CURING BEHAVIOR OF THICK-SECTIONED RTM COMPOSITES
D. J. MICHAUD, A. N. BERIS and P. S. DHURJATI
Department of Chemical Engineering and Center for Composite Materials
University of Delaware
Newark, DE 19716
Published in Journal of Composite Materials, Vol. 32, No. 14, 1998, pp 1273-1296
©1998 Technomic Publishing Co., Inc.
ABSTRACT: The successful manufacture of thick-sectioned composites is challenging, since
the highly exothermic nature of thermoset resins and limited temperature control make it difficult to
avoid detrimental thermal and cure gradients within the composite. In order to make quality parts,
it has been found experimentally that cure temperatures must be lowered as much as 50% from
those suggested for thin parts. Differential Scanning Calorimetry (DSC) experiments of a vinylester resin system at these lower temperatures revealed a significant dependence on temperature for
the maximum extent of cure. If the resin is cured isothermally at 55 °C, the final conversion of the
resin was found to only reach 70%. When the maximum extent of cure parameter was
incorporated into an empirical autocatalytic kinetic model, it was found to significantly improve the
description of the cure kinetics. Inhibitors, added to the resin to improve shelf-life, disappear
rapidly at higher cure temperatures but can double the time required to cure a thick composite
processed at 55 °C. A zeroth order kinetic relationship was developed to estimate the amount of
inhibitor in the system during the resin's cure. The inhibitor relationship and the improved kinetic
model were used in a finite difference cure simulation to successfully predict the thermal gradients
during cure of a 2.54 cm thick composite manufactured by resin transfer molding (RTM).
KEY WORDS: resin transfer molding, vinyl ester, free-radical cure, inhibitor kinetics, cure
modeling, thick laminates, thermoset composites.
1. INTRODUCTION
As the composite industry matures, the desire for thick and complexly shaped parts has
become more prevalent. The composite components of bridge structures, tank and submarine
hulls, and airplanes can require cross-sections greater than 2 cm. In the past, these parts could not
be successfully manufactured or their fabrication required costly processing procedures, long
processing times, or expensive equipment. Autoclave lay-up was one of the few processing
techniques that could be used to manufacture thick parts. As a result, many researchers worked at
optimizing the autoclave lay-up process for thick composites [1-4].
The curing of thick-sectioned parts is challenging due to the low thermal conductivity of the
composite and the high heat of reaction of many thermoset resins. This combination of high
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thermal resistance and a large heat source within the part during cure can lead to large thermal
gradients, generation of residual stresses, and polymer degradation. In order to improve the
quality of thick composites, the processing temperature needs to be controlled such that the thermal
gradients are small. This typically means that the cure temperatures need to be lower and the
processing time longer. Since the processing temperatures are necessarily lower than those for thin
parts, the chemorheology and curing kinetics may be considerably different than those observed at
higher temperatures. In order to successfully optimize the curing phase of the RTM process for
thick-sectioned composites by means of simulation, an accurate kinetic model of the resin is
required.
The fabrication of thick-sectioned parts has been aided recently by technological
improvements to resin transfer molding (RTM) and other resin infusion processes. While these
processes ease some of the manufacturing constraints by allowing more complex geometries and
shorter cycle times, a number of important processing considerations remain. A number of
researchers have developed simulations for the RTM process, although most focus on the flow
aspects of the process, assume a thin part geometry, and provide only basic kinetic analysis [5-7].
Predicting the flow of resin within anisotropic fiber mats is a very important design issue,
especially when the resin is curing during flow. In the experiments of interest to this research,
however, the curing stage of the RTM process took place after the filling stage and therefore it is
considered separate from the flow process. In the future, the use of a more accurate kinetic model,
such as proposed in this work, could increase the applicability of flow simulations under
conditions where curing occurs at low processing temperatures.
The kinetic characterization of thermoset resin systems using differential scanning
calorimetry (DSC) has been well established in the literature [8-12]. The investigation of kinetic
parameters for lower viscosity resins typical to resin transfer molding has been performed by a
number of different researchers [13-16], however the temperature ranges they have reported are
higher than those needed for successful thick-sectioned cure. It is the extension of this research to
lower temperatures of cure that is the primary focus of the present work.
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This paper focuses on predicting the cure behavior of a vinyl ester resin under the
processing conditions needed to make quality thick-sectioned composites. The kinetic behavior of
the resin for temperature ranges lower than previously studied and the effect of polymerization
inhibitors within the resin system are investigated. Once the kinetic analysis of the resin is
completed, the resulting cure simulation can be used to determine optimal processing conditions for
thick RTM composites using a methodology similar to that used by Pillai et al. [4] for the autoclave
lay-up process. Section 2 outlines the fabrication of actual 2.54 cm thick composite plates and
describes the materials used in the RTM experiments. Section 3 describes a finite difference
simulation used to predict the curing of the composites based on experimentally determined
physical and chemical parameters. Section 4 highlights the modifications required for the kinetic
models within the simulation to accurately predict cure behavior at the temperatures required for
thick-sectioned parts.
