Reaction injection molding process of glass fiber reinforced polyurethane composites

Reaction Injection Molding Process of Glass Fiber Reinforced Polyurethane Composites

DAE SU KIM*

Dept. of Chemical Engineering, Chungbuk National University 48 Kaesin-dong Cheongju, Korea 361 -763

CHRISTOPHER W. MACOSKO

Dept. of Chemical Engineering and Materials Science University of Minnesota

Minneapolis, Minnesota 55455

Structural reaction injection molding (SRIM) was used to produce polyurethane composites containing random continuous glass fiber mats. A long rectangular mold was used to cany out the SRIM experiments. 4,4‘-diphenylmethane diisocyanate and poly(propy1ene oxide) trio1 were used to formulate a thermoset polyurethane system. Dibutyltin dilaurate was used as a catalyst. A second order Arrheruus equation described the PU polymerization kinetic data obtained from the adiabatic temperature rise measurement. A viscosity as a function of temperature and conversion was developed using rheometer data. The pressure rise at the gate was measured during filling. The flow behavior within the mold was described by Dwcy’s law and the Kozeny’s equation. The temperature profile within the mold measured by thermocouples during filling and curing coincided fairly well with the simulation results. The thermal transient problem at the wall was solved using the overall. heat transfer coefficient, and it was analyzed as a function of Biot number. The dimensional stability of the fiber reinforced PU parts was excellent compared to the pure PU parts.

MTIRODUCTION RIM products contain fillers or reinforcing materials

n structural reaction injection molding (SRIM), I which is also called mat molding RIM (MM-RIM), composite RIM, or fast resin transfer molding (m, reinforcing materials such as continuous fiber mats are preplaced in an empty mold cavity before each shot. For SRIM, reactants are combined by impingement mixing just before they enter into a mold cavity. Resin must fill the heated mold quickly and wet all the fibers before much of the reaction occurs. The dis- tribution of the reactmg mixture throughout the entire cavity around the fiber bundles and the penetra- tion into the bundles must be analyzed to understand flow behavior during mold filling. The viscosity of both reactants must be low enough to attain complete mixing a t the impingement point (Re > 200) and to achieve complete fillirtg and wetting. Most commercial

T o whom correspondence shoLld be addressed.

such as chopped fibers, flakes and continuous fibers. This process is called reinforced RIM (RRIM) or filled RIM (1). The main objectives of the reinforcement are to improve dimensional stability and mechanical properties. The best properties can be obtained with long reinforcing fibers. Continuous glass fibers are more effective in reducing the coefficient of linear thermal expansion (CLTE) of RIM products, and ide- ally, the orientation of continuous fibers is not changed by the resin flow during mold filling (1). In the case of RRIM, it is difficult to control the filler orientation because it is largely affected by the flow direction.

Additional advantages of SRIM compared to FGUM are: (a) SRIM can easily exceed the maximum content of reinforcing materials for RRIM (less than 25 wtYo) because there is no need to pump reinforcing materials into the mold: glass fiber loadings of over 60 wtYo in the SRIM have been reported by Gonzalez et aL (2)

2205 POLYMER ENGINEERING AND SCIENCE, OCTOBER2OO0, Vol. 40, No. 10

Dae Su Kim and Christopher W. Macosko

and Slocum et al. (3). (b) Because of the high glass level and because long fiber can be used, the flexural modulus and tensile strength of the SFUM products are considerably larger than those of the RRIM products.

The SRIM process is very similar to a. But the major difference is that SRIM uses a typical RWI machine to fill the mold, and thus high pressure impingement mixing is needed to activate the polymerization. RTM typically uses slow reacting, heat activated formulations and injects under low pressure. Components are premixed or flow through static mixers into the mold cavity. The production rate of KIM is not as fast; SRIM is aimed for higher volume production.

It is important to know the flow behavior and thermal change of a reacting system inside a mold during filling and curing process not only to optimize process parameters such as flow rate, mold wall temperature and inlet temperature of reacting mixture, but also to predict the conditions under which incomplete filling or thermal degradation occur.

Most of the studies on SRIM have been carried out with center gated disk molds to minimize the mat slip during the mold filling. Gonzalez et al. (2) and Chen (4) used center-gated disk shaped molds with preplaced fiber mats to carry out the filling and curing study. Slocum et al. (3) recommend not to exceed 500 cm3/s to avoid the slippage of fiber mats due to the fluid during filling.

