An optimization method for the curing regime of composite materials

Abstract

This invention provides a method for optimizing the curing regime of composite materials, comprising the following steps: S1: establishing a mathematical model of the curing reaction kinetics of the resin; S2: establishing a Fourier transient heat conduction control equation containing a nonlinear internal heat source term; S3: establishing a finite element numerical model of the composite material mold and product; S4: establishing a parameter optimization model of the curing regime; S5: optimizing the parameter optimization model of the curing regime to obtain a better curing regime for the composite material product of that model; S6: verifying the curing regime of the theoretical optimization results through actual experiments. According to this invention, existing curing regimes can be optimized. For different models and types of advanced composite material products, unique and superior curing regimes can be formulated, enabling the composite material to achieve better curing effects, improving product quality while avoiding the huge time, manpower, and economic costs associated with large-scale trial-and-error experiments.

Description

Technical Field

[0001] This invention relates to the field of composite material production and manufacturing, and specifically to an optimization method for the curing process of composite materials. Background Technology

[0002] Composite materials, composed of two or more materials, exhibit significantly enhanced properties due to the complementary advantages among their components. These advantages are particularly evident in specific strength, specific modulus, high-temperature resistance, fatigue resistance, corrosion resistance, designability, and functionality, demonstrating substantial superiority over traditional single-phase materials. However, the manufacturing technology for composite materials is also more challenging, especially the molding process, which has a decisive impact on the performance of composite products. The curing process, in particular, is a key factor in the quality of composite material molding.

[0003] For the curing of thermosetting resins, the curing reaction of the resin matrix is ​​a thermally activated reaction. As the degree of curing changes, the resin successively progresses through a viscous state, a highly elastic state, and a glassy state. During the curing process, reaction time, external heating temperature, and pressure all affect the degree of resin curing. Therefore, different types of resins have a supplier-recommended curing regime, which includes a temperature-time curve. For some composite materials, certain pressure conditions are also required for better curing results.

[0004] However, relying entirely on the curing regime recommended by the supplier is not advisable in actual production. For example, for some complex composite products, the resin distribution in the structure is not uniform; that is, the resin is extremely abundant in some areas (where the thickness is greater) and extremely scarce in others (where the thickness is less). Obviously, a longer curing time or a higher temperature should be used for the thicker areas. Alternatively, the complex structure or mold of the product may require a longer time for heat to be transferred to the thicker areas through heat conduction, or a higher temperature may be required under the same temperature conditions. For some special-purpose composite materials, the resin provided by the supplier needs to be modified by adding other chemical reagents. The addition of additives will correspondingly change the original curing regime of the resin, and it is unreasonable to continue using the original curing regime in this case.

[0005] Because existing technologies cannot effectively improve the curing effect of composite materials, especially during the curing process, and the resulting cured products have technical problems such as unevenness, this invention studies and designs an optimized method for the curing regime of composite materials. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the defects in the production and manufacturing process of composite materials, especially in the curing process, where the curing effect cannot be effectively improved and the produced products have uneven curing. Thus, an optimized method for the curing regime of composite materials is provided.

[0007] To address the above problems, this invention provides an optimization method for the curing process of composite materials, comprising the following steps:

[0008] S1: Using a phenomenological model, the resin thermal experimental data are tested using a differential scanning calorimeter or differential thermal analyzer. The reaction kinetics model is fitted with the data to establish a mathematical model of the resin curing reaction kinetics.

[0009] S2: Based on the aforementioned curing reaction kinetic mathematical model, establish a Fourier transient heat conduction control equation containing the exothermic curing reaction, i.e., containing a nonlinear internal heat source term;

[0010] S3: Establish finite element numerical models of composite material molds and products based on the Fourier transient heat conduction control equations;

[0011] S4: Establish a parameter optimization model for the curing regime based on the finite element numerical model of the composite material mold and product. The optimized parameters include heating and cooling rates, heating and cooling durations, holding temperatures, holding durations, and pressures. The optimization objective is to maximize the average degree of curing of the composite material product after the curing regime is completed.

[0012] S5: Optimize the parameter optimization model of the curing regime to obtain a better curing regime for this type of composite material product, and perform theoretical verification;

[0013] S6: Verify the solidification regime based on the theoretical optimization results through actual experiments, and improve and optimize the solidification regime based on the experimental results to obtain the final solidification regime.

[0014] In some embodiments, the curing reaction kinetic model in S1 refers to an equation that links reaction time, degree of curing, and exothermic reaction and describes the state of the resin at any time during the curing reaction.

