A method for constructing a curing kinetic model of epoxy resin

Abstract

This invention provides a method for constructing a curing kinetic model of epoxy resin. The method described in this invention constructs a multi-stage n-level model that significantly improves the fitting effect on the relationship curve between the curing rate and degree of curing of epoxy resin, and simulates the temperature changes during the curing process of epoxy resin.

Description

Technical Field

[0001] This invention belongs to the field of thermosetting resin materials technology, specifically relating to a method for constructing a curing kinetic model of epoxy resin. Background Technology

[0002] In the field of thermosetting resin-based composites, curing kinetic models of thermosetting resins have important applications. Kinetic models relate the species composition, time, and temperature in the chemical reaction process to the reaction rate expression. Supported by finite element method (FEM) simulation platforms, curing kinetic models can accurately calculate the degree of curing of resin under given initial conditions, and under certain circumstances, can accurately calculate temperature changes and exothermic events during the curing process. Various industries apply thermosetting resin curing kinetics to improve the performance reliability and R&D efficiency of composite products. For example, in the fabrication of thick composite components, the exothermic curing reaction often leads to excessively high local temperatures, causing a decline in the overall component performance. Resin curing kinetic models can be used to calculate the temperature changes during the curing process in advance, providing guidance for subsequent component fabrication. Ismet Baran et al. used curing kinetic models to simulate and calculate the degree of curing and temperature changes of thermosetting resin-based composites during pultrusion molding, and further calculated the strain and stress during the curing process.

[0003] Currently, thermosetting resin formulations used in industry contain various additives, such as accelerators and fillers, which complicates curing kinetics and makes it impossible to simply study curing kinetic models based on reaction mechanisms. Therefore, phenomenological models are widely used in studying the curing kinetics of thermosetting resins. Phenomenological models capture the main characteristics of reaction kinetics while ignoring the details of how individual reactants interact. Classical phenomenological models include the n-order model, the Prout-Tompkins model, and the Kamal model. For most resin curing reaction systems, the n-order model cannot accurately describe the entire curing process. The characteristic of the n-order model is that when the temperature is constant, the greater the degree of curing, the smaller the curing rate, and the trend is singular. The Prout-Tompkins model is a typical autocatalytic model, characterized by a curing rate of zero when the degree of curing α is 0. The Kamal model is essentially a linear sum of the n-order model and the Prout-Tompkins model and is widely used to describe the isothermal curing kinetics of epoxy resins.

[0004] Current research on curing kinetic models largely focuses on analyzing factors influencing the resin curing process based on existing models or on modifications of existing models. There seems to be little enthusiasm for proposing entirely new and applicable curing kinetic models. Natalia V. Bornosuz et al., based on an n-order model, used model fitting and isoconversion methods to study the effect of epoxyphosphazene modifiers on the isothermal curing process of epoxy amines. Sestak and Berggren studied solid-phase reactions under non-isothermal conditions and proposed an empirical model. This model is derived from the Prout-Tompkins model with modifications; essentially, the Sestak-Berggren model is a typical autocatalytic model. Summary of the Invention

[0005] The purpose of this invention is to provide a method for constructing an epoxy resin curing kinetic model, thereby solving the problem that existing curing kinetic models do not perform well in fitting the curves of the relationship between curing rate and degree of curing during the epoxy resin curing process.

[0006] To achieve the above objectives, the following technical solution is adopted:

[0007] A method for constructing an epoxy resin curing kinetics model includes the following steps:

[0008] S1. Based on the non-isothermal DSC curves of the epoxy resin system at different heating rates, the degree of curing α of the epoxy resin system is obtained.

[0009] S2. Based on the degree of curing α of the epoxy resin system, a multiple n-order model of the curing rate of epoxy resin is obtained.

[0010] S3. Based on the multiple n-level model, the glass transition temperature of the resin, the thermal conductivity during the resin curing process, the specific heat capacity of the resin, and the density during the resin curing process are obtained.

[0011] In this invention, the epoxy resin system includes epoxy resin, curing agent, and defoamer.

