Cure characterisation and prediction of thermosetting epoxy for wind turbine blade manufacturing

In the wind industry, the increasing length of turbine blades and the use of thick composite sections make it vital to understand the thermoset and the underlying curing process. In this study, the curing of a specific thermoset epoxy for application in wind turbine blades is characterised by differential scanning calorimetry. The thermoset is analysed under dynamic and isothermal conditions to determine the complex cure behaviour under these various conditions. The data is fitted to determine firstly; the cure kinetics of the material through a kinetic model. Secondly; the phenomenon of the glass transition temperature Tg is studied to predict the development of Tg as a function of the degree of cure. Thirdly, a Diffusion-Kinetic model was utilised to make more accurate cure predictions based on the interaction between kinetic chemical reactions and diffusion control affecting the reaction rate through the incorporation of the glass transition temperature. A simple experimental framework for validating the diffusion-kinetic model was used to make a final validation of the model predictions on a larger scale. A set of final parameters is presented for application in a full diffusion-kinetic model for cure predictions and simulations beyond this study.


Introduction
For many years, the study of thermoset curing has been an important aspect of understanding and ensuring good composite performance.Residual stresses play an important role with respect to curing.Previous studies have shown a correlation between the level of residual stresses resulting from different curing profiles and the tensile fatigue lifetime of laminates for turbine blades [1].However, the linking of curing and residual stresses can benefit industries such as; automotive, aerospace, sport and maritime industries.
A principle for determining the characteristics of thermosets has been well established through the application of heat-flow-based Differential Scanning Calorimetry (DSC) [2].In this configuration, DSC is capable of both measuring the heat flow coming from the thermoset and the heat transferred to the thermoset to maintain the desired temperature in the sample and chamber.It is possible to determine the extent of cure from the thermoset based on the measured heat flow from the DSC device.
Furthermore, the concept of heat capacity can be easily studied with DSC.For many years, the DSC has been used to measure the glass transition temperature, which is easily observed by a change in the heat capacity of the polymer studied.The reason for the clearly observed transition is that the glass transition is a transition dependent on thermodynamical equilibrium [3].Below 2 the glass transition temperature, the thermoset is not in thermal equilibrium, resulting in the compaction of the molecular chains.As the glass transition is reached the material becomes more saturated and thus increasing the distance between the molecular chains.This can be seen as a clear step change in the heat going into the thermoset when scanned with DSC.This has resulted in very clear definitions of the glass transition temperature range and how it should be found [4].
Over the years, a number of phenomenological models for defining the curing of thermosets have been developed.Early work by M. R. Kamal and S. Sourour presented that the reaction of thermosets, and especially epoxy, follows an autocatalytic reaction [5].The authors presented a model with a term for the accelerating nature in the early stage of curing and deaccelerating for higher degrees of cure i.e., the model was autocatalytic.The model was based on a simple power law and combined with the Arrhenius reaction equation.The authors found a good fit with the experimental data for both the epoxy and polyester systems.Later, another study showed that predicting polyester behaviour could be overcome with another modified model with an additional term, making the model more accurate at higher conversions [6].
As the glass transition temperature is a thermodynamical principle, A. T. DiBenedetto [7] proposed a nonlinear relation between the glass transition temperature and the degree of cure.In which, the nonlinearity was determined by the ratio of heat capacity in the uncured and fully cured states.Further developments were made to replace this rather less definable ratio with a fitting factor [8]. Ultimately, the modifications of the relation proposed by A.T. DiBenedetto give a relationship between the glass transition temperature and the degree of cure easily applicable.The glass transition temperature is a phase transition between the glassy and rubbery states.Therefore, it is important to note that the material is thermodynamically unsaturated in the glassy state, i.e. it has less molecular mobility; thus, the material appears more rigid.The mobility increases as the material becomes increasingly saturated when reaching the glass transition temperature [3].The sink in mobility when the material enters a glassy state is also known as vitrification.Therefore, to accurately predict the curing of a thermoset where mobility is at least in part prohibited by the glass transition temperature, modifications of kinetic models are necessary.The mobility-reduced behaviour is commonly referred to as diffusion-control [9].
A simple approach to creating a diffusion-modified model is implicitly including the glass transition temperature through a critical degree of cure [10].This was later modified with a linear interpretation of the critical degree of cure to compensate for the changes in the glass transition temperature with increasing process temperature [11].Different approaches have been applied to define the diffusion control.One approach was to take the actual measured reaction rate and divide it with the model predictions, only accounting for the kinetic part of the reaction [11].The response should show that the model and the data agree as long as diffusion control is not dominant, i.e. when the measured reaction rate and the kinetic model prediction coincide.Then, as the measured reaction rate becomes lower than the model prediction, increasingly prohibited molecular mobility appears.Another approach is to use the critical degree of cure function and correlate that with the equation that describes the glass transition temperature as a function of the degree of cure [1].In this case, the relation proposed by A.T. DiBenedetto [7] was used and the degree of cure was found by setting typical cure temperatures equal to the glass transition temperature and isolating the critical degree of cure.The critical degree of cure evolution was fitted from the critical degree of cure at the different cure temperatures with a good fit.To monitor the behaviour of epoxy systems different approaches exist [12,13].These studies have compared embedded sensor technology with predictions from cure kinetic models.However, these typically neglect the presence of diffusion control in the applied cure models.
This study investigates the curing of thermoset epoxy with DSC utilising a simple and robust experimental procedure.The investigation involves the fitting of DSC data and the selection of a diffusion-kinetic model in order to better predict the curing of a larger-scale resin experiment with an embedded sensor.

