Resin flow analysis with fiber preform deformation in through thickness direction during Compression Resin Transfer Molding

Composites: Part A 41 (2010) 881–887

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Resin flow analysis with fiber preform deformation in through thickness direction during Compression Resin Transfer Molding Justin Merotte, Pavel Simacek *, Suresh G. Advani Department of Mechanical Engineering and Center for Composite Materials, University of Delaware, Newark, DE 19716, United States

a r t i c l e

i n f o

Article history: Received 4 November 2009 Received in revised form 24 February 2010 Accepted 2 March 2010

Keywords: A. Polymer–matrix composites (PMCs) C. Computational modeling E. Resin flow Compression Resin Transfer Molding

a b s t r a c t Resin flow during Compression Resin Transfer Molding (CRTM) can be best described and analyzed in three phases. In the first phase, a gap is created by holding the upper mold platen parallel to the preform surface at a fixed distance from it. The desired amount of resin injected into the gap quickly flows primarily over the preform. The second phase initiates when the injection is discontinued and the upper mold platen moves down squeezing the resin into the deforming preform until the mold surface comes in contact with the preform. Further mold closure during the final phase will compact the preform to the desired thickness and redistribute the resin to fill all empty spaces. This paper describes the second phase of the infusion. We assume that at the end of phase one; there is a uniform resin layer that covers the entire preform surface. This constrains the resin to flow in through the thickness direction during the second phase. We model this through the thickness flow as the load on the upper mold forces the resin into the preform, simultaneously compacting the preform. The constitutive equations describing the compaction of the fabric as well as its permeability are included in the analysis. A numerical solution predicting the flow front progression and the deformation is developed and experimentally verified. Non-dimensional analysis is carried out and the role of important non-dimensional parameters is investigated to identify their correlations for process optimization. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction Liquid composite molding (LCM) refers to composite manufacturing processes in which the fiber reinforcement is draped on a shaped rigid surface (lower part of the mold) and enveloped with another surface matching the final part shape and forming a closed mold. The resin is injected into the preform in the closed mold until all empty spaces between the fibers are filled with resin. Compression Resin Transfer Molding (CRTM) is a LCM process that uses a partially open rigid mold. It can be described in three distinct phases: (i) resin injection into a fixed gap located between the preform and the upper platen, (ii) gap closure along with preform compression as the upper mold platen moves down to contact with the preform and (iii) finally further compaction when the mold surface is in contact with the preform, compacting the preform to the desired thickness and redistributing the resin to fill all empty spaces. In this paper we will simplify the model by assuming that the load applied on the upper mold platen is forcing the resin into the preform uniformly in the through thickness direction. Previous work has addressed and modeled the flow during the final phase of CRTM in which the fabric deforms due to direct con-

* Corresponding author. E-mail address: [email protected] (P. Simacek). 1359-835X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesa.2010.03.001

tact with the mold [1–7]. Our previous work [8] assumed that during the phase two, as the mold platen compresses the resin layer into the preform, the preform does not deform, but this seemed to contradict some visual records of our experimental infusions. To verify the hypothesis that the preform actually deforms during this phase, we conducted several exploratory experiments with glass random mat to gage the validity of this assumption. We found that the compaction of the preform due to the fluid pressure could not be neglected, even for applied pressures as low as one atmosphere (Fig. 1). This formed the motivation of our work to analyze the resin flow during the closure of the gap as the resin is displaced into the preform progressively being deformed by the fluid pressure. To simplify the analysis we assume that there is transverse flow of resin in the z-direction only as shown in Fig. 2. This is a reasonable assumption if the through thickness permeability value is much smaller than the permeability in the gap and the injected resin volume equals or exceeds the volume of the gap. When the resin is injected during phase 1, due to the high permeability of the gap, the fluid will preferably flow in the gap, completely filling its space. This will ensure a one-dimensional flow through the thickness when the mold platen moves to close the gap. Note, however, that if the gap is too large (or resin volume too small), as the mold platen closes the gap, the resin will preferentially fill the gap before penetrating the preform, establishing the one-dimensional, through the thickness flow.

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Fig. 3. Schematic of the initial condition used in the model.

Fig. 1. Experimental measurement of the transient change in preform thickness h relative to its initial thickness hinitial during the second phase of CRTM process as the mold moves down to close the gap and displaces the resin from the decreasing gap into the preform. The tphase2 is the time period between injection and contact of mold platen with the preform.

