artigo micro_macro voids

8/12/2019 Artigo Micro_Macro Voids

http://slidepdf.com/reader/full/artigo-micromacro-voids 1/12

Optimization of injection flow rate to minimizemicro/macro-voids formation in resin transfer molded composites

E. Ruiz a, V. Achim a, S. Soukane a,*, F. Trochu a, J. Breard b

a Centre de Recherches Applique es Sur les Polyme res (CRASP), De partement de Ge nie Me canique,

E ´ cole Polytechnique de l Universite de Montre al, Canada H3C 3A7 b Laboratoire de Me canique du Havre, Universite du Havre, 25, rue Philippe Lebon, BP 540,

76058 Le Havre Cedex, France

Received 16 June 2005; accepted 16 June 2005Available online 18 August 2005

Abstract

Resin transfer molding (RTM) has become one of the most widely used processes to manufacture medium size reinforced com-posite parts. To further enhance the process yield while ensuring the best possible quality of the produced parts, physically basedoptimization procedures have to be devised. The filling of the mold remains the limiting step of the whole process, and the reductionof the filling time has an important impact on the overall cost reduction. On the other hand, the injection cycle has to be appropri-ately carried out to ensure a proper fiber impregnation. Indeed, a partial fiber impregnation leads to the creation of micro-scopic andmacro-scopic voids.

In the present work, based on a double scale flow model and the capillary number Ca, an optimization algorithm is proposed tominimize the micro/macro-voids in RTM composite parts. The optimized injection flow rate ensures an optimum Ca at the flowfront during part filling. The implemented algorithm allows the use of various constraints such as maximum capabilities of the injec-

tion equipment (i.e., maximum pressure or flow rate at the injection gates) or maximum velocity to avoid fiber washing. Bounded bythese constraints, the optimization procedure is devised to handle any injection configuration (i.e., injection gates or vents locations)for two or three-dimensional parts. The numerical model is based on a mixed (FE/CV) formulation that uses non-conforming ele-ments to ensure mass conservation. The proposed algorithm is tested for two and three-dimensional parts while emphasizing theimportant void reduction that results from the optimized injection cycle. 2005 Published by Elsevier Ltd.

Keywords: Resin transfer molding E; Modelling B; Optimization

1. Introduction

Resin transfer molding is increasingly used to manu-facture fiber reinforced composites. During the injectionphase, a liquid resin impregnates the fibers before curingand solidification. Partial impregnation of the fiber bedcreates voids in the part and as a result reduces mechan-

ical properties and surface quality [1–3]. To improve

process performance, the percentage of voids formedduring matrix infiltration must be reduced.

The fibrous reinforcements generally used in RTMhave been described in the past as dual-scale porousmedia [4]. The micro-pores are defined as the interstitialspaces between the filaments in the fiber tows, while themacro-pores are the gaps between the tows [5]. A doublescale porous medium obviously leads to a two-levelimpregnation mechanism (i.e., filling of the micro- andmacro-pores). Investigators have observed that the

0266-3538/$ - see front matter 2005 Published by Elsevier Ltd.

doi:10.1016/j.compscitech.2005.06.013

* Corresponding author. Tel.: +1 514 340 4711x5844; fax: +1 514340 5867.

E-mail address: [email protected] (S. Soukane).

Composites Science and Technology 66 (2006) 475–486

COMPOSITES

SCIENCE AND

TECHNOLOGY

www.elsevier.com/locate/compscitech

mailto:[email protected]

mailto:[email protected]



infiltration velocity influences the formation and locationof the voids in the part [4,5,10–12]. This is well explainedby the two types of forces that induce the motion of thefluid trough the dual-scale porous media: the viscous andthe capillary forces. The effect of each of these competingforces on the formation of voids can be evaluated by a

dimensionless parameter called the capillary number(Ca). Experimental studies of micro-scopic and macro-scopic infiltration have demonstrated the existence of an optimal capillary number for which the final voidcontent in the part is minimized [10,11]. Based on thisinformation, the processability window of a near-optimal infiltration stands in the vicinity of the optimalCa. This means that the impregnation velocity at anytime and position should ideally be the one that mini-mizes the micro-scopic and macro-scopic voids content.

