CURE KINETICS MODELLING AND CURE SHRINKAGE BEHAVIOUR OF A THERMOSETTING COMPOSITE Nuri Ersoy, Mehmet Tuutlu Boazici University, Mechanical Enineerin Department 3434 Bebek, Istanbul, TURKEY Nuri.Ersoy@boun.edu.tr SUMMARY Cure kinetics and throuh-the-thickness cure shrinkae of a carbon fibre-epoxy composite (AS4/855) were studied. Differential Scannin Calorimeter (DSC) scans were performed to develop a new cure kinetics model. The coefficients of thermal expansion (CTEs), the lass transition temperatures ( T ), and the cure shrinkae strains of composite samples were measured by usin a Dynamic Mechanical Analyzer (DMA). Keywords: Cure Kinetics, cure shrinkae, thermosettin resins I. INTRODUCTION Due to the orthotropic nature of the fibre reinforced composites, hih temperature processin results in shape distortions. The throuh-the-thickness thermal expansion coefficient of continuous fibre composites is much hiher than the in-plane expansion coefficients. Composite parts with curved eometry sprin-in as they come out of the mould. The throuh-the-thickness thermal and shrinkae strains are the main contributors to the sprin-in phenomenon [-5]. This makes measurement of the thermal expansion coefficient and cure shrinkae strains durin the process cycle extremely important. Hence necessary tool compensations can be made by usin models to predict the shape distortions. Durin processin of thermosettin composites, the resin transforms from a viscous fluid of monomers to first a rubbery and then to a cross linked network. Durin this process, the free space occupied by the polymer molecules reduces and this causes a chemical shrinkae which is usually referred as cure shrinkae. In order to investiate the cure development numerically, cure kinetics models specific to the resin system used in the composite were developed. The extent of the cure reactions is usually described by the deree of cure, α, which is quantified as the fraction of heat enerated to that point relative to the total heat enerated throuh the complete cure. The deree of cure can easily be determined usin standard heat flow measurements in a Differential Scannin Calorimeter (DSC) by interatin the exothermic DSC peak. The cure kinetics models developed in the literature for the 855 resin system are usually phenomenoloical and do not reveal the actual mechanism takin place durin curin [4, 6-].
The cure shrinkae of epoxy resins and composites were either measured directly by volumetric dilatometer [-5], by density chane techniques [6-8], by Thermo- Mechanical Analysis (TMA) [9, 0] or by indirect methods by curin additional layers of prepre on already cured layers [0-]. All of the direct measurement methods use small amounts of material to fit into the dilatometer or TMA cell and the material usually requires some kind of confinement such as a quartz dilatometer cell, and volumetric strains can be measured instead of orthotropic or throuh-the-thickness strains. Furthermore, the small size (usually a few millimetres) of the samples does not allow the isolation of ede effects in layered composites. Recently Garstka et al. [3] developed a method that allows direct monitorin of throuh-the-thickness strains in composite parts. This method utilizes a special tool to pressurize and to heat the sample and an optical system to measure the throuh-the-thickness strains. In this study a series of thermal scans of curin prepre samples were carried out in order to develop a cure kinetics model. Furthermore the relationship between deree of cure and the throuh-the-thickness cure shrinkae strains and coefficient of thermal expansion of partially cured composites were determined by usin standard polymer laboratory equipment such as DSC and DMA. The method used in this paper for cure shrinkae measurements is inspired from the work of Garstka et al. [3], however does not require any special equipment and allows the measurement of cure shrinkae by conventional Dynamic Mechanical Analyzer (DMA) in compression mode. Furthermore the sample size used is lare enouh (a few centimetres) so that the ede effects do not affect measurements done. II. EXPERIMENTAL. Material and Manufacturer s Recommended Cure Cycle (MRCC) The prepre used in this study is a unidirectional carbon/epoxy, produced by Hexcel Composites with a desination of AS4/855. The nominal thickness of the prepre is iven as 0.84 mm. The MRCC consists of a first ramp of o C/min up to 0 o C and a first hold at 0 o C for 60 min, a second ramp of o C/min up to 80 o C and a second hold at 80 o C for 0 min. A pressure of 0.7 MPa is applied throuhout the cycle.. Differential Scannin Calorimeter Modulated DSC (MDSC) Q00 produced by TA Instruments was used to perform the dynamic and isothermal experiments to provide a database for calculatin parameters in the model equations that describes the cure kinetics over a wide rane of erent conditions. Dynamic experiments were performed by heatin from -35 to 300 o C at,, 3, 4 and 5 o C/min. Isothermal experiments were performed by heatin from 5 o C to 0 o C, 40 o C, 60 o C, 80 o C at 5 o C/min, then holdin at the specified temperature; 0 o C for 360 min., 40 o C for 40 min, at 60 o C for 80 min, at 80 o C for 0 min. After the isothermal run, the samples were cooled 50 o C below the isothermal hold temperature and reheated to 300 o C at 5 o C/min to find the residual heats. Dynamic scans were performed by