In this paper, we will formulate a model and predict the resin impregnation and preform deformation for a case in which the preform is subjected to a fluid compaction under a prescribed applied force. The pressure field, which varies with time and with the through thickness position will be computed along with the flow front position as the mold platen moves to close the gap. An experimental validation is provided for compression of the preform under modest force. A parametric study based on non-dimensional analysis identifies the important parameters in the process. 2. Objectives and assumptions The goal of this study is to predict the compression of the fabric and the impregnation of the resin into the fabric as the mold platen pushes the resin into the preform under a prescribed force. A parametric study will identify the role of the fabric properties and the applied force on the resin impregnation dynamics. If the injection pressure during phase one is limited, the pressure compacting the preform is small and one can neglect its deformation during phase one. It is also assumed that the gap permeability is significantly higher than the preform permeability which can be easily justified. This assumption ensures that the entire gap will be filled before any impregnation into the preform provided that the volume of resin injected is at least equal to the gap volume. In phase one of the process, the gap volume is set slightly smaller than the injected resin volume. Thus, the gap will be fully filled and some resin will also impregnate the preform, as shown in Fig. 2. We assume that a linear pressure gradient exists in the filled region of the preform before the initiation of phase two as the magnitude of

this initial pressure is small and the depth of penetration is only a fraction of the initial preform thickness. As the resin covers the entire surface of the preform uniformly in the first phase and the platen moves in the thickness direction when it closes the gap, one can assume a one-dimensional flow through the thickness (see Fig. 3). Other assumptions are as follows: (i) The dry part of the preform will be assumed to be stiff [9]. It is much stiffer than the wet (and thus lubricated) part and for the pressure driven compaction its behavior does not influence the outcome, though it may influence the position of preform and the mold during the phase 2. Concerning the lubricated part of the preform, its visco-elasticity will be neglected (fiber volume fraction depends only on the applied stress). This applies only to the preform deformation. The system will still behave visco-elastically as the necessary fluid transfer governed by Darcy law still dampens the deformation. (ii) We assume that the flow follows Darcy’s law and as the Reynold’s number is much less than one, we can assume it to be quasi-steady. This allows us to solve for the steady state problem at each time step. 3. Governing equations To model the process, two ‘‘separate” equations governing the pressure distribution through the domain and the progression of the flow front need to be formulated. The applied force is recast as applied pressure as the area on which the force acts does not change during the compression process. The two parameters are related in the following way,

Pap ¼

F A

ð1Þ

where Pap is the pressure resulting from the applied force F over the preform area A. The distribution of the fluid pressures p through the domain can be described using Darcy’s law [10–12] coupled

Fig. 2. Schematic of the second phase of the CRTM process in which the resin impregnates the preform simultaneously compressing the preform even before the mold platen touches the preform.

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to the mass conservation due to the compaction of the elements by the fluid. At each time step, one finds



r 

 @e  rp ¼  g @t

K

ð2Þ

where e is the volumetric strain, K is the fabric permeability, and g is the resin viscosity. The rigorous evaluation of the deformation field requires a known stress–strain relation in both the wet and the dry fibrous preform. For the wet part, we have experimentally determined stress strain curves as described below. The dry part tends to be much stiffer and we assume it to be non-deforming as this assumption does not influence the flow under the applied force. Should the deformation be kinematically driven, this assumption must be re-evaluated as the dry preform deformation would directly influence the flow in the wet part. The volumetric strain rate on the right hand side of (2) can be written as

@ DV  @e ¼ @t @t DV

ð3Þ

where DV is an elementary volume and where the dot represents the derivative with respect to time. As the preform element of the thickness h (original thickness h0) is deformed only in the thickness direction, the right hand side of (3) can be expressed as @ DV @t

¼

DV

@h @t

h0

ð4Þ

which is essentially a linear strain description. Using the fact that the volume of reinforcement within the preform element is constant, one can express the thickness change in terms of fiber volume fraction vf change using

h¼

h0 v f 0

vf

ð5Þ

This relation is finally differentiated to obtain

v f 0 @v f @e ¼ 2 @t v f @t

ð6Þ

Here, vf0 is the initial fiber volume fraction of the fabric. This form has been used in our analysis. Description which uses nonlinear large strain will improve accuracy of predictions for large deformations. The derivative with respect to time of fiber volume fraction in Eq. (6) can be rewritten as function of compaction pressure ppref (compaction stress experienced by the fiber preforms) as follows,

