A method for optimizing the winding or layup angle of composite material curing deformation

Abstract

This invention provides a method for optimizing the winding or layup angle of composite material curing deformation, comprising the following steps: S1: establishing a mathematical model of the resin curing reaction kinetics; S2: establishing a Fourier transient heat conduction control equation containing the exothermic curing reaction; S3: establishing a finite element analysis model of the temperature field, degree of cure field, and curing deformation of the composite material curing process; S4: establishing a parameter optimization model for the winding or layup angle; S5: optimizing the parameter optimization model for the winding or layup angle to obtain a better winding or layup angle for a specific type of composite material product; S6: verifying the final winding or layup angle through actual experiments. According to this invention, this method can be applied to composite materials with different structures, sizes, and models of multi-layer multi-directional fiber winding or multi-layer layup to control the curing deformation of the product, 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 a method for optimizing the winding or layup angle of composite material curing deformation. Background Technology

[0002] Resin-based fiber-reinforced composite materials have been widely used in advanced manufacturing fields such as aerospace, automotive, military, and shipbuilding due to their advantages, including lightweight, high strength, good designability, high temperature resistance, fatigue resistance, corrosion resistance, and ease of integral molding. The curing stage in the composite material production process is one of the most critical steps affecting product quality.

[0003] During the heating, curing, and cooling processes, complex temperature and curing gradients are formed within the composite material due to factors such as the thermal expansion and contraction of the material, the chemical shrinkage of the resin matrix, and the mismatch in thermal expansion coefficients between the composite material and the mold material. To coordinate deformation, thermal stress and chemical shrinkage stress are generated within the composite material. After curing, some of the stress is released, while the rest remains in the composite material as residual stress, ultimately leading to deformation of the component after demolding, commonly referred to as the curing deformation of the composite material.

[0004] Curing deformation has a highly detrimental effect on the performance of composite components. The development of internal stress during curing can cause matrix cracking, delamination, warping, and springback deformation in composite components. Curing deformation affects the shape and dimensional accuracy of components, impacting joint fit and post-molding mechanical properties. Especially for large and complex components, curing deformation generates assembly stress, reducing the structural strength and fatigue life of the composite material, and may even directly lead to component failure.

[0005] Controlling the curing deformation of composite components is one of the key technologies in the overall structural design and molding of composite materials. Traditional methods to reduce curing deformation involve repeatedly adjusting the curing process or compensating for the deformation by machining the mold surface based on experience and process test results. However, this method is time-consuming and labor-intensive, especially for large and complex components, where mold machining and modification require significant time and materials, resulting in high costs and low efficiency.

[0006] Existing methods for reducing curing deformation of composite materials rely on experience and experimental results, involving repeated adjustments to the curing process or compensatory machining of the mold surface to offset the adverse effects of curing deformation. However, this method is time-consuming and labor-intensive, especially for large and complex components, where mold machining and modification require significant time and materials, resulting in high costs and low efficiency. Therefore, this invention researches and designs a method for optimizing the winding or layup angle of composite material curing deformation. Summary of the Invention

[0007] Therefore, the technical problem to be solved by the present invention is to overcome the shortcomings of existing methods for reducing the curing deformation of composite materials, which are time-consuming and labor-intensive, especially for large and complex components, where mold processing and correction require a lot of time and materials, resulting in high cost and low efficiency. The present invention provides a method for optimizing the winding or layup angle of composite material curing deformation.

[0008] To address the above problems, this invention provides a method for optimizing the winding or layup angle of composite material curing deformation, comprising the following steps:

[0009] 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.

[0010] 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;

[0011] S3: Based on the Fourier transient heat conduction control equation, and combined with composite material mechanics, establish a finite element analysis model of the temperature field, degree of curing field, and curing deformation of the composite material curing process;

[0012] S4: Based on the established finite element analysis model, establish a parameter optimization model for the winding or layup angle. The optimized parameter is the angle of the fiber for each layer of winding or layup. The optimization objective is to minimize the curing deformation at a certain point in the composite product or to minimize the average curing deformation in a certain area of ​​the product.

