An Analytical Vacuum-Assisted Resin 

Transfer Molding (VARTM) 

Flow Model 

by Bruce K. Fink, Kuang-Ting Hsiao, Roopesh Mathur, 

John W. Gillespie, Jr., and Suresh G. Advani 

Approved for public release; distribution is unlimited. 
The findings in this report are not to be construed as an official 

Department of the Army position unless so designated by other 

authorized documents. 

Citation of manufacturer’s or trade names does not constitute an 

official endorsement or approval of the use thereof. 

Destroy this report when it is no longer needed. Do not return 

it to the originator. 
Army Research Laboratory 

Aberdeen Proving Ground, MD 2 1005-5069 

ARL-TR-2354 October 2000 

An Analvtical Vacuum-Assisted Resin J 

Transfer Molding (VARTM) Flow Model 

Bruce K. Fink 

Weapons and Materials Research Directorate, ARL 

Kuang-Ting Hsiao, Roopesh Mathur, 

John W. Gillespie, Jr., and Suresh G. Advani 

University of Delaware 

Aooroved for oubhc release: distribution is unlimited. 
Abstract 

A closed form solution for the flow of resin in the vacuum-assisted resin transfer 

molding (VARTM) process is used extensively for affordable manufacturing of large 

composite structures, During VARTM processing, a highly permeable distribution 

medium is incorporated into the preform as a surface layer. During infusion, the resin 

flows preferentially across the surface, simultaneously through the preform, to a complex 

flow front. The analytical solution presented here provides insight into the scaling laws 

governing fdl times and resin inlet placement as a function of the properties of the 

preform, distribution media, and resin. The formulation assumes that the flow is fully 

developed and is divided into two areas: (1) a saturated region with no crossflow, and (2) 

a flow front region, which moves with a uniform velocity, where the resin is infiltrating 

into the preform from the distribution medium. The law of conservation of mass and 

Darcy’s Law for flow through porous media are applied in each region. The resulting 

equations are nondimensionalized and are solved to yield the flow front shape and the 

development of the saturated region. It is found that the flow front is parabolic in shape, 

and the length of the saturated region is proportional to the square root of the time 

elapsed. The obtained results are compared to data from full-scale simulation and show 

good agreement. The solution allows greater insight into the physics process, enables 

parametric and optimization studies, and can reduce the computational cost of full-scale, 

three-dimensional (3-D) simulations. 
1. 

2. Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 

3. 

4. 

5. Effect of Process Variables: A Parametric Study . . . . . . . . . . . .._._................................ 2 1 

5.1 Effect of Thickness Ratios.. ................................................................................. 2 1 

5.2 Effect of Permeability.. ........................................................................................ 23 

5.3 Effect of Porosity ................................................................................................. 24 

6. Conclusions _.._._.........................................................................................-............... 25 

7. 

Table of Contents 

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..-........................................................ V 

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..-...-...-..................... vii 

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..-............................................................. 1 

Analytical Solution.. ................................................................................................. 11 

Verification: Full-Scale Simulations .... . ................................................................ 19 

References .._...._._.................................................-....-...........-..............................-..-.. 3 1 

Distribution List . . .._........................-.............. Y . . . . . . . . . . . . . . . . . . . . . ..-...._...._...__................... 33 

Report Documentation Page . . . .._..........._......-.......................................................... 53 

. . . 

111 
INTENTIONALLY LEFT BLANK. 

. I 

iV 
List of Figures 

.* Figure m 

1. 

. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

. 

I 

Examples of the Broad Application Potential for VARTM Processes Including 

Shipping, Infrastructure, Land Combat Vehicle Armor, and Repair.. ....................... 

Layup of Materials in the VARTM Process .............................................................. 

Two-Layer Model of Resin Flow in the VARTM Process.. ...................................... 

Schematic of Resin Flow in the Flow Front Region for the Two-Layer 

VARTM Model .......................................................................................................... 

Illustration for Resin Mass Balance in the Flow Front Region in the 

Two-Layer Model ...................................................................................................... 

Two Mathematical Roots of hF*(X*) = 0.. ................................................................. 

Example of a Full-Scale Numerical Simulation: (a) Flow Front History and 

(b) Pressure Distribution at the Final Time Step ....................................................... 

Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Thickness Ratios .......................................................................... 

Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Permeability of Distribution Medium .......................................... 

Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of In-Plane Permeability of Fiber Preform ....................................... 

Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Transverse Permeability of Fiber Preform ................................... 

Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Porosity of Distribution Medium ................................................. 

Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Porosity of Fiber Preform.. ........................................................... 

7 

12 

17 

22 

23 

25 

26 

27 

28 

29 
bTENTIONALLY LEFT BLANK. 

vi 
l 

List of Tables 

Table m 

1. Comparison of Closed Form Solution With Results From Full-Scale Numerical 

Solution of the VARTM Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

vii 
IN’I-ENTIONALLY LEFT BLANK. 

. . . 

Vlll 
. 

1. Introduction 

The vacuum-assisted resin transfer molding (VARTM) process offers numerous cost 

advantages over traditional RTM via lower tooling costs, room temperature processing, and 

scalability to large structures. Recent advanced technology demonstrators such as the Advanced 

Enclosed Mast Sensor @EM/S) System and the composite advanced vehicle (CAV) have shown 

the potential of VARTM technology for the low-cost fabrication of large-scale structures 

requiring thick-section construction and hybrid multifunctional integral armor. The VARTM 

process is also used extensively in commercial applications such as bridge decks, rail cars, and 

yachts (Figure 1). 