Section 5 compares the improved version of the simulation with
experimental results and demonstrates the dramatic affect that the presence of fibers has on the
kinetic behavior of the resin.
2. THICK-SECTIONED RTM MANUFACTURING
A number of vinyl ester/E-glass composite slabs were fabricated in the lab to investigate the
issues involved in the thick-sectioned cure of thermoset composites. The final dimension of each
composite piece was 17.72 cm square by 2.54 cm thick. Attempts to manufacture parts of this
thickness using a cure temperature typical of thinner parts (80 °C to 100 °C) were found to
produce pieces with large delaminations through the center. Center temperatures were observed to
exceed 200 °C, which led to some polymer degradation. It was found that a much lower cure
temperature (55 °C) was required to produce pieces of satisfactory quality. Figure 1 shows the
cross-sections of two actual 2.54 cm thick composites processed at 55 °C (top) and 65 °C
(bottom). Only a 10 °C increase in curing temperature is sufficient to result in center delaminations
within the composite. Unfortunately, the lower temperatures significantly increase the curing time
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of the part due to the slower polymerization reaction and inhibitors added to the resin system to
increase shelf-life.
2.1
Components Used During Composite Manufacture
The fiber reinforcement used in fabricating the composite pieces was a 0°/90° oriented
knitted glass mat. The mat was cut into 72 sheets with the dimensions of 19.7 cm square. This
size was selected to ease placement of the sheets within the 20.32 cm square mold. Each edge of
the final composite was trimmed by 1.27 cm to eliminate the resin-rich sections produced by this
procedure. The fiber mats were composed of E-glass tows, whose fibers were coated (sized) by
the manufacturer with an undetermined component. The amount of sizing on the fibers was
approximated to be 8% by weight. This value was determined by heating a collection of fibers
(without knitting) within an oven at 550 °C for two hours and measuring the weight loss of the
fiber bundle.
A popular RTM resin, Dow Derakane 411-C50, was the only resin to be used in this
research. With a viscosity of only 100 cP, it is ideally suited to injection through fiber mats. The
411-C50 resin system contains an equal mixture by weight of an epoxy-based vinyl-ester and
styrene with an undetermined amount of inhibitory agents to increase shelf-life. The resin was
catalyzed by 1.75 wt% Witco USP-245, an organic peroxide. The kinetic parameters for this
resin system within the temperature range of 90 to 120 °C were previously evaluated by Palmese et
al. [16].
2.2 Resin Transfer Molding Apparatus and Processing
A diagram of the equipment used to manufacture the resin transfer molded parts is provided
in Figure 2. The 316 stainless steel mold (shown in a cut-away view) consists of two solid plates
to provide top and bottom surfaces and a 2.54 cm thick "picture frame" center. The "picture
frame" opening is 20.32 cm square. The center mold piece was drilled to allow the passage of up
to six thermocouples into the mold to measure internal temperatures during processing. The mold
is placed within a Wabash heat press, which is closed hydraulically until the mold surfaces contact
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the center mold frame and compress the sealing gasket that is placed on the outside rim of the
mold.
The mold is filled with room temperature resin at 240 kPa until the resin is seen exiting the
mold. The resin pressure is then slowly increased to 380 kPa. The filling stage of the process is
continued until air bubbles no longer appeared in exit tubing. This is to ensure sufficient resin
infiltration of the fiber mat and minimal voids within the final composite.
To begin curing the composite, heat is applied to the mold by water circulated through
aluminum platens on the press. The temperature of the circulating water is controlled to within
±5 °C. Due to the large heat capacity of the stainless steel mold, temperature fluctuations within
the mold are typically less than 1 °C. Temperatures within the mold are measured by J-type
thermocouples placed through the mold. The thermocouples are placed between different layers of
the fiber mat to measure through-thickness variations in temperature. In a 2.54 cm thick part,
thermocouples are placed on both top and bottom surface and at heights of 0.635 cm, 1.27 cm,
and 1.905 cm. While the above thermocouples are placed at the exact center of the composite
(10.16 cm from each mold edge), one thermocouple is typically placed at a height of 1.27 cm but
only 5.08 cm from one of the mold edges to ensure minimal heat loss from the sides of the mold.
A Macintosh computer with LabView software is used to collect the temperature data once every
second.
2.3
Flow Considerations
Since the primary focus of these experiments was to investigate the cure of thick-sectioned
composites, an effort was made to limit the effects of resin flow in the experiment. The resin was
injected at room temperature to ensure polymerization did not begin.
Furthermore, the center
portion of the mold was shaped to reduce the formation of air pockets. The entrance of the mold
was cut to provide a resin-rich region along the width of the mold, which allowed the resin to
move as a front through the fiber reinforcement. The exit side of the mold was shaped into a weir
to ensure that the majority of the mold was full before resin could begin exiting the mold.
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Although voids within the cured composites averaged 4% by volume as determined by ASTM
standard D2734, dry spots and large voids were not observed.