Cure kinetics
To study the behaviour of an epoxy thermoset resin this section will present the relevant theory applied in the study.First, the amount of reacted polymer is defined by the degree of cure, X, determined by the ratio between the reacted enthalpy, and total enthalpy of reaction, Here, H(t) is the accumulated heat released from the curing reaction up to a certain time t.
If the accumulated amount is unknown, one can determine the remaining amount (residual) instead.The total enthalpy of the reaction, H T , is the total enthalpy released by the exothermal nature of the reaction.Thus, the degree of cure X, will be in the range X ∈ [0; 1], with X = 0 for uncured and X = 1 for fully cured, respectively.To capture the kinetic reaction mechanisms, the following relation [5,6,11], is used, This model involves the temperature-dependent Arrhenius reaction relation k(T ).The relation consists of A as the preexponential factor, e a as the activation energy, and R as the universal gas constant.For the power law function, f (X), n and m are power law coefficients.
The activation energy can be found using the Kissinger's method [12,14] in where β is the heating rate and T p is the temperature at the peak of the heat flow.

Glass transition temperature
The glass transition temperature, T g , is defined in the range from an onset, over a midpoint, to the end of the transition [4].This study defines the glass transition as the midpoint value.The DiBenedetto relation [7] shown in ( 4) is used for relating the degree of cure to the glass transition temperature.
Here T g0 is the glass transition temperature for the uncured state, T g∞ is the glass transition temperature for a fully cured state.Furthermore, ξ is a fitting parameter given by the ratio of specific heat capacity ∆C p∞ /∆C p0 .The heat capacities ∆C p∞ and ∆C p0 are the difference in heat capacity for a fully cured and uncured sample at the crossing of the glass transition temperature.

Diffusion-controlled effects on cure kinetics
A model accounting for the interaction between T g and the cure evolution [11] is applied to incorporate the prohibited molecular mobility effect by diffusion control into the cure predictions The model is based on (2) modified by dividing with a term that is an exponential function including a diffusion constant C. It is related to X and the critical degree of cure X c .The critical degree of cure is the level of cure where diffusion will dominate.In this study, a linear function, of X c dependent on temperature T is applied [11], where, X cT is the critical degree of cure increase and X c0 is the initial critical degree of cure

Materials
In the presented study, an industrially available thermoset epoxy resin is investigated.The resin is a conventional diglycidyl ether of bisphenol-A (DGEBA) resin.The hardener is a modified cyclo-aliphatic-and aliphatic-amine.A mixing ratio by weight was base:hardener; 100:31, was used according to supplier guidance.

