross-section of
the fiber bundle is elliptical (Figure 2), only the thickness direction of the resin flow into the fiber bundle isconsidered (the flow in the planar direction is ignored).

Oya et al.

2135
direction. Here, Ae is the eﬀective area of the impregnated region and is approximated as
Ae ¼ llong & ltnan & jT ðtÞ

ð20Þ

These calculations are performed for warp and weft.
After updating the portion of the unimpregnated region
using equation (19), the microscopic void fraction after
compression is calculated by applying equation (14).
The compression is repeated until the sum of the surrounding resin pressure and the capillary pressure
within the fiber bundle is less than the pressure within
the microscopic void.

Multi-objective optimization

Figure 2. Schematic diagrams of microscopic void compression. (a) Before compression. (b) After compression.

The resin flow in the thickness direction into the fiber
bundle can be obtained from Darcy’s law as follows
utr ¼

KT P % Pa þ Pcap!
H % hað16Þ

where utr is the resin flow velocity in the thickness direction, Pa is the air pressure in the microscopic void, H
is the thickness of the fiber bundle, and ha is the thickness of the microscopic void. Here, ha is approximatedas follows using the portion of unimpregnated regionjT obtained by equation (11)ha ¼ H & jT

ð17Þ

Also, if the ideal gas law is applied, the pressure in
the microscopic voids can be obtained as follows
Pa ðt þ !tÞ ¼

jT ðtÞ
Pa ðtÞ
jT ðt þ !tÞ

ð18Þ

The portion of unimpregnated region after thetime step !t, jT ðt þ !tÞ, is calculated by updating asfollows
jT ðt þ !tÞ ¼ jT ðtÞ %2 & utr & Ae & !t!
" Pa ðtÞ
ð1 % Vf Þ & llong & ltnan & H

ð19Þ

where llong is the length in the longitudinal direction of
the fiber bundle and ltnan is the length in the transverse

In this study, the MOO problem was solved using a
genetic algorithm (GA). Since GA is a populationbased optimization approach, the possibility of converging to a local optimum solution is lower that with agradient-based method. Therefore, many previous studies adopted GA to optimize the injection locations.25–28 The values of the objective functions arecalculated for all sets of injection points obtained
from the multi-objective GA (MOGA). In this optimization, we considered four objective functions: filltime, weld line, total void fraction (total fraction ofmesoscopic and microscopic voids), and wasted resin.
These four objective functions are defined in FEM
simulation as follows. Fill time is the time required tofill all nodes with resin. In flow advancing simulation in
CV/FEM model, the length
P of weld line is calculated byðThelengthofweldlineÞ ¼ i fi& Vi , where i is the node
number, f is the fill fraction of resin, and V is thearea of the control volume element.25 When two flow
fronts simultaneously fill node i with opposite directions, we added value of fi& Vi to the length of weldline. Total void fraction is defined as the average mesoscopic void and microscopic void fractions of the analytical model domain obtained using equations (13) and(14). Wasted resin is the quantity that bleeds out fromthe prescribed vent nodes. Based on our previous
study,25 the dry spot is proportional to the wasted
resin; therefore, the dry spot is not added to the objective function. In addition, solutions with more than 1%
dry spots are eliminated as candidates for Pareto solutions. Hence, the obtained Pareto solutions have few
dry spot areas. In this case, all objective functions
should be minimized to optimize the process conditions. Since there are four objective functions, it is difficult to find an optimal solution that is superior toother solutions in terms of all objective functions.
Thus, in this study Pareto solutions are sought instead.
A Pareto solution is defined as a solution in which one
objective function cannot be improved without

2136

Journal of Composite Materials 54(16)Figure 3. Flowchart of filling simulation with optimization.

degrading other objective functions and there are noother solutions that are superior in all objective functions. To find the Pareto solutions, a Pareto ranking
method was used. With this method, all solutions areranked as followsrankðiÞ ¼ 1 þ n

