MODIFICATION OF TIME-TEMPERATURE-TRANSFORMATION DIAGRAM TO OBTAIN A

COMPREHENSIVE CURE MAP FOR POLYMER COMPOSITES

S.M. Sabzevari, S. Alavi-Soltani, H. Koushyar, B. Minaie* Department of Mechanical Engineering

Wichita State University Wichita, KS 67260

* Corresponding author: bob.minaie@wichita.edu, (316) 978-5613

ABSTRACT

This paper presents modification of the isothermal Time-Temperature-Transformation (TTT) cure diagram to obtain a comprehensive cure map for a commercial carbon fiber prepreg (977-2 UD). The viscoelastic and thermal properties of the prepreg for a wide range of isothermal cure temperatures were obtained using an Encapsulated Sample Rheometer (ESR) and a Differential Scanning Calorimeter (DSC). ESR was used to obtain the state of the material during cure and to identify important transitions during cure such as gelation and vitrification. ESR was also used to find the post cure transitions such as glass transition temperature (Tg). Since the conversion at gelation only depends on the chemistry of the polymer system, different definitions for the gel point were studied and the most appropriate definition based on the behavior of the prepreg during cure was selected. The minimum viscosity and Tg lines were added to TTT diagram to have a complete picture of the material state during and after isothermal cure at a wide range of cure temperatures. Minimum viscosity data can be used to design the cure pressure profile.

1. INTRODUCTION

Thermoset resins are usually used in filled or reinforced form to produce composite materials with enhanced physical and mechanical properties. Fiber-reinforced epoxy prepregs are one of the most common forms of these composite materials which have a wide variety of applications especially in aerospace industries. The prepregs are usually oven/autoclave cured using an isothermal curing process. The curing process of thermoset resins generally involves the transformation of low molecular weight liquids to high molecular weight amorphous solids by means of chemical reactions resulting in a three-dimensional structure. Viscoelastic properties of the prepreg can be used to monitor the state of the material during the cure. Here we investigate the curing process of a commercial carbon-fiber epoxy prepreg using an Encapsulated Sample Rheometer and a Differential Scanning Calorimeter (DSC).

The transformation from a viscous liquid to an amorphous solid usually encompasses two major transitions. These include the transition from liquid to rubbery state and subsequently the transition from rubbery to glassy solid state. The former transition which happens thanks to formation of the infinite cross-linked network is a sudden and irreversible phenomenon called the gelation [1]. Gel point is a characteristic of the thermoset resins and represents a physical change in their mechanical properties and does not include any change in the chemical reactions of the process [2]. As the reactions proceed, growth of the molecular chains continues towards

the construction of a complete infinite network which leads to another transition known as vitrification. At the vitrification point, the glass transition temperature of the growing chains becomes equal to the cure temperature. Vitrification marks the time at which the reaction mechanism changes from kinetic controlled to diffusion controlled [3]. As such, after the vitrification, the reaction rate dramatically drops and the glass transition temperature of the material approaches a constant value known as the final glass transition temperature (Tg∞) [4]. A good understanding of gelation and vitrification is necessary to characterize the epoxy resin systems and to design an optimal cure profile for them. This knowledge can be simplified in a comprehensive diagram called the isothermal Time-Temperature-Transformation (TTT) cure diagram [3-5].

The isothermal TTT cure diagram is a useful framework for understanding and analyzing the behavior of thermoset resin systems during an isothermal cure process. The diagram was first proposed by Gillham and Enns [6] to study the cure process of epoxy resin systems. Construction of such a diagram can be performed by plotting the experimental time to reach certain events using various isothermal cure temperatures. TTT diagram demonstrates material state changes of a thermoset resin system during the isothermal curing, including gelation and vitrification. Also other information like carbonization or thermal degradation curve, isoconversion lines, iso-viscous lines and iso-Tg lines can be added to this diagram [7]. The objective of this work was to construct the isothermal TTT cure diagram depicting the gelation and vitrification points and the iso-Tg lines for a commercial carbon-fiber epoxy prepreg (CYCOM 977-2 UD) for a wide range of isothermal cure temperatures.