Sample preparation and storage
A small batch of approximately 200 g was mixed to prepare the samples.The mixing was carried out in a small bucket over 5 minutes to ensure sufficient mixing.The mixture was degassed and pipetted into smaller 5 ml vials that were immediately quenched in a Kryogen bottle filled with liquid nitrogen.Liquid nitrogen storage serves two purposes: preventing premature curing and acting as a purge gas to protect the vials from moisture contamination during storage.DSC testing was carried out over a total time period of 4 weeks.In this period, the total enthalpy of reaction was monitored at regular intervals to verify that the material had not been reacting while storing.The sample preparation procedure was performed systematically: A vial was taken from the Kryogen container and allowed to thaw for 20 minutes before 18-20 mg of epoxy was taken from the vial and transferred to a Netzsch Concavus® pan.

DSC measurements
The DSC measurements were performed using the Netzsch TM Polyma 214.For the experiments, a protective purge gas of nitrogen was used in the main chamber of the DSC.The flow rate was set to 40 ml/min to ensure sufficient sample protection and reasonable heat conductivity.
For the purpose of investigating the curing of thermosets accurately, it is necessary to determine the curing behaviour based on both dynamic and isothermal conditions.Differential Scanning Calorimetry can with dynamic scans accurately determine; enthalpy of fusion, the peak temperature of the reaction with constant heating rates.This makes a dynamic scan ideal for fitting of Kissinger's method in (3) to determine the activation energy, e a [12].Furthermore, the dynamic scan can also determine the glass transition temperature, T g .But better results are achieved by applying temperature-modulated DSC (TM-DSC) as the glass transition temperature becomes much clearer with this approach [2].
The isothermal scan with DSC is applied to determine the reaction rate and degree of cure at various cure temperatures.This approach is applied to make sure that the cure models are fitted over a varied range of common isothermal cure temperatures.The isothermal scan can be relatively long in order to capture the transformation from a high rate of cure to a slower rate that occurs for higher levels of cure.Thus, it makes it important to use both dynamic and isothermal conditions to determine the evolution of the cure.
However, it is also a great benefit to vary the time period of the isothermal scan and in combination with a TM-DSC scan, it creates a great method for determining the evolution of T g with X.This method will be utilised in Section4 for the fitting of the DiBenedetto relation in (4).
Two techniques exist for putting samples into the DSC: The first involves the sample being mounted at room temperature and then scanned.For dynamic and TM-DSC scans, this approach has been applied.The second is to preheat the chamber before mounting the sample for scanning [15].For isothermal scans, the second approach was applied.