modulation of temperature of ±0.5 o C. Mass of prepre samples that were used in the experiments were around 6 rams..3 Coefficient of Thermal Expansion and Cure Shrinkae Measurements Five unidirectional (UD) and five cross-ply (XP) samples were prepared for the throuh-the-thickness strain measurements. Each sample was 6 layers and nominally 5 mm thick. These samples were then cured in a home-made fast response autoclave which can prorammed for the desired temperature and pressure.. The temperature proram followed the MRCC up to the end of the first dwell at 0 o C. All samples were heated from room temperature to 0 o C at a rate of o C/min, and kept at 0 o C for one hour. Then in order to obtain the equilibrium asymptotic deree of cure attainable at a specific processin temperature, the samples were heated from 0 o C to the desired temperature at a rate of o C/min and kept at this temperature for a time sufficient to attain the equilibrium asymptotic deree of cure. This hold duration was determined by the isothermal DSC experiments. The hold durations for the second dwell at the specified temperature is listed in Table. The samples were then fast cooled to room temperature in the autoclave. Table. Durations of the second isothermal holds Temperature ( o C) 0 40 60 80 Hold duration (mins.) 360 40 80 0 The samples thus manufactured were cut into 5x5 mm squares by a precise diamond cutter cooled by liquid coolant. To overcome the temperature radient between specimen and DMA equipments measurin thermocouple, the samples were drilled a mm diameter hole at the corner to accommodate the DMA equipment's control thermocouple. TA Instruments Q800 Dynamic Mechanical Analyzer was used in compression mode with the appropriate compression clamps. The sample was placed on the flat surface of the fixed bottom clamp and the movin top clamp was pressed until touchin the sample. Movin clamp applied a very small force (0. N) on the sample not to allow disenaement of the sample from the clamp, so measures dimensional chanes of the sample as displacement. Nitroen was used as purin as and liquid nitroen was used to et a controlled coolin. Reardin the temperature cycle, two sets of experiments were performed. Partially cured samples were heated from room temperature to 50 o C and cooled back to room temperature at a rate of o C/min. III. RESULTS AND DISCUSSION 3. Cure Kinetics Modelin The Modulated Differential Calorimeter enables one to distinuish between nonreversin heat flow curve (which corresponds to the heat extraction durin curin) and
reversin heat flow curve (which corresponds to the heat capacity of the sample). Fiure shows these two curves for a typical dynamic scan for a virin prepre sample, toether with the baseline. The exothermic direction is up. A straiht baseline between the onset and end of the reaction exotherm is used in this study. The lass transition temperature reveals itself as a step chane in the reversin heat flow curve around -4 o C. The heat of reaction is the total heat found by interatin the exothermic peak. It should be kept in mind that this is the heat of reaction of the composite and should be corrected for the resin content to find the total heat of reaction of the resin. Fiure. Reversin and non-reversin heat flow curves. A model which includes two parallel sinle-step reactions is used in this study. These reactions were assumed to be of n-th order, autocatalytic Prout-Tomkins type with usion control. These reactions types are proved to be well suited for cure kinetics modelin of other types of epoxy resins [4, 5] α = kα t α α α n a n ) a ( ) + k ( where k / are the temperature dependent rate constants, n / and a / are freely selectable temperature independent exponents. Althouh physical interpretation of phenomenoloical models should be avoided, Eq. () can be thouht as describin a reaction that proceeds alon two parallel branches with two erent rates, resultin in the same product, and the rates depend on the temperature as well as the deree of cure, α. The kinetic reaction equation takes into account the fact that for some conditions the lass transition temperature of the polymer increases faster than the proram temperature for the dynamic tests, or the lass transition temperature rises above the isothermal hold temperature for the isothermal holds. After the partial or complete freezin of the reaction mixture the reaction is no loner controlled by the kinetics of the chemical reaction, but by the usion processes. If usion hindrances must be considered, the Rabinowitch equation [6] can be used for calculation of the overall rate constants k / : ()
