Cure Simulation of Hemp Fiber Acrylic Based Composites During Sheet Molding Process

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1 Cure Simulation of Hemp Fiber Acrylic Based Composites During Sheet Molding Process Cure Simulation of Hemp Fiber Acrylic Based Composites During Sheet Molding Process T. Behzad and M. Sain 1 Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, Ontario, Canada Received: 12 June 2004 Accepted: 2 September 2004 SUMMARY In the present study, a new environmentally friendly thermoset resin was used to manufacture hemp fiber acrylic composites by sheet molding process for automotive applications. A finite difference method was applied to predict the cure behavior and temperature variation of hemp fiber acrylic based composites during the process. Dynamic Differential Scanning Calorimetry (DSC) was employed to determine the kinetic parameters for the curing reaction at different heating rates. It was found the experimental and predicted values are in good agreement at the lower heating rate. The thermophysical properties of the resin, fiber and composite were obtained to use in the model. The temperature profile and the degree of cure of the composite with 40% resin and 60% fiber were simulated and a comparison of numerical results with known experimental data confirms the approximate validity of the model. INTRODUCTION In the past few years, natural fibers are finding an increased interest as reinforcement in polymer matrices. Natural fiber composites are claimed to offer advantages such as low cost, low density and weight savings, reduced tool wear and low pollutant emissions. Although the mechanical properties of natural fibers are much lower than traditional fibers such as glass fiber, their specific properties, especially stiffness, are comparable to the values of those fibers 1,2. Currently, different agricultural species like hemp, kenaf, flax, pineapple leaf, have been considered for use in the production of natural fiber composites and mechanical properties have been investigated. Pervaiz et al. 3 presented the mechanical properties of hemp fiber poly propylene composite using film stacking method. The results show that hemp-based natural fiber mat thermoplastic have comparable or even higher strength properties as compared with conventional flax-based thermoplastics. Overall consequence of this study indicate that hemp based thermoplastic composites are good candidates for Corresponding author: Prof. M. Sain, Faculty of Forestry, University of Toronto, 33 Willcocks street, Toronto, Canada M5S 3B3, m.sain@utoronto.ca automotive applications. The effect of concentration and modification of fiber surface on mechanical properties of sisal/oil palm hybrid fiber reinforced rubber composites were investigated by Jacob et al. 4. It was found the alkali treatment of fibers has a pronounced effect on the extent of adhesion between fiber and matrix. From the mechanical properties the alkali treated fibers exhibited better tensile properties than untreated composites. More recently Shibata et al. 5 manufactured natural fiberreinforced biodegradable polyester composites from abaca fibers using melt mixing and injection molding process. The effect of surface treatment and fiber content on mechanical properties of composites using different biodegradable polyesters was studied. The flexural modulus of all the fiberreinforced composites increased with fiber content. Although there is a high interest to use bio-based resin such as soy-based resin for manufacturing automotive parts in short term, use of those resin must be restricted due to poor supply and cost scenario. In the thermoset polymers, the fibers are used as unidirectional tapes or mats. These are impregnated with thermosetting resins and then exposed to high temperature for curing. In the literature most of the natural fiber thermoset composites studied are produced by Resin Transfer Moulding (RTM) Polymers & Polymer Composites, Vol. 13, No. 3,