DSC cure characterisation
To get the total extent of the reaction, samples were cured with dynamic DSC scans with heating rates of 2, 5, 10, 15 and 20 K/min.The lower temperature limit was chosen as -40°C for the temperature ramp.This was chosen to ensure that the temperature ramp starts far away from any onset of reaction.The upper limit was 275°C as this was found to be below any material degradation.
Figure 1 shows the 5 scans plotted with heat flow in W/g as a function of temperature in K.In all five cases, a second ramp was performed to check for any residual cure.For the 5K/min case, the signal for this second heating ramp has been included as a dashed line in Figure 1.The second heating ramp shows that no additional cure has occurred as the signal is more or less flat.The slight bump observed on the included second ramp is the glass transition temperature.Table 1 shows all the corresponding peak temperatures T p , as well as the individual heating rates denoted β.The five scans are integrated over time from a point where the response is fairly flat, i.e. before the reaction starts and until the ramp-up ends at 275°C.This integration is interpreted   1 gives the H T values at the different heating ramps and the average value is H T = (470 ± 3)J/g.Thus, a consistent value, independent of the heating rate.It is worth noting, that these values of H T have been obtained throughout the whole test period of 4 weeks and therefore, the utilised storage facility was ideal.Similarly, the average value T g∞ = (89.0± 0.4)°C obtained, was found to be with good accuracy and well representing.Kissinger's method from equation ( 3) is used to estimate the activation energy.To do so, ln(β/T 2 p ) is plotted as a function of 1/T p . Figure 2 shows the scatter of measurement points with linear regression.The slope of the linear curve then represents the term e a /R.The fitted activation energy becomes e a = (56.23 ± 0.36)kJ/mol.curves coming from each individual scan at different T c .The approach is to use a horizontal integration baseline, starting at the end of the isothermal cure where the heat flow has stabilised.The integration is then done for the settled cure response and back to the start of the measurement.Thus, through (1) the degree of cure X and the derivative dX/dt, can be found for each scanning.From (2) a least-squares fit is performed with initial guessed parameters for A, n and m, whereas the e a found by Kissinger's method from the slope of Figure 2 was used as the initial guess for the activation energy.
Figure 3 shows the experimental values, from the DSC at different T c as points with different colours for each T c and the data fitting as dashed lines.Overall, the fitting is reasonable by a qualitative comparison of the experimental data and the model.
Table 2 compiles the parameters found by least-squares fit for the K-model from (2).The activation energy found for the isothermal fitting agrees well with the value found by Kissinger's method.This shows that predictions can be expected to perform well under both dynamic as well as isothermal conditions.
As the K-model in ( 2) is an ordinary differential equation (ODE) it can be integrated numerically, knowing the fitted parameters from Table 2.The model is integrated with respect to time and temperature from the experimental data.The K-model can then be plotted as X(t) with the experimental data for comparison of prediction.
Figure 4 shows the predictions made with (2) based on the fitting of the DSC measurements.For the different T c measured, the model seems to predict well up to around 80% of curing.For lower T c , the model somewhat overpredicts the experimental observations except for the case of 90°C and 100°C, where the same deviation is not observed.This indicates that for T c < 90°C a slowdown in the chemical reaction may be due to elements not considered.This is likely to be due to the reaction mechanism changing to a diffusion-controlled regime.As this becomes important when the glass transition temperature is greater than the cure temperature, it is important to determine the evolution of T g with cure.
4.1.2.Glass transition temperature fitting Section 3.3 described that for the determination of T g the isothermal scan followed by a TM-DSC scan was used.Appropriate T c were chosen as [60, 80 and 100]°C in time periods from 2 min to 2 h.Furthermore, T g was found, based on the data used to fit the K-model, and was also included in the fitting of T g .
The DiBennedetto relation ( 4) was used to fit the measured data, with the lowest T g measured at approximately −29°C as it was not of interest to measure lower values than this.The model was fitted with T g0 and ξ as fitting parameters and T g∞ was the known parameter in Table 1.  Figure 5 shows the measured glass transition temperatures as dots.Every measurement point is mapped with a colourmap marking at which curing temperature T c the T g has been measured.
The fitting of the DiBenedetto relation has a R 2 value of 0.997 related to the fitted data, which generally confirms a good fit.
Table 3 summarises the fitted values of the model where the fitted parameters can be for T g0 = −42.0°Cand ξ = 0.487.As the development of T g with X has been fitted, it can be used to relate the potential diffusion-controlled behaviour into the cure kinetics.Table 3. Parameters used in the DiBenedetto equation to predict the development of the glass transition temperature and the fitting coefficient.