@v f @ v f @ppref ¼ @t @ppref @t

ð7Þ

which when substituted in Eq. (6) results in,

v f 0 @ v f @ppref @e ¼ 2 @t v f @ppref @t

ð8Þ

Similarly one can express the change in permeability of the preform in the through thickness direction, Kzz, with respect to change in the thickness direction as follows

@K zz @K zz @ v f @ppref ¼ @z @ v f @ppref @z

ð9Þ

Using Eq. (2) to describe the resin flow in the z-direction and substituting Eqs. (8) and (9) in Eq. (2) results in the following governing equation,

v f 0 @ v f @ppref 1 @K zz @ v f @ppref @p K zz @ 2 p ¼ 2 þ g @ v f @ppref @z @z g @z2 v f @ppref @t

ð10Þ

Eq. (10) is a general expression which can incorporate any form of constitutive equations to describe: (i) the change in fiber volume fraction vf as a function of ppref and (ii) change in preform permeability Kzz as a function of vf . This equation allows one to solve for the pressure field within the wet preform directly if the pressure is known on both the boundaries. Note that this is not the case if the compaction is kinematically driven. In such a scenario one would need to add an equation relating the pressure in the gap with the deformation of the system. 4. Constitutive equations One must consider the stress–strain relationship in lubricated preforms to develop the relationship between ppref and vf. A significant number of compaction models that propose various forms of such a constitutive equation have been published through the years [3,13–19]. We selected the following relationship between vf and the applied stress ppref, [20]

vf

¼ v f 0 þ ðv fmax  v f 0 Þ tan h

n

ppref pf m

! ð11Þ

This model uses four parameters (vfmax, m, n and pf) unlike the power law model employed by others which uses only two parameters. The power law model [18,19] is simpler, however it neither predicts the fiber volume fraction when the compaction stresses ppref, is zero nor does it reflect the true asymptotic behavior of vf at high stress levels usually experienced in CRTM processing. This behavior is important to describe the compaction over the entire range of possible pressure values. Eq. (11) can capture this but would require evaluation of additional constants. However, these constants can be found from the same experiments and do not require any additional characterization. We conducted fiber compaction experiments with E-glass woven fabric [21]. Table 1 lists the constants that gave us the best fit with the experimental data. Fig. 4 compares the model and experimental fiber volume fractions and their derivatives with respect to the compaction stress. The experimental derivatives are calculated from the strain–stress relation as follows,

dv f dppref

!i ¼

v fiþ1  v i1 f

ð12Þ

iþ1 i1 ppref  ppref

i + 1 and i  1 represent the neighboring data points of point i. At ppref = 0, the model value of dvf/dppref is infinite, however this derivative will not be used in the system as the only locations where compacting pressure is 0 lie on the boundary. There, p is set to Pap from the boundary condition rather than Eq. (10) and vf = vf0. Fig. 4 shows the comparison of the compaction behavior between the experiment [21] and the model (Eq. (11)). One also needs a constitutive equation to describe the permeability as a function of the fabric fiber volume fraction vf. One could use one of the many available in the literature, we selected the Kozeny–Carman [10,11,22] relation to describe this change. The Kozeny–Carman equation did provide a reasonable fit for the fiber

Table 1 Parameters for compaction model described by Eq. (11). E-glass woven (24 oz) n M

vfmax vf0 Pf

0.45 0.86 0.62 0.30 4.5  105

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v f 0 gH2

experiment model

0.6

1

0.55

0.8

0.5 0.6 0.45 0.4

0.4

0.2

0

resulting fiber volume fraction

resulting fiber volume fraction derivatives

1.2

koPap tc

x 10

0.35

0

2

4

6

8

10

compaction stress (Pa)

12

14

16 x 10

0.3

4

Fig. 4. Change in fiber volume fraction and its derivative with respect to compaction pressure for E-glass woven fabric.

v

^ zz @ v f @K  ^pref @v f @p

2 f



!  ^ 2 ^ @2p ^ @v f ^ @p @p þ K zz 2 ¼ ^pref @^z @^z @^t @ p

ð21Þ

One can choose the value of tc in such a way as to make the value of the coefficient on the left hand side equal to unity, hence

v f 0 gH2

tc ¼

ð22Þ

koP ap

Interestingly, this value represents twice the time to fill a cavity between two plates separated by a distance H, filled by porous material of permeability ko with a fluid of viscosity g when injected with a constant injection pressure equal to Pap with no preform deformation. As such, it provides a reasonable first order estimate of the filling time. Substituting Eq. (22) into Eq. (21) and applying Terzaghi’s relation (20) to express the deformation as function of fluid pressure,

v

!  2 ^ ^ ^ ^ K zz @ 2 p @p @p 0 ^ ¼ K zz þ 0 v f @^z2 @^z @^t

2 f

ð23Þ

where volume fractions of our fabric with ko = 2.7  1012 m2. The procedure to find through the thickness permeability has been described in [23]

