Kinetics simulation and a novel curing procedure to avoid thermal shock during the curing process of epoxy composites

Abstract

In order to reduce the effect of the thermal shock that occurs during the curing process of epoxy resin (EP), and to improve the mechanical properties of the cured EP, a novel curing procedure for an epoxy resin system, sodium carboxymethyl cellulose (CMC)/E51 type epoxy resin (E51)/4,4-diamino diphenyl methane (DDM), was established according to the simulated results of a three-dimensional finite element model and extrapolation method. Compared to the conventional curing procedure, a cooling stage was used in the new procedure according to the simulated results to reduce the effect of the thermal shock. The experimental verification showed that even when the curing time was 30 min shorter than the conventional procedure, the new curing procedure clearly improved the mechanical properties of the cured resin. For instance, the bending strength of the specimen cured by the new procedure reached 136 MPa, which is increased by 46% when compared to the specimen cured by the conventional procedure (93.3 MPa) and the impact strength increased from 18.3 kJ m⁻² to 23.1 kJ m⁻².

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1. Introduction

Epoxy resin (EP) is one of the most important thermosetting polymers and is one of the most widely used high-performance polymeric materials.^1–3 It is also widely used as the matrix of a variety of fiber reinforced resin matrix composites.^4–7 In our previous research, we studied the CMC/E51/DDM system, and when compared to the other EP systems, components were dispersed more homogeneously in this system and the cured resin showed better interfacial properties and mechanical performance.

The curing process of the EP resin is a complex process including the heat transfer and curing reaction.^8,9 The curing process, such as the curing time and curing temperature, clearly affects the properties of the resulting cured materials.^10–12 Thermal shock is a phenomenon often occurs during the curing process of the EP and results in a significant thermal stress in the material, which reduces the mechanical properties of the final cured EP. During the curing processes of resin, the curing reactions in the resin produce large amounts of reaction heat in a relatively short period of time and the accumulated heat cannot dissipate timely due to the increased viscosity of the resin, these results in thermal shock and reduce the mechanical property of the curried resin.

In the early curing stage, the resin is in a liquid state which can release the inner thermal stress, thus we hope that the thermal shock can occur during the early stage in order to reduce the residual thermal stress in the material. However, the conventional empirical curing process cannot well control the occurrence of the thermal shock and reduce its effect. In addition, these processes are generally empirical stage-heating processes, and have no theoretical research on determining the curing time of every stage. Hence, it is important and valuable to develop a new curing procedure based on the theoretical analysis to control the occurrence of the thermal shock and reduce its effect.

A numerical simulation based on the thermal analysis kinetics is a useful approach for studying the curing process and has been widely applied to study the thermal shock phenomenon during the curing process of the EP matrix composite.^13,14 Generally, the effects of new curing procedure on thermal shock are verified by experiment results. Dynamic mechanical analysis (DMA) and mechanical property test are performed to analyze the property of the specimen cured by different procedures. Fourier transform infrared spectroscopy (FTIR) was utilized to confirm the completion of curing reaction in resin.

Twardowski utilized a one-dimensional numerical simulation to simulate the molding process of the EP matrix composite and found that the temperature of the central point (about 290 °C) was much higher than the processing temperature (130 °C).¹⁵ Bogetti established a two-dimensional finite model to simulate the curing process of a thick thermosetting resin composite with a coupled thermal and chemical kinetics formulation.¹⁶

Costa¹⁷ established a three-dimensional model and found that the thermal shock effect obviously existed in the curing process of EP matrix composite. Ding reported a three-dimensional model to simulate the stress change in composite laminates during the curing process.¹⁸ Yi utilized a nonlinear transient heat transfer finite element model to simulate the curing process of a thermosetting material, and analyzed the change in the temperature of the central point and curing degree of the material without considering the heat flow.¹⁹ However, although a variety of experimental, theoretical and analytical methods have been applied to optimize the curing process of the EP system, there is still no a suitable method for solving the problem of thermal shock.