3. NUMERICAL CURE SIMULATION OF THE RTM PROCESS
The simulation of the curing phase for the resin transfer molding process was accomplished
using a modified version of TGCURE, a cure simulation developed by Bogetti and Gillespie [2].
TGCURE was created to model the cure behavior of polyester and epoxy composites within an
autoclave environment. While the simulation is capable of analyzing arbitrarily shaped TwoDimensional cross-sections, only One-Dimensional simulations across the thickness were used in
this work.
3.1 Traditional Modeling of Thermoset Curing
The TGCURE program uses an alternating direction explicit (ADE) finite difference method
[17] to solve Fourier's anisotropic transient heat conduction equation with constant material
properties. The generalized expression with an internal heat generation source term is as follows:
ρc ⋅ c p
∂T
dq
= ∇ ⋅ ( K ⋅∇ T ) + ρc
∂t
dt
(1)
where ρc is the composite's density, cp is the composite's heat capacity, and K represents the
thermal conductivities of the composite. The heat generated by the curing resin, dq/dt, is calculated
within the simulation according to Equation (2), which assumes that the heat released by the resin
is proportional to the change in the resin's extent of cure, α . The fractional change in extent of
cure is multiplied by the resin's total heat of reaction, ∆ H rxn. The result is then weighted by the
mass fraction of the resin within the composite, mr.
dq
dα
= mr ⋅ ∆Hrxn ⋅
dt
dt
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(2)
The cure rate of the resin, as shown in Equation (3), is modeled according to the empirical
autocatalytic model used by Kamal and Sourour [8] and popularized by many other researchers [916] to describe free-radical polymerization.
dα
= ( k1 + k ⋅ α m )( 1.0 − α ) n
dt
(3)
The k 1 term is often negligible for vinyl-ester resin systems [14-16], which indicates the curing
rate is approximately zero at the beginning of the polymerization. The n exponent for free-radical
mechanisms is often assumed to be equal to (2-m) so that the overall reaction order is constant [1316]. The rate constant, k, follows an Arrhenius relations as shown in Equation (4):
− E RT )
k = A⋅ e ( A
(4)
where A is the pre-exponential factor, EA is the activation energy, and R is the gas constant.
The TGCURE simulation uses convective (Robin) boundary conditions to calculate the
surface temperature of the composite from the measured water temperature circulating within the
heat press platens. The surface temperature of the composite is required by the simulation for its
finite difference calculations, but often only the heating water temperature is known.
The
boundary conditions account for the natural convection of the water and conductivity of the mold.
Unfortunately, the heat capacity of the mold is not represented in this method. If experimental data
for the surface temperature is available, prescribed (Dirichlet) boundary conditions can be used as
an alternative.
3.2 Example of a Simulated Cure Cycle
Once the water temperature, physical parameters, and kinetic parameters are provided to the
simulation, the temperature profiles for each node are calculated. Figure 3 shows the simulated
results of a 60 °C cure cycle for a 2.54 cm thick composite. The term "60 °C cure cycle" means
that the circulating water temperature in the heat press platens was set to 60 °C and held constant
during the simulation. 7 minutes is required to raise the water temperature from 25 °C to the
required 60 °C. In Figure 3 the surface of the composite is seen to follow the temperature of the
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heating water closely. The quarter and center nodes require more time to reach 60 °C due to the
low thermal conductivity of the composite. Once the center begins to cure, the heat released by the
reacting polymer raises the center temperature of the composite and leads to a faster reaction rate.
As the cure of the resin nears completion, the temperatures within the composite again approach the
water temperature.
The simulation also predicts the extent of cure profiles for each node in the simulated
composite. Figure 4 shows the extent of cure profiles for the surface and the center nodes during
the 60 °C cure cycle. The point at which the center and surface extent of cures cross is an
important design issue for thick sectioned composites. This point signifies the time that the cure of
the composite becomes "inside-out". The closer the cross-over point is to the gel point of the resin
the lower the residual stresses will be in the final composite. A design trade-off exists between
how low the cross-over point is and the time required to cure resin.
3.3 Adaptive Time Steps
One of the modifications introduced to the simulation of the resin transfer molding process
was an adaptive time step routine to the program. The resin's cure rate at the center of a thick
composite can reach very large values and a small time step is required to capture the resin's extent
of cure correctly. As an example, the simulation of a 2.54 cm thick composite with 52 volume%
vinyl ester resin cured at 60 °C required a maximum time step of 1/32th of a second for the
temperature profile to converge to a final temperature profile.
Since a small time step is required only during a limited portion of the cure cycle, an
adaptive time step algorithm was added to the simulation. The algorithm allows for larger time
steps at the beginning of the cure cycle (1 to 2 seconds) and then reduces the time step as required
during the exothermic portion of the cure. As the curing rate for the resin lessens, the need for a
small time step is reduced and the algorithm increases the time step towards its original value as
necessary.