[0012] Furthermore, the curing agent is polyetheramine D400 and polyetheramine D230.

[0013] Furthermore, the defoamer is DF66: acetylene-modified polysiloxane emulsion.

[0014] In this invention, the mass ratio of epoxy resin, polyetheramine D400 and polyetheramine D230 is 100:14:20.

[0015] In this invention, the degree of curing α of the system in S1 is obtained by the following method:

[0016]

[0017] In the formula: —The enthalpy released by the system from time 0 to time t. ; —The total enthalpy released when the system is completely solidified. .

[0018] In this invention, the multiple n-level model in S2 is as follows:

[0019] ;

[0020] According to McLaughlin's formula:

[0021] .

[0022] Preferably, when n=3, ,

[0023] In the formula: The constant term; The coefficient of the first term; The coefficient of the quadratic term; The coefficient of the cubic term.

[0024] In some embodiments of the present invention, an equivalent transformation is performed on the multiple n-level model to obtain...

[0025]

[0026] In the formula: —The ordinate value of the intersection point of the fitted curve and the ordinate; , and —The x-coordinate value of the intersection point of the fitted curve and the x-coordinate.

[0027] Furthermore, ;

[0028] ;

[0029] ;

[0030] .

[0031] In this invention, the glass transition temperature of the resin in S3 is... Obtained through the following methods:

[0032]

[0033] In the formula: —The glass transition temperature of the resin before it has cured; — Glass transition temperature after the resin is fully cured; l — Fitting parameter.

[0034] In this invention, the thermal conductivity k during the resin curing process in S3 is obtained in the following way:

[0035]

[0036] In the formula: —The thermal conductivity of the resin before it cures; — Thermal conductivity when the resin is fully cured.

[0037] In this invention, the specific heat capacity of the resin in S3 is obtained by the following method:

[0038]

[0039] In the formula: , These respectively indicate temperatures below ( The specific heat capacity of uncured resin and cured resin at the time of curing; , These respectively indicate that the temperature is higher than ( The specific heat capacity of uncured resin and cured resin at the time of curing; This indicates that the temperature is below ( The specific heat capacity of the resin at that time; This indicates that the temperature is higher than ( The specific heat capacity of the resin at that time.

[0040] In this invention, the density ρ during the resin curing process in S3 is obtained in the following way:

[0041]

[0042] In the formula: —Density of the resin before it cures; —Density when the resin is fully cured.

[0043] The present invention has the following beneficial effects:

[0044] (1) The epoxy resin curing kinetic model construction method of the present invention constructs a multi-n-level model, which significantly improves the fitting effect of the relationship curve between epoxy resin curing rate and degree of curing, and simulates the temperature change during the epoxy resin curing process.

[0045] (2) This invention establishes a finite element model of the E44 resin curing structure and assigns a multi-level n-stage model to describe the resin curing rate, simulating the temperature changes during the epoxy resin curing process. The correctness and practicality of the multi-level n-stage model are verified from an engineering application perspective. Attached Figure Description

[0046] Figure 1This is a schematic diagram of the FBG resin curing temperature monitoring device of the present invention;

[0047] Figure 2 The differential scanning calorimeter (DSC) heat flow curves of the E44 resin of the present invention at different heating rates are shown.

[0048] Figure 3 The initial temperature of the E44 resin of this invention at different heating rates ( Peak temperature ) and termination temperature ( );

[0049] Figure 4 The differential scanning calorimetry (DSC) heat flow curves of the E44 resin of this invention at different curing temperatures are shown below.