Figure 1. Examples of the Broad Application Potential for VARTM Processes Including 

Shipping, Infrastructure, Land Combat Vehicle Armor, and Repair. 
VARTM is a composites manufacturing process that involves the layup and vacuum bagging 

of dry reinforcing fibers in fabric, tape, or bulk form as a preform in a one-sided open mold and 

impregnating the preform with liquid resin using negative pressure (i.e., a vacuum) followed by 

cure and demolding. The advantages of the VARTM process over the RTM process are 

scalability and affordability for the fabrication of large composite structures. Large parts can be 

infused rapidly using vinyl esters, phenolics, and epoxies at room temperature under vacuum 

pressure only. Consequently, tooling costs and investments are substantially reduced. VARTM 

is a completely closed system that traps volatile organic compounds (VOCs), reduces the need 

for solvents, and results in less scrap than other processes. 

The present study focuses on Seemann’s Resin Infusion Molding Process (SCRIMP) 

(Seemann 1990). In this VARTM process, a highly permeable distribution medium is 

incorporated into preform as a surface layer. During infusion, the resin flows preferentially 

across the surface and simultaneously through the preform thickness enabling large parts to be 

fabricated solely under vacuum pressure. The layup of the materials in the process is shown in 

Figure 2. 

In very large composite structures, multiple inlet gates are required to. ensure complete wetout of the part prior to gelation of the resin. Selection of distribution media, performs, and gate 

and vent locations are based on past experience for similar applications. New applications in 

which part thickness, resin, or preform characteristics change require costly trial and error 

process development. Hence, a fundamental understanding of the process physics and associated 

models represent a significant contribution to the science base for VARTM. 

Modeling and predicting the flow during the impregnation process provides insight into the 

process physics and highlights potential problems before production. In addition, flow 

prediction enables optimization of the design variables affecting the process, such as the distance 

between resin inlets (in the case of multiple lines and thickness of the diffusion layer), and 

provides rules of thumb for scaling of the prototypes. Thus, a fundamental understanding of the 

underlying science will help develop models to reduce costs, aid in selection of design 

parameters, and improve quality. 

2 
resin 

I fiber preform under vacuum 

vacuum 

layup detail 

vacuum bag 

distribution layer 

PeeI PiY 

Figure 2. Layup of Materials in the VARTM Process. 

3 
The flow of resin through porous media such as fiber preforms and resin distribution media is 

governed by Darcy’s Law: 

- Ic .VP, u=- 

IJ (1) 

where u is the Darcy’s velocity (defined as the total flow rate per total flow front area), K is the 

permeability tensor (which characterizes the ease of flow through the fiber perform), and ,LJ is 

the viscosity of the resin. This, when coupled with the continuity equation for incompressible 

flow, gives the Laplace equation for the fluid pressure field inside a region permeated by the 

fluid: 

(2) 

This equation can be discretized using finite element methods which then form the basis for 

simulation of mold-filling during the resin infusion process (Bruschke and Advani 1990, 1991a; 

Liu et al. 1996; Mohan et al. 1999). 

The flow simulations can be either two-dimensional (2-D) or three-dimensional (3-D). In 

2-D flow modeling (Bruschke and Advani 1991b; Trochu et al. 1994; Lee et al. 1994), the flow 

of resin through the thickness is considered uniform, and the finite element discretization is 

applied along the other two directions as with liquid injection molding simulation (LIMS), which 

is based on the finite element/control volume approach. In 2-D simulations, only the in-plane 

permeabilities are supplied (Simacek et al. 1998). In 3-D simulations, the pressure and flow in 

all three directions is solved, and a 3-D permeability sensor is supplied as input, as in the resin 

infusion process simulation (FUPS), which is based on finite element methods without the use of 

the control volume approach (Gallez and Advani 1996). Usually, the geometry, the material 

parameters, and the position of resin inlets and outlets are specified before the filling simulation 

is carried out. Simulation codes are used to track flow fronts and estimate the fill times. 

4 

. 

. 
. 

Parametric studies then can be conducted with simulations to design the mold and the process 

parameters. 

Closed form analytical solutions have also been derived for the resin flow under simplifying 

assumptions and for simple geometries. These solutions explain the role of various process 

variables and their interactions during processing. Indeed, a closed form solution of the resin 

flow during the VARTM process not only enables parametric studies, optimization, and 

reduction of computational expenses of full-scale simulations, but also offers insight on the 

scaleup of the process and material parameters for large structures. 

In earlier work, Tari et al. (1998) derived a closed form model for vacuum-bag RTM under 

several simplifying assumptions. They assumed that the velocity of resin in the fiber preform is 

negligible and that the region behind the flow fi-ont is uniformly saturated. In the present work, 

these assumptions were not made, so the velocity of the resin, as well as the shape of the flow 

front through the thickness of the fiber perform, are accurately captured. This is important for 

scaling purposes. 

A closed form solution for the flow of resin in the VARTM process is presented here. The 

layup is modeled as the distribution layer (high permeability material) and the structural layer 

(preform material). It is assumed that the flow is well developed and can be divided into a 

saturated region with no crossflow and a flow front region in which the resin infiltrates the 

preform from the distribution medium. The flow front region is assumed to be fully developed 

with a uniform velocity. The law of conservation of mass and Darcy’s Law for flow through 

porous media are applied in each region. The resulting equations are nondimensionalized and 

are solved to yield the flow front shape and the development of the saturated region. 