In RTM, the impregnation velocity of the fibrousreinforcement is defined as the velocity at the resin front.In practice, in order to set a given flow front velocity, the

flow rate at the injection gate needs to be controlled. Inthis study, a numerical methodology is presented tooptimize the injection flow rate and ensure that the cap-illary number takes an optimal value on the resin frontduring the filling process. The proposed methodology al-lows a fast calculation of optimal injection rates for mul-tiple opening, closing injection gates and vents even inthe non-isothermal case.

2. A dual-scale porous media

In the past, researchers have published several inves-tigations on micro- and macro-void formation [4–7].Experimental as well as numerical analyses were alsoperformed to identify and describe the mechanisms of void formation [8,9]. Breard et al. [4] presented micro-

scopic observations of composite specimens character-ized by image analysis to study their porosity and voidcontent. As shown in the micrograph of Fig. 1, a dual-scale porosity and void content can be defined and char-acterized measuring the intra-tows micro-pores ormicro-voids and the inter-tows macro-pores or macro-

voids. This dual porosity leads to an impregnationmechanism that is a consequence of a double scale flow(see Fig. 2). As depicted in Fig. 2(a), the resin can easilyflow in open channels between the tows with less viscousresistance than in the inter-tows because of the differ-ences in the local porosity. When viscous forces aredominant (i.e., for high resin velocity), micro-scopicvoids appear inside the fiber tows due to the differencebetween the viscous resistance of the tows and the openchannels. In the opposite case, if capillary forces domi-nate the fluid flow (i.e., for low resin velocity), theimpregnation is faster inside the tows than in the chan-nels (see Fig. 2(b)) and macro-voids are formed between

the tows in the open channels.As demonstrated by various authors [10–12], the per-

centage of macro/micro-void formation is a near loga-rithmic function of the fluid flow velocity (v). Labatet al. [10] measured the percentages of macro-voids(V M) and micro-voids (V m) formed during the infiltra-tion of unidirectional stitched fiberglass mats by unsatu-rated polyester resin at room temperature. Thefollowing relationships were obtained:

V M ¼ 32.28 11.8 logðvÞ; ð1Þ

V m ¼ 6.35 þ 2.35 logðvÞ. ð2Þ

This inverse logarithmic dependence plotted in Fig. 3 hasbeen experimentally corroborated and demonstrates theexistence of an optimal infiltration velocity that mini-mizes the percentage of voids in the reinforcement[5,10]. In order to quantify experimentally the mechanism

Fig. 1. Micrographs of composite specimens manufactured by RTM showing micro-void (a) and macro-void (b) formation.

476 E. Ruiz et al. / Composites Science and Technology 66 (2006) 475–486



of micro/macro-void formation, Lee and Lee [6] pro-posed a dimensionless number (v0) defined as the ratioof the superficial velocity of the macro-flow over the cap-illary velocity of the micro-flow

v0 ¼ superficial velocity of macro-flow

capillary velocity of micro-flow ; ð3Þ

when v0 = 1, there is theoretically no void formation.This relationship also indicates that more macro-voids

should be observed when v0 < 1. Alternatively, micro-voids are formed when v0 > 1. The ratio of relation (3)can be used to evaluate the effectiveness of processingconditions on the impregnation of fibers in resin transfermolding.

3. Optimal capillary number

In early investigations, the formation of micro-scopic and macro-scopic voids has been related to thecapillary number (Ca) [5–7,10–12]. Patel and Lee [5]proposed a modified capillary number (Ca*) that con-

siders the liquid/fiber contact angle and the liquid sur-face tension

Ca ¼ lv

c cos h; ð4Þ

where v is the superficial fluid velocity, l the fluid viscos-ity, c the surface tension and h the contact angle betweenthe resin and the fibers. The authors measured the voidfraction for a large number of fluids and flow velocities.When void fractions are plotted against Ca*, the exper-imental curves merged into a master characteristiccurve. Transforming the velocity dependent void con-tents of Eqs. (1) and (2) of Fig. 3 into a function of

Ca* gave the following relationships:

V M ¼ 32.28 11.8 log Cac cos h

l

; ð5Þ

V m ¼ 6.35 þ 2.35 log Cac cos h

l

. ð6Þ

Patel and Lee [12] presented also characterization resultsof capillary properties for various thermoset polymers.For an unsaturated polyester resin at room temperature,these properties are:

l ¼ 0.05462 Pa s;

c ¼ 0.0345 N m1

;h ¼ 34.