The objective of this study is to analyze the SRIM process to produce a continuous random fiber reinforced PU composite using a rectangular mold. Com- parison between measured thermal and physical data and simulation results has been carried out. The ef- fects of process parameters such as flow rate, initial mixture temperature and wall temperature on the inlet pressure rise during filling and temperature change within the mold during filling and curing are also analyzed.

ExPERxMEmAL Materiala

Isonate 143L @ow Chem. Co.) consisting of 82Oh of bifunctional MDI (4,4-diphenylmethane diisocyanate) and 18Oh of trifunctional cycloadduct, and Voranol 230-238 (Dow Chem. Co.) consisting of PPO (poly (propylene oxide)) polyol were used to formulate a thermoset PU system. Equivalent weights of the isocyanate and the polyol were 144.3 and 230.7 respectively. Functionality of the isocyanate was approximately 2.07 and that of the polyol3.0. Densities of the isocyanate and the polyol were 1.214g/cm3 and 1.033 g/cm3 at 25°C. The catalyst (TIJ used was dibutyltin dilaurate (Aldrich Chem. Co.). In this study, the catalyst level was defined as the weight percent relative to the polyol weight used.

The glass fiber mat used was OCF M8610 (Owens Cormng) continuous random fiber mat with an average

single fiber diameter of 15 pm and a fiber bundle diameter ranging from 80 to 200 pm. Density of the glass fiber was 2.560g/cm3 at 25°C.

Adiabatic Temperatare Ri.e (ATR) Meamurement

Since the reaction rate of the PU system was fast, adiabatic temperature rise (ATR) measurement was carried out to analyze the reaction kinetics. Stoichio- metric amounts of the isocyanate and the polyol were used to formulate a crosslinking thermoset PU system. A catalyst level was 0.05%. A lever arm RIM machine was used to inject both reactant streams at an initial temperature of 67°C. The Reynolds number (Re) of each reactant stream must be L 200 to ensure sufficient impingement mixing at the mixhead (1). Re of the isocyanate stream was > 1000 and that of the polyol stream > 500. Details on the RIM machine were described by Mikkelsen and Macosko (5). Ther- mocouples preplaced within the adiabatic chamber were connected to a microcomputer to receive temperature change with time. More details on the ATR measurement were also described by Camargo et d. (6) and Pannone and Macosko (7).

Rheomatric Mechanical Spectromater

Viscosity change with time during isothermal polymerization was measured using the Rheometrics Sys- tem IV and RMS-800 rheometer. Disposable parallel disk aluminum plates (diameter = 25 mm) were used. Steady shear rate was changed from 10 s-l to 1 s-l with time to obtain viscosity data over wide conversion range and to check if the bulk viscosity of the reacting PU mixture depends on the shear rate. The viscosity change during isothermal polymerization of the reacting PU system containing 0.05% catalyst was carried out at 32.42, and 55°C respectively.

Moldh?!-P--- A simple sketch of the mold used in this study is

shown in Rg. 1. The dimensions of the end gated rectangular mold cavity are 71.0 cm (length) X 10.1 cm (width) X 0.17 cm (thickness) (8). After a mold release agent was applied to the entire mold surface, the continuous random fiber mat was preplaced in the mold. The mats were cut with scissors to give a tight fit against the side walls. The mold release agent was applied for each experimental run. In order to measure the mold pressure change during mold filling, a pressure transducer (Dynisco 420A) was placed at the gate. The transducer was calibrated using a capillary rheometer (Rheo-Tester 1500, Goettfert). Each temperature controller controlled inlet reactant temperature and mold wall temperature. Two thermocouples (25mV, J type) were inserted within the mold (located at 7.5 cm and 27.5 cm from the gate) to trace the temperature change during filling and curing. The pressure transducer and thermocouples were connected to a personal computer, which collected and stored

2206 POLYMER ENGINEERING AND SCIENCE, OCTOBER 2000, Vol. 40, No. 10

RTM Process

vent

vent

vent

from Mixhead Thickness = 1.7 Unit = mm Q. 1. A sketch of the rectangular long mold used in this study.

the experimental data. The RIM machine used for the adiabatic temperature rise measurement was also used for mold filling experiments. The volumetric flow rate of the reactant mixture entering the mold was calculated from the mold filling time, mold dimension and porosity of the fiber mats.