We now report a new optimized curing procedure for the CMC/E51/DDM system by considering the three-dimensional heat transfer and chemical reaction together, different from the conventional empirical stage-heating process; the new procedure contains a cooling stage and it is established on the basis of thermal analysis kinetics and a numerical simulation. A suitable cooling stage was found to reduce the influence of the thermal shock. The effects of the new curing procedure on the total curing time and mechanical property of the cured resin are discussed based on the results of experiment verification.

2. Experimental

2.1 Materials

The diglycidyl ether of the bisphenol A type epoxy resin (E51) was provided by the Deyuan Chemistry Plant, China (epoxy value of 0.48–0.54, epoxide equivalent weight of 185–208). The curing agent was 4,4-diaminodiphenyl methane (DDM), which was provided in analytical grade by the Shanghai Crystal Pure Reagent Co. (Aladdin Reagent Co. China) (molecular weight of 198 g mol⁻¹, active hydrogen equivalent of 49.5, purity of 97%). The sodium carboxymethyl cellulose (CMC) was supplied by the Suzhou Yiming Chemical Plant, China (purity of 99%, degree of substitution of 0.2–1.5).

2.2 Preparation of the cured epoxy specimen

The mixture of CMC/E51/DDM (mass ratio 1 : 100 : 25, CMC: 0.08 g, E51: 8.00 g, DDM: 2.00 g) was well mixed at 40 °C for a few minutes, then the mixture was poured into a preheated mold. After degassing under vacuum, the curing reactions were followed by a conventional stage-heating procedure (353.15 K/2 h + 423.15 K/4 h) and by a new procedure having a cooling stage (363.15 K/0.5 h + 340.15 K/1 h + 423.15 K/4 h). After demolding, the specimens were polished for further testing.

2.3 Differential scanning calorimetry (DSC) analysis

The thermal analysis data of the curing reaction in the CMC/E51/DDM systems were obtained using a differential scanning calorimeter (DSC 200, TA Instruments, USA). A mixture of CMC, E51 and DDM was transferred to an aluminum DSC crucible for testing. For the non-isothermal run, the heating rate was 5 K min⁻¹, 10 K min⁻¹, 15 K min⁻¹ and 20 K min⁻¹, and the temperature ranged from 0 °C to 280 °C. The sample weight was 5–10 mg. All the DSC runs were carried out under N₂ flowing (50 mL min⁻¹).

2.4 Dynamic mechanical analysis (DMA)

A dynamic mechanical analysis (DMA Q800, TA Instruments, USA) was used to study the thermomechanical properties of the specimens. The rectangular specimens (35 mm × 12.7 mm × 3.14 mm) were fastened to a single cantilever clamp. The analysis was done in the three-point bending mode at a frequency of 1 Hz, an oscillation amplitude of 10 μm and at a heating rate of 3 °C min⁻¹. The specimens were heated from room temperature to 250 °C.

2.5 Mechanical property measurements

A universal testing machine (Instron 3365) was utilized to measure the bending and the tensile strength of the cured specimens. A Charpy impact testing machine (XJJ-50) was utilized to measure the non-notched impact strength of the cured specimens.

2.6 Fourier transform infrared spectroscopy (FTIR)

Completion of curing reaction in the resin was confirmed by FTIR (Spectrum 100, PerkinElmer). In the FTIR spectrum, the characteristic peaks of epoxy group at 915 cm⁻¹ disappeared. Accordingly, the peaks of primary amine at 3440 cm⁻¹ (N–H antisymmetry stretching vibration) and 771 cm⁻¹ (N–H wagging vibration) also disappeared after curing. These indicate the completion of curing reaction in the resin.

3. Thermal dynamic analyses

3.1 Thermo-chemical model

The distribution of the temperature field during the curing process is a question of heat transfer from a nonlinear internal heat source which was generated from the exothermic reaction in the matrix resin.²⁰ The macro dynamics study can estimate changes in the temperature field distribution and the curing degree field distribution, and it can also estimate the temporal and spatial regions of the occurrence of the thermal shock during the curing process of the resin. Therefore, a reasonable and reliable model is important and useful for designing a more suitable curing procedure to reduce the effect of thermal shock and improve the mechanical performance of the cured resin.