In this particular case, Eqs. (5) and (6) can now berewritten in the following form:

0

2

4

6

8

10

12

14

16

0.0001 0.001 0.01 0.1 1 10

flow velocity [m/s]

m

r c a

o - o v

i s d

% [

]

0

2

4

6

8

10

12

14

16

i m

r c o - o v

i s d

[ % ]

Fig. 3. Measured macro/micro-void fractions as a function of the axial flow velocity (from Labat et al. [10]).

Fig. 2. Impregnation mechanisms in a dual-scale porous medium:

(a) formation of macro-voids due to capillary forces (low resin velocity);(b) formation of micro-voids due to viscous forces (high resin velocity).

E. Ruiz et al. / Composites Science and Technology 66 (2006) 475–486 477



V M ¼ 28.96 11.8 logðCaÞ; ð7Þ

V m ¼ 5.69 þ 2.35 logðCaÞ. ð8Þ

The resulting macro/micro-void formation in this caseas a function of Ca* is plotted in Fig. 4. Note that belowa critical Ca*, the capillary forces dominate and create

macro-voids in the intra-tow interstitial spaces. Abovethis critical Ca*, the viscous forces dominate the infiltra-tion process and create micro-voids inside the tows. Anoptimal capillary number ðCa

optÞ exists for which thepercentage of micro/macro-voids formed during the

infiltration process is minimal. In the case of Fig. 4, avalue of Ca

opt is 0.0035.

4. Flow rate optimization

Once an optimal capillary number has been identi-fied, the methodology proposed to optimize the flowrate of the resin injected in the cavity will be presented.Considering Ca

opt as a fixed parameter that can beexperimentally measured [4–6] or numerically estimated

0

2

4

6

8

10

12

14

16

0.0001 0.001 0.01 0.1 1 10

capillary number (Ca*)

m a r c o - v o i d s [ % ]

0

2

4

6

8

10

12

14

16

m i r c o - v o i d s [ % ]

Optimum Ca*

Fig. 4. Evaluated macro/micro-void content as a function of the capillary number (Eqs. (7) and (8)). The optimal of Ca* minimizes the total voidcontent.

Fig. 5. Split of the flow front into a finite series of line elements. Based on the FE/CV approach, the area of each segment of the flow front can becomputed for each partially filled element.




Input parameters andboundary conditions

Calculate and imposethis value at the injection

gate

opt

impv

Extract the averaged Ca* atthe flow front

nii

Caaveraged ,1

*

= 1+k inj

Q

Rescale injection flow rate

using eq. (19)

Compute Darcy’s flow

Advance the flow front usingthe FE/CV approach

If*

,1*

opt ni

i CaCaaveraged ==

Loop untilmold isfilled

maxmaxmax*,,,,,,

w f injinjopt vQPCa

−

µ θ γ

Input parameters andboundary conditions

Calculate and imposethis value at the injection

gate

opt

impv


nii

Caaveraged ,1

*

=


nii

Caaveraged ,1

*

= 1+k inj

Q


using eq. (19)

1+k inj

Q


using eq. (19)

Compute Darcy’s flow

Advance the flow front usingthe FE/CV approach

If*

,1*

opt ni

i CaCaaveraged ==

If*

,1*

opt ni

i CaCaaveraged ==

Loop untilmold isfilled

maxmaxmax*,,,,,,

w f injinjopt vQPCa

−

µ θ γ

Fig. 6. Flow chart of the algorithm devised to optimize the injection flow rate.

Fig. 7. Geometrical model of the automotive part used to test the optimization algorithm.