RESULTS AND DISCUSSION

Mathematical Model

In order to model filling of a rectangular mold cavity (W: width, H: thickness and L: length), the momentum, energy and species balance equations are re- quired. In order to model filling of a center-gated disk shaped mold, Gonzalez (9) used some important as- sumptions. These and several others are used in this study.

No velocity gradient in the direction perpendicu- lar to the flow, i.c. plug flow.

Isotropic fiber mat.

Relation betwee:% pressure drop and velocity is given by Darcy’s law.

Thermal properties (cp, k) are constant.

No temperature gradient within the fibers.

Newtonian fluid.

Dispersion and conduction in the flow direction are neglected.

Molecular diffision is negligible.

Q = + w H < v x > (11

where <v,> is the average axial velocity and + porosity.

Darcy’s law is introduced instead of the momentum balance equation to analyze the relation between the pressure rise at the gate during filling and axial flow velocity. Even though the Darcy’s law was derived for the porous media packed with small particles, it can be adopted in this study because the mold cavity filled with fibers can be treated as a porous media. Many other studies (4, 9-11) have also employed Darcy’s law to analyze mold filling with preplaced fiber mats. The average velocity based on the empty channel in the flow direction through the fiber bed is proportional to the pressure gradient and the permeability, K.

where q is the viscosity of a Newtonian fluid. This relationship can be used to evaluate K of a particular packed bed by measuring Q and AP of an unreactive liquid through a rectangular channel filled with packing materials such as fiber mat. Using this method, Gonzalez (9) obtained K for the flow of water through a chopped strand fiber glass mat which is similar to the fiber mat used in this study. Chen (4) also estimated K for the flow of an oil through the same continuous random fiber mat used in this study.

Combining the above two equations, and applying the constant flow rate boundary condition, the pressure drop during filling can be expressed as follows,

The balance equations can be derived easily with

be described in terms of volumetric flow rate using the overall mass balance. where (= WHL/Q) denotes the filling time.

the above assumptioi~s. The continuity equation can AP = ?1 ( g ) 2 $ u (3) K W H

POLYMER ENGINEERING AND SCIENCE, OCTOBER 2000, Vol. 40, No. 10 2207


For the constant molding pressure condition, tfiu can be expressed as follows,

11L2 tfru = - KAP (41

and the flow rate also derived as a function of axial position (x).

(5)

The permeability depends strongly on the porosity (resin volume fraction) of packing materials. The relation between the permeability and porosity can be described using Kozeny's equation.

where d is the diameter of the particles or fibers which compose the porous media. The constant C is found to be 150-200 for the beds of packed spheres. For fiber mats, the choice of d is not easy because the strands or fiber bundles are typically not round but more like flat or ellipsoidal ribbons.

The energy balance equation is derived for the poly- merizing fluid phase and solid fiber phase separately (subscript 'f is for fluid (resin) and subscript 's' for solid (glass fiber)). Chen (4) and Gonzalez (9) used the assumption that the fibers are inert to reactants. They did not count the thermal change of the solid phase separately because they assumed that the heat transfer between resin and fiber is fast enough that equilibrium is obtained within the time scale of interest (they neglected the film heat transfer resistance). But, in the case of a highly reactive system with high porosity, temperature equilibrium between resin and fiber cannot be achieved within the time scale of interest owing to the heat transfer delay at the resin-fiber interface. So the energy balance equation is constituted for the resin and fiber phase separately in this study.

For the fluid phase,

+pfcpf(z+ <vx> dx

where hfs is the heat transfer coefficient at the interface between fluid and solid fibers and A is the surface area of the solid fiber bundles contacted to the fluid. Gonzalez (9) evaluated the heat transfer coefficient as a linear function of fluid velocity, and his results are used in this study. Assuming cylindrical geometry for fibers, the specific area of the fiber, A, can be estimated as 4/d,, where d, is the average diameter of the fiber bundles.

The chemical species balance can be expressed as a function of the isocyanate concentration. Using the chemical conversion (a), the balance equation can be expressed as follows,

where, Ris the reaction rate of PU polymerization and [NCO], is initial concentration of the isocyanate.