2. Problem Statement 

As illustrated in Figure 3, the layup of materials is modeled as two layers of permeable 

materials. The distribution layer is much thinner than the structural layer, h, << h, , where h, and 

5 
PO : injection Pressure 

Layer 1: Distribution Layer ; Flow Front Region 

I Layer 2: Structural Layer /Vacuum Pressure( = 0 

Note: d - region with transverse flow = flow front length. 

D - region without transverse flow = length behind the flow front region. 

UF - flow front velocity. 

,u - viscosity of resin. 

Figure 3. Two-Layer Model of Resin Flow in the VARTM Process. 

h,are the respective thicknesses of the two layers. The flow front in the distribution layer is 

considered uniform. The permeability of the distribution layer is K,, along the flow direction, 

and the permeabilities of the structural layer are K,,and K,, in the x and y directions, 

respectively. The constant inlet injection pressure (atmospheric pressure) is PO, and the resin 

viscosity is p . 

In the saturated region, the flow is one-dimensional (1-D) with Darcy’s velocities U, and U, 

in layers 1 and 2, respectively. The length of this saturated region is D, and the pressure at its 

boundary with the second flow region is assumed to be PD. 

The second region, illustrated in Figure 4, is the flow fi-ont region where there is transverse 

flow from the distribution layer to the structural layer. The flow front region of length d is 

assumed to maintain its shape, given by h, , and advances with a uniform horizontal velocity of 

6 
Flow Front Region 

I 

Vacuum Pressure 

t 

0 

Figure 4. Schematic of Resin Flow in the Flow Front Region for the Two-Layer VARTM 

Model. 

U,. This is the observed velocity of the resin and not the Darcy’s velocity. The transverse 

velocity of resin infiltration from the distribution layer into the structural layer is Q,. The 

horizontal velocity in the flow front region in the distribution layer u,, is with boundary 

condition u,, (x = D + d) = 0, U, . 

Since the resin is an incompressible fluid, using the continuity equation and Darcy’s Law in 

the structural layer, the governing equation for the pressure distribution is 
K 

2xX 

a2p; K a*p-() 

3X2 2YY 

?Y’ : 

Consider the following nondimensional variables: 

p’=$ ,X* =x,y* 2, 

c xc YC 

(3) 

(4) 

where x, and y, are the characteristic length scales in the longitudinal and thickness directions, 

respectively, and P, is a scaling parameter for the pressure. Introducing the dimensionless 

variables, the governing equation can be recast in dimensionless form as follows (Pillai and 

Advani 1998a, 1998b): 

K,,yf a*p* + a2p* 

-= 

K,,x,Z ax** $2 

o 

. 

(5) 

Since the resin distribution media was used in the process to enable the rapid and uniform 

distribution of the resin across the mold surface, it can be assumed that within the flow front 

region in the structural layer, the major portion of the resin flow is from the distribution layer 

into the structural layer. Hence, the flow rate in the y direction must be more significant than 

that in the x direction (i.e., Qy >> Q,). The x, in the flow fi-ont region is d, while y, is h,. If 

- 

u and v are the average Darcy’s velocities in the two directions, then 

Qy =id, 

and 

Q, =;h2. 

(6) 

Considering Darcy’s equation for the velocities, the following scaling argument can be made: 

8 
I . 

and 

v= K2, ap - K2vv p ----&.j,“-A 

Pay P h2’ 

Since QY >> Q,, from equations 6 to 8, it can be determined that: 

K*xxG- << 1 

K,,d* ’ 

(7) 

(8) 

(9) 

This allows for the neglect of the x-term in pressure equation 5 in the flow front region, which 

leads to the following result: 

and 

K2yy ap K2yy v=---= --fA-4 CL@ I-L 

At the top of the structural layer, where the flow is always Corn the distribution layer, the 

boundary condition is defined as v jyzO= z+*,,(x). Hence, in the flow fi-ont region, 

v(x) = Gy (4, 

9 
where yzY(x) is the velocity of the resin flow from the distribution to the structural layer in the 

flow front region. In the saturated region, the length scale of the flow is D in the x direction and 

h, in the y direction, where D >> h, . Since D >> d, from equation 9, 

K2Jc <<la K2A 

K2yyd2 K2,DZ 

<<l. 

So, the first term in equation 5 can be neglected, and 

Thus, the velocity in they direction in the saturated region is 

v= K2yy w K2yy ---=-- 

P ay 

cc fsW 

(11) 

(13) 

At the bottom of the structural layer in the saturated region, the resin is in contact with the 

surface of the mold, which is impermeable. Hence, the no-penetration boundary condition was 

applied (i.e., v = 0 @y = h2) in the saturated region. Therefore, 

dP 

s = fs (x) = 0 in the saturated region. (14) 

As a result, v = 0 in the saturated region everywhere in the structural layer. Since v = 0, the 

second term in pressure equation 3 becomes zero, and 

$0 spy), 

. 

10 
. 

. 

as 

-= ap @ 0 * 

So, it can be inferred that g(y) is constant, and , 

u=--- Lx ap 

P ax 

(15) 

is constant in the saturated region. Hence, from boundary conditions of P = P, @x = 0 and 

P=P,@x= D, 

ap pD-po 

dx= D 

in the saturated region. (16) 

3. Analytical Solution 

Considering the element fluid volumes shown in Figure 5 and invoking the mass balance, 

U,zy~+U2(-dhF)=UFQZZ(-dhF)~U**y =*(@*uF -u,). (17) 

A lumped mass balance in the distribution layer in the flow front region gives 

-du,,h, = ~,~,,dx 3 u,~,, = -h, - 

di- (18) 

11 
Figure 5. Illustration for Resin Mass Balance in the Flow Front Region in the Two-Layer 

Model. 