[0015] The Fourier transient heat conduction control equation for the nonlinear internal heat source term in S2 includes a combination of the heat conduction process during the curing process of the composite material, in which heat is transferred from the mold to the interior of the material, and the exothermic reaction process of the resin itself, wherein the exothermic process is not linear.

[0016] The finite element numerical model in S3 includes a structure combining a mold and a composite material product. The mold is located outside the composite material product, and there is heat conduction between the mold and the composite material product. The external environment heats the composite material product by heating the mold.

[0017] The parameter optimization model in S4 includes optimization objectives and optimization parameters. The entire solidification system can be accurately described by a few optimization parameters, and the optimization objective can be optimized by changing the optimization parameters.

[0018] The optimization described in S5 refers to the computational iterative process that makes the optimization objective reach its extreme value. The number of iterations needs to take into account the amount of computation each time, that is, the number of iterations is finite. When the difference of the optimization objective after each iteration is less than or equal to a preset value, the iteration is terminated, and the optimization objective at this time is the final result.

[0019] In some implementations, the phenomenological model in S1 takes the form of:

[0020] dα / dt = k(T)f(α) (1)

[0021] Where k(T) is a temperature-related parameter, and f(α) is a function related to the degree of curing;

[0022] Based on different forms of f(α), the phenomenological solidification kinetic model includes an n-order reaction kinetic model and an autocatalytic model, wherein the form of the n-order reaction kinetic model is as follows:

[0023] dα / dt = k(T)(1-α) n (2)

[0024]

[0025] Where n is the reaction order; k is the reaction rate in the reaction kinetic model; A is the frequency factor of the reaction kinetic model; ΔE a α is the activation energy of the reaction kinetic model; T is the temperature; t is the time; α is the degree of curing of the resin; R is the universal gas constant.

[0026] The autocatalytic model takes the following form:

[0027]

[0028]

[0029] Where k1 and k2 are the rate constants of the autocatalytic reaction model, A1 and A2 represent the two frequency factors of the model, m1 and n1 represent the reaction order of the autocatalytic model, and ΔE1 and ΔE2 represent the activation energy in the curing reaction process.

[0030] In some embodiments, the Fourier transient heat conduction governing equation for the exothermic curing reaction in S2, in Cartesian coordinates, is as follows:

[0031]

[0032] In the formula, T is the temperature; ρ c C p k ii (i = x, y, z) represent the equivalent density, specific heat, and thermal conductivity of the composite material, respectively; For internal heat source items;

[0033] The above equation can be transformed into the governing equation in any coordinate system through coordinate transformation;

[0034] The expression is:

[0035]

[0036] In the formula, ρ r H represents the density of the resin. u Let denoted as α, representing the total heat released by the resin during the curing reaction; α represents the degree of curing of the resin, indicating the ratio of the heat released at that moment to the total heat released, i.e., the proportion of heat released at time t relative to the total heat released, as shown in the following formula; dα / dt represents the instantaneous curing rate of the resin, i.e., the instantaneous reaction rate.

[0037]

[0038] Where H(t) represents the heat released by the curing reaction at time t.

[0039] In some implementations, S3 first establishes a geometric analysis model for composite material products of different configurations and types. To facilitate finite element calculations, the initial finite element model is then simplified. After the geometric model is established, different material properties and thermal conductivity parameters at the interface are set for the mold and the product. Subsequently, the geometric model is meshed, and the mesh must meet both the calculation accuracy requirements and the calculation cost requirements.

[0040] In some implementations, during the curing deformation simulation in S3, the slight changes in fiber density due to thermal expansion and contraction are ignored, and only the changes in resin due to curing shrinkage are considered. The volume shrinkage rate of the resin is measured experimentally, and then a fitting formula for the density of the composite material is obtained.

[0041] In some implementations, the density of the composite material is calculated using a mixing ratio formula in S3:

[0042] ρ = ρ f Vf + ρ m (1 - V f (10)

[0043] Where, ρ m ρ represents the density of the resin. f ρ represents fiber density, V represents composite material density. f Indicates the percentage of fiber volume;

[0044] The specific heat capacity of the composite material is calculated using the mixing law:

[0045]

[0046] Among them, C f For the specific heat of the fiber, C m V is the specific heat of the resin. m This represents the volume percentage of the resin.