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The adaptive time step algorithm was implemented by setting a maximum allowable curing
rate, ∆αmax, and an acceptable minimum curing rate, ∆αmin. When the value of ∆αmax is violated
at any node within the simulation, the time step within the simulation is halved. The time step is
doubled (until the original value is reached) when the curing rate at every node within the
simulation falls below ∆αmin. The simulations in this paper use a starting time step of 1 second, a
maximum allowable curing rate of 0.0005 per time step, and a minimum acceptable curing rate of
0.0001 per time step.
While this approach was found to be important for vinyl ester resins, improvement of the
simulation's temperature prediction was also seen for polyester and epoxy resin systems. The
adaptive time step algorithm produces smoother temperature profiles and assures convergence. It
is useful for any simulation package used to predict the cure of highly exothermic resins to have a
similar feature to control the time step size.
3.4 Kinetic Parameters
The original kinetic equations within the TGCURE simulation were designed for rather
simple resin systems that follow the autocatalytic cure behavior shown in Equation (3).
This
particular expression for the resin kinetics was found to be insufficient when used to predict
internal composite temperatures using literature values for the same resin system as reported by
Palmese et al. [16]. While the simpler kinetic model was adequate for temperature above 90 °C,
these relationships do not seem to hold at the lower processing temperatures required for thicksectioned parts. The discrepancy in predicting the center temperature of a composite can be shown
in Figure 5.
The peak temperatures within the simulated composite are greatly over-predicted and occur
much earlier than those seen during actual experiments. The processing temperature for the
composite presented in Figure 5 was 53 °C, which is 37 °C less than the lowest temperature
measured by Palmese et al. [16]. The problems within the simulation and its kinetic representation
9
motivated a study of the resin system's kinetic parameters at temperatures lower than previously
studied.
4. LOW TEMPERATURE KINETICS OF VINYL ESTER RESIN
Differential Scanning Calorimetry (DSC) was used to experimentally determine the kinetic
parameters of the Dow Derakane 411-C50 vinyl-ester resin system that included isothermal cure
temperatures below 90 °C. A DuPont Model 9900 thermal analyzer calibrated with high-purity
indium was used for these experiments. Catalyzed resin samples weighing between 6 and 12 mg
were placed in sealed pans. After the experiment, each pan was weighed to ensure styrene was not
lost from the sample pan during the polymerization. All experiments were done under a dry
nitrogen atmosphere.
The kinetic parameters for the resin were found using Equation (2) and through non-linear
regression of an empirical autocatalytic model, shown in Equation (5), according to the procedure
developed by Kamal and Sourour [8]. This manner of determining the kinetic parameters of a
thermoset resin has been well documented in the literature [8-16,18]. Equation (2) was used to
convert the DSC heat flow data to cure rate data by dividing the heat flow values by the ultimate
heat of reaction for the resin. The resin's ultimate heat of reaction, 423 ± 5 J/g, was found by
slowly ramping resin samples to 250 °C and integrating to find the total heat released by the resin.
This value compares to that of 425 J/g reported by Palmese et al. [16] for the same resin system.
4.1 Maximum Extent of Cure
Since the latter half of a thermoset resin cure is often diffusion controlled, the cure reaction
can reach a steady plateau before full conversion is achieved. The final conversion of the resin, or
its maximum extent of cure, is therefore temperature dependent up to a temperature that is high
enough to provide sufficient molecular mobility to react all the species within the system. The
situation is further complicated by the possibility that the ultimate conversion of a multi-component
resin is dependent on its temperature history. Depending on the respective reaction rates for the
homopolymerization of each component and the copolymerization between two components, the
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final cross-linked structure can change dramatically as a function of temperature. Horie et al. [18]
reported this behavior in a polyester fumarate/styrene resin system and showed that the resin's final
conversion went through a maximum with increasing temperature.
Kamal and Sourour [8] accounted for the incomplete cure of a resin by using a temperature
dependent reducing parameter. A more straight-forward method was introduced by Lam et al. [14]
to account for this phenomenon. Instead of subtracting the extent of cure from unity in Equation
(3), they replaced the unity term with a temperature dependent variable, α max (αu in their
terminology).
dα
= k ⋅ α m ( α max − α ) 2 − m
dt
(5)
They found a significant temperature dependence for two unsaturated polyester systems.
Interestingly enough, they also studied Dow Derakane 411-45, which contains the same vinyl ester
component as the resin system used in this research but 5% less styrene. They reported very little
temperature dependence on the resin's maximum extent of cure.
The temperature range they
reported, 100 to 120 °C, was not wide enough to draw any significant conclusions, since this
phenomenon is most apparent at low temperatures. Lee and Lee [15] also investigated 411-45 for
the temperature range of 86.1 °C to 127.1 °C and reported a maximum extent of cure of 0.93 at
86.1 °C. A maximum extent of cure was not reported by Palmese et al. [16] who investigated the
Dow Derakane 411-C50 resin system between 90 °C and 120 °C.