[8,9], the optimal impregnation velocity ðvoptimpÞ can be cal-

culated as follows:

voptimp ¼

Caoptc cos h

l . ð9Þ

Based on volume averaged values, Darcys law is often

used to model the resin flow through fibrous reinforce-ments. It establishes the relationship between the fluidvelocity and the pressure gradient $P

Fig. 8. Flow front positions in time for the three isothermalsimulations: (a) constant injection pressure; (b) constant injection flowrate; (c) optimized injection flow rate.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600

injection time [sec]

i n j e t c i o n f l o w

t a r

e

- e 1

[ 5

m

/ 3

] s

0E+00

2E-03

4E-03

6E-03

8E-03

1E-02

C a

a l l i p

r y

m u n

b e r a t f l w o

f r

t n o(a)

(b)

(c)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600


i n j e t c i o n f l o w

t a r

e

- e 1

[ 5

m

/ 3

] s

0E+00

2E-03

4E-03

6E-03

8E-03

1E-02

C a

a l l i p

r y

m u n

b e r a t f l w o

f r

t n o(a)

(b)

(c)

Fig. 9. Injection flow rate and capillary number on the flow front forthe simulation at constant injection pressure: (a) and (c) micro-voidsdue to high fluid velocity; region (b) forms macro-voids due to lowfluid velocity.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 100 200 300 400 500 600


i n j e c t i o n

l f o w r a e t

1 e 5 -

m [

3 / s ]

0E+00

2E-03

4E-03

6E-03

8E-03

1E-02

C a

a l l i p

r y

m u n

b e r a t f l

f w o

r

t n o(a)

(b)

(c)

y

(a)

(b)

(c)

Fig. 10. Injection flow rate and capillary number at the flow front forthe simulation at constant injection flow rate: (a) and (c) form micro-voids due to high fluid velocity; region (b) forms macro-voids due tolow fluid velocity.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 100 200 300 400 500 600


i n j e c t i o n

l f o w r a e t

1 e 5 -

m [

3 / s ]

0E+00

2E-03

4E-03

6E-03

8E-03

1E-02

C a

a l l i p

r y

m u n

b e r a t f l

w

o

f r

t n o

Fig. 11. Injection flow rate and capillary number on the flow front forthe optimized injection flow rate simulation.




~vfront ¼ ½ K

l/r P ; ð10Þ

where ~vfront is the fluid macro-scopic velocity at the flowfront, [K ] is the permeability tensor of the porous med-ium, l is the resin viscosity and / is the total porosity of the dual-scale porous medium. Assuming that the mi-

cro/macro-voids appear in the partially saturated re-gions, near the flow front the injection flow rate canbe optimized by setting the front velocity equal to theoptimal impregnation velocity

k~voptfrontk ¼ v

optimp. ð11Þ

If a fully saturated flow is considered, the equation of mass conservation for the fluid phase can be written as

divðq~vÞ ¼ 0; ð12Þ

where q is the density of the fluid and ~v is the filtrationfluid velocity (i.e., the velocity at which the fluid actuallytravels in the pores rather than the macro-scopically ob-served velocity, ~vfront ¼ ~v=/). If the mold deformation isneglected, the global mass balance of the fluid indicatesthat the flow rate Qfront across the fluid flow front isequal to the flow rate at the injection gate Qinj

Qfront ¼ Qinj. ð13Þ

Considering the areas of the injection gate Ainj and of the flow front Afront, the flow rates can be, respectively,expressed as:

Qinj ¼ Ainjk~vinjk; ð14Þ

Qfront ¼ Afrontk~vfrontk. ð15Þ

The unsteady flow conditions developed during RTMmold filling can be numerically solved by considering asuccession of quasi steady-state approximations. In thefinite elements formulation used in this work [13,14],the problem is divided into a sequence of spatial andtransient analyses. As depicted in Fig. 5, if the flow frontis split into a finite number n of sections, Eqs. (13)–(15)can be expanded as follows:

Qfront ¼Xn

i¼1

Aik~vik

/i

¼ Ainjk~vinjk ¼ Qinj; ð16Þ

where Ai , ~vi, /i denote, respectively, the area of the

cross-section, the fluid velocity and the porosity of a fi-nite portion of the flow front ðPn

i¼1 Ai ¼ AfrontÞ.To ensure full saturation in the fibrous preform, all

flow front velocities k~vik must be equal to the optimalimpregnation velocity at each time. This can be achievedby feeding back a new injection flow rate based on thefollowing relationship:

Qinjjk þ1 ¼ k~vopt

frontk

k~vi=/iki¼1;n

D E Xn

i¼1

Aik~vik

/i

0@

1A

k

; ð17Þ

where k means the actual time step and k + 1 the nextpredicted time step and hk~vi=/iki¼1;ni is the averaged

resin velocity at the flow front. Using the assumptionsof Eq. (16), the expression of the injection flow rateQinj|k +1 reduces to

Qinjjk þ1 ¼v

optimpQinj

k~vi=/iki¼1;nD E

0

@

1

Ak

. ð18Þ

Including Eqs. (4), (9) and (11), Eq. (18) can now be ex-pressed as a function of the capillary number

Fig. 12. Distribution of voids content obtained for the three simula-tions tested. (a) constant injection pressure or (b) flow rate show a highvoid distribution; (c) the optimized flow rate minimizes the voidformation. The computer times required for each analysis shows thatthe optimization requires double the time required for a standardfilling simulation.




Qinjjk þ1 ¼Ca

optQinj

kCai ki¼1;n

D E0@

1A

k

; ð19Þ

where hkCai ki¼1;ni is the averaged capillary number at

the flow front.Eq. (19) represents the correction of the injection flow

rate for the time increment k + 1 to ensure an optimalcapillary number on the fluid front (i.e., maximizingimpregnation of the fibrous preform).

5. Optimization constraints

The proposed optimization of the injection processdoes not only depend on the fiber impregnation. Otherrestrictions may be applied so that the capillary numberat the flow front differs from the optimal value. One of these restrictions is the maximum flow rate allowed by

the injection machinery. Moreover, the maximum injec-tion pressure permitted by the system may also limit theperformance of the optimization. It is well known thatfor large fluid velocities, viscous forces are high enoughto deform the fibrous reinforcement (a phenomenonusually called fiber washing ). Fiber washing limits in factthe maximum allowed fluid velocity. All these con-straints can be summed up as follows:

Optimization constraints :

Qinj 6 Qmaxinj ;

P inj 6 P maxinj ;

viji¼1;n 6 vmax f w;

8><

>:ð20Þ

where Qmaxinj is the maximum allowed injection flow rate,

P maxinj is the maximum injection pressure and vmax

f w is themaximum permitted flow velocity to avoid fiber wash-ing. The final optimization procedure consists of solvingEq. (19) subject to the constraints of Eq. (20).

6. Numerical procedure

The numerical solution is based on a finite elementapproximation [13] of the equation that governs thefluid flow combined with an iterative procedure to cor-rect the injection flow rate according to Eq. (19). Asdepicted in the flow chart of Fig. 6, the algorithm startswith the filling simulation and imposes the optimalimpregnation velocity vopt

imp at the injection gate. Notethat vopt

imp is evaluated by Eq. (9) from the user definedfluid–solid interaction parameters: Ca

opt, c, h and l. Atthis time step, the averaged flow front velocity is

extracted from the finite element solution. This velocityis then used in Eq. (19) to rescale the injection flow rate.For each time step, a closed loop iteration is performeduntil the averaged capillary number

Pn

i¼1kCai k=n in the

vicinity of the flow front approaches Caopt. The resulting

injection flow rate is used as boundary condition toadvance the flow front to a new transient positiondefined by the filling algorithm. Finally, a new time stepis computed. The process is ended when filling is com-pleted or until the boundary conditions reach equilib-rium (i.e., vents closed and compressed air inside themold).

Fig. 13. Three-dimensional model filled by non-isothermal optimization of the injection flow rate.




7. Application examples

To illustrate the capability of the proposed optimiza-tion methodology, two application examples will be pre-sented. The first one consists of an automotive part1.6 m long by 1.2 m wide and 3 mm thick (see Fig. 7).The numerical model contains 2950 triangular elementsand 1560 nodes with a central injection gate. To high-light the advantages of the proposed optimization meth-odology, three isothermal simulations where performedat constant injection pressure, constant injection flowrate and with the optimized injection flow rate. Fig. 8shows the resulting flow front positions in time for thethree simulations. Note that the filling times are of thesame order of magnitude for the three cases.