ð21Þ

where i is the solution number and n is the number ofother solutions that are superior to the ranked solution
in all objective functions. A solution having rank ¼ 1 isregarded as a Pareto solution.
The design variables of the MOO problem are thetwo injection locations, and an FEM element is used toexpress the gate (i.e. the injection radius is equal to theelement size). Therefore, variation range in gate location is same as element size. Figure 3 presents a flowchart of our simulation. As shown in the figure, we

obtained Pareto solutions of injection location by calculating GA and resin-filling simulation alternatively.
We used GA through a real-encoded algorithm.21 Thisalgorithm gives us optimized injection locations as continuous coordinates. On the other hand, an injection
location for resin filling simulation is positioned at
the center of an element in FEM model, and can takeposition discretely. For the gate of the resin-filling
simulation, we selected the element that has the closest
position to the optimized injection location. Therefore,
slight diﬀerences exist between the obtained design variables and the simulated injection locations. However,
we consider these diﬀerences to be small enough toneglect. For the parameters in MOGA, the crossover
rate was 1.0, and the mutation rate was 0.1. The crossover and the mutation processes generate optimized
injection locations both inside and outside the model.
We rejected injection location outside the system toOya et al.
avoid unrealistic solution. We continued the MOGA
until we reached 150 generations. In each generation,
40 new genes were added. Figure 3 presents a flowchartof our simulation.

Experiment method
In this study, we conducted an RTM experiment andmolded FRP in addition to analytical investigations.
The two purposes of the experiment were determinationof the permeability of the global flow for fiber preformand qualitative validation of the distribution of the void
fraction for molded FRP. In this section, we discuss the
setup of equipment for the RTM experiment, themethod to determine permeability, and the procedure
to observe voids.

Resin injection experiment and determinationof permeability
To determine the permeability for global flow, we conducted one-point radial injection in fabric. Figure 4(a)is a schematic diagram of the experiment apparatus,and Figure 4(b) is a photograph of the mold that was
actually used. There is a gate at the center of the mold,and a vent is provided near the corner of the mold. The
mold consisted of two 25 cm ( 25 cm transparent glass
plates and two plates were connected using a sealanttape to seal the inside of the mold. Before sealing themold, it was necessary to place the fiber preform as
reinforcement for FRP in the mold (preforming). In
this study, we adopted a plain-woven glass fiber preform as reinforcement; it was cut into 18 cm ( 18 cm soas to match to the size of the mold. Glass fiber preforms
have been used in many studies that conducted permeability measurement experiments.29–31 A commerciallyavailable polyester resin was set on the gate side after
mixing with a suitable curing agent.
To inject the resin, the pressure inside the mold must
be lower than the pressure at a gate. Therefore, in thisstudy, a vacuum pump was connected to the vent side,and negative pressure was applied to the mold to generate a pressure gradient. A regulator was connected
between the vacuum pump and the vent, and the negative pressure was set at 50 kPa, which is the same as theinjection pressure that we applied in the simulation.
The resin was then injected under constant pressure.
This experiment was performed at room temperature(298 K) so as to delay curing of the resin.
To determine the permeability, it is necessary to
track the advancement of the flow front position of
the resin with the lapse of time. Using a transparent
glass plate for the mold, we can capture the behaviorof the resin in the mold using a video camera set at the
top of the mold. From the relationship between the2137
time and the flow front position taken by the video
camera, permeability is calculated by the following
equation32
Kn ¼

o
i
!ð1 % Vf Þ h 2 n )x*
x 2 ln% 1 þ r2
4t!P
r

ð22Þ

where Kn is the permeability in the global flow, t is theelapsed time, x is the distance from the gate, and r is theinjection radius. Immediately after the start of injection, the calculated permeability is unstable; however,its value becomes almost constant as time elapses. The
permeability measured in the experiment is used for thefilling simulation.