[0047] The thermal conductivity of the composite material along the fiber direction is obtained from the mixing law:

[0048] K L = K f V f + K m (1 - V f (12)

[0049] The thermal conductivity perpendicular to the fiber direction is calculated using the Springer-Tsai model by the following formula:

[0050]

[0051] In the formula,

[0052] In some implementations, the curing regime of the composite material product in S4 is expressed by vectors l and m:

[0053]

[0054] Where l1, l2, l3 and m1, m2, m3, m4, m5 are the heating and cooling rates and the time nodes used to control the heating, cooling, and heat preservation, respectively, and T is the temperature rise and fall rate and the time node used to control the temperature rise and fall and heat preservation, respectively. amb The ambient temperature.

[0055] In some implementations, the optimized formula for the parameter optimization model of the curing regime described in S4 is as follows:

[0056] find:l,m

[0057]

[0058] st:

[0059] l min ≤l≤l max

[0060] m min ≤l≤m max (9)

[0061] Where l and m are the parameter vectors to be optimized, specifically including heating and cooling rates, heating and cooling durations, holding temperatures, holding durations, pressure, etc.; l min m min Let l be the lower bound of the parameter vector to be optimized. max m max α is the upper bound of the parameter vector to be optimized; AVG (l)| t＝t_end This represents the average degree of curing of the composite material product after the curing process is completed.

[0062] In some embodiments, the composite material includes thermosetting resin-based composite materials and / or thermoplastic resin-based composite materials.

[0063] The method for optimizing the curing process of composite materials provided by this invention has the following beneficial effects:

[0064] This invention utilizes resin thermal experimental data to establish a relatively accurate mathematical model of the resin curing reaction kinetics, which is beneficial to the accuracy of numerical calculations. Starting from resin curing kinetics and Fourier's law of heat conduction, and combining it with finite element numerical analysis, this invention establishes an analysis model of the temperature field and degree of cure field during the composite material curing process, enabling full-time analysis of the temperature field and degree of cure field for composite materials with arbitrarily complex configurations. This invention parameterizes the curing regime and utilizes parameter optimization techniques to optimize existing curing regimes. In particular, for advanced composite material products of different models and types, it can formulate unique and superior curing regimes, improving product quality while avoiding the huge time, manpower, and economic costs associated with large-scale trial-and-error experiments. After obtaining the theoretically optimized solution, this invention, combined with actual experiments, ultimately obtains a practically effective composite material curing regime. Attached Figure Description

[0065] Figure 1 This is a flowchart illustrating the implementation of the optimized method for the curing regime of composite materials according to the present invention.

[0066] Figure 2 This is a schematic diagram of the finite element model of the present invention applied to a certain example (corresponding to S3);

[0067] Figure 3 This is a temperature field distribution diagram of a composite material obtained at a certain moment in a certain example using the present invention;

[0068] Figure 4This is a field distribution diagram of the degree of curing of a composite material at a certain moment, obtained using the present invention in a certain example;

[0069] Figure 5 This is a curve showing the degree of curing and curing speed at a certain point inside the composite material during the curing process obtained in a certain example of the present invention (indicating the changes in curing sufficiency and curing speed over time);

[0070] Figure 6 The present invention uses several different curing temperature curves obtained by parameterizing the temperature in the curing process. Detailed Implementation

[0071] In the description of this invention, it should be noted that the terms "inner" and "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0072] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," "contact," and "communication" should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0073] In this invention, terms such as curing reaction kinetic model, Fourier's law of heat conduction, finite element numerical analysis method, and parameter optimization method are inherent terms known to those skilled in the art and need not be limited in any way.

[0074] like Figure 1-6 As shown, the present invention provides an optimization method for the curing regime of composite materials, which includes the following steps:

[0075] S1: Using a phenomenological model, the resin thermal experimental data are tested using a differential scanning calorimeter (DSC) or differential thermal analyzer (DTA), and the reaction kinetic model is fitted to establish a mathematical model of the resin curing reaction kinetics.

[0076] S2: Based on the aforementioned curing reaction kinetic mathematical model, establish a Fourier transient heat conduction control equation containing the exothermic curing reaction, i.e., containing a nonlinear internal heat source term;

[0077] S3: Establish finite element numerical models of composite material molds and products based on the Fourier transient heat conduction control equations;

[0078] S4: Establish a parameter optimization model for the curing regime based on the finite element numerical model of the composite material mold and product. The optimized parameters include heating and cooling rates, heating and cooling durations, holding temperatures, holding durations, and pressures. The optimization objective is to maximize the average degree of curing of the composite material product after the curing regime is completed.

[0079] S5: Optimize the parameter optimization model of the curing regime to obtain a better curing regime for this type of composite material product, and perform theoretical verification;

[0080] S6: Verify the solidification regime based on the theoretical optimization results through actual experiments, and improve and optimize the solidification regime based on the experimental results to obtain the final solidification regime.