[0050] Figure 5 This is the real-time exothermic curve of the E44 resin of the present invention at different curing temperatures;

[0051] Figure 6 This is a curing degree curve of the E44 resin of the present invention at different curing temperatures;

[0052] Figure 7 This is a curing rate curve of the E44 resin of the present invention at different curing temperatures;

[0053] Figure 8 To fit the curing rate-degree of cure curves of E44 resin at different curing temperatures using the n-level model of this invention;

[0054] Figure 9 To fit the curing rate-degree of cure curves of E44 resin at different curing temperatures using the Prout-Tompkins model of this invention;

[0055] Figure 10 To fit the curing rate-degree of cure curves of E44 resin at different curing temperatures using the multiple n-level model of this invention;

[0056] Figure 11 This invention extends the fitting curve of the multiple n-level model;

[0057] Figure 12 This is the fitting result of the equivalent transformation multiple n-level model of the present invention;

[0058] Figure 13 Parameters of the present invention , The functional relationship with temperature T;

[0059] Figure 14 Parameters of the present invention , The functional relationship with temperature T;

[0060] Figure 15 The glass transition temperatures of E44 resin at different degrees of curing according to this invention;

[0061] Figure 16 The specific heat capacity of uncured and fully cured E44 resin in this invention varies with temperature;

[0062] Figure 17 This refers to the temperature changes of the experimental chamber and the temperature at the center point B during the curing of E44 resin over time.

[0063] Figure 18 This is the finite element model of the E44 resin curing structure of the present invention;

[0064] Figure 19 This is the temperature spatial distribution of the E44 resin cured structure at 1500s according to the present invention;

[0065] Figure 20 This is a comparison of the numerical simulation and experimental temperature history curves for the curing structure point B of E44 resin in this invention. Detailed Implementation

[0066] This invention provides a method for constructing a curing kinetic model for epoxy resin. Without considering the curing reaction mechanism, it utilizes the concept of a phenomenological model to seek a curing kinetic model that can highly accurately describe the relationship between the curing rate, degree of cure, and temperature of epoxy resin. The mathematical form of this model is simple and practical, and can be used in real-world engineering applications. Specifically, addressing the problem that classical curing kinetic models cannot adequately fit the curve of the relationship between curing rate and degree of cure during the curing process of epoxy resin E44, a new curing kinetic model is proposed. This new curing kinetic model shows significantly better fitting results than other curing kinetic models.

[0067] A method for constructing an epoxy resin curing kinetics model includes the following steps:

[0068] S1. Based on the non-isothermal DSC curves of the epoxy resin system at different heating rates, the degree of curing α of the epoxy resin system is obtained.

[0069] The specific process is as follows:

[0070] In this embodiment of the invention, the epoxy resin component includes component A (epoxy resin E44, model WSR6101) and component B (curing agent polyetheramine D400, polyetheramine D230, and defoamer DF66: acetylene-modified polysiloxane emulsion). Epoxy resin E44 was purchased from the China Academy of Engineering Physics, polyetheramine D400 from Shanghai Aladdin Reagent Co., Ltd., polyetheramine D230 from Shanghai Maclean Biochemical Technology Co., Ltd., and the defoamer from Tianjin Yunwei Technology Co., Ltd. All materials are industrial grade.

[0071] (1) Sample preparation

[0072] Preparation of curing kinetics test samples: First, weigh a certain amount of epoxy resin E44 and preheat it in an oven at 45℃ for 30 minutes. Then, add polyetheramine D400 and polyetheramine D230 in sequence according to the mass ratio of epoxy resin E44, polyetheramine D400 and polyetheramine D230 of 100:14:20. Add defoamer dropwise at a ratio of 6 drops per 100g of epoxy resin E44. Stir for 10 minutes, mix evenly, and vacuum for 15 minutes.

[0073] Sample preparation for thermal conductivity test: The uniformly mixed epoxy resin was poured into a stainless steel mold and cured at 95℃ for 12h to make a fully cured cylindrical sample with a height of 5mm and a diameter of 40mm.

[0074] (2) Curing kinetics analysis

[0075] Curing reaction kinetics analysis: The curing reaction kinetics of the resin were tested using a differential scanning calorimeter (DSC2500, TA Instruments, USA). Approximately 5–10 mg of uncured sample was weighed, and nitrogen flow rate was 50 mL / min. The heating rates for non-isothermal DSC tests were 5 °C / min, 10 °C / min, and 15 °C / min, with a heating range of 30–250 °C. The isothermal DSC tests were conducted at temperatures of 55 °C, 60 °C, 65 °C, 70 °C, 75 °C, and 80 °C, with a holding time of 6 hours.