Observation of mesoscopic voids
After performing the resin injection experiment, theresin impregnated in the fiber preform cured at room
temperature. In the case of RTM, it means that molding of FRP is completed at the time when curing of theresin is completed. After curing, the molded glass fiber
reinforced plastic (GFRP) is removed from the mold.
In the mesoscopic void observation, we used digitalmicroscope (model VH-5500; Keyence Co. Ltd.,
Osaka). The window size is 2.95 mm ( 2.36 mm. In
order to observe voids generated by the air entrapment,
the surface of GFRP was observed. However, it is difficult to examine all void distributions in GFRP.
Figure 4(c) represents observation points at 10 mm,
30 mm, and 50 mm from injection point for warp andweft directions.

Result and discussion
Numerical test for distributions in mesoscopic andmicroscopic voids by unidirectional flow
To verify the validity of our numerical analysis, RTM
filling simulation for simple unidirectional flow was carried out. In the model shown in Figure 5(a), element
size is (12.5 mm)2 and total element number is 3200.
Unidirectional flow was realized by replacing all elements at the left edge of the simulation model with gates
and those at the right edge with vents. The distance
between gate and vent was set to 1 m. Table 1 lists
the material properties used for resin, and Table 2
lists those for fabric. Figure 6 plots the relationshipbetween the void fraction and the distance from thegate obtained by our analysis Figure 6(a) and analysis
by Park et al. Figure 6(b).12 Several parameters (e.g.
permeability) used in our analysis were obtained byfitting in order to conform to the analysis conditionsof the thesis.12 Our results are in good agreement withthose of Park et al.

2138

Journal of Composite Materials 54(16)Figure 4. (a) Schematic diagram of the set-up of the RTM experiment. (b) Picture of mold. (c) Schematic diagram of the observation
points of a mesoscopic void.
RTM: Resin transfer molding.

Figure 5. Simulation models of filling simulation. (a) Rectangle model for uniaxial injection. (b) Square model for radial injection.

Our results (Figure 6) provide us with some important suggestions for void formation. First, no mesoscopic voids are generated near gates, because theglobal flow near the gate is faster than the flow in theintra-bundle. As the distance from the gate increases,
the global flow becomes slower and the flow in theintra-bundle becomes faster. As a result, mesoscopic
voids form between the fiber bundles. However, many
microscopic voids are generated near the gate, and void
fraction decreases as distance from the gate increases.
This is because the flow in the intra-bundle is slow near
the gate, and air is confined in the intra-bundle. These
results confirm that the sum of the mesoscopic void

fraction and the microscopic void fraction is the smallest in the vicinity midway between the gate and thevent. In fact, the minimum total void fraction is
obtained 0.6 m from the gate. At that value, it isassumed that the global flow velocity is close to theflow velocity in the intra-bundle.
To obtain more general insight that does not dependon system size, the relationship between the generalmodified capillary number expressed by equation (1)and the void fraction was investigated. Figure 7 plots
the relationship between the modified capillary number
and the void fraction. As the modified capillary number
increases, microscopic voids increase and mesoscopic

Oya et al.

2139

Table 1. Resin properties used in this study.
Density % (kg/m3)
Viscosity ! (Pa&s)
Surface tension " (N/m)
Contact angle # (degree)

1100
0.15
0.031730

voids decrease; their magnitude relationship reverses at
0.0004. Since the order of the value is consistent withthe results published in many previous studies, we canconfirm again that this numerical simulation can accurately reproduce void formation.

Analysis of the distribution of mesoscopic andmicroscopic voids using one-point radial injection
Table 2. Fabric properties used in this study.
Fiber volume fraction of preform %f (%)
Fiber volume fraction inside warp
bundle Vf,wp (%)
Fiber volume fraction inside weftbundle Vf,wt (%)
Warp volume fraction &f,wp (%)
Weft volume fraction &f,wt (%)
Fiber diameter df (m)Longitudinal length of bundle L (m)Transverse length W (m)Height of bundle H (m)Global permeability of perform forx direction Kx (m2)Global permeability of perform fory direction Ky (m2)

58
64
64
45.3
45.3
1:4 ( 10%5
5:5 ( 10%3
4:5 ( 10%3
5:0 ( 10%4
7:0 ( 10%11
3:0 ( 10%11