The quality of the injected part can be evaluatedthrough the averaged capillary numbers on the flowfront (i.e., Ca* at the impregnation front). Fig. 9depicts the averaged Ca* and the injection flow rateobtained in the first simulation at constant injectionpressure. At the beginning of the injection, a high

Ca* is observed which induces the formation of micro-voids (see Fig. 9). Then, the Ca* decreases to avalue below Ca

opt, indicating that macro-voids are

Fig. 14. Resin distribution and temperature field across the part thickness for the non-isothermal optimization of the injection flow rate.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0 20 40 60 80 100 120


i n j e c t i o n

l f o w r a e t

1 e 7 -

m [

3 / s ]

1E-04

1E-03

1E-02

C a

a l l i p

r y

m u n

b e r a t f l

w

o

f r

t n o

Fig. 15. Injection flow rate and capillary number on the flow front forthe optimized injection rate.




created in this region. At the end of injection, the Ca*grows up again entrapping micro-voids.

In the second case (see Fig. 10), although a constantflow rate is imposed as injection boundary condition, theCa* on the flow front varies during mold filling. TheCa* profile obtained in this simulation exhibits a similar

behavior than in the previous analysis. In both cases,macro- and micro-voids are formed as a result of thevarying flow front velocities at different locations alongthe part. The last evaluation concerns the optimizationof the injection flow rate. As can be seen in Fig. 11,the optimization algorithm yields a constant Ca* on

Fig. 16. Distribution of void in the part for the: (a) non-isothermal injection at constant injection pressure; (b) constant injection flow rate; and (c)the optimized flow rate. While constant pressure and/or flow rate injections show a high void distribution, the optimized flow rate minimizes the voidcontent.




the resin flow front. For the isothermal analysis per-formed here, this means that the impregnation fronthas a constant resin velocity during injection. To ensurea maximum impregnation of the reinforcement, theinjection flow rate shown in Fig. 11 should be used tomanufacture this part.

As previously discussed, the percentage of macro/micro-voids contained in the part can be considered asrepresentative of the part structural integrity. The totalpercentage of voids in a composite part needs to bereduced to increase mechanical properties and decreasepart defects. Fig. 12 shows a comparison of the distribu-tion of total voids inside the part after filling. For bothuncontrolled injections (i.e., constant injection pressureor flow rate), a circular distribution of voids can beobserved (see images (a) and (b) in Fig. 12). A maximumof 4% of voids resulted from these uncontrolled injec-tions whereas, using the injection optimization algo-rithm, the macro/micro-voids were reduced to a

minimum as depicted in Fig. 9(c). These results showthat the proposed methodology is a useful tool to in-crease performance by minimizing the void formation.Note that the computer time required by the optimiza-tion algorithm is around twice that of uncontrolled fill-ing simulations.

The second test consists of a three-dimensional partused to run non-isothermal filling simulations. Asshown in Fig. 13, the geometrical model contains22,590 tetrahedral elements with 6392 nodes. Differentmold, fibers and resin temperatures were used as wellas a temperature dependent resin viscosity. In the

non-isothermal case, the resin properties vary acrossthe part thickness due to the non-uniform temperaturefield. As a consequence, the Ca* will not only dependon fluid velocity but also on temperature dependentmaterial properties (i.e., resin viscosity and capillaryparameters). Fig. 14 shows the non-isothermal flowsolution for the optimized injection flow rate. The resindistribution and temperature field across the part aredisplayed at three filling times. It can be seen in thecross-section that the temperature field varies in timetrough the part thickness. Fig. 15 depicts the resultedCa* at the flow front and the optimized injection flowrate for this case. Note that even under non-isothermalconditions, the capillary number at the flow front re-mains constant and equal to Ca

opt. Finally, Fig. 16compares the distribution of voids within the part forthree different analyses: (a) injection at constant pres-sure; (b) injection at constant flow rate; and (c) opti-mized injection flow rate. For both constant injectionconditions, the percentage of macro/micro-voids dis-tributed along the part is of almost 10%, with maxi-mum values in the core of the part. The optimizedinjection rate shows an important reduction of voidswith a small distribution of voids mainly in the partcorners. These results demonstrate that the proposed

optimization algorithm has a consistent solution evenfor non-isothermal analyses.