From equations 17 and 18, the result is 

%, = -h d” Ix = $q@2uF -4,). h?x (19) 

Applying Darcy’s Law in the y direction in the flow front region and using equations 17 and 

18, 

and 

12 
This leads to the following equation for 4 (x’) , the pressure field in the distribution medium in 

the flow front region: 

&*)=h,~(@,u, -u2+ 

2YY 

(21) 

A similar mass balance in the flow front region, including both the structural and the distribution 

layers, yields 

U,h, +U,h, =U,(@, h, +@ 2 h,). 

Applying Darcy’s Law in the saturated region with 1 -D flow, 

and 

K2, PO - PLI u, =- 

K 

P D 

3 u, =u,x. 

K 2xX 

In combination with equation 22, 

(22) 

(23) 

(24) 

The previous set of equations can be nondimensionalized using the following nondimensional 

variables: 

13 
x-D h; +x* =- 

2 h2 ’ 

(25) 

and 

4* =$I* =$,p* =$ - 

2 2 0 

This gives the following system of equations: 

and 

(26) 

(27) 

(28) 

(29) 

- 

Here, ti2UF p* = - 

KLJO 

is obtained from the nondimensional Darcy’s Law. The boundary conditions 

14 
on UT, are Use= U,*.U~:(~*)= $1. The boundary conditions on h; (0) = l,h; (d’ ) = 0. The 

pressure boundary conditions are <* (0) = Pi,c* (d’ )= 0. 

Integrating equation 29 and applying the boundary condition ulx (0) = U,*,U;, (d’ ) = @I , 

In combination with equation 26, 

dl?’ tt a 1= 

dx* -CL Ulx = cc h; (x’ )+ @, 1 . (31) 

Combining equations 29 and 3 1, the following nonlinear ODE with boundary conditions 

hi (0) = 1, hi (d * ) = 0 result in: 

,““;;1. . 

2 2 

(32) 

This ODE is of the form given by (y2)” = ay + b. It can be solved using the substitution 

dY p=d,,y.=pdp dy (Murphy 19W This usually yields a solution in a quadratic form. 

The quadratic form hi (x’ ) = ax2 + /3x* + y can be substituted into the above equation to find the 

solution using the first boundary condition hi (0) = 1 and matching the coefficients of the powers 

of x* on either side. Then the second boundary condition, hi(d*) = 0, can be used to determine 

d * . This gives a quadratic equation for d * having two roots. Both roots are positive, but if the 

larger one were chosen, then the flow front profile would be physically impossible (Figure 6). 

Hence, the smaller root gives the following unique solution: 

15 
K* 2YY 

a=- 

6h,* ’ 

and 

y=l. 

Thus, 

K* *2 h;(n’)=--$, 

1 

and since hi (d’ ) = 0, d * can be determined as 

(33) 

(34) 

(35) 

Substituting the form h;(x*) = ax** + /3x* + y in equation 29, the pressure can be 

determined as follows: 

p’ = -b2 -dJ* 

1 K’ 

[2ax*’ + 3a/?x” + (p’ + 2a)x* + pl 

7-YY 

(36) 

Applying the boundary condition 4’ (0) = Pi gives 

16 
-- 

\ 

Xf = d* Nonphysical Region 

Flow Front Shape: &(x*) 

Figure 6. Two Mathematical Roots of hi* = 0. Note That Only the Smaller Root Is 

Physically Possible. 

Using the nondimensional form of Darcy’s Equation in the saturated region, 

u* = G, 1-p; --s U;D * P* 

2 p* D* 

---.=1--p l o2 -u; G, + w;, 

K’ 2xX K’ %Y 3h; @2-u; - 

To find Uisubstituted with p* is 

@2UF _ 1 -- 

‘* = KlxxPo rLY+A ’ 

17 

(37) 

(38) 
where 

u; r=- 

K* 2.w 

and 

From equation 38, the flow fi-ont velocity is 

&,& 1 -- Q- @, 170*+/c 

but U, =$, D and D’ = - ; hence, the previous equation becomes 

h2 

dD Klx,Po 1 

-- 

-z- ph, ID-+-Ah, - 

(41) 

Solving the resulting differential equation for D(t), 

t-t, =C,(D’-D’)+C,(D-D,) , (42) 

where C, = rkf 

=Lpo 

a,ndC,=- 

Kl& 

The variable t, is the time it takes for the flow front 

region to become fully developed, while D, is the entry length for the development of the flow 

front region. Solving for D(t), 

18 
(/1 h*)Z + 2;pp (t-to +C,D,2 +C*D,)-Ah, 

D(t) = 

Ixr 0 

l- (43) 

Equations 42 and 43 are important for the design of the VARTM process. The results 

obtained are compared to full-scale, finite-element-based simulations using LIMS 4.0 and are 

presented in the next section. A parametric study is presented to shed light on how one can scale 

the parameters in the VARTM process. 