Measurementof
permeability
in
an
RTM
experiment. Measurement of permeability in an RTM
experiment was performed three times. The part
impregnated with resin is symmetrical, so the vent position does not influence the direction of resin flow.
Table 3 lists the results for warp direction and weft
direction. Permeability in the warp direction diﬀer
from that in the weft direction. The diﬀerence in permeability is mainly due to the anisotropy of the glass
fiber mat. The thickness of the fiber bundle diﬀers
between the weft and warp directions, which causes
the permeability diﬀerence. Errors between the averagevalue and the measured value are within 15%, which iswithin the allowable range. A subsequent simulation
was carried out using these average permeability values.
Prediction of the distribution of void fractions using numericalsimulation. In this section, void distribution is investigated for one-point radial injection in plain-woven
fabric. The material properties are the same as those

Figure 6. Void fraction vs. distance from the gate. (a) This simulation. (b) Park et al.12

Figure 7. Void fraction vs. modified capillary number. (a) This simulation. (b) Park et al.12

2140

Journal of Composite Materials 54(16)Table 3. Global permeability obtained by RTM experiments of
one-point injection.

1
2
3
Averagevalue

Kx (m2)Ky (m2)Error(%) (Kx )Error(%) (Ky )2:10 ( 10%11
2:05 ( 10%11
1:66 ( 10%11
1:94 ( 10%11

5:33 ( 10%12
4:65 ( 10%12
4:21 ( 10%12
4:73 ( 10%12

11.89
9.23
%11.50
%

14.93
9.23
%11.50%

RTM: resin transfer molding.

in the above simulation (Tables 1 and 2), except for the
global permeability of the preform, which is adapted as
an experimental value. In the simulation of one-point
radial injection RTM, Figure 5(b) represents a squaremodel with a side of 180 mm, which is the same size asthat in our experiment. The size of each element is(3 mm)2. The number of elements of the FEM simulation is 3600, and the number of nodes is 3721. To matchthe experiment conditions, resin was injected fromthe center of the model, the boundary conditions
for the gate were imposed on the nodes corresponding
to the injection radius of 3 mm, and the vacuum pressure was set at 50 kPa. The element at the upper rightvertex of the model was set to vent. Figure 8 illustrates
the distributions of void fractions for mesoscopic andmicroscopic voids obtained by numerical simulation. In
this figure, red indicates higher void fractions and blue
indicates lower ones. One key feature in this figure issimilar to the result obtained in unidirectional flow: themesoscopic void fraction increases when the distancefrom the gate increases, whereas the opposite is true
for the microscopic void. This feature is consistent
with previous experiment studies.11
Since a constant-pressure injection strategy isapplied to the gate, the negative pressure gradientdecreases with the advance of the flow front. Basedon equation (2), resin velocity is proportional to pressure gradient; thus, decrease in the pressure gradient isrelated to low resin velocity. Near the gate, pressure
gradient was higher and the viscous force was dominant
in void generation; however, a low-pressure gradientwas found near the wall, and the capillary eﬀect
became dominant in this area. If the capillary force isdominant, the flow in the intra-bundle is faster thanthat in the inter-bundle; consequently, mesoscopic
voids occur. Therefore, the fraction of mesoscopic
voids increases with an increase in distance. With
one-point injection in the bulk case (the boundary of
the system is not considered), the distance from the gate
point is essential for void distribution. In contrast, withmulti-gate injection in a system with a boundary, void
distributions are assumed to be aﬀected by bothdistance and gate arrangement in the system becauseof acceleration of the flow due to conjunctions initiatedat the gates. In the following section, optimum (two)gate positions are investigated using the MOO method
where flow analysis is combined with GA.
Observation of void in GFRP. To validate the simulated distribution of mesoscopic voids, Figure 9 depicts the surfaces of molded GFRP at the observation points in
Figure 5(c). There is no mesoscopic void near the gate
for both warp and weft directions (left figures).
However, mesoscopic voids increase with distancefrom the injection point (center and right figures).
Furthermore, more mesoscopic voids are observed in
the weft direction than in the warp direction. The distance and orientation dependences of void formation
are consistent with our simulation result (Figure 8(a)).
Therefore, our simulation can qualitatively reproduce
the experiment. In this study, we observed only mesoscopic void content. In order to obtain distribution of
microscopic void distribution, we have to observe themicrostructure of the specimen with high resolution
method, such as X-ray computed tomography.33 To
observe microscopic void is one of our future tasks.