The basic equation for the macro dynamics is a heat conduction equation in a nonlinear internal heat transfer system.

where ρ, C and H represent the average density, heat capacity and enthalpy of the curing reaction, respectively; K_xx, K_yy, K_zz represent the thermal conductivity of the composite in the X, Y, Z directions, respectively, and da/dt is the curing rate.

Generally, a kinetic analysis of the thermosetting resins cured by a non-isothermal process is characterized by the following rate equation:²¹

where k is the rate constant as a function of the temperature, A is the pre-exponential factor, E is the activation energy, R is the gas constant, a is the conversion and f(a) represents the function of the curing degree which is associated with the reaction mechanism and represents the kinetic model.

In general, the curing kinetics of an epoxy resin is studied by using an n^th-order model or Sestak–Berggren (SB) autocatalytic model.²² In a previous study, we found that the SB autocatalytic model was suitable for the CMC/E51/DDM system.²³ The SB autocatalytic model is shown as:²⁴

where m and n are the reaction orders.

The unknown parameters, such as A, E, m, and n in eqn (2) and (3), were calculated using the previous kinetic equations based on the non-isothermal DSC data. The specific curing kinetic model of the CMC/E51/DDM system was them as the following equation:

In this study, we established a three-dimensional finite element model based on the above equations and the previous study.²⁵ The physical conditions were set as follows: the temperature change of the upper and lower surfaces of the material was set as shown in Fig. 1, while the other surface was set as adiabatic. The initial temperature of the material was set at 293.15 K. The other necessary parameters of the system are shown in Table 1, no. 1. The specimen was considered a laminate with the size of 15.24 cm × 15.24 cm and 2.54 cm thick.

Fig. 1 The simulated curves of the central point temperature (T) versus curing time (t) by our model (black square) and the reported results of ref. 26 (white square).

Table 1 Physical parameters in the model for simulating curing process of resin

No.	Resin system	ρ (kg m^−3)	C (J kg^−1 K^−1)	Kxx (W m^−1 K^−1)	Kyy (W m^−1 K^−1)	Kzz (W m^−1 K^−1)	H (J kg^−1)
a Reported in ref. 26.
1	CMC/E51/DDM	1162	1560	0.2223	0.2223	0.2223	379 000
2^a	Glass/polyester	1890	1260	0.4326	0.4326	0.2163	77 500

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3.2 Model verification

In order to verify the reliability of the established model, a reported resin system of glass fiber/polyester²⁶ was selected as the reference. The relations of the central point temperature (T) and the central point curing degree (α) versus curing time (t) in the reference system were simulated by using our model and by the reported model (Fig. 1 and 2) under the same physical parameters (Table 1, no. 2).

Fig. 2 The simulated curves of curing degree (a) in the central point (black square) versus time (t) and the reported results of ref. 26 (white square).

As shown in Fig. 1, the simulated curves of central point temperature and central point curing degree versus the curing time by the two models (Fig. 2) are almost consistent. The new model afforded the similar simulation results as the reported one,²⁶ which indicate that the new established model is reasonable and reliable and it is suitable to simulate and analyze the curing process to give the guidance for designing a better curing procedure.

4. Results and discussion

4.1 Simulation of the effect of processing temperature on thermal shock

The generation and accumulation of the reaction heat during the curing process could cause a remarkable thermal shock. If thermal shock occurs in the early stage of the curing reaction, it will be favorable to release the reaction heat and inner stress so as to reduce the influence of the thermal shock on the materials.

Temperature is an important factor for the EP curing process. If an unsuitable temperature program is selected, it will produce defects and residual stress in the material due to the thermal shock, which results in reduced mechanical properties of the cured material. Therefore, it is very important to analyze the effect of the curing temperature on the thermal shock so as to determine a suitable temperature program to reduce the effect of the thermal shock.¹²

The curing process of the CMC/E51/DDM system was simulated by utilizing the model. The physical parameters were assumed as constant during the EP curing reaction.²³ The curing temperature range was set as from 293.15 K to 343.15 K, 353.15 K and 363.15 K. Fig. 3A and B show the simulated curves of the temperature and curing degree of the central point versus the curing time at different curing temperatures.