[0076] a. Non-isothermal DSC curve test.

[0077] from Figure 2 The starting temperature at which the resin undergoes a curing reaction at different heating rates can be obtained. Peak temperature ) and termination temperature ( ),like Figure 3 As shown. With increasing heating rate, , and All these values ​​increase accordingly, and the exothermic peak of the system shifts to higher temperatures. By extrapolation, the characteristic temperature can be extrapolated to the characteristic temperature corresponding to a heating rate of 0. Thus, the characteristic temperature at a heating rate of 0 is obtained. , and The temperatures were 51.38℃, 99.19℃, and 158.56℃, respectively.

[0078] Assuming the degree of epoxy resin reactivity is proportional to the enthalpy released during the curing reaction on the DSC curve, the degree of curing α can be calculated by the ratio of the exothermic peak area at time t to the total heat released during the curing reaction.

[0079] (1)

[0080] In the formula: —The enthalpy released by the system from time 0 to time t. ; —The total enthalpy released when the system is completely solidified. .from Figure 2 The total enthalpy of the system at speeds of 5℃ / min, 10℃ / min, and 15℃ / min were respectively... , and The total enthalpy at the three heating rates was close, indicating that the reaction system had completely reacted during the heating DSC test. The average of the three total enthalpies was taken. It is the total enthalpy released when the system is completely solidified.

[0081] b. Isothermal DSC test

[0082] Isothermal DSC curves of epoxy resin at different temperatures are shown below. Figure 4 As shown, the peak value of the isothermal DSC curve increases with increasing curing temperature. This is because the increased temperature enhances the molecular reactivity within the system, and the more vigorous the group reaction, the more heat is released per unit time. Figure 4 The real-time exothermic curves at each curing temperature are obtained by integrating the intermediate-temperature DSC curve over time, such as... Figure 5 According to equation (1), from Figure 5 Real-time curing degree curves at various temperatures can be obtained, such as Figure 6 It was found that as the temperature increased, the degree of curing the system could achieve was closer to 1. Finally... Figure 6 The curing rate curves at various temperatures are obtained by differentiating the curing degree curves with respect to time, such as... Figure 7 It can be seen that as the temperature increases, the resin reaction rate increases at the same degree of curing.

[0083] S2. Based on the degree of curing α of the epoxy resin system, a multiple n-order model of the curing rate of epoxy resin is obtained.

[0084] Classical curing kinetics model

[0085] according to Figure 6 and Figure 7 The curing rate of the system at various temperatures can be obtained. The relationship between the curing degree (α) and the curing degree (α) was nonlinearly fitted using the n-level model (2), the Prout-Tompkins model (3), and the Kamal model (4) in turn.

[0086] (2)

[0087] (3)

[0088] (4)

[0089] Where: m, n—reaction order; , , , —Reaction rate constant. For ease of analysis, three temperatures (65℃, 70℃, and 75℃) were selected from the curing rate versus degree of cure curves at six temperatures for fitting analysis of the curing kinetics model.

[0090] The results of fitting the n-level model are as follows: Figure 8 The fitted curves are generally concave, while the original curves are generally convex. The correlation coefficient R of the fitted curves at 65℃, 70℃, and 75℃ is... 2 The values ​​are 0.95098, 0.968787, and 0.98505, respectively, indicating that there is a significant difference between the fitted curve and the original curve, and the fitting accuracy of the n-level model is not high.

[0091] In the Prout-Tompkins model, a reaction order m equal to 0 represents an n-order model. However, when the reaction order m is not equal to 0, the Prout-Tompkins model becomes an autocatalytic model, meaning that when the degree of curing is 0, the curing rate is also 0. Clearly, the resin curing system in this experiment is not an autocatalytic reaction, therefore the Prout-Tompkins model cannot be used to fit the original curve.

[0092] The Kamal model is essentially a linear combination of the n-level model and the Prout-Tompkins model, and its fitting result is as follows: Figure 9 The correlation coefficients of the fitted curves at 65℃, 70℃, and 75℃. The fitting accuracy of the Kamal model was 0.99421, 0.99648, and 0.99891, respectively, showing a significant improvement over the n-level model. However, the fitting accuracy of the Kamal model decreased as the temperature decreased, with the most significant difference between the fitted curve and the original curve at 65℃. This suggests that other, more suitable curing kinetic models are needed for fitting.

