Department of Applied Mathematics and Statistics. State University of New York at Stony Brook. Stony Brook, NY 11794-3600, USA. A P Jardine and J S Madsen.
POROSITY MIGRATION IN RTM 1 W K Chui, J Glimm and F M Tangerman Department of Applied Mathematics and Statistics State University of New York at Stony Brook Stony Brook, NY 11794-3600, USA A P Jardine and J S Madsen Department of Materials Science State University of New York at Stony Brook Stony Brook, NY 11794-2275, USA T M Donnellan and R Leek Northrop Grumman Advanced Technology & Development Center Bethpage, NY 11714, USA
ABSTRACT
The reduction of porosity is an important requirement in the manufacture of reliable composite components. In the Resin Transfer Molding (RTM) process, porosity results from the formation and growth of gas bubbles during the ll and cure stages of the process. Understanding the dynamics of the formation and motion of these bubbles will allow design of RTM processes that provide optimum quality and performance. In this paper, we demonstrate that an unsaturated ow model for gas bubble migration is in qualitative agreement with experimental results.
1 INTRODUCTION The high cost of autoclave-processed composites has led to interest in alternative processing concepts. Resin transfer molding (RTM) is one particularly attractive technique for many applications since it combines cost savings with potential performance improvements (e.g., 3-D strength characteristics). In the past, tool design decisions, component design decisions, and processing cycles for composites have been develThe work at Stony Brook was nancially supported by the Northrop Grumman ATDC and by NSF grant number DMS-9312098. The Northrop Grumman portion of the work was partially supported by ARPA Technology Development Agreement No. MDA972-93-0007 that is being administered by the USAF Wright Laboratory Materials Directorate. 1
oped through experience and trial-and-error approaches. One problem with RTM as a composite fabrication technology is that the industrial experience base is limited. In the RTM process, the important process characteristics are the mold ll behavior and the resin cure behavior. At the macroscopic level, variations in ow conductivity can result in nonuniform ow fronts and potentially large areas of dry pre-form after the ll process is complete. An analysis of the macroscopic ll behavior provides information on the mold lling time as well as on the potential for large-scale process defects. The modeling has mostly involved Darcy-law-based descriptions of the macroscopic ow [1,2,3,4,5,6,7,8,9,10]. The mat structure promotes the development of a heterogeneous ow eld composed of inter-tow and intra-tow ow that can result in porosity entrapment in the interstices of the tow structure. Porosity can signi cantly a ect the composite mechanical performance [11]. Various workers have studied porosity formation that results from this heterogeneous ow [3,7,12]. An additional important consideration is the mobility of bubbles that have formed in the ll process prior to resin cure. Models for bubble mobility would allow process design for reduction of porosity concentration in any composite system. In this paper, we demonstrate that a class of continuum models accurately predicts the ow and distribution of macro bubbles. Local pressure is considered a mobilizing factor: as the local pressure increases, bubbles shrink in size, and their mobility is increased. We propose a class of macroscopic porous media models to describe the bubble distribution during the mold lling phase. These models contain a single free parameter that is mat dependent. It is shown that these models produce reasonably good correlation to experimentally observed behavior. For a detailed discussion of the theoretical and experimental results we refer to [13].
2 THEORY The general form of the mathematical models we adopt in this paper is based on the simplest unsaturated ow models, as found in the porous media literature [14]. Our macroscopic parameters are pressure P and the saturations Sr and Sa of the resin and the macro bubble phase
relative to the available pore space. Clearly: + Sa = 1: (1) The available pore space is characterized by the ber volume fraction , assumed constant throughout the mat. The absolute concentration of the resin and macro bubble phase are de ned by Sr and Sa, respectively. We treat the resin and the macro bubble phase as incompressible and obtain a conservation law for each of the phases: @t ( Sr ) + div (qr ) = 0 (2) @t ( Sa) + div (qa) = 0 (3) Sr
and qa denote the phase volumetric velocities and are given by Darcy's law [14,15]:
qr
qr qa
= krel;r K r P r
= krel;a K r P a
(4) (5)
r and a denote the phase viscosities, krel;r and krel;a denote relative phase permeabilities, and K denotes the absolute mat permeability. The relative permeabilities, krel;r and krel;a, take values between 0 and 1. The conservation form of these equations implies that at any time there will be a sharp discontinuity in the resin saturation at the resin front. The resin saturation ahead of this front is zero, while the resin saturation immediately behind the resin front is determined by conservation of resin volume [14,13,16]. The resin saturation behind the front increases continuously to 1.0 as the distance from the front increases.