[0081] This invention establishes a relatively accurate mathematical model of the resin curing reaction kinetics by utilizing resin thermal experimental data, which is beneficial to the accuracy of numerical calculations (corresponding to S1). Starting from resin curing kinetics and Fourier's law of heat conduction, and combining it with the finite element numerical analysis method, this invention establishes an analysis model of the temperature field and degree of curing field during the composite material curing process. This enables full-time analysis of the temperature field and degree of curing field for composite materials with arbitrary complex configurations (effectively achieved through the finite element models established in S1-S3). This invention parameterizes the curing regime and utilizes parameter optimization techniques to optimize existing curing regimes. In particular, for advanced composite material products of different models and types, it can formulate unique and superior curing regimes, improving product quality while avoiding the huge time, manpower, and economic costs associated with large-scale trial-and-error experiments (corresponding to S4-S5, proposing an optimization model and effectively achieving optimization based on the finite element model). After obtaining the theoretical optimization solution, this invention, combined with actual experiments, finally obtains a practically effective composite material curing regime, enabling composite materials to achieve better curing results.

[0082] To address the technical problems in the production and manufacturing of composite materials, particularly the inability to effectively improve the curing effect during the curing process, resulting in uneven curing of the produced products, this invention proposes an optimization method for the curing regime of composite materials. Starting from resin curing kinetics and Fourier's law of heat conduction, and combining this with finite element numerical analysis, an analytical model of the temperature field and degree of curing field of the composite material curing process is established. This enables full-time analysis of the temperature field and degree of curing field of composite materials with arbitrary complex configurations. Based on this, parameter optimization techniques can be used to optimize existing curing regimes, improve the degree of curing of composite materials, and achieve better curing results (more complete and uniform curing of the product).

[0083] Reference Figure 6Formulas (14) and (9) describe the entire curing regime through two parameters: vector l and m, namely the heating and cooling rate and the time node used to control the heating and cooling and the heat preservation. Figure 6 These are several sets of different curing temperature profiles under different parameters. The final curing regime is the optimal set of parameters such as l, m, or pressure, i.e., the optimized set of parameters that can fully describe the curing regime (which includes temperature profiles, pressure, and other parameters). Using the curing regime described by these optimized parameters to produce composite material products results in product quality superior to products produced using the initial curing regime. By optimizing the curing regime, the product cures more thoroughly and uniformly.

[0084] In some embodiments, the curing reaction kinetic model in S1 refers to an equation that links reaction time, degree of curing, and exothermic reaction and describes the state of the resin at any time during the curing reaction.

[0085] The Fourier transient heat conduction control equation for the nonlinear internal heat source term in S2 includes a combination of the heat conduction process during the curing process of the composite material, in which heat is transferred from the mold to the interior of the material, and the exothermic reaction process of the resin itself, wherein the exothermic process is not linear.

[0086] The finite element numerical model in S3 includes a structure combining a mold and a composite material product. The mold is located outside the composite material product, and there is heat conduction between the mold and the composite material product. The external environment heats the composite material product by heating the mold.

[0087] The parameter optimization model in S4 includes optimization objectives and optimization parameters. The entire solidification system can be accurately described by a few optimization parameters, and the optimization objective can be optimized by changing the optimization parameters.

[0088] The optimization described in S5 refers to the computational iterative process that makes the optimization objective reach its extreme value. The number of iterations needs to take into account the amount of computation each time, that is, the number of iterations is finite. When the difference of the optimization objective after each iteration is less than or equal to a preset value, the iteration is terminated, and the optimization objective at this time is the final result.

[0089] This invention, whether using DSC or DTA, primarily tests the exothermic data of the resin curing reaction. The curing reaction kinetic model refers to the equation that links reaction time, degree of curing, and exothermic reaction, describing the state of the resin at any moment during the curing reaction. It is an equation that must be established to calculate the degree of curing and the curing rate. The curing process of the resin in this invention is exothermic, and the molding of the composite material requires external heat, i.e., an external temperature. Therefore, the curing process of the composite material is not simply a heat conduction process where external heat is transferred to the interior of the material through the mold; the exothermic reaction of the resin itself must be taken into account, and this exothermic process is not linear. Therefore, it is necessary to establish a Fourier transient heat conduction control equation containing a nonlinear internal heat source term. The finite element model of this invention includes the mold and the composite product, i.e., the mold is on the outside and the product is inside. There is heat conduction between the two materials, meaning that the external temperature heats the mold, and the mold then heats the product. The parameter optimization model of this invention includes optimization objectives and optimization parameters. The entire curing process can be accurately described by a few optimization parameters, and the optimization objective is optimized by changing these parameters. After establishing the S4 optimization model of this invention, the optimal parameters need to be obtained through optimization, that is, the parameters that achieve the extreme value of the optimization objective, which is the better curing process. This optimization refers to the iterative calculation process that makes the optimization objective reach its extreme value. The number of iterations needs to take into account the amount of computation each time; that is, the number of iterations is not infinite. When the difference in the optimization objective is not significant after each iteration, or is less than or equal to a certain decimal, the iteration can be stopped, and the optimization objective at this point is considered the final result.