[0013] S5: Optimize the parameter optimization model of the winding or layup angle to obtain a better winding or layup angle for a specific type of composite material product, and perform theoretical verification.

[0014] S6: Verify the winding or layup angle of the theoretical optimization results through actual experiments, and improve and optimize it based on the experimental results to obtain the final winding or layup angle.

[0015] 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.

[0016] The Fourier transient heat conduction control equation for the nonlinear internal heat source term in S2 includes the combination of the heat conduction process from the outside to the inside of the material through the mold during the curing process of the composite material and the exothermic reaction process of the resin itself, and the exothermic process is not linear.

[0017] The parameter optimization model in S4 includes an optimization objective and optimization parameters. The optimization parameters are the fiber angles of each layer of winding or laying. By changing the optimization parameters, the optimization objective can be optimized to the maximum.

[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, and let α be the degree of curing of the resin, representing the ratio of the heat released at time t 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 is 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, 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.

[0040] S3 considers the curing deformation of composite products, i.e., the mechanical behavior of the products, and requires the establishment of a constitutive equation for composite materials that takes into account temperature and degree of curing:

[0041]

[0042] Where σ ij ε represents the stress component of the composite material; kl This represents the total strain of the composite material; Q represents the chemical shrinkage strain of a material; ijkl This represents the stiffness coefficient of the material.

[0043] In some implementations, the performance parameters of the unidirectional composite material in S3 are expressed by a combination of resin and fiber properties and calculated using the following model:

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051]

[0052]

[0053] In the formula, E, G, and ν represent the elastic modulus, shear modulus, and Poisson's ratio, respectively. The subscripts m and f represent the resin and fiber, respectively. The subscripts 1, 2, and 3 represent the direction, where 1 is parallel to the fiber direction.

[0054] In some embodiments, S3 may also employ a homogenization method to calculate the mechanical and thermal properties of the composite material; and / or, in S3, the change in the elastic modulus of the fiber during the curing reaction is ignored, while the change in the elastic modulus of the resin during the curing reaction is fitted using empirical formulas before and after the degree of curing and the gel point.

[0055] In some embodiments, the density of the composite material in S3 changes as the curing reaction proceeds. The volume shrinkage rate of the resin is experimentally measured, and a fitting formula for the resin density is obtained. The thermal expansion effect of the fiber is ignored, that is, the change in fiber density during the entire curing process is ignored. Then, the density of the composite material is calculated using the mixing ratio formula.

[0056] The density of the composite material is calculated using the mixing ratio formula in S3:

[0057] ρ=ρ f V f +ρ m (1-V f (19)

[0058] 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;

[0059] The specific heat capacity of the composite material in S3 is calculated using the mixing law:

[0060]

[0061] 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.

[0062] The thermal conductivity of the composite material along the fiber direction is obtained from the mixing law:

[0063] K L =K f V f +K m (1-V f ) (twenty one)

[0064] The thermal conductivity perpendicular to the fiber direction is calculated using the Springer-Tsai model by the following formula:

[0065]

[0066] In the formula,

[0067] In some embodiments, the coefficients of thermal expansion of the unidirectional composite material used in S3 along the fiber direction and perpendicular to the fiber direction are:

[0068]

[0069] α2=(α 2f +ν 12 α 1f V f +(α m +ν m α m (1-V) f )-[ν 12f V f +ν m (1-V f )]·α1 (24)

[0070] α2=α3 (25)

[0071] In the formula, α 1f α is the coefficient of thermal expansion of the fiber parallel to the fiber direction. 2f E is the coefficient of thermal expansion perpendicular to the fiber direction. 1f E represents the elastic modulus of the fiber parallel to its direction. m Indicates the elastic modulus of the resin, ν m Indicates the Poisson's ratio of the resin, ν 12f V represents the Poisson's ratio of the fiber 12 plane. f This indicates the fiber volume fraction.