Gate optimization for two-point injection
The optimum gate position for RTM with the twopoint injection is determined by the MOO constructedin section Multi-objective optimization. As depicted in
Figure 5(b), two vents were placed at two-edge elementsin the diagonal direction. The design variables andobjective functions of the MOO problem are introduced in Section Multi-objective optimization. The
material properties are listed in Tables 1 and 2, andthe permeability and the vacuum pressure are thesame as those for the one-point injection describedabove. First, convergence of the optimization in GA
was checked. Figure 10 plots the relationship between
fill time and weld line for each generation. The black
dotted curve indicates the Pareto front over 150 generations. This figure indicates there are few Pareto front
movements from 100 generations to 150 generations;thus, the Pareto front has achieved convergence at
150 generations. Hence, our optimization suﬃciently
converged, and 150 generations were selected as the
maximum number of calculated generations for thisoptimization.
Figure 11 presents a scatter-plot matrix of 192
Pareto solutions obtained from the optimization
result. The values in this figure indicate Pearson’s coefficient, which represents the strength of correlation, andthe graphs present the correlation diagrams for eachobjective function. As Pearson’s coeﬃcient approaches
1, the relationship between two objective functions

Oya et al.

2141

Figure 8. Distributions of each void for radial injection. (a) Mesoscopic void. (b) Microscopic void (warp). (c) Microscopic
void (weft).

Figure 9. Observations of mesoscopic voids at different distance from the injection point. Figures from left to right are at 10 mm,
30 mm and 50 mm for (a) warp and (b) weft directions. Red circles denote representative mesoscopic voids.

Figure 10. Pareto solutions movement with respect togenerations.

Figure 11. Scatter plot matrix of objective functions. (Values
indicate Pearson’s correlation coefficient.)

2142
exhibits strong positive correlation; in contrast, as it
approaches –1, the relationship exhibits strong negative
correlation. A positive correlation was found between
fill time and wasted resin. Since wasted resin is analyzed
as the scalar product of the time and flow rate in ventnodes, any increment of fill time causes resin bleeding.
Hence, these relationships obtained from optimization
are reasonable. Fill time and total voids also had apositive correlation, because the global flow velocity
at the flow front decreases as time passes, causing theformation of mesoscopic voids. In contrast, negative
correlations were found between the weld line andtotal voids, and between fill time and weld line. These
negative correlations suggest trade-oﬀ relations thatlead not to global solution but to Pareto solutions.

Journal of Composite Materials 54(16)To extract more detailed information about the optimization results, Pareto solutions in gate arrangements
are clustered using SOM.
Figure 12(a) is an SOM-Ward cluster figure of threeclusters, and their representative gate positions are
drawn on the map of each cluster. All representativegate positions are arranged diagonally opposite to thevent. These diﬀerences are only the distances between
the gates, and this distance is increased in the order ofcluster 2, 1 and 3. Figure 12(b) plots the parallel coordinates that correspond to each cluster, and normalized
values of the objective functions are indicated on the
y-axis. Detailed characteristics in each cluster are summarized as follows. In cluster 1, all objective functions
have relatively average values. In cluster 2, the weld line

Figure 12. Results of MOO calculations: (a) SOM-ward of Pareto solutions with representative gate arrangements. (b) Parallel
coordinates for each cluster.
MOO: multi-objective optimization; SOM: self-organizing map.