2 T. Behzad and M. Sain technique. Richardson and Zhang conducted an experimental study of RTM process for nonwoven hemp-phenolic composite 6. It was found that the injection pressure and fiber concentration have significant effects on the complete perform impregnation. Moreover, the effects of nonwoven hemp on the mechanical properties of phenolics and their microstructural features were investigated. There was a significant increase in flexural strength and modulus with the introduction of nonwoven hemp. Also, hemp fiber-reinforced polyester composites were manufactured using RTM process and the mechanical behavior of the composite investigated by Sebe et al. 7. No major problem was took place during the process and very good results for hemp fiber-reinforced polyester composites were obtained. Surface modification of hemp fiber did not affect the flexural stress at break of the composite but was detrimental to toughness. From this review it can be noticed that most of the papers focus on the mechanical properties of natural fiber composites using a specific process. Most of the numerical studies deal with composites reinforced with synthetic fibers using RTM technique. Lim et al. 8 presented a three-dimensional analysis of resin flow for RTM process using the control volume finite element method to predict the degree of cure and temperature for thick parts. Numerical and experimental results were found to be in good agreement. The modeling and simulation of resin flow, heat transfer and the curing of multilayer thermoset composites during processing were studied by Blest et al. 9. Another work was presented by Chiu et al. 10 on the heat transfer and resin reaction simulation and compared with an experimental analysis. There is little work on providing a model predicting the cure behavior of natural fiber composites and optimizing process conditions. For the first time, Rouison et al. 11 provided a model predicting the cure behavior of natural fiber composites using a curing model based on the one-dimensional Fourier s heat conduction equation. The model could be used to optimize the process and to produce highly cured parts in a minimum time. In the previous study, a new environmentally friendly acrylic resin was characterized to optimize the curing conditions 12. In this work, firstly n th order equation was used to determine the kinetic parameters for the curing reaction of the resin. These results were used to simulate the cure behavior of this resin in a sheet molding process. Secondly, the resin was used to manufacture hemp fiber acrylic based composites. Hemp fibers were impregnated by the resin solution and then the dry mats were used for sheet molding process. The main purpose of this project is to provide a model predicting the cure behavior and temperature variations of hemp fiber acrylic based composites during the process and evaluate the predicted values with experimental results. Materials EXPERIMENTAL In this study, a new commercial water-based acrylic resin (viscosity at 23 C = mp.s), a binder for natural fiber composites, was used. It contains polycarboxylic acid with a polyhydric alcohol as a crosslinking agent. Hemp fiber used in this work was kindly supplied by the Hempline Company. Dynamic Kinetic Analysis of an Acrylic Resin The experiments were carried out using a Differential Scanning Calorimeter (DSC) TA instruments Q1000 (DSC) in the dynamic mode following wellestablished procedures 13. Indium was used for temperature calibration and nitrogen as the flushing gas. Standard aluminum D.S.C. pans were used. Sample weights were between 10 to 20 mg. Because of the water content, the resin was dried by vacuum rotary system before using for dynamic scans. Non-isothermal experiments on uncured samples were conducted at 5, 10 and 15 C min -1 from 30 C up to 350 C. A straight line was established to quantify the areas above the endothermic curves. These calculations were performed by the D.S.C. software. Vacuum Resin Impregnation and Sheet Molding Process One of the major issues in development of composites is dispersion of the fibers in the matrix. The incorporation of cellulosic fibers in polymers leads to poor dispersion of the fibers due to strong interfiber hydrogen bonding, which holds the fibers together. This lack of fiber dispersion can result 236 Polymers & Polymer Composites, Vol. 13, No. 3, 2005