[0090] S1-S5 of this invention are all for obtaining optimized results through theoretical calculations. S6 is for actual experiments. For example, the same product can be cured using the original curing regime and the optimized curing regime respectively. After curing, the performance of the product is tested and compared.

[0091] In some implementations, the phenomenological model in S1 takes the form of:

[0092] dα / dt = k(T)f(α) (1)

[0093] Where k(T) is a temperature-related parameter, and f(α) is a function related to the degree of curing;

[0094] Based on different forms of f(α), the phenomenological solidification kinetic model includes an n-order reaction kinetic model and an autocatalytic model, wherein the form of the n-order reaction kinetic model is as follows:

[0095] dα / dt = k(T)(1-α) n (2)

[0096]

[0097] Where n is the reaction order; k is the reaction rate in the reaction kinetic model; A is the frequency factor of the reaction kinetic model; ΔE a α is the activation energy of the reaction kinetic model; T is the temperature; t is the time; α is the degree of curing of the resin; R is the universal gas constant.

[0098] The autocatalytic model takes the following form:

[0099]

[0100]

[0101] Where k1 and k2 are the rate constants of the autocatalytic reaction model, A1 and A2 represent the two frequency factors of the model, m1 and n1 represent the reaction order of the autocatalytic model, and ΔE1 and ΔE2 represent the activation energy in the curing reaction process.

[0102] This invention relates to the phenomenological model used in S1, which employs differential scanning calorimetry (DSC) or differential thermal analysis (DTA) to test resin thermal experimental data, fits the reaction kinetic model to the data, and establishes a specific model-building method for the curing reaction kinetics of the resin. This method can accurately obtain the curing reaction kinetics mathematical model of the resin.

[0103] In some embodiments, the Fourier transient heat conduction governing equation for the exothermic curing reaction in S2, in Cartesian coordinates, is as follows:

[0104]

[0105] In the formula, T is the temperature; ρ c C p k ii (i = x, y, z) represent the equivalent density, specific heat, and thermal conductivity of the composite material, respectively; For internal heat source items;

[0106] The above equation can be transformed into the governing equation in any coordinate system through coordinate transformation;

[0107] The expression is:

[0108]

[0109] In the formula, ρ r H represents the density of the resin. uLet denoted as α, representing the total heat released by the resin during the curing reaction; α represents the degree of curing of the resin, indicating the ratio of the heat released at that moment to the total heat released, i.e., the proportion of heat released at time t relative to the total heat released, as shown in the following formula; dα / dt represents the instantaneous curing rate of the resin, i.e., the instantaneous reaction rate.

[0110]

[0111] Where H(t) represents the heat released by the curing reaction at time t.

[0112] This is the specific equation-establishing method and approach of the present invention corresponding to the mathematical model of curing reaction kinetics in S2, which establishes the Fourier transient heat conduction control equation containing the exothermic curing reaction, i.e., containing a nonlinear internal heat source term. This method can accurately obtain the Fourier transient heat conduction control equation for the exothermic curing reaction. In formula (6) The term "internal heat source" is the governing term in the Fourier transient heat conduction equation. Equation (6) does not expand the internal heat source term because the internal heat source in this invention is the exothermic reaction of the resin curing reaction. Therefore, Equation (6)... That is, the internal heat source term can be expressed by formula (7), where ρ in formula (7) r (1-V f )H u These are parameters that are easy to obtain, and It is the expression of formula (2) or formula (4), that is, the reaction kinetic model established in S1.

[0113] Furthermore, solving the Fourier transient heat conduction control equation in S2 requires thermal boundary conditions, which, when applied to finite element numerical calculations, means that reasonable thermal boundary conditions need to be set in the finite element numerical model in S3.