where chem k / are the chemical reaction rates, = + () chem k/ k/ k/ k / are the usion rates. The chemical rate constant is described in the form of Arhenius equation: { E RT} k chem / = A/ exp / (3) where A / are the pre-exponential factors, E / are activation eneries, R is the universal as constant, and T is the absolute temperature in derees Kelvin. The concrete form of the temperature function for / is absolutely unimportant. However, it should be such that the experimental input necessary for the calculation of the selected function is the easily accessible lass transition temperature. Therefore, for temperatures above the lass temperature T ( T > T ) the WLF equation can be used as proposed by Wise et al. [7]: Below T ( T < T k C( T T ) k / ( T ) = K/ exp (4) ( C + T T ) ) dependence is accordin Arrhenius equation as proposed by Flammersheim and Opfermann [4, 5]: with E k / ( T ) = K/ exp (5) R T T E R C T = (6) C where K / and C and C are the model parameters to be found. At formulas are continuous up to the first derivative. T = T both For the fit of reaction curves, it is postulated that k / may be erent for each usion controlled reaction, but C and C are lobal, which means that they are valid for all reactions steps/branches. An additional function of T (α ) is needed for the kinetic evaluation of the usion controlled systems. T as a function of deree of cure is found by fittin the data to the followin equation proposed by Hesekamp [8]: α T ( α) = T (0) exp (7) α The constants,, and T (0) can be found to be 0.994,.66 and -.05 o C respectively by a least square fit of the T vs. α data, as in Fiure.
Fiure. Glass transition temperature versus deree of cure The parameters of the model listed in Table were found usin the NETZSCH Termokinetics Software [9] which utilized a multivariate non-linear reression scheme. Fiure 3 shows the predictions of the model toether with the oriinal nonreversin heat flow curves. The model fits the experimental data very well as can be seen from this fiure. Parameter lo (A ) Table. Cure kinetics model parameters E n a lo ( k ) lo (A ) E n a lo ( k ) C C Unit s - kj/mol 4 0 s - s - kj/mol s - K Value 0. 5 0.338 5.53-4.35 4.94 65.8.4 0.473-4.94 8.40 3.6 Fiure 3. Measured and model fitted heat flow curves
3. Thermal expansion and cure shrinkae It has been found that the thermal expansion of the clamp is sinificant durin the measurement of thermo-chemical strain response of the composite, so the response of the samples should be corrected by usin the clamp response as a baseline. The baseline corrected response of the crossply specimen precured at 60 o C is shown in Fiure 4. Here several features of the thermal strain response of the composite can be distinuished: Durin heatin the partially cured composite expands due to increasin temperature and then underoes a lassy-to-rubbery transformation ( T (heatin) ); it then continues to expand in the rubbery phase with a reater CTE until the cure shrinkae starts to compete with the expansion. The reaction ends and since increasin temperature keeps the composite in the rubbery state, the composites continues expandin with almost the same rate as before the cure reaction. Cure shrinkae strain can be found by extrapolatin the expansion response before cure shrinkae and subtractin from this the thermal response after cure reaction as shown in Fiure 4. Upon coolin, the composite underoes a lass transition at around T of fully cured composite. Fiure 4. Baseline corrected thermal strain response of crossply specimen. The thermal strain responses of composites with erent initial derees of cure are compared in Fiure 5 for unidirectional and crossply composites durin the heatin stae. Different derees of cure are obtained by precurin the composites at various isothermal temperatures at which the composite cures up to an equilibrium deree of cure as explained in the experimental part. It can be seen that as the deree of cure increases, the lassy-to-rubbery transformation temperature is shifted to hiher temperatures, and the cure shrinkae strain decreases. The measured transition temperature for unidirectional and crossply samples is almost the same, however the CTEs before and after T and the cure shrinkae strains are larer for crossply samples.