3 Cure Simulation of Hemp Fiber Acrylic Based Composites During Sheet Molding Process in clumping and agglomeration of cellulose fibers which lead to inferior mechanical properties. variations of the resin s heat capacity were taken in the range of 35 ºC to 190 ºC. In this work, hemp fibers were randomly oriented in a perforated screen and the acrylic resin solution was circulated to impregnate the fibers with the solution. Vacuum filtration was applied to remove excess solution. (US pat. APPL. No. 60/562,444) After circulation of the resin solution, the wet mat was displaced on a polyester sheet and then kept in the oven at 55 C for 48 hrs to remove all moisture content and to complete thickening process (maturation), if any. The mat would be ready for sheet molding process after the maturation period. Finally, to manufacture the composite the impregnated mat was cured at 180 C for 10 minutes using a hydraulic press with 1500psi pressure to obtain the highest compaction. After heating cycle, the temperature of the composite was cooled down inside the press to around 70 C using water cooling system to prevent any blister formation due to any moisture content. The final composite was removed from the press and prepared for mechanical properties measurements. The evaluation of temperature was recorded at the center of the composite using J type thermocouples. Thermo Physical Properties To predict the curing behavior of the resin during processing accurately, thermophysical properties of the composites have to be determined. The evaluation of heat capacity with temperature for hemp fibers was measured using a Differential Scanning Calorimeter (DSC) TA instruments DSC Q The non-cured resin s heat capacity was obtained as well by a similar experiment. The The density of uncured resin was given 1.53 g/cm 3 and the densities of the cured resin and composites with 60% fiber content were measured by weighing samples of well known volumes. The apparent density of the composites was also carried out by the water displacement method (Archimedean density) which consisted of weighting samples in air and in water (ASTM C693). This method allows determination of the density in air compared to its displacement in distilled water. The thermal conductivity of the composite with 60% fiber was measured as well using the method was adapted from a technique presented in Davidson and James s work 14 and is illustrated in Figure 1. A set-up was designed to make one-dimensional heat flow through the samples. A temperature differential was created across a pair of the samples using a thin film resistive heater. In order to distribute heat uniformly, a steel plate was placed on either side of the heater, while a second pair of steel plates prevented convective heat loss directly from the samples to the environment. A thin layer of a thermal compound was applied between all components to ensure good thermal contact. The steel plates and the samples had the same cross-sectional area as the heater and insulation was placed around the edges of the samples to minimize lateral heat flow. Two thermocouples were placed on each side of one of the samples in the set-up. All four thermocouples were connected to an acquisition system, which was connected to a computer to store the recorded temperatures. After reaching to steady state, the average temperature differential from the last Figure 1. The experimental set-up used for the thermal conductivity measurement of the composite Styrofoam insulation Thermocouples Steel plates Composite samples A thin heater Polymers & Polymer Composites, Vol. 13, No. 3,

4 T. Behzad and M. Sain 10 min of heating was used to calculate the thermal conductivity of the composite. Crosslink Density Measurements In order to measure the crosslink density of the matrix of the composite the Flory-Rehner equation was used. The samples of approximately 1 cm square shape and 2 mm thickness were cut, weighed accurately and allowed to swell in excess of solvent (water) at room temperature for specific period (24 hr). Samples after swelling were taken out, wiped out solvent adhering to the surface and weighed immediately at the room temperature. The weight of the samples after complete drying was also found out. Volume fraction of resin (υ) was then calculates using the equation 15 : υ= (D FT )ρ r _1 (D FT )ρ r _1 + A 0 ρ S _1 Where T = Initial weight of the sample D = Deswollen weight of the samples F = Weight fraction of insoluble components ρ r = Density of the resin A 0 = weight of the solvent absorbed by the sample ρ s = Density of the solvent Sheet Molding of Natural Fiber Composites: Cure Simulation 1) Kinetic Study of an Environmentally Friendly Acrylic Resin One of the most widely accepted methods for determining cure kinetics of a thermoset resin system is differential scanning calorimetry (DSC) 16,17. For the calculation of the reaction rate (dα/dt) and the degree of conversion (α) the variation of the calorimetric signal according to the time or