The maximum extent of cure of the neat 411-C50 resin system was found by DSC to be
much less than unity at the temperatures typical in thick-sectioned cure. At an isothermal cure of
55 °C, the resin was found to reach only 70% conversion. Figure 6 shows the resin's maximum
extent of cure dependence on temperature within the range of 55 to 105 °C.
The following
empirical linear relationship was fit to the experimental data to approximate the resin's maximum
extent of cure. For values of T greater than 125.8 °C, the value of αmax is taken to be 1.0.
α max = 0.439 + 0.00446 ⋅ T [° C ]
11
(6)
4.2
Differences in Kinetic Constants
Once the maximum extent of cure of a DSC run was determined, Equation (5) could be
used to evaluate the kinetic parameters of the resin. The use of αmax greatly improves the fit of the
autocatalytic model, particularly at temperatures below 100 °C.
The kinetic parameters of the neat resin system for the temperature range of 55 to 120 °C
were found to be significantly different than those published by Palmese et al. [16] for a higher
temperature range, 90 to 120 °C. Figure 7 provides a comparison between the rate constants
found during this research and those from the literature. Table 1 highlights the changes in kinetic
parameter values between the two temperature ranges.
It can be observed in Figure 8 that the rate constant relationship for the resin evidently goes
through three distinct stages. The kinetic parameters for the three different regions can be found in
Table 2. The data between 85 and 120 °C appear to be very close to that reported by Palmese et al.
The data between 55 °C and 70 °C seem to have an activation energy (slope) close to the higher
temperature range but a significantly different pre-exponential factor. The rate constants between
those two ranges do not have a strong temperature dependence, possibly due to a gradual shift in
reaction mechanisms within this temperature range. A change in mechanism is also evident in the
m exponent value of the autocatalytic expression. The experimental values for the m exponent are
shown in Figure 9. While the average value of m is 0.85, a better representation of the m exponent
would be a step function with a value of 0.91 between 55 °C and 87.5 °C and 0.74 between
87.5 °C and 120 °C.
4.3
Influence of Inhibitors on Resin System
Inhibitors are placed within resin systems to increase shelf-life by combining with the free-
radicals that initiate polymerization of the resin. Inhibitory agents within the investigated resin
system were found to significantly increase the processing time of thick-sectioned parts. While
these inhibitors disappear quickly under normal processing temperatures, the kinetics of inhibitor
deactivation can be very slow at the lower temperatures required to successfully cure thick parts.
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Unfortunately, the kinetic analysis of a commercial resin system is complex since the
concentrations and types of inhibitors within the resin system are unknown and subject to change
by the manufacturer.
Flory [19] provides a detailed discussion on inhibitor chemistry, particularly for the
inhibition of styrene due to benzoquinone. Of the resin/inhibitor systems discussed by Flory,
many exhibited zeroth order disappearance of the inhibitor, which means that the rate of
consumption of the inhibitor is independent of its concentration. If the inhibitor concentration, Z,
is scaled by its original concentration, Z 0 , the change in the relative inhibitor concentration, Z/Z 0,
is given by Equation (7). The rate constant, kinhib, is assumed to follow an Arrhenius relationship
similar to that shown in Equation (4).
d
Z
Z0
= − kinhib
dt
(7)
The time lag observed during a DSC run before heat is detected by the cell, otherwise
known as the induction time, can be measured at each temperature. At 55 °C, an induction time of
6 hours was observed. Assuming that the polymerization of the resin can begin once the inhibitor
concentration reaches zero, the rate constant, k inhib , for a particular temperature can be calculated
by Equation (8).
kinhib =
1
(8)
tinduction
The Arrhenius behavior of the inhibitor's rate constant is shown in Figure 10.
The
Arrhenius parameters for k inhib , A inhib and E A,inhib , can be determined from the experimental
induction times for different isothermal cure temperatures.
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Following from Equation (7) and
expanding k inhib , Equation (9) can be used in the cure simulation to estimate the inhibitor
concentration within the vinyl ester resin system for a particular time step, dt.
( −18990 T [ K ] ) ⋅ dt [min]
22
( Z Z0 ) i + 1 = ( Z Z0 ) i − 3.732 ⋅ 10 [ 1 / min] ⋅ e
(9)
5. COMPARISON OF THE IMPROVED SIMULATION TO RTM
EXPERIMENTS
5.1
Verification of Physical Parameters
It was important to verify the physical parameters within the simulation independent of the
kinetic parameters.
This was done by first curing a composite, then cooling it to room
temperature, and finally ramping the mold temperature to 70 °C.
Figure 11 shows that the
physical parameters were adequate in describing the temperatures within an actual composite
during heating. Since the simulation does not account for the heat capacity of the mold, some
discrepancy is expected. Some deviation of the parameters from experiment to experiment is also
expected considering the variable nature of the resin system and the void content of the composite.
Table 3 presents the physical parameters used in the simulation in order to simulate the RTM
experiments described in Section 2.
5.2
Modifications to TGCURE Simulation
The maximum extent of cure relationship was added to the TGCURE simulation by placing
the α max term into the autocatalytic model according to Equation (5).