[0072] In some implementations, the parameter optimization model in S4 is formulated as follows:

[0073] find:l

[0074]

[0075]

[0076]

[0077] l min ≤l≤l max (26)

[0078] Where l is the parameter vector to be optimized, representing the vector composed of the fiber angles of each layer of winding or laying; u AVG (l) represents the optimization objective, indicating the mean displacement of a certain region related to the optimization parameters; the first two equations of the optimization constraints are the Fourier heat conduction equation containing a chemical exothermic term and the mechanical constitutive equation including the effects of temperature and degree of curing, respectively; min , l max These are the lower and upper bounds of the parameter vector to be optimized, respectively.

[0079] The method for optimizing the winding or layup angle of composite material curing deformation provided by this invention has the following beneficial effects:

[0080] This invention offers five 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, based on resin curing kinetics and Fourier's law of heat conduction, this invention, combined with composite material mechanics and finite element numerical analysis, establishes analytical models for the temperature field, degree of cure field, and curing deformation during the curing process of composite materials with multi-layer multi-directional fiber winding or multi-layer layup. This enables full-time analysis of these parameters. Third, by parameterizing the winding or layup angle and utilizing parameter optimization techniques, this invention effectively controls the curing deformation of composite material products through optimization of the winding or layup angle. Fourth, this method is applicable to control the curing deformation of multi-layer multi-directional fiber winding or multi-layer layup composite materials of different structures, sizes, and models, demonstrating good applicability. Fifth, compared to traditional process improvement methods that rely solely on experience and extensive experimentation, this method combines theoretical calculations with experiments, improving product quality while avoiding the significant time, manpower, and economic costs associated with large-scale trial-and-error experiments. Attached Figure Description

[0081] Figure 1 This is a flowchart illustrating the implementation of the optimized method for curing deformation of composite materials according to the present invention.

[0082] Figure 2 This is a schematic diagram of the geometric model of the present invention applied to a certain example;

[0083] Figure 3 This is a schematic diagram of a finite element mesh model applied to a specific example of the present invention;

[0084] Figure 4 This is a schematic diagram of a local coordinate system used in a certain example of the present invention; (the spatial rectangular Cartesian coordinate system is not applicable. For products such as irregular curved surfaces, a local coordinate system needs to be established. The arrows in the figure indicate multiple different coordinate systems established at multiple different locations).

[0085] Figure 5 This is a schematic diagram of the layup angle of a multilayer composite material; (the diagonal lines in the diagram indicate the direction of the fibers. By changing the layup angle, the amount of curing deformation can be reduced).

[0086] Figure 6 This is a schematic diagram of a multilayer layup of the present invention in a certain example (meaning that after the composite material is laid up in multiple layers, different gray levels represent different winding or layup angles). Detailed Implementation

[0087] 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.

[0088] 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.

[0089] 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.

[0090] like Figure 1-6 As shown, this invention provides a method for optimizing the winding or layup angle of composite material curing deformation (winding or layup angle refers to the winding angle or layup angle), which includes the following steps:

[0091] 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.

[0092] 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;

[0093] S3: Based on the previous two steps, according to the Fourier transient heat conduction control equation, and combined with composite material mechanics, establish a finite element analysis model of the temperature field, degree of curing field and curing deformation of the composite material curing process;

[0094] S4: Based on the established finite element analysis model, establish a parameter optimization model for the winding or layup angle. The optimized parameter is the angle of the fiber for each layer of winding or layup. The optimization objective is to minimize the curing deformation at a certain point in the composite product or to minimize the average curing deformation in a certain area of ​​the product.

[0095] S5: Optimize the parameter optimization model of the winding or layup angle to obtain a better winding or layup angle for a specific type of composite material product, and perform theoretical verification.

[0096] S6: Verify the winding or layup angle of the theoretical optimization results through actual experiments, and improve and optimize it based on the experimental results to obtain the final winding or layup angle.