2. EXPERIMENTATION

2.1 Material The studied epoxy prepreg was CYCOM 977-2 UD which is a 177oC curing toughened epoxy resin reinforced by unidirectional (UD) carbon fiber. For rheometer tests, samples were prepared in room temperature with a stack sequence of [0,90,90,0]S consisting of 28 plies. Circular samples with the diameter of 41.3 mm, average thickness of 3 mm and average weight of 6.7 gr were tested under different isothermal cure temperatures. For DSC tests, same material was used while the weight of each sample was around 10 mg.

2.2 Rheology experiments Experimental data reported in this work such as storage modulus (G′) and loss modulus (G″) were obtained using a shear rheometer (Alpha Technologies, ATD 2000 encapsulation rheometer) with parallel plates. Experiments were performed under strain-controlled condition with strain amplitude of 0.05 degrees and frequency of 1Hz. Isothermal cure profiles ranged from 116 °C to 188 °C with 5.6 °C increments followed by the glass transition temperature test [8] to obtain the final Tg . Each test was subject to high pressure condition (2000-4000 KPa) and long enough time to ensure that the final conversion has been achieved (more than 500 min depending on the cure temperature).

2.3 Thermal experiments DSC measurements were performed using a TA Instrument Q2000 DSC which was precisely calibrated with a high purity indium standard. Dry Nitrogen was used as the purge gas. Samples with a weight of about 10 mg were enclosed in aluminum pans and cured directly in the unit cell. DSC experiments were carried out using the same temperature profiles used for rheometry tests in order to find the correlation between sample Tg and conversion obtained using both instruments. All the experiments were followed by a glass transition test [9]. Fractional conversion at any time can be calculated by dividing the energy released up to that time by the total energy released by a fully cured sample.

To determine the initial glass transition temperature of the uncured sample (Tgo) and the final glass transition temperature of the fully cured sample (Tg∞), a total of four consecutive dynamic scans at a heating rate of 10oC/min were performed using the DSC. The first dynamic scan started at -20oC and ended at the room temperature and the following dynamic scans started at the room temperature and ended at 290oC. Tgo and Tg∞ were obtained with the first and the last dynamic scans, respectively. The second and third dynamic scans were performed to fully cure the sample. The glass transition temperatures for the partially cured samples were obtained using DSC dynamic scans from the room temperature to 290oC at a heating rate of 10oC/min. Before the Tg test, samples were partially cured at five different isothermal temperatures (116°C, 132°C, 149°C, 160°C and 177°C) with dwell times ranging from 15min to 550min.

3. RESULTS

3.1 Gelation Gelation is a characteristic of the thermoset resins; an irreversible phenomenon during the cure of these materials which characterizes the incipient formation of an infinite network. As the chemical reactions proceed, the molecular weight of the polymer increases and eventually several chains become linked together into networks of infinite molecular weight. Beyond the gel point, resin is no longer processable and starts to transform from a viscous liquid to a rubbery gel [1].

Gelation takes place at a well-defined stage during the cure process and is only dependent on the stoichiometry, functionality and reactivity of the reactants. This phenomenon usually appears between 55% and 80% conversion [1]. According to Flory’s expression (1953), gelation occurs at a certain critical conversion (αg) for a given epoxy system regardless of the cure temperature [10-13]. Gelation is a physical transition in the status of the material and does not slow down the curing process. Therefore, it cannot be determined using techniques related to DSC and TG which are only sensitive to chemical reactions [1].

In the current work, we investigated several methods that are usually used to obtain the gel point. These methods are dependent on the experimental data provided by the rheometer. Based on viscoelastic properties, gelation can be defined as [11-12,14]:

• The point at which viscosity tends to infinity. • The point at which the storage modulus (G′) passes the loss modulus (G″); tanδ = 1. • The maximum of the tanδ curve.

• The point at which tanδ drops rapidly.

Figure 1 illustrates gelation time vs. isothermal cure temperature obtained using the aforementioned definitions. As this figure shows, for isothermal cure temperatures near the final glass transition temperature of the prepreg (Tg∞=186oC), various definitions result in same values of the gel time. Since, at lower cure temperatures respect to Tg∞, rate of reaction is low and chemical reactions proceed gradually, viscoelastic properties of the material extent in a wide span of the time and show their variations clearly. This will cause the gel time obtained based on various definitions to diverge. In the case of elevated cure temperatures near Tg∞ with higher rate of reactions, however, these properties evolve rapidly, leaving a small room for any difference to be reflected in gel time values.