The value of α max is
calculated as a function of temperature for each time step using Equation (6). The value of α max
was not allowed to exceed 1.0 and should the extent of cure value for an particular node in the
simulation exceed the current value of αmax, the cure rate was set to 0.
The inhibitor deactivation kinetics were implemented in the TGCURE simulation by
calculating the relative inhibitor concentration for each node in the simulation according to Equation
(9). The cure rate for a particular node is set to 0 until the inhibitor concentration reaches 0 for that
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node. Once the inhibitor disappears, the cure rate is calculated by the autocatalytic model and the
resin begins to polymerize.
Figure 12 compares the center (1.27 cm) composite temperature observed during an RTM
experiment with the results of the modified simulation using the kinetic parameters determined in
Section 4. When the neat resin parameters are used, however, the new expressions do not initially
seem to improve the accuracy of the simulation.
5.3
Further Modifications to Inhibitor Kinetics
The most obvious discrepancy in Figure 12 is the time required to cure the resin. Although
there is some delay in the cure due to inhibitors, the delay does not correspond to that observed
during differential scanning calorimetry (DSC) with neat resin samples. The fibers within the
composite are either absorbing inhibitors or greatly promoting the deactivation of the inhibitors.
It was found through trial and error that reducing the initial relative inhibitor concentration,
Z/Z 0, from Equation (9) to 0.15 and retaining the same Arrhenius parameters provides good
agreement to actual experiments within the cure temperature range needed for thick-sectioned parts
(50 to 70 °C). The 85% reduction in inhibitors would only be valid for this resin and glass
combination and could be significantly affected by the age of the resin, resin catalyst level, and the
processing temperature.
Some of the data presented by Lem and Han [20] indicates a decrease of induction time for
an unsaturated polyester resin with increased levels of an inorganic filler, calcium carbonate.
While not directly reported by the authors, data from their figures reporting resin extent of cure
with time show an approximately 50% reduction in the induction time when the weight percent of
filler is increased from 25% to 50%. Palmese et al. [16] discuss the possibility of inhibitor
absorption on the fibers for the vinyl-ester/styrene resin system, but do not report induction times
of the resin cure for fibers with different sizings. In their work, absorption of inhibitors was given
as the reason why an increase in cure rate was observed for glass-modified systems. The method
used in [16] to evaluate the kinetics of fiber containing resin samples was limited to a fiber volume
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fraction of 20%, which is significantly less than the 40% to 60% fraction found in RTM
composites. Until such time that the kinetic mechanisms of the inhibitors within a composite are
understood, the use of computer simulations to fit phenomenological models such as Equation (9)
to experimental RTM data will remain an important technique.
5.4 Further Modifications to Cure Kinetics
The temperature peak at the center of the simulated composite in Figure 12 is still seen to
over-predict the experiment, despite the addition of a maximum extent of cure relationship. The
35 °C difference indicates that not as much heat was released within the composite as was
expected. However, it was found by trial and error that reducing the maximum extent of cure
relationship by 30% overall allows the simulation to predict the temperature peak within an actual
composite. The new maximum extent of cure can be evaluated from the neat resin value through
Equation (10).
α max, apparent = 0.7 ⋅ α max, neat
(10)
It has been reported by Ishida and Koenig [21] that the amount of unreacted polyester resin
within a polyester/styrene sample increases with the glass powder content. At a fiber weight
percent of 65% they report that 2.5 times the amount of polyester remains uncured at the end of the
polymerization reaction in comparison to the neat resin sample. They also report that the mobility
of styrene, due to its smaller molecular size, is not as restricted by the glass surfaces and so the
amount of glass fibers has a negligible effect on the residual concentration of unreacted styrene.
The work of Lem and Han [20] also support a reduction in the final extent of cure for a resin with
increased filler content.
5.5
Final Verification of Simulation
With these new empirical relationships for the inhibitor and cure kinetics, the simulation
was much improved in predicting the center temperature profile of a 2.54 cm thick composite
during a 53 °C cure cycle, as can be seen in Figure 13. The modified kinetic parameters used for
the 53 °C cure cycle were then used to predict the center temperature of a similar composite during
16
a 68 °C cure cycle. As can be seen in Figure 14, the simulation can still reasonably predict the
temperatures within the composite even though the exothermic temperature rise was observed in
1/3 the time and 50 °C hotter than the 53 °C cure cycle. It is not likely that the processing
temperature of this resin system for thick-sectioned cure would exceed 68 °C, since delaminations
were observed at this temperature.
6. CONCLUSIONS
A number of important and new issues concerning the kinetic behavior of vinyl-ester resin
systems have become apparent during the manufacture of thick-sectioned parts by resin transfer
molding (RTM). This novel behavior is primarily due to the lower processing temperatures
required to produce quality thick-sectioned parts. The observed kinetic behavior of the neat vinylester resin system below 85 °C is significantly different than previously reported by other
researchers. At the lower curing temperatures, a significant portion of the resin remains uncured.