4. Verification: Full-Scale Simulations 

The results obtained can be compared to finite-element-based simulations of the filling 

process in VARTM. LIMS 4.0 was used for simulation of the tilling process for five different 

cases, with different values for permeabilities and fiber volume fractions for the distribution and 

structural layers, respectively, and length of part, D. Each part was modeled using finite 

elements and the filling process simulated as a constant pressure injection at 1 atm at one comer 

of the part. The viscosity of the resin, the thicknesses of the structural and distribution layers, 

and the permeability of the distribution layer were held constant. The fill times and the values of 

d were determined and compared to those obtained from the closed form solution. The results 

are tabulated in Table 1. The fill time from the analytical solution was found to be within 2% of 

the value from the full-scale numerical simulation, while the value of d was within 12% of the 

value from simulation. For all cases, the condition K2,h-i 

K*,d2 

<< 1 -. was maintained for a valid 

analytical solution. 

The flow front history and the pressure contours at the final time are plotted for Case 1 in 

Figure 7. It can be observed that the flow front is constant in shape, while the lines of constant 

pressure in the saturated region are equally spaced and vertical to the x axis, thus verifying the 

assumptions of constant flow front shape and linear variation in pressure in the saturated region. 

19 
Table 1. Comparison of Closed Form Solution With Results From Full-Scale Numerical 

Solution of the VARTM Process 

t-to 

(s) 

% Error” 

hse Parameters LIMS 4.0 Closed Form Closed Form 

Solution LIMS 4.0 Solution d 

(%) (i) 

1 Kzxx = 8.8E-7 cm 2 8.9 9.8 44.9 44.8 9.7 -0.3 

Kz~ = 4.4E-7 cm2 

01 = 0.99, $2 = 0.50 

D-Do = 40.0 cm 

2 K2xx = 8.8E-7 cm2 29.2 30.9 19.1 19.4 5.7 1.5 

K2yy = 4.4E-8 cm2 

$1 = 0.99, $2 = 0.50 

D-Do = 19.0 cm 

3 Kzxx = 8.8E-7 cm 2 3.0 3.1 54.2 54.5 2.9 0.5 

K2, = 4.4E-6 cm2 

$1 = o-99,+2 = 0.50 

D-Do = 47.0 cm 

4 Kzxx= 8.8E-7 cm 2 9.2 10.1 71.7 72.1 10.2 0.6 

Kzfl = 4.4E-7 cm2 

4, = 0.99, @2 = 0.80 

D-Do = 40.3 cm 

5 Kzxx= 8.8E-7 cm 2 9.0 10.0 44.2 44.5 11.6 0.7 

Kzyy = 4.4E-7 cm2 

0, = 0.70, $2 = 0.50 

D-Do = 40.0 cm 

jte: The following variables were used in all cases: 

PO = lE6 g/cm-s2, 

p = 1 g/cm-s 

h, = 0.01 cm, 

h2=1cm, 

Klxx = IE-3 cm2, and 

Do-O cm for all the cases. 

a Based on results from LIMS 4.0. 

20 
5. Effect of Process Variables: A Parametric Study 

The process variables that affect the flow of resin are broadly classified into geometric 

parameters (such as thickness) and material properties (such as permeability and porosity of the 

two layers). These process variables influence the time to fill a mold of a given length. A 

parametric study of these effects allows for better design and analysis of the VARTM 

manufacturing process. In the present section, the effect of a number of process variables on the 

fill times and flow velocity was studied. The baseline values used for the study are: 

P, =latm,p=lcp, 

h, = 1.00 cm, h, = 0.025 cm, 

K ,xx =8.8x10-4cm2,K,, = 8.8x10-‘cm’,K,, =1.47x10-‘cm’, and 

a, = 0.99, cp, = 0.50. 

In the plots for each parameter, the flow front velocity (UF) and the time taken (t) are plotted 

against D for different values of the parameter. Note that the time axis is reversed; therefore, the 

lines for t start from zero at the top of the graph. 

5.1 Effect of Thickness Ratios. The effect of the ratio of the thickness of the distribution 

medium to that of the structural layer, hJ = + , is considered. Figure 8 plots the flow front 

velocity, U,, vs. D for different thickness ritios. As h,’ increases, the flow front velocity 

increases while the fill time decreases for a given length D. This is because as the thickness of 

the highly permeable distribution medium relative to that of the structural layer increases, the 

resin flow rate in the distribution medium increases. Since the diffusion material is used to 

distribute resin in the part and ensure mold filling, an increase in h,* will cause an increase in 

flow front velocity and a decrease in fill time. 

For the case of h; = 0.1, encountered with thin section composite parts, U, shows a slower 

decrease with D than with the other cases. With thick-section composite parts where h,’ + 0, 

21 
0.1 

0 

-0.1 

-0.2 

-0.3 

-0.4 

-0.5 

-0.6 

-0.7 

-0.8 

-0.9 

-1 

0.1 

0 

-0.1 

-0.2 

-0.3 

,-0.4 

% -0.5 

-0.6 

-0.7 

-0.8 

-0.9 

-1 0 

-I -I t 

(a) Flow Front History 

(b) Pressure Distribution at the Final Time Step 

Figure 7. Example of a Full-Scale Numerical Simulation: (a) Flow Front History and 

(b) Pressure Distribution at the Final Time Step. 

22 
8 * 

. 7 

6 

\ 

\ 

-+--UF(h,/h2=0.1) 

--i- -UF(h,/h2=0.025) 

-t -UF(hl/hz=0.00625) 

-t- t-t0(h,/h2=0. 1) 

-f- t-to(h,/h2=0.025) 

et-t0(h,/hz=0.00625) 

0 

1500 

2000 

2500 

0 50 100 150 200 250 

Wm) 

Figure 8. Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Thickness Ratios. 