[0093] Construction of a multi-level n-stage model for curing kinetics:

[0094] Theoretically, a perfect curing kinetic model exists that can accurately fit the curing rate-curing relationship of E44 resin. Finding this perfect curing kinetic model would be extremely difficult, and even if it were found, it would be incredibly complex. Let's assume this perfect model is as follows:

[0095] (5)

[0096] Therefore, according to McLaughlin's formula:

[0097] (6)

[0098] Approximately:

[0099] (7)

[0100] The approximate Ideal(α) expression has too many parameters, making it difficult to apply to practical fitting. Further simplification of the Ideal(α) expression is needed, allowing n=3. Theoretically, the perfectly solidified dynamic model, after approximate simplification, can then be expressed as:

[0101] (8)

[0102] In the formula: The constant term; The coefficient of the first-order term; The coefficient of the quadratic term; The coefficients of the cubic term. Mathematically, the simplified model is a linear combination of multiple different n-level models, so this model is named the multiple n-level model.

[0103] The fitting results of the multi-level n-stage model are as follows Figure 10 As shown, the correlation coefficient R of the fitted curves at 65℃, 70℃, and 75℃ is... 2 The correlation coefficients are 0.99982, 0.99966, and 0.99941, respectively. It can be seen that the fitting accuracy of the new solidification kinetic model is significantly improved compared to the Kamal model, and its fitting correlation coefficient is [missing information]. All are greater than 0.999. However, this curing kinetics model has a drawback: the four parameters in the model cannot be effectively linked to the resin curing reaction mechanism.

[0104] To address the drawbacks of multiple n-level models, a mathematical transformation is needed. Figure 11 The fitted curve in the model is extended by expanding the range of the horizontal axis to -1.0 to 2.0, resulting in the following: Figure 11 The attached curve extension plot is shown below. Figure 11 As can be seen, the fitted curve intersects the horizontal axis at three points. This provides a methodological approach for mathematical transformation of the newly solidified kinetic model, namely, the following equivalent transformation:

[0105] (9)

[0106] In the formula: —The ordinate value of the intersection point of the fitted curve and the ordinate; , and —The x-coordinate value of the intersection point of the fitted curve and the x-coordinate.

[0107] The equivalent transformed multi-n-level model was refitted, and the fitting result was consistent with the fitting result before the transformation. The fitting result is as follows: Figure 12 Parameters at various temperatures , , and The fitted values ​​are shown in Table 1. Parameters A value greater than 0 indicates a higher curing reaction temperature, and is positively correlated with temperature T; parameter The parameter should be less than 0. The values ​​should be greater than 1, and the smaller these two parameter values ​​are, the higher the curing temperature reaction, indicating a negative correlation with temperature T; parameters This represents the maximum degree of curing that the resin curing reaction can achieve at a certain temperature. Its value increases with increasing temperature and gradually approaches 1. The relationship between the four parameters in the curing kinetics model and temperature cannot be accurately described by a simple linear relationship; further appropriate mathematical expressions are needed to describe the relationship between each parameter and temperature.

[0108]

[0109] by and Plot scatter plots for 1 / T separately, and then perform linear fitting on the scatter plots, such as... Figure 13 The relationship between the two parameters and temperature is obtained as follows:

[0110] (10)

[0111] (11)

[0112] by and Plot scatter plots for T separately, then use the model and Perform nonlinear fitting on the scatter plots respectively, such as Figure 14 The relationship between the two parameters and temperature is obtained as follows:

[0113] (12)

[0114] (13)

[0115] From parameters Greater than 0, parameter Less than 0, parameter Greater than 1 and parameters A value greater than 0 and less than 1 can be used to determine the minimum applicable temperature for this curing kinetic model to describe the curing process of E44 resin. for . This represents the temperature at which the resin begins to react. When the curing temperature is less than... If the curing rate is 0, then the curing rate is 0. T is obtained by the previous extrapolation method when the heating rate is 0. i The difference of only 2.46℃ further illustrates the accuracy of the new curing kinetics model in describing the resin curing characteristics, and also reflects the limitations of classical curing kinetics, as classical curing kinetics models generally cannot clearly give the applicable temperature range.