[0097] This invention has the following five beneficial effects: First, by utilizing resin thermal experimental data, a relatively accurate mathematical model of the resin curing reaction kinetics can be established, which is beneficial to the accuracy of numerical calculations (corresponding to S1). Second, based on resin curing kinetics and Fourier's law of heat conduction, this invention, for composite material products with multi-layer multi-directional fiber winding or multi-layer layup, combines composite material mechanics and finite element numerical analysis methods to establish analytical models of the temperature field, degree of cure field, and curing deformation during the composite material curing process. This achieves full-time analysis of the temperature field, degree of cure field, and curing deformation of composite material products with multi-layer multi-directional fiber winding or multi-layer layup (established through S1-S3). (Effective implementation of finite element model); This invention parameterizes the winding or layup angle and utilizes parameter optimization technology to effectively control the curing deformation of composite material products through the optimization of multi-layer winding or layup angles (corresponding to S5); This method can be applied to control the curing deformation of composite materials with different structures, sizes, and models of multi-layer multi-directional fiber winding or multi-layer layup, and has good applicability (corresponding to S4-S5); Compared with traditional process improvement methods that rely solely on experience and a large number of experiments, this method combines theoretical calculation results with experiments, improving product quality while avoiding the huge time, manpower, and economic costs brought about by large-scale trial and error experiments.

[0098] The existing methods for reducing curing deformation of composite materials rely on experience and experimental results, involving repeated adjustments to the curing process or compensatory machining of the mold surface to offset the adverse effects of curing deformation. However, this method is time-consuming and labor-intensive, especially for large and complex components, where mold machining and correction require significant time and materials, resulting in high costs and low efficiency. This invention proposes a method for optimizing the winding or layup angle of composite material curing deformation. Based on resin curing kinetics and Fourier's law of heat conduction, and considering multi-layer multi-directional fiber winding or multi-layer layup composite material products, this invention combines composite mechanics and finite element numerical analysis to establish analytical models of the temperature field, degree of cure field, and curing deformation during the composite material curing process. This enables full-time analysis of the temperature field, degree of cure field, and curing deformation of multi-layer multi-directional fiber winding or multi-layer layup composite material products. Furthermore, by utilizing parameter optimization techniques, curing deformation can be effectively controlled through optimization of the winding or layup angle, effectively improving product yield and avoiding the need for repeated adjustments or compensatory machining of the mold surface due to curing deformation. This significantly reduces time and materials, lowers costs, and improves the efficiency of the curing process.

[0099] This invention is mainly aimed at composite material products with multi-layer multi-directional fiber winding or multi-layer layup. By optimizing the winding or layup angle, the curing deformation of composite material components can be effectively controlled. Controlling the curing deformation of composite material components is a key technology for the overall structural design and molding of composite materials.

[0100] In existing composite material molding processes, firstly, curing deformation occurs gradually during the curing process, and secondly, this curing deformation cannot be eliminated. This invention, targeting composite materials produced by winding or layup, effectively controls curing deformation by varying the winding or layup angle, thereby significantly improving product yield. For example... Figure 2 In medium-sized structures, some areas may warp after the structure is formed. By changing or optimizing the winding or layup angle, this deformation can be reduced and brought within the allowable range of quality requirements.

[0101] In some embodiments, the curing reaction kinetic model in S1 links reaction time, degree of curing, and exothermic reaction, and is an equation used to describe the state of the resin at any time during the curing reaction.

[0102] The Fourier transient heat conduction control equation for the nonlinear internal heat source term in S2 includes the combination of the heat conduction process from the outside to the inside of the material through the mold during the curing process of the composite material and the exothermic reaction process of the resin itself, and the exothermic process is not linear.

[0103] The parameter optimization model in S4 includes an optimization objective and optimization parameters. The optimization parameters are the fiber angles of each layer of winding or laying. By changing the optimization parameters, the optimization objective can be optimized to the maximum.

[0104] 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.

[0105] This invention, whether using DSC or DTA, primarily tests the exothermic data of the resin curing reaction. The curing reaction kinetic model links reaction time, degree of curing, and exothermic reaction, and is an equation used to describe 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 material through the mold; the exothermic reaction of the resin itself must be taken into account. Moreover, this exothermic process is not linear, so a Fourier transient heat conduction control equation containing a nonlinear internal heat source term must be established. The finite element model of this invention is capable of analyzing the temperature field, degree of curing field, and curing deformation. The parameter optimization model of this invention includes an optimization objective and optimization parameters. The optimization parameters are typically the fiber angles of each layer of winding or layup. The optimization objective is optimized by varying these parameters. After the S4 optimization model is established, the optimal parameters are obtained through S5 optimization, which are the parameters that achieve the extreme value of the optimization objective, i.e., a better method for controlling curing deformation (better winding or layup angles). This S5 optimization refers to the iterative calculation process that brings the optimization objective to its extreme value. The number of iterations needs to consider the computational load of each iteration; 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.