the temperature has to be known. The basic assumption for the application of DSC is that the measured heat flow, dh/dt, is proportional to the reaction rate, dα/dt. Without knowing the exact reaction mechanism, the rate of the curing reaction under study is often described according to the following equation: dα dt = dh 1 dt H 0 = k ( 1 α) n = Ae E a /RT (1 α) n (1) where k is the reaction constant and is usually assumed to be of the Arrhenius form, A is frequency factor, R the universal gas constant, E the activation energy, T the absolute temperature, n order of the reaction, H the amount of heat consumed by the reaction up to time t and H 0 is the total amount of heat consumed over the entire reaction. By expressing the scanning rate as β = dt/dt, this expression can be written in the logarithmic form: ln β dα = ln A E a dt RT + nln ( 1 α) (2) A multilinear regression can be performed to calculate the values of E a, A, n. 2) Model Theory In this study a one-dimensional curing model was used to predict the temperature variation and degree of cure in the composite during the compression molding process. A few assumptions were considered to simplify the problem: - It was assumed that the resin start to cure after closing the press, since the temperature of composite during the closing was less than 100 C at which the resin did not cure immediately. - Due to the presence of fibers, the thickness of the composite assumed to be constant, so the effect of resin shrinkage was neglected. - It was assumed that there were no radiation and convective heat transfer with air during curing. The edge surface of composite which exposed to air is negligible compare with the total surface of the composite. Based on Fourier s heat conduction equation for onedimensional, transient heat transfer and an internal heat consumption term using the assumption considered above the temperature variation can be obtained 9,18 : T ρ c C pc t = k 2 T x x Q 2 t (3) Where ρ c, C pc and k x are the density, heat capacity and thermal conductivity of the composite material respectively. The heat consumption sink represents the endothermic effect of the curing reaction. This term is directly related to the rate of cure by the following equation: 238 Polymers & Polymer Composites, Vol. 13, No. 3, 2005

5 Cure Simulation of Hemp Fiber Acrylic Based Composites During Sheet Molding Process dq dt =ρv H dα r r 0 dt (4) where α is the degree of cure, H 0 is the heat of reaction per unit mass of resin, V r is the volume fraction of resin in the composite, ρ r is the density of the resin and dα/dt the rate of cure reaction. As it mentioned earlier, the curing rate of the resin was studied by DSC using the following n th order model: dα dt = k(1 α)n = Aexp E a (1 α) n (5) RT To integrate the related equations the Crank- Nicholson finite difference method was applied 19. For a one-dimensional problem this method was shown to be stable with time step size. In numerical analysis, finite increments of space and time are considered. First, the x axis perpendicular to the composite is chosen and the upper and lower surface of the composite were considered as the boundaries of the domain (i=1 and i=n). The domain was divided in N-1 equal intervals with the grid size being Δx=L/(N-1), where L is the thickness of composite. In the time domain the grid size was Δt and the index j was used to count the time such as t j =j(δt). The partial differential equations were evaluated at time t j +Δt/2: 2 T x 2 i, j+1/2 T t i, j+1/2 1 T i+1,j 2.T i, j +T i 1,j 2 x T i, j+1 T i, j t + T 2.T +T i+1,j+1 i, j+1 i+1,j+1 ( ) ( 2 x) 2 (6) (7) The sink term in the Equation (3) was evaluated at time t j using equation (5) as an approximation, giving: T ρ c C pc t i, j+1/2 2 T = k x x 2 i.,j+1/2 Q t i, j (8) The temperature at the surfaces (i=1 and i=n) were known as constant and used as boundary conditions. For i=2 N-1, this system was solved for each j. The Thomas algorithm was applied to solve a (N-2, N-2) tridiagonal matrix. The cure rate was calculated from equation (5) and a dichotomy method was used to compute the degree of cure at each node at t j +Δt. A MATLAB code was written to solve all these equations and compute the evaluation of temperature, degree of cure and cure rate in the composite during a typical experiment. The platen temperature and initial temperature of the composite were measured experimentally and used as boundary and initial conditions to increase