K zz ðv f Þ ¼ ko

ð1  v f Þ3

v 2f

v 0f ¼

5. Non-dimensional analysis In order to identify the key parameters, a non-dimensional analysis was carried out where dependent and independent variables have been selected as follows,

^L ¼ L H

ð15Þ

^ zz ¼ K zz K ko

ð16Þ

z H

ð17Þ

^t ¼ t tc

ð18Þ

^ ¼1p ^pref ¼ p

p pap

ð19Þ

Eq. (19) has been derived from Terzaghi’s relation [10,11,24] which states that the total applied pressure is distributed between the resin pressure, p and the compaction stress, ppref. Hence,

ppref ¼ Pap  p

¼

@v f ^pref @p 

v fmax  v f 0 mPmax



nPap

    n1 ^pref Pap ^pref Pap p 2 p 1 þ tan h tan h mP max mPmax ð25Þ

ð14Þ

where L is the depth of penetration of the fluid into the preform relative to the upper surface of the preform and / = (1  vf) is the porosity of the fabric.

^z ¼

ð24Þ

and

ð13Þ

To determine the flow front position, the flow front advancement is computed from the averaged velocity provided by Darcy’s law at the flow front position:

@L ðK zz Þz¼L @p  ¼ @t g/z¼L @zz¼L

2 3 ^ ^ 0 ¼ @ K zz ¼ 3ð1  v f Þ v f  2ð1  v f Þ K zz 3 @v f vf

ð20Þ

Using Eq. (15)–(17), one can write the non-dimensional form of Eq. (10) as,

Using Eq. (15)–(18) and substituting Eq. (22), the dimensionless version of Eq. (14) is,

^ zz Þ v f 0 @ p ^ ðK @ ^L z¼L ¼ /z¼L @^zz¼L @^t

ð26Þ

where the subscript z = L represents the values at flow front position.

6. Numerical solution As Eq. (23) is non-linear, we will use a finite differences scheme with fluid pressure at each node as our primary variable for the calculations. As the resin progresses in the preform only in the transverse through thickness direction, one can increase the size of the domain at each time step to accommodate this moving resin boundary. The element size will increase as well. To solve Eqs. (23) and (26), we use the finite differences scheme. The derivatives are discretized as follows,

^ti1 ^t  p ^ p @p ¼ iþ1 2D^z @^z

ð27Þ

tþ1 ^tþ1 ^tþ1 ^iþ1 ^ p  2p þp @2p i i1 ¼ @^z2 D^z2

ð28Þ

^ti ^tþ1  p ^ p @p ¼ i @^t D^t

ð29Þ

The previous expressions are substituted into Eq. (23) and its finite differences form becomes,

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v 2f

^0 K zz

 t  ^ zz p ^tþ1 ^tþ1 ^tþ1 ^ti1 2 K ^iþ1  p p iþ1 þ pi1  2pi þ 0 vf 2D^z D^z2

!! ¼

^tþ1 ^tþ1 p p i i D^t ð30Þ

The secondary unknowns (fiber volume fraction, permeability ^ti . Note that the first order and their derivatives) are computed for p differentiation raised to a square is expressed at the time t while the second derivative with respect to z is at t + 1. The motivation of this choice is to restrict the solution technique to a semi-implicit scheme. The system should be more stable than the fully explicit one without dealing with the complex formulation and iteration difficulties encountered in fully implicit schemes. By sorting the pressures at time t and t + 1 and by grouping the coefficients by the individual nodal values one finds,

^0 v0 K zz f tþ1 ^tiþ1  p ^ti1 Þ2 þ bp ^ti ¼ p ^tþ1 ^iþ1 ^tþ1 ðp ðb þ 2Þ  p p i i1 ^ zz 4K

ð31Þ

where

ð32Þ

f

This equation is valid for every internal node i. At boundaries i = 0 and i = iL, one apply the following boundary conditions,

p^z¼0 ¼ 1

ð33Þ

p^z¼^L ¼ 0

ð34Þ

The best way to solve this system of equations is to express it as a matrix including every space step,

1

0

6 6 1 6 6 6 60 6 6 60 6 6 60 6 6. 6. 4.