(a) (b) Fiure 5. Thermal strain response of (a) unidirectional and (b) crossply samples precured at erent temperatures. The CTEs at the lassy and rubbery states as well as T durin heatin and curin are iven in Table 3. It can also be seen from Table 3 that the cure shrinkae strains of the crossply samples are almost twice of CTEs of unidirectional samples. The T measured durin curin is almost the same as the value reported in the manufacturer s data sheet [30]. The CTE increases dramatically upon lass transition and the rubbery CTEs are 4-5 larer than the lassy CTEs. Table 3. Properties of the composite measured from the thermal strain response. Precure T Lay-up α T < T ) T (heatin) α T > T ) (coolin) ( ( T ε cure C µm/(m C) C µm/(m C) C % 0 UD 7.99 3.74 84.80 05.95 0.64 XP 34.37 38.58 58. 00.85 0.97 40 UD 8.83 6. 9.44 98.84 0.4 XP 38.47 58.50 66.4 96.84 0.78 60 UD 9.37 86.54 8.6 98.7 0. XP 9.88 75.38 63.0 97.09 0.40 80 UD.50 0.3 0.4 95.64 0.04 XP 35.00 97.9 55.7 00.85 0. fully cured UD 6.73 93.36 97.47 - - XP 4.89 90.0 47.0 - -
IV. CONCLUSION The cure kinetics of the epoxy resin was successfully modeled by a rate equation describin a reaction that proceeds alon two parallel branches with two erent rates, resultin in the same product, and the rates depend on the temperature as well as the deree of cure. The proposed model enables to capture all features of the reaction exotherm and the freezin of reaction as the lass transition of the resin approaches the process temperature and the reaction shifts from autocatalytic to usion controlled. A method has been proposed that allows the measurement of throuh-the-thickness cure shrinkae strains durin curin of the composite by usin a compression clamp in conventional DMA equipment. The thermal response of the partially cured composite samples shows that the resin underoes a transition from lassy to a rubbery state, which shifts to hiher temperatures dependin on the deree of cure. The coefficients of thermal expansion in the thouh-the-thickness direction is found to be relatively independent of the deree of cure, however, they increase considerably after lassy-to rubbery transition. Further curin takes place at the rubbery state causin cure shrinkae strains that are inversely proportional to the previous deree of the cure of the resin. The throuh-the-thickness cure shrinkae strains in crossply laminates are measured to be about twice of the strains in unidirectional laminates, because the fibers provide a constraint for shrinkae in both in-plane directions in crossply laminates whereas only in one direction in unidirectional laminates. ACKNOWLEDGEMENTS The authors acknowlede the support of Boazici University Research Fund under project code 09A60P. References. D.W. Radford, T.S. Rennick, J. Reinf. Plast. Compos., 9, 6 4 (000).. D. A. Darrow, Jr. and L. W Smith, J. Compos. Mater., 36, 407-49 (00). 3. C. Albert, G. Fernlund, Compos. Sci. Technol., 6, 895 9 (00). 4. N. Ersoy, K. Potter, M.R. Wisnom and M.J. Cle, Composites Part A, 36, 700-706 (005). 5. M.R. Wisnom, N. Ersoy, K.D. Potter, J. Compos. Mater., 4, 3-34 (007). 6. M. Buczek, D. Mason, C. W. Lee, A. Saunders, Proactive control of curin composites, Proceedins of the 44th International SAMPE Symposium, Lon Beach, CA, May 999. 7. J. Player, M. Roylance, W. Zukas, D.K. Roylance, UTL consolidation and out-ofautoclave curin of thick composite structures, 3nd International SAMPE Technical Conference, Boston, MA, USA; 5-9 Nov. 000, 757-767. 8. P. Hubert, A. Johnston, A. Poursartip, K. Nelson, Cure kinetics and viscosity
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