8. Conclusions

This study concerns the relationship between injection

flow rates (or pressures) and void formation in compositeparts manufactured by Resin Transfer Molding. Thequality of composite parts is strongly dependent on thepercent of macro/micro-voids contained. In this work,an optimization methodology was presented to reducethe percent of macro/micro-voids formed during RTMmanufacturing. The optimization is based on the analysisof the capillary number at the fluid flow front position.Once this capillary number is calculated, the injectionflow rate is corrected at each time step to ensure an opti-mal capillary number at the flow front (i.e., the capillarynumber for which the fibrous preform is totally impreg-

nated). To demonstrate the abilities of the numericalmethod, two test cases were presented: an isothermaland a non-isothermal three-dimensional injection opti-mization. The two optimizations were compared withfilling simulations at constant injection pressure and flowrate. In the two tested cases, the optimization showed aminimization of the macro/micro-voids for similar fillingtimes. It can be finally concluded that the injection opti-mization proposed in this work is a useful tool to in-crease the performance of injection molded compositeparts by minimizing the percent of voids formed withinthe fibrous reinforcement.

References

[1] Varna J, Joffe R, Berglung LA, Lundstrom TS. Effect of voids onfailure mechanisms in RTM laminates. Compos Sci Technol1995;53:241–9.

[2] Gowayed YA. The effect of voids on the elastic properties of textilereinforced composites. J Compos Technol Res 1997;19(3): 168–73.

[3] Goodwin AA, Howe CA, Paton RJ. The role of voids in reducingthe interlaminar shear strength in RTM laminates. In: Interna-tional conference on composite materials ICCM-11, Gold Coast,Australia, 14–18th July; 1997.

[4] Breard J, Henzel Y, Trochu F, Gauvin R. Analysis of dynamicflows through porous media. Part I: Comparison between

saturated and unsaturated flows in fibrous reinforcements. PolymCompos 2003;24(3):391–408.

[5] Patel N, Lee LJ. Effects of fiber mat architecture on voidformation and removal in liquid composite molding. PolymCompos 1995;16(5):386–99.

[6] Lee G-W, Lee K-J. Mechanism of void formation in compositeprocessing with woven fabrics. Polym Polym Compos 2003;11(7):563–72.

[7] Mahale AD, PrudHomme RK, Rebenfield L. Characterization of voids formed during liquid impregnation of non-woven multifil-ament glass networks as related to composite processing. ComposManufact 1993;4(4):199–207.

[8] Spaid M, Phelan F. Modeling void formation dynamics in fibrousporous media with the lattice Boltzmann method. CompositesPart A 1998;29A:749–55.




[9] Benetruy C, Hilaire B, Pabiot J. Tow impregnation model andvoid formation mechanism during RTM. J Compos Mater1998;32(3):223–45.

[10] Labat L, Breard J, Pillut-Lesavre S, Bouquet G. Void forma-tion prevision in LCM parts. Eur Phys J, Appl Phys 2001;16:157–64.

[11] Patel N, Lee LJ. Modeling of void formation in liquid compositemolding. Part II: Model development and impregnation. PolymCompos 1996;17(1):104–14.

[12] Patel N, Lee LJ. Modeling of void formation in liquid compositemolding. Part I: Wettability analysis. Polym Compos1996;17(1):96–103.

[13] Remacle J-F, Breard J, Trochu F. A natural way to simulate flowdriven injections in liquid composite molding. Proc CADCOMP98, Comput Meth Compos Mater 1998;6:97–107.

[14] Trochu F, Gauvin R, Gao D-M. Numerical analysis of the resintransfer molding process by the finite element method. Adv PolymTechnol 1993;12(4):329–42.


artigo micro_macro voids

Documents