the accuracy of the modeling work. RESULTS AND DISCUSSION Dynamic Scans Typical dynamic scans at different heating rates were shown in the previous work. Also, the average value of the heat of reaction was obtained 491 J/g. As mentioned earlier, a multilinear regression was performed on equation 2 to obtain kinetics parameters at different heating rates. These values are presented in Table 1. To check the validity of the model the experimental and predicted values of curing rates can be compared. The main assumptions which are made in this case are that the sample is so small and the heating rate used in DSC is so low that the temperature throughout the sample is always uniform and about the same as that of the calorimeter. This means that the rate of heat transfer by conduction through the sample is very low compared to the rate of heating selected in the DSC. Therefore, as it can be noticed from Figure 2, the experimental and calculated curing rates are in good agreement at lower heating rate. At the heating rate of 5 C/min, the correlation coefficient is 96% which is fairly acceptable. The values which obtained at the heating rate of 5 C/min were used for cure simulation of the composite. Thermophysical Properties Figure 3 show that the fiber s C increased from p 1.07 J/g.K to almost 1.7 J/g.K with increasing Table 1. Values obtained from multilinear regression with non-isothermal data Scanning rate (ºC min -1 ) Activation energy (KJ/ mol) Order of reaction Ln (Frequency factor) Polymers & Polymer Composites, Vol. 13, No. 3,

6 T. Behzad and M. Sain Figure 2. comparison of experimental and calculated curing rate for acrylic resin Figure 3. Heat capacity of the hemp fibers measured by DSC in the range 50 C to 200 C Figure 4. Variation of the non-cured resin heat capacity with temperature temperature from 70 C to 200 C. The variation of the fiber s heat capacity could be fitted quite well by a polynomial of the second order in the range 70 C to 200 C: C pf =-3e -6.T T (9) The density of hemp fiber was obtained from literature to be 1.48 g/cm 3 in this study to evaluate the volume fractions of fibers in the composite. It can be seen from Figure 4 that the heat capacity of the uncured resin increased linearly with temperature in the range of 35 C to 190 C. The values vary from 1.03 J/g.K to 3.43 J/g.K approximately. These variations could not be neglected in the model and the following linear relationship was used as the resin s heat capacity in J/g.K: C pr = T (10) To predict accurately the temperature variations in the composite the heat capacities of the composite materials were needed as well. It was therefore decided to evaluate the heat capacity of the composite using the rule of mixture with equations 9 and 10: pc (T) = C pf (T).m f + C pr (T).m r,, (11) where m f and m r are the mass fraction of the fiber and resin, respectively. The density of the uncured resin was given 1.53 g/cm 3. Weighing the known volume of the cured resin, the density was measured 1.45 g/cm 3. It can be seen the difference between the density of uncured and cured samples is negligible. Therefore, the density of the resin was kept constant for the modeling and equal 240 Polymers & Polymer Composites, Vol. 13, No. 3, 2005

7 Cure Simulation of Hemp Fiber Acrylic Based Composites During Sheet Molding Process to 1.5 g/cm 3. The density of the composite with 60% fiber and 40% resin was measured almost 1.32 g/cm 3. The apparent density of the composite was found 1.4 g/cm 3. It can be seen that the composite density difference between two methods was not dramatic (5%). So, the density of the composite was assumed to be 1.35 g/cm 3 for the modeling. The thermal conductivity of the samples which consisted of 60% hemp fiber and 40% resin was calculated from the following expression in W/m. C: k = Qx A T (12) where Q is the heat flow through the sample [W], x is the thickness of the sample in the direction of heat flow [m], A is the cross-sectional area of the sample [m 2 ] and ΔT is the steady state temperature drop across the sample [ C]. The heat flow through each sample was considered to be half the power consumed by the heater because of the symmetry of the experimental set-up, i.e. Q = 0.5 V 2 R (13) with 60% fiber system at the center of the mold is presented in Figure 6. This experiment was performed with a constant surface temperature of approximately 185 C. It could be noted that the predicted temperature at the center