Determination of diffusion characteristics for curing
Determining the change from a cure kinetic model reaction without diffusion behaviour to a diffusion-controlled cure kinetic model is described by ( 5) [11].This model will be used to modify the predictions from the Kmodel.The model involves the term X c , the critical degree of cure.The method of determining this crossover, from one molecular mobility mechanism to another, is to set T g = T c and, through find the corresponding degree of cure [1].The value of X found is then interpreted as the critical degree of cure X c at the given T c .
Figure 6 illustrates the determined values of X c as a function of T c from 293 K to 353 K i.e., 20°C to 80°C.The line is the fitted linear regression of (6) and the overall fit is good.Table 4 lists the fitting parameters.The slope corresponds to X cT and takes into account an increase or decrease in X c with the cure temperature.The initial critical value X c0 = −0.885 is invalid for temperatures below −105°C as X is non-physical below zero.The remaining unknown in (5) is the diffusion coefficient C. By fixing the parameters found for the K-model in Table 2 and the critical degree of cure function in Table 4 the diffusion coefficient C, is found.The diffusion coefficient is found to be C = 43.7.
Figure 7 shows the Diffusion-Kinetic model (DK-model) based on (5).The predictions by the DK-model seem to better adapt the DSC measurements for levels of conversion above X = 0.8.For T c at 40°C to 60°C the prediction at high conversion follows the DSC data well.For T c at 70°C and 80°C, the model slightly overpredicts compared to the data.However, the predictions are still improved compared to the K-model predictions in Figure 3.For 90°C and 100°C, the predictions seem to be unaffected by the diffusion term, since molecular mobility is not significantly prohibited at these cure temperatures.It is relevant to compare the kinetic model (K-model) in (2), and the diffusion-modified (DK-model) from (5).To justify a good comparison, one should look at isothermal curing for longer time periods.
Figure 8 shows the development of curing at the same T c as in Figure 7, over a logarithmic time period of up to 200 h. Figure 8 visualises that for curing at lower temperatures, the Kmodel seems to over-predict X compared with the measurements from the DSC.However, the DK-model predicts significantly slower speeds as the reactions slows down due to the prohibited molecular-mobility by the glass transition temperature.Thus, it is infeasible to expect the Table 4. Fitting parameters found for the evolution of the critical degree of cure with the glass transition temperature.The previous section dealt with the analysis and fitting of measurements performed with Differential Scanning Calorimetry.This section will deal with the in situ monitoring of a neat resin plate manufactured with the industrially available resin system.The kinetic model (Kmodel) and diffusion-kinetic model (DK-model) will be applied and validated on this in situ monitored neat resin plate to investigate their applicability on larger components.

Experimental procedure
The neat resin plate is cured in an industrial-scale universal oven.The neat resin plate is consist of a zip-bag of 150 x 200 mm.The plate is placed in the middle of the oven and a thermocouple is placed so it will measure the temperature of the thermoset in situ.At the top and bottom of the oven, thermocouples are placed approx.100 mm from the oven surfaces to monitor the temperature variation across the oven.Just before starting the experiment, the thermoset is mixed, following the procedure in Section 3.1.The thermoset is degassed and infused into the bag with a syringe.The thickness of the neat resin plate is approximately 4 mm at the end of cure.
In addition to the neat plate, a concavus® aluminium DSC pan is also placed in the oven, filled with 20.0 mg of the remaining thermoset.This DSC sample was cured simultaneously and thus has experienced the same cure profile.This DSC sample served as a validation sample, since T g and the possible residual enthalpy H R could be determined immediately after the cure ended.Table 5 tabulates the parameters used for the cure profile applied.
To assist the cure profile listed in Table 5 a letter annotation is adopted for illustration purposes for explaining the cure profile steps.Figure 9 shows the temperature, as a function of time, registered by the thermocouple inside the resin, for which, the predictions of X will be based.Thinner dotted lines have been used to illustrate the temperature of the air in the oven around the neat resin plate.Figure 9 illustrates both models; the kinetic (K-model) from (2) as a green dashed line, and the diffusion-modified kinetic model (DK-model) as a green dash-dotted line based on (5).Similarly, two orange curves illustrate the T g predictions based on the two models.At the end of the predictions, two larger dots mark the measured DSC values from the DSC sample cured simultaneously with the neat resin plate.Both models in Figure 9, agree at the early stages of X and start to deviate after approximately 8 hours.The DK-model slows down compared to the K-model, which is also reflected in the glass transition temperature development.This behaviour is expected as it was confirmed in Figure 8 that for longer isothermal cure time the K-model is less conservative with respect to X compared to the DK-model.As the temperature is elevated during B , both models predict an increase in reaction rate.Furthermore, the speed is higher for the DK-model, as it almost catches up with the kinetic model as the temperature enters C .This is expected  as the T c crosses T g and the DK-model becomes more dominated by kinetic reactions.The glass transition temperature is naturally affected by the development of X and the fact that T g (X) is a non-linear relation.The difference in the predicted X by the two models has a great effect on T g .Figure 9 illustrates this as T g predicted during A shows a significant difference between the two models.During the heat-up at B , the difference becomes small as observed and as the temperature enters the next isotherm C the two predictions start to deviate again.Although, the difference in X is not significant, it affects the glass transition temperature achieved at the end of the cure.The DSC sample, cured along the neat resin plate was scanned with TM-DSC and the residual enthalpy of reaction H R and T g was found.The found H R was used to determine X DSC through (1) and plotted together with T g,DSC at the end of the curing.
Table 6 compiles the values found by scanning the DSC sample together with the final values predicted by the two models at the end of the cool-down D where the thermoset has returned to a temperature near room temperature.The values measured with the DSC, are not far away from either of the predictions.As the H R found with the DSC is attached with some uncertainty due to the low response measured with the DSC.This makes it difficult to determine where the limits for integrating the residual enthalpy should be.Thus, the glass transition temperature is a more stable entity to determine as it is easily observed through the TM-DSC response.The T g,DSC found was very close to the predictions from the DK-model, confirming that under these