Oya et al.
is optimized at the expense of the fill time and the total
voids. In cluster 3, the fill time, wasted resin, and total
voids are superior, although the weld line has a higher
value. The characteristics in these clusters correspondto the relations obtained using the scatter-plot matrix.
Based on Figure 12(a) and (b), the relationshipbetween gate location and objective function is
obtained. If the distance between two gates is short(e.g. Figure 12(b) cluster 2), the weld line tends to be
short, and a longer fill time and a greater total void
fraction are found. For the multi-injection model,
the following conditions are generally required
to reduce the fill time and the wasted resin simultaneously. First, each gate equally occupies the region(i.e. the perpendicular bisector of the straight line connecting the two gate positions divides the system area

Figure 13. Distribution of mesoscopic and microscopic voids.

Figure 14. Objective function vs. distance between gates.

2143
equally). Next, each gate is located at the center ofgravity of the region. Without considering flow conjugation from two diﬀerent injection points, the first condition is suﬃcient to reduce the wasted resin; however,the second condition is also necessary to reduce the filltime. Clusters 1, 2, and 3 satisfy the first condition.
Clusters 3, 1, and 2 are close to the second conditionsin that order, and the representative gate position incluster 3 is excellent with respect to fill time. A weld
line is defined as a region where two flow fronts collide,and it is inversely proportional to gate distance.
Therefore, from the viewpoint of the distance between
gates, a trade-oﬀ relationship can be obtained between
weld line and fill time. The following section discusses
the relationship between gate arrangement and eachvoid considering flow conjunction.
Figure 13 illustrates the spatial distributions of
mesoscopic and microscopic voids for a representativegate arrangement of each cluster. The features observedby comparing clusters 1, 2, and 3 are summarized asfollows. Mesoscopic void increases in order of thecloseness between gates, whereas microscopic void
does not depend on the distance between gates. Only
when the distance between gates is suﬃciently small isthe microscopic void clearly reduced by overlapping ofvoids that emerged from diﬀerent injection points.
When two gate positions are independently located in
the system, resin flow velocity increases due to the joining of the resins, which also leads to reduction of mesoscopic voids. Therefore, the total amount of mesoscopic

2144
and microscopic voids is not a simple proportional relationship with respect to distance, and there seems to bean appropriate distance to optimize the objectivefunctions.
Each objective function in MOO was investigatedwhen the distance between gates was changed while
keeping the diagonal arrangement. Figure 14 plots therelationship between the two-gate distance and eachobjective function. The optimum distance with respect
to fill time, total void fraction, and wasted resin is from
0.1 m to 0.15 m. When each gate position is located at
the center of gravity of each region of a whole system,
the distance is 0.126 m, which corresponds to our
obtained distance. Hence, to minimize fill time,
wasted resin, and total void simultaneously, the gate
position at the center of gravity of the two areas divided
by the line connecting vents is regarded as the reference
for appropriate molding. Flow conjunction is assumed
to change the appropriate distance slightly from
0.126 m, due to the increase of flow speed and decreaseof mesoscopic voids. However, when considering weld
line and wasted resin, one injection location at thecenter of a mold is the appropriate condition, although
the mesoscopic void becomes large. In conclusion, adiagonal arrangement with an appropriate distance isrequired for appropriate molding depending on polymer resins. Finally, it should be noted that this study
evaluated a quality of a product only by total void content and weld line for simplification. However, previous
studies reported that not only total void content but
also void localization, void location, and void shape
are important for the quality.34,35 This point will be
studied in the near future.

Conclusion
This study proposed a simulation-based MOO framework of RTM for a woven fabric, and observed thevoid distribution to validate the proposed approach.
This framework was realized by combining MOGAs
and flow dynamics simulation including microscopic
and mesoscopic void formations, which are inherent
phenomena in molding inside woven fabric. First, weverified the void-formation model by conducting
unidirectional flow simulation. The calculated void
fractions almost agreed with the previous results by
the authors who proposed the void-formation model.
Next, the experiment and the numerical simulation for
one-point radial injection were performed. Our experiment extracted the permeability of GFRP as a parameter for the filling simulation. Furthermore, observation
successfully captured features of void distribution. (1)The mesoscopic void in the warp direction is smaller
than that in the weft direction. (2) The mesoscopic void
increases with distance from the injection point.