[0106] The equation of S3 of this invention is substituted into the specific product to solve (formulas (19)-(22) are the formulas used to calculate material parameters in the finite element model of S3); S4 is built on the basis of S3. This invention not only solves the temperature field and the curing degree field, but also solves the curing deformation (mechanical problem). The final optimization process is achieved through formula (9). Formula (9) solves the mechanical behavior (constitutive equation). Formulas (10)-(18) are used to describe the material properties related to the mechanics of composite materials. Formulas (23)-(25) are thermodynamic equations. Formula (26) describes the optimization model (find a suitable l to minimize the optimization target u (displacement, i.e., curing deformation) to minimize curing deformation to the greatest extent; l is the parameter vector to be optimized in formula (26).

[0107] 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 deformation method and the optimized curing deformation method, respectively. After curing, the performance of the product is tested and compared.

[0108] In some implementations, the phenomenological model in S1 takes the form of:

[0109] dα / dt = k(T)f(α) (1)

[0110] Where k(T) is a temperature-related parameter, and f(α) is a function related to the degree of curing;

[0111] 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:

[0112] dα / dt = k(T)(1-α) n (2)

[0113]

[0114] 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.

[0115] The autocatalytic model takes the following form:

[0116]

[0117]

[0118] 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.

[0119] 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.

[0120] In some embodiments, the Fourier transient heat conduction governing equation for the exothermic curing reaction in S2, in Cartesian coordinates, is as follows:

[0121]

[0122] 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;

[0123] The above equation can be transformed into the governing equation in any coordinate system through coordinate transformation;

[0124] The expression is:

[0125]

[0126] 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.

[0127]

[0128] Where H(t) represents the heat released by the curing reaction at time t.

[0129] 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.

[0130] 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 analysis model in S3.

[0131] In some embodiments, 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 simultaneously meet the requirements for computational accuracy and computational cost. In S3 of this invention, the curing deformation of the composite material product, i.e., the mechanical behavior of the product, needs to be considered, requiring the establishment of a constitutive equation for the composite material that considers temperature and degree of curing.

[0132]

[0133] Where σ ij ε represents the stress component of the composite material; kl This represents the total strain of the composite material; Q represents the chemical shrinkage strain of a material; ijkl This represents the stiffness coefficient of the material.

[0134] Formula (9) of this invention describes the mechanical behavior of the composite material, that is, the constitutive equation required to calculate the mechanical behavior. Formulas (1)-(5) describe the equations related to the curing reaction kinetics, and formulas (6)-(8) describe the Fourier transient heat conduction equations containing the exothermic curing reaction. In this process, heat will cause thermal strain, that is, heat will cause mechanical deformation of the material.

[0135] S3 of this invention is based on the Fourier transient heat conduction control equation and combined with composite material mechanics to establish a finite element analysis model of the temperature field, curing degree field and curing deformation of the composite material curing process. The equation is substituted into the specific product to solve (formulas (19)-(22) are the formulas used to calculate material parameters in the finite element model in S3); S4 is established on the basis of S3. This invention not only needs to solve the temperature field and curing degree field, but also needs to solve the curing deformation (mechanical problem). The final optimization process is achieved through formula (26). Formula (9) solves the mechanical behavior (constitutive equation), formulas (10)-(18) are to describe the material properties related to composite material mechanics, formulas (20)-(25) are thermodynamic equations; formula (26) describes the optimized model (finding a suitable l to minimize the optimization target u (displacement, i.e., curing deformation) to minimize curing deformation to the greatest extent; l is the parameter vector to be optimized in formula (26).