0

0 ..

.

..

.









0

0

 .. . .. . .. .

0 .. . .. .

3

2

ptþ1 0 ptþ1 1 ptþ1 2

3

2

^Ltþ1  ^Lt ^ti ^t  p p i i ¼ c iþ1 D^z D^t

ð36Þ

where

ð1  v fap Þ2

v 2fap

ð38Þ

The strain is calculated for each element. The sum of all the infinitesimal deformations over the domain will give the global deformation.

In order to validate the one-dimensional solution, an experimental setup using constant applied pressure was developed. The setup consists of a semi-circular cavity with a glass wall for the straight edge. This allows us to observe the evolution of the key components (flow front, preform top, molds) during the process of CRTM. A plate of similar shape is used as the top plate. The mold and plate form a male female combination. In this setup, the bottom mold moves vertically up and the upper plate is stationary. The movement of the mold is achieved by placing the mold on an inflatable rubber tube. This rubber tube is attached to a pressure

1 

3

^0 v0 K zz f

For the initial pressure distribution, we assume that some fluid penetration has occurred during phase 1; it involves a linear pressure distribution over its length. Substituting discretized derivatives into Eq. (26),

c¼

vf0 1 vf

2 7 6 7 7 b1 pt1  K^ pt2  pt0 7 6 7 6 7 zz 7 6 7 6 7 6 7 6 7 6 0 0 ^  7 K zz v f  2 7 6 7 6 t t t 7 b p  p  p 7 6 7 6 b2 þ 2 1 0 2 2 ^ zz 3 1 7 K 7 6 7 6 7 7 6 .. 7 6 .. .. .. 7 .  ¼ 7 7 6 .. 7 . . . 0 7 6 . 7 6 7 7 6 .. 7 6 .. .. .. 7 6 .. 7 6 . 7 6 7 . . . 0 7 6 7 6 . 7 7 6 tþ1 7 6 ^0 v0  .. 2 7 K 7 4 pN1 5 6 zz f t t t 7 . 0 1 bN1 þ 2 1 5 p  p  p b 5 4 N1 N1 ^ zz N N2 K ptþ1 N 0 0 0 0 1 0

b1 þ 2 1 1

e¼

7. Experimental validation

D^z2 v 0f b¼ ^ zz v 2 D^t K

2

The non-dimensional time step of 5  104 was utilized and no stability issues were noted. In order to validate or invalidate the observation made in Fig. 1, one needs to compute the deformation of the preform occurring during the process by converting the fluid pressure at each node into a strain. To do so, Terzaghi’s relation (20) is used to obtain the stress in the preform ppref from the fluid pressure p. Once ppref is known, the corresponding fiber volume fraction of each element is known by averaging the stresses at the two neighboring nodes and by applying Eq. (11). One needs then to integrate with respect to time the infinitesimal stress strain relation given by Eq. (6)

v 3f 0 ð1  v f 0 Þ3

ð37Þ

vfap is the fiber volume fraction corresponding to a applied pressure of Pap without any fluid pressure. To solve the problem, the new domain is determined by solving Eq. (36) at each time step. The new mesh of fixed size (100 elements) is then generated over the extended domain, the initial values are interpolated and pressures are solved using Eq. (35).

ð35Þ

bucket containing water. By injecting at constant pressure (10 psi) the water into the rubber tube, the lower part of the mold is pushed upwards with constant force of 386 N (Fig. 5). A series of five experiments have been conducted with E-glass woven fabric 24 oz as a reference material due to its very small variability in its properties. The initial thickness as well as the initial weight, number of layers and resin viscosity were measured for each experiment. For each experiment, 15 layers of woven E-glass (about 14 mm thick) were placed into the mold. The gap was set to 4 mm. Dyed corn syrup was injected using a syringe to cover the entire surface and fill the gap. Viscosity of the fluid was about 0.4 Pa s at room temperature. The final filling time and deformation were recorded until the preform came in contact with the tooling. The same parameters have been set as inputs in the simulation. The experimental results and the simulation outputs are compared (filling time (Fig. 6) and final thickness (Fig. 7)). In Fig. 6, the model errors bars represent the variability in filling time due to the variability of the measured permeability while the experiment errors bars represent the inaccuracy of the contact

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fects, as the compaction behavior was measured at slow compaction rates. 8. Parametric study

Fig. 5. One-dimensional phase two experimental setup.