The initial conditions are,

T f ( x z ) = T d at t = O

a(x, z ) = 0 at t = 0 (1 1)

T, (x. Z) = T, (x) = T& at t = 0

At the mold entrance, it is assumed that the incoming fluid is mixed perfectly and totally unreacted. The boundary conditions are,

Tf(z. t ) = Tp at x = 0

a (z. t ) = 0 at x = 0 (12)

- _ a' - 0 at z = 0 (symmetry at center) az

Since there is no flow during curing, only two balance equations of energy and chemical species are re- quired. The convection term is just omitted from the balance equations for the filling stage. Thus for fluid phase, the energy balance equation is,

where pf and p, are densities, Cpf and C,, are heat ca- pacities, Tf and T, are temperatures, AH- is the heat of reaction for the pure PU polymerization, a is conversion of the isocyanate, and k is the effective thermal conductivity defined as follows.

Gonzalez (9) found this relation was in good agree- ment with his experimental observations.

For solid phase,

temperature profile

/ coolant (water)

hm

Fig. 2. A schematic representation of the temperature field through the mdd wall


RIM Process

For solid phase, the energy balance equation is same as that of the filling sitage (Eq 9). The species balance equation becomes,

-=- l R da dt [ NCO], (14)

The final values (conversion, fluid temperature and solid temperature) of the filling stage were used as the initial values for the curing stage.

Heat Transfer Throu,gh the Wall

Assuming the isotheimal wall, Chen (4) fit fairly well the temperature profile within a center-gated disk shaped mold during ciiring because the reaction rate of a cyanate system he used was slow. The isothermal boundary condition has been adopted successfully in several other studies (8, 9). Even though they are good approximations for some cases, the isothermal wall or adiabatic wall cannot be applied in this study for a proper simulation of the filling and curing process. The PU reaction is fast and the heat generated by the exothermic PU reaction significantly affects the temperature profile within the mold wall. In turn the calculated temperature profile within the mold cavity is affected by the thermal boundary conditions. Some portion of the heat generated by the PU reaction is transferred through the wall, and some portion of the heat is <also accumulated temporarily within the mold.

Fgwe 2 represents the temperature field in the polymer-mold-cooling stream for a case with wall temperature lower than the entering polymer fluid (exothermic reaction). The transient heat transfer problems for the polymer fluid and mold wall can be expressed with di- mensionless variables using an overall heat transfer coefficient as follows.

Tf 22 Hu where, TI* = - z* = - Bi = 7-. The inverse of

T f o ’ H’ 2k the overall heat transfer coefficient is

The transient problem can be simplified by assuming isothermal wall if the heat transfer rate from the polymer to the mold wall is very small in comparison to the heat conduction rate in the wall. But, for a typical RIM cycle this condition is not easily satisfied, which is consistent with the reported mold temperature changes between cycles (1).

Gonzalez (9) considered heat transfer through the wall using an overall heat transfer coefficient. Using the overall heat transfer coefficient seems like a good approach because it is not easy to count exactly the three heat transfer components individually. He used

Merent overall heat transfer coefficients for the filling stage and curing stage. For the filling stage, he used a velocity dependent heat transfer coefficient to express heat transfer through the resin-fiber interface, and the same heat transfer coefficient was also used to analyze heat transfer through resin-mold wall interface. But, for the curing stage, he used a pseudo-homogeneous model at the resin-mold wall interface, and ignored the film heat transfer resistance (hfs = in- finity). So the overall heat transfer coefficient for the curing stage was much larger than that for the filling stage because h, was considerably smaller than (0.52J/cm/K/s for Al (9)) or h, (4.2 X 10-2J/cm2/K/s (9)). The pseudo-homogeneous model does not seem like a good approach for this highly reactive PU SRIM process because the overall heat transfer coefficient through the wall must be larger during the filling stage owing to the fluid flow. Since the mold wall temperature is controlled by water flowing inside the mold wall and the mold is made from aluminum (H, = 0.5 cm) of high thermal conductivity, heat transfer at the wall is almost governed by hf,. So the film heat transfer resistance cannot be ignored in considering heat transfer through the wall.