[0136] In some implementations, the performance parameters of the unidirectional composite material in S3 are expressed by a combination of resin and fiber properties and calculated using the following model:

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146] In the formula, E, G, and ν represent the elastic modulus, shear modulus, and Poisson's ratio, respectively. The subscripts m and f represent the resin and fiber, respectively. The subscripts 1, 2, and 3 represent the direction, where 1 is parallel to the fiber direction.

[0147] In some embodiments, S3 may also employ a homogenization method to calculate the mechanical and thermal properties of the composite material; and / or, in S3, the change in the elastic modulus of the fiber during the curing reaction is ignored, while the change in the elastic modulus of the resin during the curing reaction is fitted using empirical formulas before and after the degree of curing and the gel point.

[0148] In some embodiments, the density of the composite material in S3 changes as the curing reaction proceeds. The volume shrinkage rate of the resin is experimentally measured, and a fitting formula for the resin density is obtained. The thermal expansion effect of the fiber is ignored, that is, the change in fiber density during the entire curing process is ignored. Then, the density of the composite material is calculated using the mixing ratio formula.

[0149] The density of the composite material is calculated using the mixing ratio formula in S3:

[0150] ρ=ρ f V f +ρ m (1-V f (19)

[0151] 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;

[0152] The specific heat capacity of the composite material in S3 is calculated using the mixing law:

[0153]

[0154] 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.

[0155] The thermal conductivity of the composite material along the fiber direction is obtained from the mixing law:

[0156] K L =K f V f +K m (1-V f ) (twenty one)

[0157] The thermal conductivity perpendicular to the fiber direction is calculated using the Springer-Tsai model by the following formula:

[0158]

[0159] In the formula,

[0160] Formula (19) of this invention is a calculation formula after density mixing. Formulas (19) to (22) 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.

[0161] In some embodiments, the coefficients of thermal expansion of the unidirectional composite material used in S3 along the fiber direction and perpendicular to the fiber direction are:

[0162]

[0163] α2=(α 2f +ν 12 α 1f V f +(α m +ν m α m (1-V) f )-[ν 12f V f +ν m (1-V f )]·α1(24)

[0164] α2 = α3 (25)

[0165] In the formula, α1f α is the coefficient of thermal expansion of the fiber parallel to the fiber direction. 2f E is the coefficient of thermal expansion perpendicular to the fiber direction. 1f E represents the elastic modulus of the fiber parallel to its direction. m Indicates the elastic modulus of the resin, ν m Indicates the Poisson's ratio of the resin, ν 12f V represents the Poisson's ratio of the fiber 12 plane. f This indicates the fiber volume fraction.

[0166] The coefficient of thermal expansion of the resin in this invention is constant in all directions, but the fibers inside the component are different in the longitudinal and longitudinal directions. The coefficient of thermal expansion of the fibers is determined by the coefficients of thermal expansion of both the resin and the fibers. Therefore, the coefficients of thermal expansion of the composite material are also different in the two directions. The coefficients of thermal expansion of the unidirectional composite material used in this study are more complex along the fiber direction and perpendicular to the fiber direction. Therefore, formulas (23)-(25) are used to solve for the coefficient of thermal expansion.

[0167] In some implementations, the parameter optimization model in S4 is formulated as follows:

[0168] find:l

[0169]

[0170]

[0171]

[0172] l min ≤l≤l max (26)

[0173] Where l is the parameter vector to be optimized, representing the vector composed of the fiber angles of each layer of winding or laying; u AVG (l) represents the optimization objective, indicating the mean displacement of a certain region related to the optimization parameters; the first two equations of the optimization constraints are the Fourier heat conduction equation containing a chemical exothermic term and the mechanical constitutive equation including the effects of temperature and degree of curing, respectively; min , l max These are the lower and upper bounds of the parameter vector to be optimized, respectively.

[0174] After calculating the anisotropic material properties of the composite material of this invention, these properties are input into the finite element model. The complete finite element model in this step includes the geometric model of the composite material, material properties, thermal and mechanical boundary conditions, and a mesh model. Schematic diagrams of the geometric model and mesh model are shown below. Figure 2 , 3 As shown.