[0116] In theory, the applicability of multiple n-level models is very broad. When describing curing reactions with different reaction characteristics, the parameters of a multiple n-level model can be interpreted in different ways. When obtaining a multiple n-level model based on the Maclaurin formula, different n values ​​can be used to obtain different n-level models to meet specific needs. However, the larger the n value, the greater the analytical difficulty.

[0117] S3. The glass transition temperature of the resin was obtained based on the multiple n-level model. The thermal conductivity k during the resin curing process, the specific heat capacity C of the resin, and the density ρ of the resin during the curing process.

[0118] Specifically:

[0119] (1) Glass transition temperature

[0120] Glass transition temperature test: Six groups of uniformly mixed resin samples were cured at 90℃ for 2 min, 5 min, 10 min, 20 min, 40 min, and 80 min, respectively. The glass transition temperature and degree of cure of the six groups of samples after curing were then measured using a differential scanning calorimeter. The sample size was approximately 5-10 mg, the nitrogen flow rate was 50 mL / min, the heating rate was 10℃ / min, and the heating range was [not specified]. .

[0121] The glass transition temperatures of six groups of samples with different degrees of cure were measured using DSC, such as... Figure 15 By fitting the equation using the DiBenedetto equation, as shown in the following formula, we can obtain... for , for l is 0.591.

[0122] (14)

[0123] In the formula: —The glass transition temperature of the resin before it has cured; — Glass transition temperature after the resin is fully cured; l — Fitting parameter.

[0124] (2) Thermal conductivity

[0125] Thermal conductivity testing: The thermal conductivity of the resin samples was tested using a thermal constant analyzer (TPS2500S, Hot Disk, Sweden). The probe of the thermal constant analyzer was immersed in a uniformly mixed, uncured resin sample to measure the thermal conductivity of the uncured resin sample. The probe of the thermal constant analyzer was clamped between the bottom surfaces of two fully cured cylindrical resin samples to measure the thermal conductivity of the fully cured resin sample.

[0126] The thermal conductivity of the uncured and fully cured resins at room temperature was measured to be 0.174 W / (m·K) and 0.203 W / (m·K), respectively, using a thermal constant analyzer. Ignoring the effect of temperature on thermal conductivity and assuming a linear correlation between thermal conductivity and degree of cure, the thermal conductivity k during the resin curing process is expressed by the following formula:

[0127] (15)

[0128] In the formula: —The thermal conductivity of the resin before it cures; — Thermal conductivity when the resin is fully cured.

[0129] (3) Specific heat capacity

[0130] Specific heat capacity test: The specific heat capacity of the resin was tested using a differential scanning calorimeter. Approximately [amount missing] of the fully cured sample was weighed. Nitrogen flow rate The heating rate is The test temperature range is Weigh approximately [amount] of the uncured sample. Nitrogen flow rate The heating rate is The test temperature range is .

[0131] Figure 16 These are the specific heat capacity test results for fully cured and uncured resin samples. The specific heat capacity of the resin system increases significantly before and after the glass transition temperature. To facilitate a mathematical description of the change in resin specific heat capacity, it is assumed that the resin at temperatures below (…). ) or higher than ( At a temperature of ( ), the specific heat capacity is linearly related to the degree of cure and is independent of temperature; when the temperature is ( ), )and( When the specific heat capacity is between 0 and 1, it is linearly related to temperature, so the expression for the specific heat capacity of the resin can be obtained:

[0132] (16)

[0133] In the formula: , These respectively indicate temperatures below ( The specific heat capacity of uncured resin and cured resin at the time of curing; , These respectively indicate that the temperature is higher than ( The specific heat capacity of uncured resin and cured resin at the time of curing; This indicates that the temperature is below ( The specific heat capacity of the resin at that time; This indicates that the temperature is higher than ( The specific heat capacity of the resin at that time. , respectively and , , They are respectively and T1 is .