The transient heat transfer problems at the mold wall were solved by using the boundary conditions such that the heat transfer is dependent on the overall heat transfer coefficient, and it was analyzed as a function of Biot number, Bi. Bi for the filing stage (about 1.3 X lo5) was larger than that for the curing stage (3.0 x lo4) to compensate for the convective heat transfer to the wall during filling. When Bi is high enough, the case is equivalent to the isothermal wall. When Bi is low enough, it is equivalent to the adiabatic wall.

The hfs value evaluated by Gonzalez has linear relationship to the average linear fluid velocity with a proportional constant of 4.38 X 10-5J/cm3/K and 2.0 X 10-5J/cm2/K/s at velocity 0. Typical values for hfs are 5.9 x to 5.9 X 10-2J/cm2/K/s for viscous fluids and 5.9 x 1C2 to 1.17J/cm2/K/s for water (12). Gon- zalez’s results are considerably smaller than the liter- ature values. But it is valuable because it was obtained experimentally using the fiber packed mold. So, his results were employed in this study to esti- mate heat transfer at the resin-fiber interface. For the curing stage, h, = 2.0 X 10-5J/cm2/K/s was used for the resin-fiber interface.

Chemorheology

A reaction kinetic equation and a viscosity function are needed to simulate the filling and curing process of a molding process. Since the chemical conversion of a functional group is related to the change of heat evolution, the reaction kinetics of polymer systems can be analyzed indirectly by dynamic scanning calorimetry (DSC) or adiabatic temperature rise (Am) measurement, which calculate the chemical conversion by measuring the heat evolution caused by the

POLYMER ENGINEERING AND SCIENCE, OCTOBER 2000, VOI. 4 4 NO. 10 2209

Dae Su K i m and Christopher W. Macosko

180

160

140

120

100

80

60 0 5 10 15 20 25 30

Time [s] Fig. 3. Comparison between the model prediction and the experimental adiabatic temperature rise data for the PU system containing 0.05% catalyst (T,d &&

exothermic polymerization. Since the polymerization rate of the typical PU RIM system is fast, the ATR measurement technique has been recommended in studying the reaction kinetics of PU systems (1, 6, 7).

An Arrhenius type simple second order reaction kinetic equation described well the reaction path of the PU system containing 0.05% catalyst. The best fitting kinetic parameters were determined by Marquette's multivariable nonlinear regression (13) and Runge- Kutta integration. The following kinetic equation was used.

Comparison between experimental adiabatic temperature rise data and kinetic model prediction is shown in Rg. 3. The model reaction kinetic equation fit well the experimental adiabatic temperature rise data.

The viscosity change of a reactive polymer system during polymerhtion affects sgmfhnt ly the process- ability of the polymer in many polymer processing applications such as RIM, RTM, SRIM. compression molding and pultrusion. It is important to understand precisely the rheological behavior of a reactive polymer system during polymer processing to determine optimum process parameters such as filling time, flow rate, initial and wall temperature. etc.

In order to model a reactive polymer process, a viscosity function that can express the relationship between viscosity change and process condition (temperature and shear rate if viscosity of the polymer system is dependent on shear rate) as well as the de- gree of polymerization (conversion) is necessary. The viscosity change of the PU system used in this study with reaction time was not affected by shear rate. For a similar PU system (Isonate 143L + PPO-EO + BDO), Castro and Macosko (14) also reported that the viscosity was independent of shear rate. So the following empirical viscosity function proposed by Castro and Macosko (15) was employed in this study to analyze the viscosity change of the PU system during polymerization.

where q,m = A,, exp (2) , agel is the conversion at

gelation point, and a and b are empirical constants.

The Vogel relation, q,O = 4 exp also be used instead of Arrhenius temperature dependence. However, the viscosity function (Eq 18) with the Arrhenius equation has been employed in this study since it is well known that it is more appropri- ate for viscosity well above Tg (16). The Castro and Macosko equation with the Arrhenius equation was

).can ( c + d(T - Tg)

221 0 POLYMER ENGINEERING AND SCIENCE, OCTOBER 2000, Vol. 40, No. 10

RIM Process

80

60 r\ [Pa.s]

40

20

0 0 100 200 300 400 500

Time [sec] Fig. 4. Comparison between the model prediction and the RMS viscosity data measured at 32.42, and 50°C respectively for the PU system containing 0.05% catalyst level .

also adopted to fit the viscosity change of the rubber modified epoxy system as a function of reaction temperature and conversion ( 17).