U, falls rapidly. In order to fill such a part efficiently, the distance between the gates (0) has to 

be small; thus, the number of gates required increases. Therefore, the solution provides insight 

into the scaling laws required for manufacturing thick-section composites by VARTM. 

5.2 Effect of Permeability. The permeability values of importance are: ICI*,, the 

permeability of the distribution layer in the longitudinal x direction, and K;, and Klw, the 

permeabilities of the structural layer in the longitudinal x and thickness y directions. As seen in 

23 
Figures 9-l 1, as the permeability values increase, the time to fill decreases, and the flow front 

velocity increases. As the permeability values increase, the resistance of the material to the resin 

flow decreases. Hence, the net flow rates are higher, and the time to till decreases, while the 

flow front velocity increases. Since the flow rate in the distribution layer is higher, the effect of 

K,*, is significantly more than that of K;, and Ki, . These effects can also be observed from 

the plots shown. This has important ramifications on the selection and the thickness of 

distribution media. 

5.3 Effect of Porosity. The porosity of a fiber preform is defined as the fraction of the total 

volume of the material not occupied by the fibers. In composite manufacturing, the 

complementary term, volume fraction, was more commonly used. The volume fraction is 

defined as the fraction of the fiber preform occupied by the fibers and is related to the porosity 

by the relation V/ = 1 - CD. The porosity also affects the permeability of the material. However, 

this coupling has not been accounted for in the present work. 

The porosity values considered here are CD,, the porosity of the distribution layer, and cD~, 

the porosity of the structural layer. As observed from Figure 12, 0, did not significantly affect 

the time to fill and the flow front velocity. In Figure 13, as Oz increases, the flow-front velocity 

decreases, and the fill time significantly increases. This is because the fraction of the total part 

volume occupied by the thin layer of diffusion material is very low compared to that occupied by 

the fiber preform in the structural layer. Hence, increasing the porosity of the diffusion material 

does not have a significant effect. Whereas, if cD~ increases, the volume of the structural layer 

(which is unoccupied by the fiber perform) significantly increases. This additional volume must 

be filled by the resin, thus requiring more time to fill it and therefore slowing down the flow 

front. 

24 
. 

9 

8 

7 

t -+- ~. 

I 

\ 

UF (K,,, = 3.52E-3cm*) * 

\ ~ t-b (I&, = 2.2E-4cm*) 

t-h (I& = 8.8E-4cin*) 

\- 

\ t-b (I& = 3.52E-3cm*) 

i ‘\ 

a ? 

4 “+c 

1000 

1500. 

3z 

M 

2000 

2500 

3000 

0 50 100 150 200 250 

Wm) 

Figure 9. Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Permeability of Distribution Medium. 

6. Conclusions 

A closed form solution for flow of resin in the VARTM process has been developed. This 

process is explained by a two-layer model comprised of a distribution layer and a structural 

layer, containing fiber preform. The flow is divided into a saturated region where there is no 

25 
6 

5 

4 

P 

5 3 

5 

2 

1 

0 

i - -+ - Ur (IQ,, = 5SE-8 cm2) 

s 

k 

--A- - Ur (I& = 8.8E-7 cm2) 

-+ - Ur (I& = 3.52E-6 cm2) 

0 50 100 150 200 250 

Wcm) 

Figure 10. Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of In-Plane Permeability of Fiber Preform, 

crossflow, and a flow front region with a steady shape and uniform velocity where the driving 

flow emanates from the distribution layer to the structural layer. It is assumed that the thickness 

of the distribution layer is much smaller than that of the structural layer, and that the length of 

the flow front region is much smaller than that of the saturated region. It is also assumed that the 

crossflow in the flow front region is much higher than the flow from the saturated region into the 

flow front region. Darcy’s Law regarding flow in porous media and mass balances at different 

sections was used to formulate a system of differential equations, and a closed form solution was 

26 
z 3 

E 

= 2.5 

5 

2 

1.5 

1 

0.5 

0 

, 

I \ 

4 -+--UF (lC& = 9.1875E-9 cm2) 

4 

A 

- +--UF (I&, = 3.675E-8 cm2) 

- * -uF (Kzyy = 1.47E-7 cm2) 

\ \ 

$4 \ 

-t-b (I&,, = 9.1875E-9 cm2) 

\, \, et-t, (K2,,,, = 3.675E-8 cm2) 

50 100 

D (cm) 

100 

200 

300 

400 

z 

500 = 

600 

700 

800 

900 

1000 

150 200 250 

Figure 11. Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Transverse Permeability of Fiber Preform. 

found. The model predicted the shape and development of the flow front given the material 

properties, the geometric parameters, the pressure at the inlet, and the viscosity. The obtained 

results were verified by comparing them with full-scale simulations. The parametric study 

indicated trends that reflect the physics of the flow process and identified the parameters that 

27 
3.5 

1.5 

1 

0.5 

0 

-t- UF (porosity = 0.6) 

- i- - UF (porosity = 0.7) 

- *- - UF (porosity = 0.8) 

-t-b (porosity = 0.6) 

+ t-b (porosity = 0.7) 

-t-t-b (porosity = 0.8) 

100 

200 

300 

400 z 

w 

500 

600 

800 

0 50 100 150 200 250 

D @ml 

Figure 12. Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Porosity of Distribution Medium. 

significantly affect the filling process. Subsquent solutions provided physical insight into the 

manufacturing process and can be used for scaling, design, and optimization of the VARTM 

process. 

. 

28 
8 

. 