Fig. 3 The simulated curves of temperature (A) and curing degree (B) of the central point versus the curing time at different curing temperatures.

The simulation results in Fig. 3A show that in the early stage of the curing reaction (0–1000 s), the curing temperature did not clearly influence the central point temperature in the material. However, in the middle stage of the curing reaction, it significantly affected the occurrence time and range of the thermal shock. At the curing temperature of 343.15 K, the peak temperature of the thermal shock was 461.22 K and appeared at 4900 s (Fig. 3A, cylinder), which was 118.07 K higher than the boundary temperature (343.15 K). However, when 363.15 K was selected as the curing temperature, the peak temperature of the thermal shock increased to 555.86 K and appeared at 2020 s (Fig. 3A, square). It was amazing that even when the curing temperature only increased 20 K from 343.15 K to 363.15 K, the peak temperature of the thermal shock increased 94.64 K (from 461.22 K to 555.86 K) and appeared 2880 s earlier (from 4900 s to 2020 s). According to these simulated results, we can conclude that the occurrence and peak temperature of the thermal shock were quite sensitive to the curing temperature.

As shown in Fig. 3B, the curing degree of the central point (α) increased very slowly during the early stage (0–1000 s), then it sharply increased to saturation. The curing degree of the central point was not clearly influenced by the curing temperature in the early stage. However, the total curing time was clearly influenced by the curing temperature. By increasing the curing temperature from 343.15 K to 363.15 K, the total curing time of the central point was shortened from 4000 s to 1020 s (Fig. 3B). Therefore, increasing the curing temperature could clearly increase the curing rate and shorten the curing time, although it had no such clear influence during the early stage of the curing process.

4.2 Simulation of the effect of the heating rate on the thermal shock

In order to study the effect of the heating rate on the thermal shock, the heating rate was set to 1.0 K min⁻¹, 1.5 K min⁻¹ and 2.0 K min⁻¹. The temperature range was 293.15–533.15 K. The simulated curves of the temperature and curing degree at the central point versus the curing time under different heating rates are shown in Fig. 4.

Fig. 4 The simulated curves of temperature (A) and curing degree (B) of the central point versus the curing time at different heating rates.

According to the simulated results shown in Fig. 4, the curing process could be roughly separated into three stages, i.e., the early stage, the thermal shock stage and the post curing stage. The heating rate did not clearly influence the central point temperature in the early stage and the post curing stage. This was because that in the early stage, the viscosity was low which can easily release any inner stress and reaction heating, and in the post curing stage, the curing reaction was almost completed and the temperature at the central point was mainly affected by the thermal transfer.

In the case of the thermal shock stage, the temperature at the central point sharply increased with the appearance of the thermal shock. In this stage, with the curing temperature increase, a large amount of reaction heat was produced and accumulated in the materials which accelerated the curing reaction, and this acceleration of the curing reaction produced more reaction heat and caused the rapid change in the system viscosity, and finally, the thermal shock appeared. Fig. 4A shows that the heating rate clearly affected the temporal region of the thermal shock; the higher heating rate could make the thermal shock appear earlier and shorten the curing time.

Curves of the curing degree of the central point and boundary point versus time at the different heating rates are shown in Fig. 4B and 5. The tendency of the effects of the heating rate and curing temperature on the curing degree are the same.

Fig. 5 Curves of the curing degree of the boundary point versus time at the different heating rates.

Additionally, in comparison with Fig. 4B and 5, it can be seen that the curing degree of the boundary point was higher than that of the central point during the early curing stage, because in this stage, the boundary point had the faster reaction rate due to its higher temperature than the central point. As the reaction further proceeded, the curing degree of the central point quickly increased and exceeded the boundary point.

4.3 Optimization of curing procedure of CMC/E51/DDM system

In general, the EP curing procedure is determined by the extrapolation method and on an empirical basis.^25,27,28 In this study, the specific curing procedure was determined by combining the extrapolation with the simulated results of the three-dimensional finite element model.