[0114] In some implementations, in step S3, a geometric analysis model is first established for composite material products of different configurations and types. To facilitate finite element calculations, the initial finite element model is then simplified. After the geometric model is established, different material properties and thermal conductivity parameters at the interface are set for the mold and the product. Subsequently, the geometric model is meshed, and the mesh must simultaneously meet the requirements of computational accuracy and computational cost. The finite element numerical model of the composite material mold and product described in step S3 of this invention includes the geometric model, material properties, boundary conditions, load conditions, and finite element mesh model of the mold and product. Step S3 mainly focuses on establishing the finite element model, which relies on the finite element method. This method is a mature approach. Therefore, in this step, the finite element model is established using this method based on the actual situation (geometric model, material properties, boundary conditions, load conditions, and finite element mesh model).

[0115] In some implementations, during the curing deformation simulation in S3, the slight changes in fiber density due to thermal expansion and contraction are ignored, and only the changes in resin due to curing shrinkage are considered. The volume shrinkage rate of the resin is measured experimentally, and then the fitting formula for the resin density is obtained.

[0116] S3 of the present invention: Establishing a finite element numerical model of composite material molds and products.

[0117] In this step, a geometric analysis model needs to be established for composite material products with different configurations and types. To facilitate finite element calculations, the initial finite element model needs to be simplified. After the geometric model is established, different material properties and thermal conductivity parameters at the interfaces need to be set for parts such as molds and products. Subsequently, the geometric model needs to be meshed, and the mesh must meet both the requirements for computational accuracy and computational cost.

[0118] The density of composite materials changes during the curing process. Due to the chemical shrinkage of the resin matrix during curing, the density gradually increases, and the density of the fibers undergoes slight changes due to thermal expansion and contraction. In the curing deformation simulation, the slight changes in fiber density due to thermal expansion and contraction are ignored, and only the changes caused by resin shrinkage during curing are considered.

[0119] The volume shrinkage rate of the resin can be measured experimentally, and then a fitting formula for the resin density can be obtained.

[0120] Ignoring the thermal expansion effect of the fibers, i.e., ignoring the change in fiber density throughout the curing process, the density of the composite material can then be calculated using the mixing ratio formula:

[0121] ρ = ρ f V f + ρ m (1 - V f (10).

[0122] In some implementations, the density of the composite material is calculated using a mixing ratio formula in S3:

[0123] ρ=ρ f V f +ρ m (1-V f (10)

[0124] Where, ρ m ρ represents the density of the resin. f ρ represents fiber density, V represents composite material density. f Indicates the percentage of fiber volume;

[0125] The specific heat capacity of the composite material is calculated using the mixing law:

[0126]

[0127] Among them, C f For the specific heat of the fiber, C m V is the specific heat of the resin. m This represents the volume percentage of the resin.

[0128] The thermal conductivity of the composite material along the fiber direction is obtained from the mixing law:

[0129] K L =K f V f +K m (1-V f (12)

[0130] The thermal conductivity perpendicular to the fiber direction is calculated using the Springer-Tsai model by the following formula:

[0131]

[0132] In the formula,

[0133] Formula (10) of this invention is a calculation formula after density mixing. Formulas (10) to (13) are all mixed calculation formulas for material properties. They include the calculation of the density, specific heat, and thermal conductivity of the composite material. Since the composite material in this invention refers to fiber-reinforced resin-based composite material, the composite material contains resin and fiber. The overall density, specific heat, thermal conductivity, and other parameters of the material need to be calculated by mixing the properties of both. Density, specific heat, and thermal conductivity are material properties of composite materials and are necessary for establishing the finite element calculation model in S3. With these parameters, the Fourier heat conduction formula of formula (6) can be solved.

[0134] In some implementations, the curing regime of the composite material product in S4 is expressed by vectors l and m:

[0135]

[0136] Where l1, l2, l3 and m1, m2, m3, m4, m5 are the heating and cooling rates and the time nodes used to control the heating, cooling, and heat preservation, respectively, and T is the temperature rise and fall rate and the time node used to control the temperature rise and fall and heat preservation, respectively. amb The ambient temperature.

[0137] Formula (14) of this invention describes the curing regime through vectors l and m. After plotting formula (14) as a graph, it is as follows: Figure 6 Different l and m parameters correspond to different curves, i.e. different curing regimes.

[0138] In some implementations, the optimized formula for the parameter optimization model of the curing regime described in S4 is as follows:

[0139] find:l,m

[0140]

[0141] st:

[0142] l min ≤l≤l max

[0143] m min ≤l≤m max (9)

[0144] Where l and m are the parameter vectors to be optimized, specifically including heating and cooling rates, heating and cooling durations, holding temperatures, holding durations, pressure, etc.; l min m min Let l be the lower bound of the parameter vector to be optimized. max m max α is the upper bound of the parameter vector to be optimized; AVG (l)| t＝t_end This represents the average degree of curing of the composite material product after the curing process is completed.