[0175] To lay up or wind multilayer composite materials in this example, a local coordinate system needs to be established on this example, such as... Figure 4 As shown.

[0176] Therefore, in S4 of this invention: establish a parameter optimization model for the winding or layup angle, wherein the optimized parameter is the fiber angle of each winding or layup layer; the optimization objective is to minimize the curing deformation at a certain point in the composite material product or to minimize the average curing deformation in a certain area of ​​the product.

[0177] The formula (26) of this invention is an optimized formulation, that is, under certain constraints, by changing the l parameter, the optimization objective is made to obtain the optimal value, that is, the average value of the curing degree deformation of the composite material product is minimized.

[0178] This invention offers five 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, based on resin curing kinetics and Fourier's law of heat conduction, this invention, combined with composite material mechanics and finite element numerical analysis, establishes analytical models for the temperature field, degree of cure field, and curing deformation during the curing process of composite materials with multi-layer multi-directional fiber winding or multi-layer layup. This enables full-time analysis of these parameters. Third, by parameterizing the winding or layup angle and utilizing parameter optimization techniques, this invention effectively controls the curing deformation of composite material products through optimization of the winding or layup angle. Fourth, this method is applicable to control the curing deformation of multi-layer multi-directional fiber winding or multi-layer layup composite materials of different structures, sizes, and models, demonstrating good applicability. Fifth, compared to traditional process improvement methods that rely solely on experience and extensive experimentation, this method combines theoretical calculations with experiments, improving product quality while avoiding the significant time, manpower, and economic costs associated with large-scale trial-and-error experiments.

[0179] 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. A method of optimizing the winding or layup angle of a cured composite material deformation, characterized in that: The method comprises the following steps: S1: using an empirical model, testing resin thermal experimental data by a differential scanning calorimeter or a differential thermal analyzer, fitting data of a reaction kinetics model, and establishing a resin curing reaction kinetics mathematical model; S2: establishing a Fourier transient heat conduction control equation containing a curing reaction exothermic, i.e., containing a nonlinear internal heat source term, according to the curing reaction kinetics mathematical model; S3: according to the Fourier transient heat conduction control equation, combining mechanics of composites to establish a finite element analysis model of a temperature field, a curing degree field and a curing deformation of a curing process of the composites; S4: according to the established finite element analysis model, establishing a parameter optimization model of winding or layering angle, the optimized parameter being a fiber angle of each layer of winding or layering, and the optimization target being to minimize the curing deformation of a certain place of the composite product or to minimize the average value of the curing deformation of a certain region of the product; S5: performing optimization on the parameter optimization model of the winding or layering angle to finally obtain an optimal winding or layering angle of a specific type of composite product and perform theoretical checking; S6: verifying the winding or layering angle of the theoretical optimization result through actual test, and perfecting and optimizing the winding or layering angle according to the test result to obtain a final winding or layering angle; The parameter optimization model in S4 comprises an optimization template and an optimization parameter, the parameter being a winding or layering angle described by several variables, and the optimization target being optimized by changing the optimization parameter; The optimization in S5 refers to a calculation iteration process in which the optimization target reaches an extreme value, the number of iterations needs to consider the size of the calculation amount each time, i.e., the number of iterations is limited, and when the difference of the optimization target is less than or equal to a preset value after each iteration, the iteration is exited, and the optimization target at this time is the final result; The optimization formula of the parameter optimization model in S4 is as follows: where l is the vector of parameters to be optimized, and l AVG (l) is the optimization objective, which represents the mean value of the displacement of a certain region related to the optimization parameters; the first two equations before optimization are the Fourier heat conduction equation containing the chemical exothermic term and the mechanical constitutive equation containing the influence of temperature and degree of cure; l min , l max are the lower and upper limits of the vector of parameters to be optimized, respectively.