Figure 4 shows the viscosity change with curing time during isothermal polymerization at 32, 42, and 50°C for the PU system. The viscosity data measured usmg the FWS-800 parallel plate rheometer are shown as symbols. Each curve indicates model prediction calculated by the above viscosity function. Parameters of the viscosity function (Eq 18) were determined through regression. Best fitting parameters of the viscosity function considwing thermal (temperature dependence) and physical (conversion dependence) ef- fects were: A,, = 4.546 X lo4 Pa.s, E,, = 38690J/mol, age, = 0.684, a = 2.94, and b = -1.18. The conversion at gel point (0.684) was calculated theoretically by the following Macosko’s equation ( 1).

age[ = k0- 1) VOH- 1) Y2 (19)

where fNco (2.07) and foH (3.00) are functionality of the isocyanate and the polyol respectively.

polymerization until the chemical reaction is finished. The pressure change during filling was measured using a pressure transducer, and temperature change with curing time was also monitored by thermocouples at two axial positions.

The material properties used for the mold filling simulation are summarized in Table 1. The grid size used in the computation scheme using finite difference method (FDM) was one mold thickness (H).

Some information (process conditions and formula- tion) for molding experiments are summarized in Table 2. In order to study faster reacting systems, mold filling experiments for PU systems with higher catalyst levels (0.40% and 0.10Yo) were also carried out. The reaction kinetic equations for the PU systems with higher catalyst levels are referred from our previ- ous study (18). Porosity was calculated by measuring the weight of fiber and composite respectively. The porosity of the mold channel containing one mat layer was 0.913, and 0.826 for two mats.

Comparioon Between Holding Experimental Data and Modal Prediction

Table 1. Properties of the PU and Glass Fiber Used for Modeling.

Parameter PU Fiber For a constant flow rate process, the pressure rise at the mold entrance during filling of a packed mold is Density (p) [g/cm3] related to the viscosity change and to porosity. The Heat capacity (C ) [J/g/K] 1.84 (8) 0.774

Thermal conducthy [J/g/s/K] 0.0017 (8) 0.036 temperature and conversion profile within the mold Heat of reaction [J/mol] 66,530 cavity changes continuously because of the exothermic

1.103 2.56

-

POLYMER ENGINEERING AND SCIENCE, OCTOBER 2000, Vol. 40, No. 10 221 1


Table 2. Summary of the SRlM Experiments.

ExP# TXCI TwT, Wl %TI, h,,tSI Q[cc/s] L[cm] Matt C KtcmS

Exp# 1 60 60 0.40 2.03 47.1 1 61 1 112 1.760 X lo4 Exp# 2 44 43 0.10 3.00 15.15 29 1 162 1.217 X lo4 Exp# 3 67 65 0.05 4.45 25.01 71 1 180 1.095 X lo4 Exp# 4 70 70 0.05 4.30 25.88 71 1 117 1.684 X lo4 Exp# 5 75 75 0.05 4.20 23.98 71 2 112 3.257 X lo4 EXD# 6 80 80 0.05 1.65 61.75 71 1 114 1.744 x 10-4

The pressure rise during filling could be predicted using Darcy's law and Kozeny's equation fairly well. Figwe 5a-f show the mold pressure rise predictions together with experimental data (Exp# 1-6). The model predicts well the experimental pressure rise at the gate in the case of Exp# 1, 2, and 6. In the case of Exp# 3, 4, and 5, the model overpredicts the experimental pressure rise data. This deviation seemed to be caused by some experimental errors. There was some leaking through the thermocouple holes as the mold pressure was increasing over about 50 psi. Slip- page of the fiber mats could also introduce some errors but it was small compared to the errors caused by leaking. In the case of Exp# 2, even though temperature change and pressure rise were measured si- multaneously, there was no leaking through the thermocouple holes because the molding pressure was not so high (under 4Opsi). There were large deviations in the case of Exp# 5 (2 mat layers) because leaking was larger than any other experiments owing to low porosity. Considerable fiber slippage was observed only for Exp# 1 because sufficient molding pressure was developed during filling. The initial position of the fiber mat before filling near the gate slipped about 4 cm during filling in the flow direction. Fluctuation in the experimental pressure rise data for Exp# 1 (Fig. 54 during the period of 1-1.5 seconds was considered due to the fiber slippage.