Figure 1. Gelation time determined based on different definitions vs. isothermal cure temperature.

Figure 2 shows the fractional conversion corresponding to the gelation time vs. isothermal cure temperatures. Despite of the fact that gelation occurs at a certain critical conversion according to the Flory’s theory, for the current epoxy resin system none of the gelation definitions lead to a constant value for αg. As Figure 2 shows, αg increases with increasing the isothermal cure temperature. Same behavior has been observed by Núňez [7] for other epoxy systems.

Here despite of the Núňez point of view, we believe that the common reaction rate equation cannot be used for the calculation of the apparent activation energy. The following equation is usually used to describe the behavior of the epoxy resin system during the cure process [2-3].

( ) ( )αα fAedtd RTaE−= [1]

where A is a constant, T is the isothermal curing temperature, is the apparent activation energy for the overall curing reaction, R is the universal gas constant and f(α) is the conversion function independent of the cure temperature.

Integration of the Eq. 1 from α = 0 to α = αg , and taking natural logarithms, gives:

( ) RTEtA

fd a

g

g

−+=∫=

lnlnln0

α

α αα [2]

This equation can only be used when conversion at gelation is constant (αg = const.). Apparent activation energy for 977-2 UD cannot be calculated using this equation since αg is not the same for different isothermal cure temperatures.

Figure 2. Fractional conversion corresponding to gelation vs. cure temperature using Figure 1

data.

3.2 Viscosity Controlling viscosity of the resin during curing process in an autoclave allows optimization of resin infiltration in fibers and hence improvement of densification in shorter times [15]. Complex viscosity of the current resin system was calculated by measuring the viscoelastic properties. The complex viscosity is considered to be almost the same as shear viscosity defined by Cox-Merz rule [16-17]. Here we used the following equation to calculate the complex viscosity [18-19]:

ηηη ′′′−′= j* [3]

ωη /G ′′=′ and ωη /G′=′′ [4]

where η* the complex viscosity, η′ and η″ are the real and the imaginary (dynamic) parts of the viscosity, respectively and is the angular frequency of the system. According to the Cox-Merz rule:

( ) ( ) ( ) ( ){ } 2/122* /ωηωηγη G′+′⋅==& [5]

Shear viscosity ( )γη & and complex viscosity can be assumed equal ignoring the distinction between the linear behavior in small amplitude oscillatory and the non-linear behavior in steady shear tests [17]. γ& is the shear rate in the above equation.

Figure 3 illustrates complex viscosity vs. cure time in logarithmic scale for different isothermal cure temperatures. As this figure shows, the minimum viscosity time is the same for all cure cycles. This is because the viscosity of the prepreg reaches its minimum value during the fast ramp up (28 °C/min) stage right before the start of the isothermal curing. The point at which viscosity rises and tends to infinity has been considered as the gel point in many studies [20-21]. Figure 4 shows the onset of infinite viscosity vs. cure temperature using Figure 3 data. As it can be seen, gelation occurs at a constant viscosity (around 180 KPa.s) independent of the cure temperature.

Figure 3. Complex viscosity vs. time in logarithmic scale at different isothermal cure temperatures.

Figure 4. Onset of the infinite viscosity vs. cure temperature using Figure 1 data.

3.3 Vitrification After the transformation from the viscous liquid to an elastic gel, curing process of the epoxy system undergoes another transition called Vitrification. Vitrification is the onset of transformation from the elastic gel to the glassy solid. At this point, glass transition temperature of the material reaches the isothermal cure temperature (Tg = Tcure) and reaction becomes diffusion controlled. Curing process of a thermoset resin initially starts by chemical reactions which are primarily kinetically controlled. After the vitrification, low concentration of the reaction agents causes reaction to become diffusion controlled [3-4]. Vitrification can be usually calculated using either thermal or viscoelastic properties. In this study, we used three different definitions based on viscoelastic properties which are commonly used to find this transition. These include [22]:

• The inflection point of the transition in the storage modulus. • The maximum value of the loss modulus. • The onset of the plateau value of the storage modulus.