[0134] (4) Density

[0135] Density testing: The density values ​​of the resin samples in their uncured and fully cured states were tested using a solid-liquid density meter (AR-300GY, China Dahometer). Based on the principle of the water displacement method, the density of the liquid uncured resin sample and the density of the solid fully cured resin sample can be tested separately.

[0136] The densities of uncured and fully cured resin at room temperature were measured using a solid-liquid density tester. and Assuming a linear relationship between density and degree of cure, the density of the resin during the curing process is expressed by the following formula:

[0137] (17)

[0138] In the formula: —Density of the resin before it cures; —Density when the resin is fully cured.

[0139] Resin simulation verification of multiple n-level models

[0140] A three-dimensional finite element model of epoxy resin curing in an aluminum alloy mold was established. A multi-level n-stage model describing the resin curing rate was adopted to simulate the temperature change during the epoxy resin curing process. The actual epoxy resin curing temperature change measured by the FBG sensor was compared with the simulated temperature change to verify the correctness and practicality of the multi-level n-stage model.

[0141] FBG monitoring of resin curing temperature: A uniformly mixed epoxy resin is poured into an aluminum alloy mold. The mold's casting groove is 6mm deep, and its length and width are both 48mm. An FBG sensor (center wavelength 1535pm, Beijing Tongwei Technology) is placed in the center of the mold's casting groove to monitor temperature changes during resin curing. The device is as follows: Figure 1 As shown, a fiber optic grating demodulator (SM130, Micron Optics, USA) was used to obtain the changes in the wavelength of light inside the FBG caused by temperature changes during the resin curing process. An aluminum alloy mold filled with resin was placed in a rapid temperature change test chamber (250CES, Chongqing Artek Technology). The temperature conditions inside the chamber were 70℃ / 3h, and the wavelength change of the light beam inside the FBG was synchronized with the temperature change inside the resin.

[0142] (1) Establishing a finite element model

[0143] Because the constitutive model built into ABAQUS cannot reflect the exothermic phenomenon of resin curing, a user subroutine was developed to establish a constitutive model describing the exothermic phenomenon of resin curing. In the subroutine UMAT, the resin curing degree change is first defined using a multi-n-level model, then the exothermic phenomenon of resin curing is defined according to equation (1), and finally the glass transition temperature, thermal conductivity, specific heat capacity, and density of the resin are defined sequentially according to equations (14) to (17). Based on the symmetry of the spatial geometry, a 1 / 4 three-dimensional model of resin curing in an aluminum alloy mold is established in ABAQUS, and the DC3D8 element type is selected for mesh generation, such as... Figure 18 Point B is the spatial center of the resin in the mold, and it is used as the observation point in both numerical simulation and experimental testing. In the 1 / 4 model, adiabatic boundary conditions are applied to the surfaces on either side of point B, while convective heat transfer boundary conditions are applied to the other surfaces. The convective heat transfer coefficients of the metal mold surface and the resin surface are respectively... and , and according to Figure 17 The temperature change curve inside the test chamber is set to reflect the outer surface temperature of the model. Contact heat conduction is set at the resin-metal mold contact surface, with a conductivity coefficient set to [value missing]. During the simulation, the maximum time increment for each step was 10 seconds. A total of four different simulations were performed. In all four simulations, the edge length of the metal mold mesh element was 0.5 mm, and four different edge lengths were selected for the resin mesh element: 0.5 mm, 1 mm, 6 mm, and 12 mm.