The permeability (K) data for each experiment was estimated from the initial slope of the pressure rise data, and summarized in Table 2. The Kozeny's constant (C) for each experiment was calculated by Eq 6 using the permeability, and summarized also in Table 2. The constant changed somewhat accordmg to the process conditions, and ranged between 110 and 180. Considering the fact that C is found to be 150-200 for the beds of packed spheres (1). this result was rea- sonable. It is usually not easy to determine the diameter of fiber strands because they are actually not rounded. The average fiber bundle diameter of 140 pm was used for the simulation in this study. Gonza- lez (2) estimated K for the strand diameter of 54 pm (AKM, PPG industries) and obtained C = 180. Martin and Son (lo) reported K values similar to the Gonza- la 's result for corn syrup flowing through a continuous random fiber mat (OCF M8605, Owens Corning). Gauvin and coworkers (1 1) also reported K values on the same mat using a slightly shear thinning poly- ester resin. They found that K depended strongly on the porosity especially at high porosity range.

Comparisons between the experimental temperature profiles and model predictions are shown in Fig. 6a and b for Exp# 2 and Fig. 7a and b for Exp# 3. The experimental data were plotted with open circles and the model predictions were indicated as six solid lines (from the center to the wall with the interval of 0.017cm). "lbo thermocouples were located within the mold at x = 7.5 and 27.5 cm. It was difficult to define the exact thermocouple position in the mold thickness direction because the mold thickness was very thin (0.17 cm) compared to the thermocouple diameter. The thickness of the thermocouples was about 0.05 cm. The thermocouples were attached on the mold wall surface using an insulation tape with thickness of about 0.01 cm because they did not work when they were contacted directly to the mold wall surface because of electrical interference. So the centers of the thermocouples were considered to be located at 0.035 2 0.005 cm from the mold wall surface. In order to ensure the thermocouple position, position of the front thermocouple (x = 7.5 cm) in the thickness direction for Exp# 3 was measured with a caliper after slicing the thermocouple position of the PU SRIM part. The center of the thermocouple was located at 0.033 cm from the mold wall surface. The experimental temperature data shown in Rg. 6a, b and Fig. 74 b agreed fairly well with the simulation results for the position 0.034 cm away from the mold wall surface.

Figure 6a, 6b, 7a, and 7b, show that the two thermocouples were reading the initial solid fiber temperature until the reactant mixture reached each thermocouple position. After the reacting mixture reached the thermocouple position, the temperature at the thermocouple position was retained constantly until the end of the filling stage since the reactants passing the thermocouples experienced almost same thermal history during the period flowing between the gate and thermocouple position. The experimental temperature data shown in Fig. 6a was almost constant during the period (1-3 seconds). The temperatures at both thermocouple positions started to increase rapidly as soon as mold was full. Most of the experimental temperature profiles showed an inflection point at the end of filling. The temperature went up as a result of accumulated heat of reaction.

There are two competing factors affecting the temperature profiles: heat accumulation due to the exothermic heat of reaction, and heat transfer through the mold wall. The maximum temperature was at- tained after about 10 seconds from starting filling at


RIM Process

140 7 I 120

.- 100 CI

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the center in the thickness direction. The heat accumulation effect was bigger than the heat transfer effect before the maximum temperature point. But after the maximum temperature point, the situation be- came opposite.

All the experimental temperature profile data measured during the filling and curing stage showed similar patterns. With the two Biot numbers to analyze heat transfer for the resin-mold wall interface, 1.3 X lo5 for the filling stage and 3.0 X lo4 for the curing



48 I 1

5 L

47

46

45

44

43

42

- I.a cm r r i

wall

F 0 5 10 15 20

Time [s]

5

47

46

45

44

43

42 0 5 10 15 20

Time [s] Fig. 6. Temperature change with time for Exp# 2 duringming and curing stage at two axial positions. (4 x = 7.5 cm x = 27.5 n

stage, the simulation model predicted fairly well the temperature profiles. A small Biot number represents an adiabatic wall, while a large Biot number corre- sponds to an isothermal boundary approximately.

Typical polymer processing conditions lie between these two extremes [somewhat closer to the isothermal boundary (l)]. However, even though the two Biot numbers used in this study seemed to be large


RIM Process

Fig. 7.