The main parameters, such as the initial thermal decomposition temperature (T_d), glass transition temperature (T_g) and theoretical gel curing degree (a_gel) should be identified before simulating the curing process. a_gel is different for the different epoxy-curing agent systems, but it is not affected by temperature and can be calculated by the following equation:

where f_A is the amount of active amino hydrogen of the curing agent molecule; f_E represents the number of epoxy groups in an EP molecule.

In the case of the CMC/E51/DDM system, a_gel was about 0.577, T_g generally was 423.15 K, and T_d was about 573.15 K. T_p and t_p represent the peak temperature and peak time of the thermal shock, respectively, and t_gel represents the time to reach the curing degree of the gel at the boundary point.

The optimization of curing procedure should follow some basic principles; i.e., to avoid decomposition and deformation of the material, the T_p should be lower than T_d; since the effect of the thermal shock in the early stage (before gelation of EP) is small, t_p should be earlier than t_gel; and the curing temperature in the post curing stage should be close to the T_g. Therefore, the curing temperature based on the above conditions should be as high as possible during the entire curing process from the viewpoint of improving the production efficiency and energy saving.

Since the simulated results indicate that the curing temperature and heating rate had almost no influence on the thermal shock during the early stage of the curing reaction (0–2000 s in Fig. 3 and 4), it is wise to utilize a preheated mold which could provide the system with a higher curing temperature to accelerate the curing reaction at this stage.

For the thermal shock stage, since the thermal shock appears and the system temperature sharply increased in this stage, the best way to reduce the effect of the thermal shock is to reduce the system temperature as much as possible based on maintaining the reaction activity. In other words, it is necessary to have a cooling stage in the region of the thermal shock to release its effect. In order to keep the reactivity of the system, the curing temperature should not be lower than the initial curing temperature (T_i) which was obtained by an extrapolation method.

During the post curing stage (5500–14 000 s), the curing temperature should be close to the T_g of the cured material or slightly higher than it, because the curing reaction is almost finished and the heat transfer effect played the key role. The purpose of this stage is to improve the curing degree and release the thermal stress. Additionally, the heating rate from the thermal shock stage to the post curing stage should be slow in order to reduce the thermal stress.

Based on these analyses of the simulated results and basic principles for optimization, we established a novel optimized curing process having a cooling stage for the CMC/E51/DDM system, which was 363.15 K/0.5 h + 340.15 K/1 h + 423.15 K/4 h (Fig. 6A, black circle). In contrast, the conventional curing process of the CMC/E51/DDM system was 353.15 K/2 h + 423.15 K/4 h (Fig. 6A, white circle). In comparison to the conventional procedure, in the new optimized procedure, the early stage temperature was 10 K higher which could accelerate the early curing reaction, and the biggest difference in the new procedure from the conventional one was that the new procedure contained a cooling stage that was 23 K lower than the temperature of the early stage, which was designed to reduce the effect of thermal shock. The region of the cooling stage was decided according to the simulated thermal shock region. In addition, the total curing time of the new procedure was 30 minutes shorter than the conventional one.

Fig. 6 Comparison of the conventional curing procedure and the optimized curing procedure for CMC/E51/DDM; (A) the conventional and the optimized procedure, (B) simulated curves of central point temperature versus curing time, (C) simulated curves of curing degree of central point versus curing time; (D) simulated curves of curing degree at boundary point versus curing time.

To verify the advantages of the new curing procedure, we simulated the curing processes under the new and conventional curing procedures (Fig. 6). As shown in Fig. 6B, in the conventional curing procedure (Fig. 6B, white circle), the peak temperature of the thermal shock (518 K) appeared at 4160 s. However, the peak temperature of 476 K appeared at 2940 s in the new curing procedure. In the new curing procedure, the T_p was 42 K lower and the t_p was 1220 s earlier than those for the conventional procedure (Fig. 6B). This indicated that the cooling stage could make the thermal shock occur earlier and could also reduce the thermal shock temperature; this should be beneficial to the property of the cured materials. In addition, the total curing time of the new curing procedure was shorter than the conventional curing procedure (Fig. 6C and D). In summary, the new optimized curing procedure containing a cooling stage could not only reduce the thermal shock effect but also shorten the curing time. Therefore, it was a more suitable procedure for the CMC/E51/DDM system than the conventional curing procedure.