The activation energy of the resin also appears to be smaller.
However, probably the most
significant low temperature behavior is the slow deactivation of the inhibitors with the resin
system. Knowledge of the inhibitor's kinetic behavior is important in modeling the process to
determine the time lag before the resin begins curing and to characterize possible inhibitor gradients
within the part. While most of the resin's kinetic parameters and inhibitor deactivation kinetic
parameters can be experimentally determined from the neat resin using DSC, the scaling parameter
for the maximum extent of cure relationship and the initial inhibitor concentration need to be
evaluated from actual RTM experiments.
The presence of fibers within a composite can
dramatically affect the curing behavior of the resin and current analysis techniques have not been
able to adequately describe this behavior.
Although the present work has successfully modeled two thick-sectioned RTM cure cycles,
it did so by relying heavily on experimental data and trial and error fitting of two parameters.
These data were used to fit phenomenological models that are specific to the system under
investigation. More work is required at a more fundamental level to address kinetics and structure
17
formation during curing to allow for models of more general applicability and higher predictive
capability.
7. ACKNOWLEDGMENTS
Financial support for this work was provided by the Army Research Office/University
Research Initiative through the Center for Composite Materials, University of Delaware. The
authors are grateful to Dr. Travis Bogetti for the use of the TGCURE code. The authors would
also like to thank the reviewers for their helpful suggestions.
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Curing of Composites. J. Compos. Mat., 25(12):1542-1587.
4.
Pillai, V. K., A. N. Beris, and P. S. Dhurjati. 1997. Intelligent Curing of Thick
Composites Using a Knowledge-Based System. J. Compos. Mat., 31(1):22-51.
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Bruschke, M. V. and S. G. Advani. 1990. A Finite Element/Control Volume Approach to
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Wymer, S. A. and R. S. Engel. 1994. A Numerical Study of Nonisothermal Resin Flow in
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Boccard, A., W. I. Lee, and G. S. Springer. 1995. Model for Determining the Vent
Locations and the Fill Time of Resin Transfer Molds. J. Compos. Mat., 29(3):306-333.
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Kamal, M. R. and S. Sourour. 1973. Kinetics and Thermal Characterization of Thermoset
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9.
Dutta, A. and M. E. Ryan. 1979. Effect of Fillers on Kinetics of Epoxy Cure. J. Appl.
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Fiberite 977-3 and 977-2 Thermosetting Resins. J. Reinf. Plas. Compos., 14:847-865.
18
13. Han, C. D. and K. Lem. 1983. Curing Kinetics of Unsaturated Polyester and Vinyl Ester
Resins. ACS Symposium Series: Chemorheology of Thermosetting Polymers, 227:201221.
14. Lam, P. W. K., H. P. Plaumann, and T. Tran. 1990. An Improved Kinetic Model for the
Autocatalytic Curing of Styrene-Based Thermoset Resins. J. Appl. Poly., 41:3043-3057.
15. Lee, J. H. and J. W. Lee. 1994. Kinetic Parameters Estimation for Cure Reaction of Epoxy
Based Vinyl Ester Resin. Polym. Eng. Sci., 34(9):742-749.
16. Palmese, G. R., O. A. Andersen, and V. M. Karbhari. 1997. Effect of Glass Fiber Sizing
on the Cure Kinetics of Vinyl Ester Resins. J. Appl. Poly., In Press.
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Numerical Methods. J. Heat Transfer, 88(4):421-427.
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19
Table 1: Experimental Kinetic Model Parameters for Neat Dow 411-C50
Temperature Range, °C
Palmese et al. [16]
55 to 120
90 to 120
8
5.50⋅10
9.62⋅10 1 0
60600
77400
0.85
0.66
Kinetic Model Parameter
Arrhenius A-factor, A [1/minute]
Activation Energy, EA [J/mole]
m Exponent for Autocatalytic Model
Table 2: Experimental Kinetic Model Parameters in Different Regimes
Kinetic Model Parameter
Arrhenius A-factor, A [1/minute]
Activation Energy, EA [J/mole]
m Exponent for Autocatalytic Model
Temperature Range, °C
55 to 70
70 to 85 85 to 120
10
6.69⋅10
1.89⋅10 5 1.62⋅10 1 1
73700
37600
78200
0.90
0.91
0.74
Table 3: Physical Model Parameters Used in the RTM Cure Simulation