Fig. 6. Prediction of normalized deformation (H = 15 mm) and its comparison with experimental results for 24 oz. E-glass fabric.

From Eqs. (23) and (26), we can identify four parameters that do influence the flow front and the compaction of the preform. They are listed in Table 2 along with their physical significance. The material properties and the final geometry being usually fixed by the mechanical properties desired, only the influence of X will be studied. The essential issue is to analyze it as follows: the applied pressure can be increased and will lead to faster filling time but it will also increase the process cost. Is there any transition where the improvements obtained by increasing the pressure are less significant as compared to the cost associated with use of large pressure machines? Two points are to be noted. First, the ‘‘optimum” will depend on the particulars of the process, so here we are only interested if the rate of improvements decrease sharply at a certain pressure value. Second, as the paper analyzes only the second stage, one would need to consider the subsequent stage to obtain valid recommendations. In order to identify the role of X, several numerical experiments varying the applied force while maintaining the material properties (C = 0.3, vf0 = 0.3, n = 0.45, m = 0.86) constant were carried out. The impact of this variation on the two outputs: deformation and filling time is shown in Figs. 8 and 9. Final thickness, hfinal, is non-dimensionalized with respect to the initial thickness H. The fill time will not be non-dimensionalized as the characteristic time is a function of the applied pressure. The gap size is fixed and different amounts of forces are applied on the resin on top of the preform in order to squeeze it into the material. The filling time and final deformation are recorded when all the resin has penetrated the preform (calculated for vffinal = 0.45 at the end of the process). Initially, increasing X increases the compaction of the fabric and more importantly significantly lowers the fill time. However with

Fig. 7. Prediction of normalized fill time (tc = 2.014 s) and its comparison with experimental results for 24 oz. E-glass fabric.

time determination. Similarly, in Fig. 7, the model error bars represent the variability in deformation due to the compaction behavior while the experiment error bars represent the inaccuracy of the contact position measurement. The variability of permeability and deformation was assumed to be ±10%, according to our general experience. The model seems to be more compliant than the experiment. This might really be a result of neglecting viscous compaction ef-

Fig. 8. Influence of non-dimensional parameter X (ratio of available stress to maximum possible) on the final deformation.

Table 2 Non-dimensional parameters in the process. Non-dimensional parameter

Physical significance

X ¼ PPapf

Ratio of available stress and shape parameter pf to compact the preform. The shape parameter is the measure of the ‘‘maximal” compaction stress – the stress that no longer produces significant increase in preform compaction Parameters describing the preform compaction as a function of fiber volume fraction Initial fiber volume fraction Preform compliance

n, m

vf0 C = vfmax  vf0

J. Merotte et al. / Composites: Part A 41 (2010) 881–887

887

additional force increase produces ever decreasing return and therefore optimal processing force can be evaluated for individual cases based on this asymptotic behavior. Acknowledgement The authors gratefully acknowledge the support provided by the National Science Foundation under Award number 0856399. References

Fig. 9. Influence of non-dimensional parameter X (ratio of available stress to maximum possible) on the filling time.

further increase, its influence on the fill time improvement decreases relative to the increase of the force, and consequently, the tooling cost. This supports the assertion that there is some optimal value of applied pressure. For higher values, the improvements are marginal. This behavior has already been observed in the third phase of CRTM when a prescribed force is applied to a saturated preform and displaces the fluid horizontally [20]. Obviously, for a particular process one should evaluate both stages and include the process particulars, such as possible gains from higher processing rates and compare them with expenses incurred from need for stronger tools and assembly to withstand higher pressures. Another way to decrease the fill time of the second phase is to increase the initial depth of penetration of the fluid. This will decrease the gap size and therefore decrease the amount of resin to squeeze into the preform during phase two. As the final deformation is calculated using the final depth of penetration (which depends on the total volume of resin), the final thickness will be unchanged. However, the gain in time made in phase two will be offset by the increase in time required to complete phase one as one must inject the resin into the preform further in phase one under low pressure. Analysis of the phase one is thus a pre-requisite for such an analysis.

9. Conclusions In this paper, a model has been developed to predict the compaction behavior of the preform and describe the penetration of the resin in the thickness direction in a deforming preform which occurs during the phase two of the CRTM process. Five experiments have been conducted to validate the model’s results. The experimental behavior was properly predicted within the limits of the variability in permeability and compaction properties of the fabric. To investigate the influence of the initial parameters (preform properties, process variables), a parametric study was conducted which revealed that while a significant improvement in filling time is possible with modest increase of the applied force,

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