The vitrification time for different isothermal cure temperatures obtained using the above mentioned definitions is shown in Figure 5. As it is observable, values obtained based on the first two definitions overlap and are about 50 min less than the corresponding values obtained using the third definition. At the vitrification, reaction reaches the final stage and its mechanism changes from the kinetic controlled to the diffusion controlled resulting in a perceptible decrease in the rate of reaction. As such, in contrast to the gelation, in which the reaction rate corresponding to the gel point changes with the cure temperature, at the vitrification the process reaches a steady state and the reaction rate does not change with the cure temperature. As a result, the corresponding values of vitrification time obtained based on different definitions have a constant difference for various isothermal cure temperatures.

Figure 5. Vitrification time determined based on different definitions vs. isothermal cure temperature.

Figure 6 shows the fractional conversion at vitrification vs. cure temperature using the data in Figure 5. According to this figure, fractional conversion at vitrification increases with increasing

the isothermal cure temperature. As such, similar to the aforementioned observation for gelation, the apparent activation energy for vitrification cannot be calculated using the reaction rate equation.

Figure 6. Fractional conversion corresponding to vitrification vs. cure temperature using Figure 5 data.

3.4 Tg vs. conversion The relationship between the glass transition temperature and the conversion of thermoset resins has been a topic of interest in many studies. Many authors found a unique one-to-one relationship between the values of Tg and α and the empirical DiBenedetto equation reported by Nielsen has been broadly used to fit the experimental Tg vs. α data [3, 7, 13-14, 23]. The experimental final Tg and α data vs. isothermal cure temperature are shown in Figure 7. As it has been previously reported by the other studies, the relationship between the Tg and α should be independent of the cure temperature. This concept is clearly observable in Figures 7 and 8. According to Adabbo and Williams approach using the DiBenedetto equation, Tg and conversion relation can be expressed as [3, 5, 23]:

( )( )α

α2

21

11 CCC

TTT

go

gog

−−−=

− [6]

where Tg is the glass transition temperature, Tgo is the initial glass transition temperature of the uncured material (equal to –2.5 °C for 977-2 UD), C1 and C2 are constants and α is conversion. This equation implies a unique relationship between Tg and conversion. For the epoxy prepreg in this study, C1 and C2 were calculated to be 1.92 and 1.08, respectively. This equation can be used to calculate values of Tg vs. conversion or vice versa at any stage of the curing process.

Figure 7. Final glass transition temperature and final conversion vs. cure temperature.

Figure 8. Final glass transition temperature vs. final conversion corresponding to different

isothermal cure temperatures.

3.5 Isothermal Time-Temperature-Transformation Cure Diagram Isothermal TTT cure diagram encompassing gelation, vitrification, minimum viscosity time, Tgo, Tg∞, gelTg and iso-Tg lines was constructed for 977-2 UD (Figure 9). Iso-Tg lines are useful for tracking the state of the material at any time during the isothermal curing process. As it was discussed earlier, Tg has a unique one-to-one relationship with the conversion and hence it also can be used to describe the fractional conversion at different times.

Minimum viscosity time at different isothermal cure temperatures was added to the isothermal TTT cure diagram to determine the moment at which cure pressure can be applied to the system. According to Loos and Springer [20], the time at which the prepreg layer adjacent to the bleeder reaches its minimum viscosity is the latest moment to apply the cure pressure. Therefore, the isothermal TTT cure diagram can be used to design not only the cure temperature, but also the cure pressure as well.

Figure 9. Isothermal Time-Temperature-Transformation cure diagram.

4. CONCLUSIONS

In the current study, we investigated different definitions for gelation and vitrification based on viscoelastic properties. Fractional conversions corresponding to gelation and vitrification were obtained using DSC data. It was concluded that for 977-2 UD, the conversion corresponding to gelation does not follow the Flory’s equation and is dependent on the isothermal cure temperature. As such, the apparent activation energy for gelation and vitrification cannot be calculated using the reaction rate equation. Complex viscosity of the prepreg vs. cure time was obtained for various isothermal cure temperatures using the Cox and Merz method. It was demonstrated that the onset of infinite complex viscosity which marks formation of the infinite cross-linked network is independent of the isothermal cure temperature. The correlation between final Tg and conversion was obtained using the DiBenedetto equation and the parameters of the equation were calculated. It was shown that for the 977-2 UD, similar to many other thermoset resins, there is a unique one-to-one relationship between Tg and conversion. Iso-Tg lines were added to the isothermal TTT diagram for 977-2 UD. The TTT diagram was further improved by adding minimum viscosity line. This line can be used to design the cure pressure profile.

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