6 

5 

2 

1 

0 

- +- -UF (porosity = 0.3) 

- -A- -UF (porosity = 0.4) 

-t -UF (porosity = 0.5) 

.+ t-b (porosity = 0.3) 

+ t-b (porosity = 0.4) 

-)- t-b (porosity = 0.5) 

0 50 100 150 200 250. 

D (cm) 

400 z 

c, 

500 

600 

800 

Figure 13. Flow Front Velocity and Fill Time as a Function of Length of the Saturated 

Region: Effect of Porosity of Fiber Preform. 

29 
INTENTIONALLYLEFTBLANK. 

. I 

30 
7. References 

Bruschke, M. V., and S. G. Advani. “A Finite Element/Control Volume Approach to Mold 

Filling in Anisotropic Porous Media.” Polymer Composites, vol. 11, pp. 398-405, 1990. 

Bruschke, M. V., and S. G. Advani. “A Numerical Approach to Model Non-Isothermal, Viscous 

Flow With Free Surfaces Through Fibrous Media.” International Journal of Numerical 

Methods in Fluids, vol. 19, pp. 575-603, 1991a. 

Bruschke, M. V., and S. G. Advani. “RTM: Filling Simulation of Complex 

Three-Dimensional Shell-Like Structures.” SAMPE Quarterly, vol. 3, no. 1, pp- 2-l 1, 

1991b. 

Gallez, X. E., and S. G. Advani. “Numerical Simulations for Impregnation of Fiber Preforms in 

Composites Manufacturing.” Proceedings of the Fourth International Conference on Flow 

Processes in Composite Materials, University of Wales, 1996. 

Lee L. J., W. B. Young, and R. J. Lin. “Mold Filling and Cure Modeling of RTM and SCRlMP 

Processes.” Composite Structures, vol. 27, pp. 1-2, 1994. 

Liu, D., S. Bickerton, and S. G. Advani. “Modeling and Simulation of RTM: Gate Control, 

Venting and Dry Spot Prediction.” Composites Part A, vol. 27A, pp. 135-141, 1996. 

Mohan, R. V., N. D. Ngo, and K. K. Tamma. “On a Pure Finite Element Based Methodology for 

Resin Transfer Mold Filling Simulations.” Polymer and Engineering Science, vol. 39, no. 1, 

pp. 2843,1999. 

Murphy, G. M. Ordinary Dz@rential Equations and Their Solutions. Princeton, NJ: Van 

Nostrand, 1960. 

Pillai, K. M., and S. G. Advani. “Numerical Simulation of Unsaturated Flow in Woven or 

Stitched Fiber Mats in Resin Transfer Molding.” Polymer Composites, vol. 19, no. 1, 

pp. 71-80,1998a. 

Pillai, K. M., and S. G. Advani. “A Model for Unsaturated Flow in Woven or Stitched Fiber 

Mats in Resin Transfer Molding.” Journal of Composite Materials, vol. 32, no. 19, 

pp. 1753-1783,1998b. 

Seemann, W. H., II. “Plastic Transfer Molding Techniques for the Production of Fiber 

Reinforced Plastic Structures.” U.S. Patent 4,902,2 15, 1990. 

Simacek, P., E. M. Sozer, and S. G. Advani. “User Manual for DRAPE 1 .l and LIMS 4.0.” 

Technical Report 98-01, Center for Composite Materials, University of Delaware, 1998. 

31 
Tari, M. J., J. P. Irnbert, M. Y. Lin, A. S. Lavine, and H. T. Hahn. “Analysis of Resin Transfer 

Molding With High Permeability Layers.” Journal of Manufacturing Science and 

Engineering, vol. 120, pp- 609-616, 1998. 

Trochu, F., R. Gauvin, D. M. Gao, and J. F. Boudreault. “RTMFLOT-An Integrated Software 

Environment for the Computer Simulation of the Resin Transfer Molding Process.” Journal 

of Reinforced PIastics and Composites, vol. 13, no. 3, pp. 262-270, 1994. 

. I 

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201 MILL ST 

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C BAKIS 

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HTHAHN 

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245 HAMMOND BLDG 

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PURDUE UNIV 

SCHOOL OF AERO & ASTRO 

CTSUN 

W LAFAYETTE IN 47907-1282 

STANFORD UNIV 

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& AEROBALLISTICS 

S TSAI 

DURANT BLDG 

STANFORD CA 94305 

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J M WHITNEY 

COLLEGE PARK AVE 

DAYTON OH 45469-0240 

UNIV OF DELAWARE 

CTR FOR COMPOSITE MTRLS 

J GILLESPIE 

M SANTARE 

G PALMESE 

S YARLAGADDA 

S ADVANI 

D HEIDER 

D KUKICH 

20 1 SPENCER LABORATORY 

NEWARK DE 19716 

UNIV OF ILLINOIS AT 

URBANA CHAMPAIGN 

NATIONAL CENTER 

FOR COMPOSITE 

MATERIALS RESEARCH 

J ECONOMY 

216 TALBOT LABORATORY 

104 S WRIGHT ST 

URBANA IL 61801 

NORTH CAROLINA STATE UNIV 

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47 

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THE UNIV OF 

TEXAS AT AUSTIN 

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J PRICE 

A WALLS 

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VA POLYTECHNICAL 

INST & STATE UNIV 

DEPT OF ESM 

MWHYER 

K REIFSNIDER 

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BLACKSBURG VA 24061-0219 

UNIV OF MARYLAND 

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AJVIZZJNI 

COLLEGE PARK MD 20742 

DREXEL UNIV 

ASDWANG 

32ND & CHESTNUT ST 

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AMSRL WM MA 

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RYTN 

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E RJGAS 

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AMSRL WM MB ALC 

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ECHIN 

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NO. OF 

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48 
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S WALSH 