4.4 Experimental verification

In order to verify the advantages of the new optimized curing procedure, the CMC/E51/DDM system was cured under the new (363.15 K/0.5 h + 340.15 K/1 h + 423.15 K/4 h) and conventional procedure (353.15 K/2 h + 423.15 K/4 h). Mechanical performances of the specimen cured by different procedure were compared.

Fig. 7 shows the DMA results of the cured specimen of CMC/E51/DDM resin, for the specimen cured by optimized curing procedure, its glass transition temperature (T_g) is around 180 °C, which is about 10 °C higher than that of the specimen cured by the conventional procedure (169.5 °C). It was possibly caused by the fact that the optimized procedure afforded a smaller residue press and made the curing process and the formed network more perfect.

Fig. 7 DMA analysis of CMC/E51/DDM system for the different curing procedures.

The mechanical performances, such as bending, tensile and impact strength, of the cured materials prepared by the different procedures were compared in Table 2 and Fig. 8. When compared to the specimen prepared by the conventional curing procedure, the bending strength of the specimen prepared by new curing procedure reached 136 MPa, which increased by 46% (93.3 MPa), the impact strength increased by 26.2% (from 18.3 kJ m⁻² to 23.1 kJ m⁻²), the tensile strength increased by 14% (from 58.3 MPa to 66.6 MPa).

Table 2 Mechanical properties of CMC/E51/DDM specimen prepared by the conventional and optimized curing procedures^a

Mechanical properties	Curing procedure
	Conventional procedure	Optimized procedure
a The results of strengths were measured in the three-point mode impact strengths were measured in the single-point mode.
Bending strength (MPa)	93.3	136
Tensile strength (MPa)	58.3	66.6
Impact strength (kJ m^−2)	18.3	23.1

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Fig. 8 Mechanical properties of CMC/E51/DDM specimen prepared by different procedures.

In summary, even the total curing time was 30 min shorter than the conventional procedure, the new curing procedure could clearly enhance the mechanical performances of the cured CMC/E51/DDM materials. These results indicated that the new procedure having a cooling stage could even improve the mechanical property to a level of physical blending or chemical modification, and it was the more suitable curing procedure for the CMC/E51/DDM system. This procedure is also suitable for general epoxy resin system and is valuable for industrial practice.

5. Conclusion

The curing process of the CMC/E51/DDM system and thermal shock phenomenon during the curing process were studied by a three-dimensional finite element model. Based on the numerical analysis and simulation of the curing process, a new optimized curing procedure having a cooling stage was established to reduce the effect of the thermal shock. The simulated results showed that when compared to the conventional procedure, the peak temperature of the thermal shock (T_p) clearly decreased and the peak time t_p was 20 min earlier. Moreover, the total curing time was shortened by 30 min. The experimental verification showed that the new procedure could clearly improve the mechanical properties and the T_g of the cured materials. For instance, by utilizing the new curing procedure, the bending strength of cured resin increased from 93.3 MPa to 136 MPa and the impact strength increased from 18.3 kJ m⁻² to 23.1 kJ m⁻². These results indicated that the new procedure having a cooling stage was the more suitable curing process for the CMC/E51/DDM system. This provided a new thinking and method for curing of the EP resin system, and is very valuable for practical applications. This new curing procedure has great potential not only in EP system, but also other resin system, and is valuable for industrial application.

Acknowledgements

We acknowledge the financial support from the National Natural Science Foundation of China (21576060, 21574033, and 51373044), National Natural Science Foundation of Heilongjiang province, China (LC201404 and E2016019), the Fundamental Research Funds of Datong (2015109), and the Fundamental Research Funds for the Central Universities (HEUCFZ1018, HEUCF20161004, and HEUCFQ1417).

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