Surface Convective Boundary Condition, 1/m
Transverse Thermal Conductivity, W/m•°C
Heat Capacity, J/g•°C
Density, g/ml
Resin Mass Fraction
20
2600
0.25
1.205
1.69
0.335
LIST OF FIGURES
Figure 1: Comparison of Two 2.54 cm Thick Composite Cross-Sections Cured at 55 °C (Top)
and 65 °C (Bottom)
Figure 2: Cut-Away View of RTM Experimental Apparatus
Figure 3: Simulated Temperatures Within a Composite For a 60 °C Cure Cycle
Figure 4: Simulated Extent of Cures Within a Composite For a 60 °C Cure Cycle
Figure 5: Comparison of an Actual RTM Experiment and the Original TGCURE Simulation
Figure 6: Temperature Dependence of the Resin's Maximum Extent of Cure
Figure 7: Arrhenius Relationship of the Vinyl Ester Resin System
Figure 8: Effect of Reaction Mechanism Change on Kinetic Rate Constants
Figure 9: Effect of Reaction Mechanism Change on Autocatalytic 'm' Exponent
Figure 10: Arrhenius Relationship of Inhibitor Within the Vinyl Ester Resin System
Figure 11: Experimental and Simulated Temperatures of a Heating Ramp to 70 °C
Figure 12: Comparison of RTM Experiment and Improved Simulation With Neat Resin
Parameters
Figure 13: Comparison of RTM Experiment and Improved Simulation With Empirical Parameters
Figure 14: Comparison of an Actual RTM Experiment and Simulation for a 68 °C Cure Cycle
21
Figure 1: Comparison of Two 2.54 cm Thick Composite Cross-Sections
Cured at 55 °C (Top) and 65 °C (Bottom)
Stainless Steel Mold
Thermocouples to Data Acquisition
Polyurethane
Tubing
Polyurethane
Tubing
Compressed
Air
Resin
Source
Resin
Collection
Resin
Figure 2: Cut-Away View of RTM Experimental Apparatus
22
Temperature, oC
140
120
Water Temperature
Surface Temperature
100
Quarter (1/4") Temperature
Center (1/2") Temperature
80
60
40
20
0
20
40
60
80
100
Time, minutes
Figure 3: Simulated Temperatures Within a Composite For a 60 °C Cure Cycle
0.8
Extent of Cure, α
0.7
Surface Extent of Cure
0.6
Center (1/2") Extent of Cure
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
80
100
Time, minutes
Figure 4: Simulated Extent of Cures Within a Composite For a 60 °C Cure Cycle
23
180
Water Temperature
160
Temperature, oC
Center (1/2") Simulation
140
Center (1/2") Experimental Data
120
100
80
60
40
20
0
25
50
75
100
125
150
Time, minutes
Maximum Extent of Cure, αmax
Figure 5: Comparison of an Actual RTM Experiment and the Original TGCURE Simulation
0.95
0.90
0.85
0.80
0.75
α max= 0.439 + 0.00446 * T[ oC]
0.70
0.65
0.60
50
60
70
80
90
100
110
Temperature, oC
Figure 6: Temperature Dependence of the Resin's Maximum Extent of Cure
24
Autocatalytic Rate Constant, 1/min
10
Exp. Rate Constant, 55 to 120 oC
Lit. Rate Constant, 90 to 120 oC
1.0
0.10
0.0025
0.0026
0.0027
0.0028
0.0029
0.0030
0.0031
Inverse Temperature, 1/K
Autocatalytic Rate Constant, 1/min
Figure 7: Arrhenius Relationship of the Vinyl Ester Resin System
10
1.0
0.10
0.0025
0.0026
0.0027
0.0028
0.0029
0.0030
0.0031
Inverse Temperature, 1/K
Figure 8: Effect of Reaction Mechanism Change on Kinetic Rate Constants
25
Autocatalytic Exponent, m
1.25
Experimental Data
Average Value (0.85)
Step Function (0.91 & 0.74)
1.00
0.75
0.50
50
60
70
80
90
100
Temperature,
o
110
120
130
C
Inhibitor Rate Constant, 1/min
Figure 9: Effect of Reaction Mechanism Change on Autocatalytic 'm' Exponent
1
0.1
0.01
0.001
0.00285
0.00290
0.00295
0.00300
0.00305
Inverse Temperature, 1/K
Figure 10: Arrhenius Relationship of Inhibitor Within the Vinyl Ester Resin System
26
80
Temperature,
o
C
70
60
50
Heating Water Temp
1/4" Thermocouple - Exp.
1/2" Thermocouple - Exp.
1/4" Simulation
1/2" Simulation
40
30
20
0
5
10
15
20
25
30
35
Time, minutes
Figure 11: Experimental and Simulated Temperatures of a Heating Ramp to 70 °C
Temperature, oC
140
Water Temperature
Center (1/2") Simulation
120
Center (1/2") Experimental Data
100
80
60
40
20
0
100
200
300
400
500
600
Time, minutes
Figure 12: Comparison of RTM Experiment and Improved Simulation with Neat Resin Parameters
27
120
Temperature, oC
100
80
60
Water Temperature
40
Center (1/2") Simulation
Center (1/2") Experimental Data
20
0
25
50
75
100
125
150
Time, minutes
Figure 13: Comparison of RTM Experiment and Improved Simulation With Empirical Parameters
160
Temperature, oC
140
120
100
80
60
Water Temperature
Center (1/2") Simulation
Center (1/2") Experimental Data
40
20
0
10
20
30
40
50
60
Time, minutes
Figure 14: Comparison of an Actual RTM Experiment and Simulation for a 68 °C Cure Cycle
28