R u 0 Y

w"

isi i+" e

Temper& re

76

74

72

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6 4 L ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 1 ' ' 10 5 10 15 20

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x = 27.5 cm 74

0.085cm 0.069

72 0.052

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64 0 5 10 15 20

Time [IS] ' charge with time for Ex@ 3 mm and curing stage at two axial positions. [d x = 7.5 cm (b) x = 27.5 crn

enough to meet the isothermal boundary condition, the wall was not the isothermal boundary because the heat generated by the fast exothermic PU polymerization might give a temperature gradient inside of the

wall and the time scale of interest was very small in this study. There was not enough time to establish zero temperature gradient inside of the wall because the heat generation due to reaction was fast and



u" F e

130 t / I E M 3

120 1 x = 7.5 em z = 0.034 cm lrom the wall

110

100

90

80

70

/ I / I

isothermel wall

6 0 ~ " ' " " " ' " " ' " " 0 5 10 15 20

Time [s] Flg. 8. Efikct of thermal boundary wnditions on the model prediction for Exp# 3.

continuous. The effect of thermal boundary conditions at the wall on the simulated temperature profile is shown in RCJ. 8 (Exp# 3, x = 7.5 cm). The SFUM processing conditions used in this study are closer to the isothermal wall like typical polymer processing conditions.

One reason for reinforcing polymers is to improve dimensional stability. The experimental results showed remarkable improvement in dimensional stability. The dimensional stability was measured by comparing the mold dimension with the molded composite dimension at room temperature. The linear shrinkage of the pure PU part containing no fiber mats was about 8.5 X cm/cm in the axial direction. But the shrinkage of the PU composite containing the random fiber mat (one or two) was almost negligible (less than 5.0 X 1W cm/cm). The polymer composite containing random fiber mats can be used in many applications, such as the automobile industry, because it has high dimensional stability.

coNcLusIo~s

The SFUM process for fabricating random continuous glass fiber reinforced PU composites was studied through the molding experiments and simulation modeling. The reaction kinetics of the PU system was studied using the adiabatic temperature rise measurement method. The Arrhenius type simple second order reaction kinetic equation could explain well the

reaction kinetics of the PU system. The viscosity function for the PU system was also obtained from the viscosity data measured using the rheometrics mechanical spectrometer. Darcy's law could explain well the flow behavior of the polymer fluid during mold filling. The pressure rise during filling was predicted rea- sonably by Darcy's law with the Kozeny's constants of 1 10-180. The experimental temperature profile measured at two axial positions agreed well with the simulation result. A remarkable improvement in dimensional stability was observed by measuring the linear shrinkage ratio of both the pure and the fiber reinforced PU parts.

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REFERENCES C. W. Macosko, RIM Fundamentals of Reaction Iy&n Molding, Hanser (1989). V. M. Gonzalez and C. W. Macosko, Polym Comp., 4, 190 (1983). G. H. Slocum. N. H. Nodelman, C. E. Fluharty, and D. W. Schumacher. Structural RIM: Successful Combination of RIM Process and Fiber Reinforcement, Amer. SOC. Mat., Adv. Comp. Conf., Dearborn, Mich. (1986). Y. T. Chen, Resin Transfer Molding of Liquid Dicyanate: Chernorheology, Molding Experiments, and Wetting Visu- alization, PhD thesis, Univ. of Minnesota (1993). K. J. Mikkelsen and C. W. Macosko, J. EIast h t , 21, 29 (1989). R. E. Camargo, V. M. Gonzalez. C. W. Macosko, and M. Tirrell, Rubber Chem Tech, S6, 774 (1983). M. C. Pannone and C. W. Macosko, J. AppL Pdym sci, S4, 2409 (1987). J. M. Castro, Mold FiUing and Curing Studies for the Polyurethane RIM Process, PhD thes is , Univ. of Min- nesota (1980). V. M. Gonzalez, Studies of Reactiue Polymer Processing with Fiberglass Reinforcement, PhD thesis, Univ. of Min- nesota (1983). G. Q. Martin and J. S . Sons, Fluid Mechanics of Mold FiUing for Fiber Reinforced Plastics. h e r . SOC. Mat., Adv. Comp. Conf., Dearborn, Mich. (1986). R. Gauvin a n d M. Chibani, J. Reinf. Plat . . 6, 267 (1987).

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Reaction injection molding process of glass fiber reinforced polyurethane composites