Conclusion
This study presents a procedure for analysing the curing and glass transition temperature of a thermoset epoxy system.Based on the data analysis, predictions from a simple kinetic model were made.This model was found to lack some accuracy when the thermoset was cured isothermally for a long time.To accommodate this, the glass transition temperature development was investigated and a diffusion-modified kinetic model was proposed to take into account the glass transition temperature.This diffusion-modified kinetic model showed that accounting for the diffusion control for cure temperatures below the glass transition was important to make reasonable predictions for long cure times.The model also showed that when curing at lower temperatures relative to the glass transition temperature this behaviour became more dominant, and thus the model was also found to be relevant at low cure temperatures.Based on the two models, an experimental validation was made by curing a neat resin panel and predicting in situ the degree of cure and glass transition temperature based on thermocouple data over time.The predictions were verified by a DSC sample cured simultaneously with the neat resin plate.The result of scanning the DSC sample immediately after the experiment showed that the value of the glass transition temperature, as midpoint values, was in good agreement with the diffusion kinetic model prediction.Thus, this study has shown a relatively simple experimental procedure.The study demonstrated several techniques to fit the data measured with DSC and in the end, presented a diffusion-modified kinetic model able to predict the extent of cure in the studied thermoset with good results.Table 7 lists a set of recommendable parameters for future predictions of an epoxy thermoset for application in wind turbine blade manufacturing.Table 7. Final parameters recommended for simulation of X and T g of the resin system.

Figure 1 .
Figure 1.Dynamic scans of uncured samples at different heating rates as solid line and the DSC signal from a second heating ramp at 5K/min to check for any residual cure -dashed line.

Figure 3 .
Figure 3. Least squares fit of the kinetic model (K-model) with the experimental values as dots and full lines for the fit.

Figure 4 .
Figure 4. Predictions based on fitted parameters from the kinetic model with DSC measurements for different T c .

Figure 5 .
Figure 5. Fitting of the DiBenedetto relation to predict the glass transition temperature development with curing.The colorbar shows the cure temperatures reflected in the colour of the dots.

Figure 6 .
Figure 6.Fitting of the critical cure development based on T c .

A
Isothermal -Pre-cure.B Heat-up before post-cure.C Isothermal -Post-cure.D Cool-down after post-cure.

Figure 9 .
Figure 9. Prediction of X and T g as a function of time from the in situ measurement of temperature and time.The temperature profile measured inside the neat resin plate is shown, together with the temperature in the oven, above and below the plate, indicated by the two thin lines.Predictions are based on both models investigated and include the values of the DSC sample at the end of the cure.

Table 1 .
Heating rate β, Peak temperature T p , total enthalpies of reaction H T and final glass transition temperatures T g∞ .β K/min T p [°C] H T [J/g] T g∞ [°C] enthalpy of reaction H T .A TM-DSC scan has been performed as a second dynamic scan to determine, what is taken as the final glass transition temperature T g∞ .Table

Table 2 .
Fitting parameters for the kinetic model.

Table 5 .
Cure profiles applied for the sample cured.

Table 6 .
Summarised final values of X and T g for the two predictions of the neat resin panel as well as the control sample measured with DSC.DSC measurement K-model prediction DK-model prediction