Journal of Composite Materials 54(16)These results qualitatively guarantee the accuracy of
our simulation. Finally, MOO was demonstrated forthe flat plate model with two vents at diagonal cornersof the system. Our result confirmed trade-oﬀ relationships of weld line with fill time, wasted resin, and total
amount of void; however, we found positive correlations among fill time, total void fraction, and wasted
resin. Furthermore, SOM extracted the design role for
optimum injection locations (i.e. the arrangement of
two gates on the perpendicular bisector of the straightline connecting the vents is appropriate for all molding
characteristics). This arrangement does not seem todepend on the permeability ratio between two perpendicular directions of the preform. We also found thatthe distance between two injection locations has a significant eﬀect in minimizing mold characteristics. The
results obtained above will be useful for optimum molddesign in actual RTM of a woven fabric-reinforced
composite in the future. This study investigated only
the flat plate model; however, our framework andresults will help determine optimum molding conditions
even in complicated shape molding.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest withrespect to the research, authorship, and/or publication of thisarticle.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication ofthis article: The Cross-Ministerial Strategic Innovation
Promotion Program and the Ministry of Education,
Culture, Sports, Science and Technology of Japan underGrant-in-Aid Scientific Research (C) No. 15K06597. Toray
Industries, Inc. also supported this work.

ORCID iDs
Yutaka Oya
https://orcid.org/0000-0003-2136-6004
Ryosuke Matsuzaki
https://orcid.org/0000-0001-82371638

References
1. Soutis C. Carbon fiber reinforced plastics in aircraft construction. Mat Sci Eng A 2005; 412: 171–176.
2. Pillai KM and Advani SG. Numerical simulation of unsaturated flow in woven fiber preforms during the resin transfer molding process. Polym Compos 1998; 19: 71–80.
3. Pillai KM. Governing equations for unsaturated flow
through woven fiber mats. Part 1. Isothermal flows.
Compos A Appl Sci Manuf 2002; 33: 1007–1019.
4. Tan H and Pillai KM. Multiscale modeling of unsaturated
flow in dual-scale fiber preforms of liquid composite molding I: Isothermal flows. Compos A Appl Sci Manuf 2012;
43: 1–13.

Oya et al.
5. Dimitrovova Z and Advani SG. Mesolevel analysis of thetransition region formation and evolution during theliquid composite molding process. Comput Struct 2004;
82: 1333–1347.
6. Schell JSU, Deleglise M, Binetruy C, et al. Numericalprediction and experimental characterisation of mesoscale-voids in liquid composite moulding. Compos A
Appl Sci Manuf 2007; 38: 2460–2470.
7. Jinlian H, Yi L and Xueming S. Study on void formationin multi-layer woven fabrics. Compos A Appl Sci Manuf
2004; 35: 595–603.
8. Varna J, Joffe R, Berglund LA, et al. Effect of voids on
failure mechanisms in RTM laminates. Compos Sci
Technol 1995; 53: 241–249.
9. Leclerc JS and Ruiz E. Porosity reduction using optimized flow velocity in Resin Transfer Molding. Compos
A Appl Sci Manuf 2008; 39: 1859–68.
10. Lee DH, Lee W Il and Kang MK. Analysis and minimization of void formation during resin transfer molding
process. Compos Sci Technol 2006; 66: 3281–3289.
11. Kang MK, Lee W Il and Hahn HT. Formation of microvoids during resin-transfer molding process. Compos Sci
Technol 2000; 60: 2427–2434.
12. Park CH, Lebel A, Saouab A, et al. Modeling and simulation of voids and saturation in liquid composite molding processes. Compos A Appl Sci Manuf 2011; 42:
658–668.
13. Lawrence JM, Neacsu V and Advani SG. Modeling theimpact of capillary pressure and air entrapment on fiber
tow saturation during resin infusion in LCM. Compos A
Appl Sci Manuf 2009; 40: 1053–1064.
14. Matsuzaki R, Kobayashi S, Todoroki A, et al. Flow control by progressive forecasting using numerical simulation during vacuum-assisted resin transfer molding.
Compos A Appl Sci Manuf 2013; 45: 79–87.
15. Foley ME. Modeling the effect of fiber diameter and fiber
bundle count on tow impregnation during liquid molding
processes. J Compos Mater 2005; 39: 1045–1065.
16. Okabe T, Matsutani H, Honda T, et al. Numerical simulation of microscopic flow in a fiber bundle using themoving particle semi-implicit method. Compos A Appl
Sci Manuf 2012; 43: 1765–1774.
17. Devalve C and Pitchumani R. Simulation of void formation in liquid composite molding processes. Compos A
Appl Sci Manuf 2013; 51: 22–32.
18. Yashiro S, Nakashima D, Oya Y, et al. Particle simulation of dual-scale flow in resin transfer molding for process analysis. Compos A Appl Sci Manuf 2019; 121:
283–288.
19. Garcia JA, Gascon Li, Chinesta F, et al. An efficientsolver of the saturation equation in liquid composite
molding processes. Int Mater Form 2010; 3: S1295–S1302.
20. Matuzaki R, Seto D, Naito M, et al. Analytical prediction of void formation in geometrically anisotropic