[0144] (2) Comparison of simulation and experimental results

[0145] Figure 19 The temperature spatial distribution of the E44 resin cured structure at 1500s is shown, where the edge length of the resin mesh unit is 0.5mm. It can be seen that the temperature peak appears in the area around the center point B of the structure. Figure 20 A comparison of the temperature history curves at point B obtained from numerical simulation and experimental testing is presented. It can be seen that in the initial heating stage, reaching the same temperature requires approximately 100 seconds longer for simulations using different mesh density models compared to the experimental time. During the temperature peak appearance stage, the simulated temperature peaks differ depending on the mesh density. Higher mesh density results in a higher temperature peak, and the peak position gradually shifts to the right to approach the experimental peak, although this trend gradually weakens. The simulated temperature curve with the highest mesh density has a maximum value 1.5℃ higher than the experimental maximum. In the later stages of the resin reaction, the simulated and experimental temperatures are essentially the same. Overall, the simulated and experimental temperature curves from different mesh density models are very close. This indicates that establishing a constitutive model describing the exothermic reaction during resin curing is reasonable for simulating the exothermic phenomenon during resin curing. The core of the constitutive model describing the exothermic reaction during resin curing is a multiple n-order model. The practical application of the curing exothermic constitutive model in temperature simulation effectively verifies the correctness and practicality of the multiple n-order model and also demonstrates the reliability of the various resin performance parameters provided in this invention.

[0146] The above description discloses only preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. Therefore, equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A method for constructing a curing kinetic model of epoxy resin, characterized in that, Includes the following steps: S1. Based on the non-isothermal DSC curves of the epoxy resin system at different heating rates, the degree of curing α of the epoxy resin system is obtained. S2. Based on the degree of curing α of the epoxy resin system, a multiple n-order model of the curing rate of epoxy resin is obtained. S3. The glass transition temperature of the resin was obtained based on the multiple n-level model. The thermal conductivity k during the resin curing process, the specific heat capacity C of the resin, and the density ρ of the resin during the curing process.

2. The method for constructing an epoxy resin curing kinetic model according to claim 1, characterized in that, The epoxy resin system includes epoxy resin, curing agent, and defoamer.

3. The method for constructing an epoxy resin curing kinetic model according to claim 1, characterized in that, The degree of curing α of the system in S1 is obtained in the following way: In the formula: —The enthalpy released by the system from time 0 to time t. ; —The total enthalpy released when the system is completely solidified. .

4. The method for constructing an epoxy resin curing kinetic model according to claim 2, characterized in that, The multi-n-level model in S2 is as follows: ； According to McLaughlin's formula: 。 5. The method for constructing an epoxy resin curing kinetic model according to claim 4, characterized in that, When n=3 , In the formula: The constant term; The coefficient of the first-order term; The coefficient of the quadratic term; The coefficient of the cubic term.

6. The method for constructing an epoxy resin curing kinetic model according to claim 4 or 5, characterized in that, By performing an equivalent transformation on the multi-n-level model, we obtain In the formula: —The ordinate value of the intersection point of the fitted curve and the ordinate; , and —The x-coordinate value of the intersection point of the fitted curve and the x-axis; in, ; ； ； 。 7. The method for constructing an epoxy resin curing kinetic model according to claim 4 or 5, characterized in that, The glass transition temperature T of resin in S3 g Obtained through the following methods: In the formula: —The glass transition temperature of the resin before it is cured; — Glass transition temperature after the resin is fully cured; l — Fitting parameter.

8. The method for constructing an epoxy resin curing kinetic model according to claim 4 or 5, characterized in that, The thermal conductivity k of the resin during the curing process in S3 is obtained in the following way: In the formula: —The thermal conductivity of the resin before it cures; — Thermal conductivity when the resin is fully cured.

9. The method for constructing an epoxy resin curing kinetic model according to claim 4 or 5, characterized in that, The specific heat capacity of the resin in S3 was obtained in the following way: In the formula: , These respectively indicate temperatures below ( The specific heat capacity of uncured resin and cured resin at the time of curing; , These respectively indicate that the temperature is higher than ( The specific heat capacity of uncured resin and cured resin at the time of curing; This indicates that the temperature is below ( The specific heat capacity of the resin at that time; This indicates that the temperature is higher than ( The specific heat capacity of the resin at that time.

10. The method for constructing an epoxy resin curing kinetic model according to claim 4 or 5, characterized in that, The density ρ during the resin curing process in S3 is obtained in the following way: In the formula: —Density of the resin before it cures; —Density when the resin is fully cured.

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