of composite were around 20 C less than the temperatures measured at the center of the part. The first part of the curve, when the center of the part heated up by conduction, was very well predicted. It can be found that the rate of temperature increasing will drop at the temperature around 140 C where the endothermic cure reaction started. After 3 min the temperature of the composite will reach to 185 C. Some discrepancies could be explained by the approximations made to describe the thermophysical parameters of the system. The density and the heat conductivity may vary during the process with the state of cure of the resin. Moreover, the initial distribution in the composite may not be uniform and the temperature of the platen may slightly change with time. Figure 5. Experimental temperature profile at the center of the composite where V and R are the voltage drop across the heater [V] and the resistance of the heater [Ω] respectively, measured with a multimeter. The average ΔT from the last 10 min of temperature measurements was 2.39 C. The thermal conductivity of the hemp fiber acrylic based composite is calculated W/m. C. Sheet Molding of Natural Fiber Composites The evaluation of temperature at the center of the composite was monitored using type J thermocouple. Once the press was closed the temperature of the center of the composite was started to record every 5 seconds. Due to the low thickness of the composite and high temperature of the press the initial temperature of the center of the composite was around 75 ± 5 C. A typical temperature profile at this location is presented in Figure 5. It can be seen that the temperature increased quite fast till the point where it reached the set point. A comparison between the experimental data and predicted result collected for the composite Figure 6. Comparison of experiment and simulation for 60% fiber composite at the centre of the composite Temperature, center ( C) Model 90 Experimental Time (s) Polymers & Polymer Composites, Vol. 13, No. 3,

8 T. Behzad and M. Sain Due to the small thickness of the composite, it was very difficult to keep the thermocouple exactly at the center of the composite, so there is the possibility of the movement of the thermocouple toward the surfaces of the composite which were closer to the platens. The model predicted the degree of cure and the rate of cure of the resin with time as well, as shown in Figure 7. The curing rate of the resin increased sharply with time to reach a maximum after almost 1 min or at a degree of cure of around 20%. After this point the rate of cure decreased slowly with time. The model predicted a degree of cure of almost 100% after 10 minutes. To validate this prediction, the same composite under same conditions were prepared at different curing times and the crosslink density of samples was measured. Crosslink density is the most definitive value to represent cure. It is a quantitative measure of the number of crosslinks that exist in a given volume in the thermosetting polymer. This value is related to the degree of cure. The degree of cure represents a certain level of crosslinking, but the value obtained for the degree of cure is relative. According to the theory of Flory and Rehner, for a perfect network, crosslink density υ x is calculated by using the following equation 12 : υ x ln ( 1 υ)+υ+χ = 1 υ 2 υ 1/3 υ/2 ϕ 1 ( ) (14) Where υ x is the number of moles of elastically effective network chains per cubic centimeter, υ is the volume fraction of the polymer in swollen matrix, ϕ 1 is the molar volume of the solvent and χ 1 is the Flory-Huggins interaction parameter between solvent and polymer. Using χ 1 equal to from the literature, data for volume fraction of swollen sample υ, crosslink density υ x of the composites at different curing times between 1 min to 12 min at 180 C were calculated. Data for volume fraction of swollen sample υ and crosslink density υ x at different curing times between 1 min to 12 min at 180 C are calculated and presented in Table 2. The data reported in Table 2 indicates that the cure time have a significant effect on the crosslink density of the cured sample. The crosslink density of the acrylic resin increases from to mol ml -1 with increasing the curing time from 1 min to 10 min at 180 C. It can be noticed that the rate of increasing of the crosslink density decreased after 5 min curing time. Also, as the curing time increased from 10 min to 12 min the crosslink density decreased from to mol ml -1 which can be due to decomposition of the resin. Table 2. Volume fraction and Crosslink density of the resin in the composite at different curing times Curing time (min) Volume fraction Crosslink density 10 3 (mol/ml) Figure 7. Evaluation of the degree of cure and the rate of cure with time at the center of the composite for 40% resin system Degree of cure Degree of cure Rate of cure Time (s) Rate of cure 242 Polymers & Polymer Composites, Vol. 13, No. 3, 2005