2145
woven fabrics during resin transfer molding. Compos
Sci Technol 2015; 107: 154–161.
21. Oyama A, Obayashi S and Nakahashi K. Real-coded
adaptive range genetic algorithm applied to transonicwing optimization. Appl Soft Comput 2001; 1: 179–187.
22. Ghiasi H, Pasini D and Lessard L. Pareto frontier for
simultaneous structural and manufacturing optimizationof a composite part. Struct Multidiscip Optim 2010; 40:
497–511.
23. Matsuzaki R, Ishikawa T, Okabe T, et al. Stiffness andpermeability multi-objective optimization of carbonfiber-reinforced plastic mesostructures using homogenization method. J Compos Mater 2018; 0: 1–16.
24. Kohonen T. The self-organizing map. Neurocomputing
1998; 21: 1–6.
25. Okabe T, Oya Y, Yamamoto G, et al. Multi-objective
optimization for resin transfer moulding process.
Compos A Appl Sci Manuf 2016; 92: 1–9.
26. Mathur R, Advani SG and Fink BK. Use of genetic algorithms to optimize gate and vent locations for the resintransfer molding process. Polym Compos 1999; 20:
167–178.
27. Kim BY, Nam GJ and Lee JW. Optimization of filling
process in RTM using a genetic algorithm and experimental design method. Polym Compos 2002; 23: 72–86.
28. Ratle F, Achim V and Trochu F. Evolutionary operatorsfor optimal gate location in liquid composite moulding.
Appl Soft Comput J 2009; 9: 817–823.
29. Kuentzer N, Simacek P, Advani SG, et al. Permeability
characterization of dual scale fibrous porous media.
Compos A Appl Sci Manuf 2006; 37: 2057–2068.
30. Scholz S, Gillespie JW and Heider D. Measurement oftransverse permeability using gaseous and liquid flow.
Compos A Appl Sci Manuf 2007; 38: 2034–2040.
31. Wu X, Li J and Shenoi RA. A new method to determine
fiber transverse permeability. J Compos Mater 2007; 41:
747–756.
32. Weitzenböck J, Shenoi R and Wilson P. Radial flow permeability measurement. Part A: Theory. Compos A Appl
Sci Manuf 1999; 30: 781–796.
33. Plank B, Mayr G, Reh G, et al. Evaluation and visualization of shape factors in dependence of the void content
within CFRP by means of X-ray computed tomography.
In: 11th European conference on non-destructive testing,
6–10 October 2014, Prague, Czech Republic.
34. Olivier P, Cottu JP and Ferret B. Effects of cure cycle
pressure and voids on some mechanical properties ofcarbon/epoxy laminates. Composites 1995; 26: 509–515.
35. Mehdikhani M, Gorbatikh L, Verpoest I, et al. Voidsin fiber-reinforced polymer composites: a review
on their formation, characteristics, and effects onmechanical performance. J Comp Mat 2019; 53:
1579–1669.