[0145] Formula (9) of the present invention is an optimized formula, that is, under certain constraints, by changing the parameters l and m, the optimization objective is made to obtain the optimal value, that is, the average curing degree of the composite material product is maximized.

[0146] S5 of the present invention: Through optimization, a better curing regime for this type of composite material product is finally obtained, and theoretical verification is performed.

[0147] S6: Verify the solidification regime of the theoretical optimization results through actual experiments, and further improve and optimize the solidification regime based on the experimental results to obtain the final solidification regime.

[0148] Formulas (1)-(5) of this invention are specific methods for establishing the model in S1; formula (6) substitutes the equations in S1 into S2, and formula (7) is a conversion of formula (6). Expanding, formula (7) is substituted into formula (6), and formula (8) is the integral of formula (2) or (4) over time.

[0149] S3 is solved by substituting the equation into the specific product (formulas (10)-(13) are all formulas used to calculate material parameters in the finite element model of S3); S4 is built on the basis of S3, and the final optimization process is achieved through formula (9); formula (14) in S4 is a formula describing the curing regime of composite materials ( Figure 6(Black solid line in the middle), Formula (9) describes the optimized model (finding suitable l and m to maximize the optimization objective α (degree of curing), where l and m are the parameterized curing regimes in Formula (14).

[0150] In some embodiments, the composite material includes thermosetting resin-based composite materials and / or thermoplastic resin-based composite materials.

[0151] This invention offers four key advantages: First, by utilizing resin thermal experimental data, it establishes a relatively accurate mathematical model of the resin curing reaction kinetics, improving the accuracy of numerical calculations. Second, starting from resin curing kinetics and Fourier's law of heat conduction, and combining it with finite element numerical analysis, this invention establishes an analysis model of the temperature field and degree of curing field during the composite material curing process, enabling full-time analysis of the temperature field and degree of curing field for composite materials with arbitrary complex configurations. Third, by parameterizing the curing regime and utilizing parameter optimization techniques, this invention can optimize existing curing regimes, particularly for advanced composite material products of different models and types, allowing for the development of unique and superior curing regimes, improving product quality while avoiding the enormous time, manpower, and economic costs associated with large-scale trial-and-error experiments. Fourth, after obtaining the theoretically optimized solution, this invention, combined with actual experiments, ultimately yields a practically effective composite material curing regime.

[0152] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention. The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the protection scope of the present invention.

Claims

1. An optimization method for the curing regime of composite materials, characterized in that: Includes the following steps: S1: Using a phenomenological model, the resin thermal experimental data are tested using a differential scanning calorimeter or differential thermal analyzer. The reaction kinetics model is fitted with the data to establish a mathematical model of the resin curing reaction kinetics. S2: Based on the aforementioned curing reaction kinetic mathematical model, establish a Fourier transient heat conduction control equation containing the exothermic curing reaction, i.e., containing a nonlinear internal heat source term; S3: Establish a finite element numerical model of the composite material mold and product based on the Fourier transient heat conduction control equation; the finite element numerical model in S3 includes a structure combining the mold and the composite material product, the mold is located outside the composite material product, there is heat conduction between the mold and the composite material product, and the outside heats the composite material product by heating the mold; S4: Establish a parameter optimization model for the curing regime based on the finite element numerical model of the composite material mold and product. The optimized parameters include heating and cooling rates, heating and cooling durations, holding temperatures, holding durations, and pressures. The optimization objective is to maximize the average degree of curing of the composite material product after the curing regime is completed. S5: Optimize the parameter optimization model of the curing regime to obtain a better curing regime for a specific type of composite material product, and perform theoretical verification; S6: Verify the solidification regime of the theoretical optimization results through actual experiments, and improve and optimize the solidification regime based on the experimental results to obtain the final solidification regime; The parameter optimization model in S4 includes optimization objectives and optimization parameters. The entire solidification system can be accurately described by a few optimization parameters, and the optimization objective can be optimized by changing the optimization parameters. Vector for curing regime of composite material products in S4 l , m Express: （14） in, l 1. l 2. l 3 and m 1. m 2. m 3. m 4. m 5 represents the heating and cooling rates and the time points used to control heating, cooling, and heat preservation, respectively. T amb The ambient temperature; The optimized formula for the parameter optimization model of the curing regime described in S4 is as follows: （9） in, l , m The parameter vector to be optimized includes heating and cooling rates, heating and cooling durations, holding temperature, holding duration, and pressure. l min , m min Let be the lower bound of the parameter vector to be optimized. l max , m max This represents the upper limit of the parameter vector to be optimized; α AVG ( l )| t=t_end This represents the average degree of curing of the composite material product after the curing process is completed.