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W GILLICH 

T HAVEL 

J RUNYEON 

M BUTUUNS 

E HORWATH 

B GOOCH 

W BRUCHEY 

AMSRL WM TC 

R COATES 

AMSRL WM TD 

A DAS GUF’TA 

T HADUCH 

T MOYNIHAN 

F GREGORY 

A RAJENDRAN 

M R4FTENBERG 

M BOTELER 

T WEERASOORIYA 

D DANDEKAR 

A DIETRICH 

AMSRL WM TE 

A NIILER 

J POWELL 

AMSRL SS SD 

H WALLACE 

AMSRL SS SE R 

R CHASE 

AMSRL SS SE DS 

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AMSRL SE L 

R WEINR4UB 

J DESMOND 

D WOODBURY 

49 
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LTD 

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MERL 

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UK 

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UK 

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MUNICH 

GERMANY 

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P N JONES 

D SCOTT 

M HINTON 

SEVEN OAKS KENT TN 147BP 

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IRO CANADA 

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ROYAL MILITARY COLLEGE OF 

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WKS 

w LANZ 

ALLMENDSTRASSE 86 

3602 THUN 

SWITZERLAND 

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TECHNOLOGY 

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FACULTY OF MECHANICAL ENGR 

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LANGE IUEIWEG 137 

PO BOX 45 

2280 AA RIJSWIJK 

THE NETHERLANDS 

FOA NATL DEFENSE RESEARCH 

ESTAB 

DIR DEPT OF WEAPONS & 

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S 172 90 STOCKHOLM 

SWEDEN 

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3602 THUN 

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RAFAEL 

ARMAMENT DEVELOPMENT 

AUTH 

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HAIFA 3 102 1 ISRAEL 

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BOX 201 

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51 

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1 B HIRSCH 

TACHKEMONY ST 6 

NETAMUA 42611 

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DYNAMICS SYSTEMS 

M HELD 

PO BOX 1340 

D 86523 SCHROBENHAUSEN 

GERMANY 
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OMB No. 07060188 

Public reporting burden for *his ccAleRion of infomution is esfimated to avenge 1 hour per response, includmg the time for reviewing InStruCtions. searching existing data Sources, 

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT NPE AND DATES COVERED 

October 2000 Final, January 1997-July 1999 

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

An Analytical Vacuum-Assisted Resin Transfer Molding (VARTM) Flow Model 62105AH84 

6. AUTHOR(S) 

Bruce K. Fink, Kuang-Ting Hsiao,* Roopesh Mathur; John W. Gillespie, Jr.,* 

and Suresh G. Advani* 

7. PERFORMING ORGANlZATlON NAME(S) AND ADDRESS 6. PERFORMING ORGANIZATION 

U.S. Army Research Laboratory REPORT NUMBER 

ATTN: AMSRL-WM-MB 

Aberdeen Proving Ground, MD 21005-5069 ARL-TR-2354 

9. SPONSORING/MONITORING AGENCY NAMES(S) AND ADDRESS 10.SPONSORING/MONlTORlNG 

AGENCY REPORT NUMBER 

11. SUPPLEMENTARY NOTES 

l University of Delaware, Newark, DE 197 16 

12a. DISTRIBUTlON/AVAlLABlLlN STATEMENT 12b. DISTRIBUTION CODE 

Approved for public release; distribution is unlimited. 

13. ASSTRACT(Maximum 200 words) 

A closed form solution for the flow of resin in the vacuum-assisted resin transfer molding (VARTM) process is used 

extensively for affordable manufacturing of large composite structures. During VARTM processing, a highly permeable 

distribution medium is incorporated into the preform as a surface layer. During infusion, the resin flows preferentially 

across the surface, simultaneously through the preform, to a complex flow front. The analytical solution presented here 

provides insight into the scaling laws goveming fill times and resin inlet placement as a function of the properties of the 

preform, distribution media, and resin. The formulation assumes that the flow is fully developed and is divided into two 

areas: (1) a saturated region with no crossflow, and (2) a flow front region, which moves with a uniform velocity, where 

the resin is infiltrating into the preform from the distribution medium. The law of conservation of mass and Darcy’s Law 

for flow through porous media are applied in each region. The resulting equations are nondimensionalized and are 

solved to yield the flow front shape and the development of the saturated region. It is found that the flow front is 

parabolic in shape, and the length of the saturated region is proportional to the square root of the time elapsed. The 

obtained results are compared to data from full-scale simulation and show good agreement. The solution allows greater 

insight into the physics process, enables parametric and optimization studies, and can reduce the computational cost of 

full-scale, three-dimensional (3-D) simulations. 

14. SUBJECT TERMS 15. NUMBER OF PAGES 

composite material, vacuum-assisted resin transfer molding, flow modeling 

16. PRICE CODE 

17. SECURIN CLASSIFICATION 18. SECURIN CLASSIFICATION 19. stxuRirY CLASSIFICATION 20. LIMITATION OF ABSTRACT 

OF REPORT OF THIS PAGE OF ABSTRACT 

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL 

NSN 7540-01-280-5500 53 Standard Form 298 (Rev. 2-89) 

Prescribed by ANSI Std. 239-l 8 298-l 02 
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54 
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1. ARL Report Number/Author ARL-TR-2354 (Fink) Date of Report October 2000 

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