9 Cure Simulation of Hemp Fiber Acrylic Based Composites During Sheet Molding Process To validate the predicted degree of cure from the model, the crosslink density obtained from above mentioned results were used. It was assumed the sample with the highest amount of crosslink density has been completely cured (α=1), so the degree of crosslink was considered to be one for this sample. A comparison between the experimental data and predicted values for the composite with 40% resin and 60% fiber with 2.2 mm thickness is presented in Figure 8. The predicted degrees of cure were in very good agreement with the experimental data. After 5 min, more than 90% of the reaction was completed and there is a slow rate of increasing of reaction from 5 to 10 min. CONCLUSIONS In this study, the kinetic parameters of an environmentally friendly acrylic resin were obtained using DSC. Hemp fiber acrylic based composites were prepared using the sheet molding process. Some of the thermophysical properties of the resin, fiber and composite were studied. The curing behavior of the composite was predicted during processing using a curing model based on the onedimensional Fourier s heat conduction equation. Due to the high cure temperature and difficulty to measure the temperature at the center of the composites, some discrepancies were observed between predicted and experimental values of temperature. The degree of cure in the composite was also predicted. The degree of cure was found to be 100% which is acceptable for these materials. The crosslink density of the composite at different curing times was measured to evaluate the predicted values of degree of cure. A comparison of numerical results with known experimental data confirms the approximate validity of the model. ACKNOWLEDGEMENT The authors would like to acknowledge (1) NCE- Auto 21 st Century for their financial support of this work and (2) Dr. Ning Yan for providing the Differential Scanning Calorimeter. REFERENCES 1. Wambua, P., Ivens, J. and Verpoest, I., Composite science and technology, 63, (2003), Joshi, S.V., Drzal, L.T., Mohanty, A.K. and Arora, S., Composites: Part A, 35, (2004), Pervaiz, M. and Sain, M.M., Macromolecular materials and engineering, 288, (2003), Jacob, M., Thomas, S. and Varughese, K.T., Composite science and technology, 64, (2004), Shibata, M., Ozawa, K., Teramoto, N., Yosomiya, R. and Takeishi, H., Macromolecular materials and engineering, 288, (2003), Richardson, M. and Zhang, Z., Reinforced plastics,45, (2001), Sebe, G., Cetin, N.S., Hill, C.A.S. and Hughes, M., Applied composites materials, 7, (2000), Lim, S.T. and Lee, W.I., 60, (2000), Blest, D.S., Duffy, B.R., McKee, S. and Zulkifle, A.K., Composites: Part A, 30, (1999), Figure 8. Comparison of experimental degree of crosslink and predicted data Polymers & Polymer Composites, Vol. 13, No. 3,

10 T. Behzad and M. Sain 10. Chiu, H.T., Yu, B., Chen, S.C. and Lee, L.J., Chemical engineering science, 55, (2000), Rouison, D., Sain, M., and Couturier, M., Composites science and technology, 64, (2004), Behzad, T. and Sain, M., Journal of applied polymer science, 92, (2004), Turi, E.A., Thermal characterization of polymeric materials, Academic press: New York, 1981, Davidson, S.R.H. and Sherar, M.D., Taylor & Francis health sciences, 19, (2003), Panthapulakkal, F.S., Studies on short polyester fiber-polyurethane elastomer composite with different interfacial bonding agents, PhD thesis, Cochin university of science and technology, India, (1998) 16. Ishida, H. and Rodriguez, Y., Polymer, 35, (1995), Chu, F., McKenna, T. and Shidu, L., European polymer journal, 33, (1997), Vergnaud, J.M. and Bouzon, J., Cure of thermosetting resins: modeling and experiment, Springer-Verlag, London, (1992). 19. Chapra, S.C. and Canale, R.P., Numerical methods for engineering: with programming and software applications, Boston: WCD/ McGraw-Hill, (1998), Chapter Polymers & Polymer Composites, Vol. 13, No. 3, 2005