For successful modeling of an RTM ll process, the modeling of the relative permeability parameters is critical. The experimental e orts and modeling are directed to nding the relationship of these parameters to measurable process conditions. We adopt simple models for the relative permeabilities krel;r and krel;a . In the RTM process, resin saturations are typically high, i.e., > 90% and vary over only a small range. A sensible assessment for krel;r is that it is close to one and standard choices are linear (krel;r (Sr ) = Sr ) and quadratic (krel;r (Sr ) = Sr2). In our conceptual model bubbles are created during mold lling at the front, at a constant volume at origination Vo , independent of the outlet pressure Pout . These bubbles are more or less round with diameter on the order of a tow spacing. The mobility of a bubble is
determined by its size. In response to change in local resin pressure, its size decreases, enhancing its mobility. The gas in the bubble is assumed to be ideal: P V = Pout Vo . Therefore, the mobility of the air phase depends on the rescaled pressure: P
= PP : out
(6)
A bubble becomes mobile when its size reaches a critical volume Vc . Vc is a resin/air/ ber-mat property and a critical pressure Pc is required for the bubble to become mobile: = Pc = Pout VVo : (7) c The reduced critical pressure is constant and a mat property. There is a zone behind the resin front where the bubbles have not yet moved. At the boundary of this zone, in the resin-rich region, the pressure equals the critical pressure. Pc
In our model krel;a depends on saturation and rescaled pressure. In order to model the immobility of bubbles which are too large, we propose a residual air saturation Sa;resid(P ), describing the saturation of the air contained in immobile bubbles and which depends on the rescaled pressure. We propose that krel;a depends only on the reduced saturation Sa;red: = S1a ?? SSa;resid((PP)) : (8) a;resid Such a reduced saturation is common in the oil-recovery literature, but its pressure dependence is a novel aspect of this work. Standard choices for krel;a are linear or quadratic in the reduced saturation. Sa;red
In the remainder of this paper we demonstrate that for RTM experiments, described below and in [17], the residual air saturation can be chosen to provide a good match to data. These experiments were performed in rectangular molds, with inlet and outlet ports at either end. Resin was injected at the inlet port, and inlet and outlet pressures were held constant during the experiment. The experiment was stopped just when the resin front was about to leave the ber mat (at breakthrough). Care was taken that the resin did not cure during ll. The resin was cured at atmospheric pressure, and a bubble measurement was made at various cross sections in the mold.