2. The method for optimizing the curing regime of composite materials according to claim 1, characterized in that: The curing reaction kinetic model described in S1 refers to the equation that links reaction time, degree of curing, and exothermic reaction, and is used to describe the state of the resin at any time during the curing reaction. The Fourier transient heat conduction control equation for the nonlinear internal heat source term in S2 includes a combination of the heat conduction process during the curing process of the composite material, in which heat is transferred from the mold to the interior of the material, and the exothermic reaction process of the resin itself, wherein the exothermic process is not linear. The optimization described in S5 refers to the computational iterative process that makes the optimization objective reach its extreme value. The number of iterations needs to take into account the amount of computation each time, that is, the number of iterations is finite. When the difference of the optimization objective after each iteration is less than or equal to a preset value, the iteration is terminated, and the optimization objective at this time is the final result.

3. The method for optimizing the curing regime of composite materials according to claim 1, characterized in that: The phenomenological model in S1 takes the form of: （1） in, For parameters related to temperature, It is a function related to the degree of cure; According to different forms Phenomenological solidification dynamics model includes n First-order reaction kinetics model and autocatalytic model, among which n The form of the first-order reaction kinetic model is: （2） （3） in, n The reaction order is [number]. k The reaction rate is the reaction rate in the reaction kinetic model. A For the frequency factor of the reaction kinetic model; The activation energy is the reaction kinetic model value; T is the temperature, and t is the time. R represents the degree of curing of the resin; R is the universal gas constant. The autocatalytic model takes the following form: （4） ( i = 1,2) （5） in, and The rate constant for the autocatalytic reaction model is... and This represents the two frequency factors of the model. and This indicates the reaction order in the autocatalytic model. and This represents the activation energy during the curing reaction process.

4. The method for optimizing the curing regime of a composite material according to claim 1, characterized in that: The Fourier transient heat conduction governing equation for the exothermic curing reaction in S2, in Cartesian coordinates, is as follows: （6） In the formula, T For temperature; , , ( i = x, y, z ) are the equivalent density, specific heat, and thermal conductivity of the composite material, respectively; For internal heat source items; The above equation can be transformed into the governing equation in any coordinate system through coordinate transformation; The expression is: （7） In the formula, The density of the resin; This represents the total heat released by the resin during the curing reaction. Let be the degree of curing of the resin, and represent the ratio of the heat released at time t to the total heat released, which indicates the degree of curing of the resin. t The proportion of heat released at any given moment relative to the total heat released is given by the following formula; This refers to the instantaneous curing rate of the resin, which is also the instantaneous reaction rate. （8） in, for t The heat released during the curing reaction.

5. The method for optimizing the curing regime of composite materials according to claim 1, characterized in that: In S3, a geometric analysis model is first established for composite material products with different configurations and types. To facilitate finite element calculations, the initial finite element model is then simplified. After the geometric model is established, different material properties and thermal conductivity parameters at the interface are set for the mold and the product. Subsequently, the geometric model is meshed, and the mesh must meet both the calculation accuracy requirements and the calculation cost requirements.

6. The method for optimizing the curing regime of composite materials according to claim 5, characterized in that: In the S3 simulation of curing deformation, the slight changes in fiber density due to thermal expansion and contraction are ignored. Only the changes in resin due to curing shrinkage are considered. The volume shrinkage rate of the resin is measured experimentally, and then the fitting formula for the density of the composite material is obtained.

7. The method for optimizing the curing regime of composite materials according to claim 6, characterized in that: The density of the composite material is calculated using the mixing ratio formula in S3: （10） in, Indicates resin density, Indicates fiber density, Indicates the density of composite materials. Indicates the percentage of fiber volume; The specific heat capacity of the composite material is calculated using the mixing law: （11） in, For the specific heat of the fiber, For the specific heat of the resin, This represents the volume percentage of the resin. The thermal conductivity of the composite material along the fiber direction is obtained from the mixing law: （12） The thermal conductivity perpendicular to the fiber direction is calculated using the Springer-Tsai model by the following formula: （13） In the formula, .

8. The method for optimizing the curing regime of the composite material as described in any one of claims 1-7, characterized in that: The composite material includes thermosetting resin-based composite materials and / or thermoplastic resin-based composite materials.

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