Curing produces a distinction between the macro bubble content during and after the experiment. During mold lling the pressure varies through the mold, while curing occurs at a constant pressure. The aftercure bubble fraction, denoted by Va, is measured experimentally as a function of location, but can be thought of as a function of pressure, namely the pressure just prior to raising the pressure to cure pressure. It depends on only the rescaled pressure P = PP and: P Sa;resid (P ) = Pcure Va (P ): (9) out
Our procedure for matching Sa;resid (P ) to data is through a piecewise linear model for the after-cure bubble fraction Va(P ), which requires three parameters: maximum volume fraction Vmax, and rescaled pressures P 1 and P 2 (Figure 1). 10
8
V (%) a 6
4
V max
2
0
1
P1 P 2 Rescaled Pressure
Figure 1: The piecewise linear model used to t the residual saturation to the experimental data. Shown is the model for the after-cure bubble fraction Va (P ). The parameters are the maximum bubble fraction Vmax, and pressures P 1 and P 2. The upper and lower limits of the pressure line are rescaled inlet pressure P in and rescaled outlet pressure P out = 1, respectively. Our model asserts that the maximum bubble fraction Vmax depends linearly on P cure = PP , and that P 1 and P 2 are mat constants. cure out
We test this assertion by reducing the after-cure macro bubble distribution in the following manner:
1. Rescale Vmax by a factor P cure . 2. Rescale the normalized distance direction (from 0 to 1) by a fac[P ]
tor P in ? 1 = P This rescaling is essentially a transformation from normalized distances to rescaled pressures. out
Figure 2 shows how, through a suitable choice of parameters for residual saturation, the experimental data from [17] are reproduced, while gure 3 shows their rescaling. 10 Outlet Pressure: 1 atm Outlet Pressure: 0.5 atm
8
Outlet Pressure: 0.3 atm
Va (%) 6
4
2
0 0
0.2
0.4
0.6
0.8
1
Normalized Distance to Outlet
Figure 2: Comparison of macro bubble content pro les for three experiments obtained from [17]. In these experiments, the pressure di erence between inlet and outlet was held at 5 atmospheres and the outlet pressure varied: 1, 0.5, and 0.3 atmosphere. The ber mat was a unidirectional fabric (Brochier Lyvertex 21130) at a ber volume fraction of 59%.
3 EXPERIMENTAL The pre-forms for the experiments were constructed from 15 plies of style 1564 berglass fabric manufactured by North American Textile Corporation. Fabric areal weight was measured at 0.03738 grams per square centimeter. The fabric was an orthogonal plain weave with a count of 20 warp yarns by 15 ll yarns per 2.54 cm. Warp and ll have the same ECG 150-4/2 yarn structure. Our panels had a nal
10 Outlet Pressure: 1 atm Outlet Pressure: 0.5 atm
8
Outlet Pressure: 0.3 atm
Reduced Va 6
4
2
0 0
0.2
0.4
0.6
0.8
1
Reduced Normalized Distance To Outlet
Figure 3: Rescaled data from [17]'s experiments, using atmospheric cure pressure. The pressure drop in each of these experiments was 5.0 atm. In this gure, the outlet pressure is as indicated. The rescaled data lie on a common curve as in Figure 1. ber volume content of 51.0%. The resin system was a Derakane epoxy vinyl ester. The molds had overall dimensions of 25.4 12.7 2.54 cm and a atness tolerance of 0.005 cm. The uncatalyzed resin, which had been de-gassed for thirty minutes at 6:66 10?3 P a, was immediately catalyzed and injected at a constant pressure and controlled mold evacuation level. Resin viscosities varied from 365-504 10?3 Ns=M 2 . The experiment was performed at room temperature using a conventional pressure pot, pressure regulator, vacuum pump, and vacuum regulator. The uid ow direction was parallel to warp bers, and normal to ll bers. The experiment was stopped at breakthrough, after which the resin was cured at atmospheric pressure. After completion of the cure, the panel was removed from the mold and was sectioned as shown in Figure 4. The bubble area fraction of each section was determined by scanning each photomicrograph into a Macintosh IIx computer system with a Silverscanner II. Each photomicrograph was scanned using Colorit 3.0 software, and NIH image analysis software was used to process the image. Table 1 shows the porosity distribution and levels as a function of the parameters examined. The results are given in percentage of the total cross-sectional area covered by macroscopic voids.
1.27 cm
7.62
6.35
5.08
3.81
2.54
1.27
7.62 cm
Inlet end
Outlet end
Figure 4: Sectioning of cured panels for photomicrographs. PANEL SIZED 2 8 7 1 9 UNSIZED 3 6 4 5
Pout
[P] 7.62 6.35 5.08 3.81 2.54 1.27 (atm) (atm) (%) (%) (%) (%) (%) (%)
1 1 3/4 1/2 1/38
3.5 5.5 3.5 3.5 5.5
0 0 0 0 0
1 1 0 0 0
2 2
1 3/4 1/2 1/4
3.5 3.5 3.5 3.5
0 0 0 0
0 0 0 0
1 0 0 0