2. The winding or layering angle optimization method of the curing deformation of the composites according to claim 1, characterized in that: The curing reaction kinetics mathematical model in S1 refers to an equation established by combining the curing degree, the curing speed and the temperature of the resin, and is used to calculate the curing degree and the curing speed; The Fourier transient heat conduction control equation of the nonlinear internal heat source term in S2 comprises a heat conduction process in which the composites in a curing process transfer heat from the outside to the inside of the material through a mold and a reaction exothermic process of the resin itself, and the exothermic process is nonlinear.

3. The winding or layering angle optimization method of the curing deformation of the composites according to claim 1 or 2, characterized in that: The form of the empirical model in S1 is as follows: dα / dt=k(T)f(α) (1) wherein k(T) is a parameter related to the temperature, and f(α) is a function related to the curing degree; According to different forms of f(α), the empirical curing kinetics model comprises an n-order reaction kinetics model and a self-catalytic model, wherein the form of the n-order reaction kinetics model is as follows: da / dt = k(T)(l - a) n (2) where n is the reaction order; k is the reaction rate of the reaction kinetic model, A is the frequency factor of the reaction kinetic model; ΔE a is the activation energy of the reaction kinetic model; T is the temperature, t is the time; a is the degree of curing of the resin; R is the universal gas constant; The form of the self-catalytic model is as follows: 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, ΔE1 and ΔE2 represent the activation energy in the process of curing reaction.

4. The method of claim 1 or 2, wherein the winding or ply angle optimization method of the curing deformation of the composite material is characterized in that: The Fourier transient heat conduction control equation of the curing reaction exothermic in S2 is in the form of a Cartesian coordinate system: where T is the temperature; p c , C p , k ii (i = x, y, z) are the equivalent density, specific heat and thermal conductivity of the anisotropic material of the composite, respectively; is the internal heat source term; The above formula is converted into a control equation in any coordinate system by coordinate transformation; The expression is: In the formula, ρ r H represents the density of the resin. u α represents the total heat released by the resin during the curing reaction; α is the degree of curing of the resin, which represents the ratio of the heat released at time t to the total heat released, i.e., the proportion of heat released at time t to the total heat released, as shown in the following formula; dα / dt is the instantaneous curing rate of the resin, i.e., the instantaneous reaction rate. where H(t) is the heat released by the curing reaction at time t.

5. The method of claim 1 or 2, wherein the winding or ply angle optimization method of the curing deformation of the composite material is characterized in that: In S3, a geometric analysis model is first established for different configurations and types of composite material products for the convenience of finite element calculation, and then the initial finite element model is simplified. After the geometric model is established, different material properties and heat conduction parameters at the interface of the mold and the product are set; thereafter, the geometric model is meshed, and the meshing needs to meet both the calculation accuracy requirement and the calculation cost requirement; In S3, the curing deformation of the composite material product, i.e., the mechanical behavior of the product, needs to establish a composite material constitutive equation considering temperature and degree of curing: where σ ij represents the stress component of the composite material; ε kl represents the total strain of the composite material; represents the chemical shrinkage strain of the material; Q ijkl represents the stiffness coefficient of the material.

6. The method of claim 5, wherein the winding or ply angle optimization method of the curing deformation of the composite material is characterized in that: In S3, the performance parameters of the unidirectional composite material are represented by the combination of the performance of the resin and the fiber, and the following model is used to calculate: In the formula, E, G, and v represent the elastic modulus, shear modulus, and Poisson's ratio, the subscripts m and f represent the resin and the fiber, and the subscripts 1, 2, and 3 represent the directions, wherein 1 is parallel to the fiber direction.

7. A method of winding or ply angle optimization for cure distortion of a composite material according to claim 6, characterized in that: In S3, the homogenization method can also be used to calculate the mechanical and thermal performance parameters of the composite material; and / or, in S3, the change of the elastic modulus of the fiber in the curing reaction is ignored, and the change of the elastic modulus of the resin in the curing reaction process is fitted by the degree of curing and the empirical formula before and after the gel point.

8. The method of claim 6, wherein the winding or ply angle optimization method of the curing deformation of the composite material is characterized in that: In S3, the density of the composite material in the curing process changes with the progress of the curing reaction, the volume shrinkage rate of the resin is measured by experiment, and then the fitting formula of the resin density is obtained. The thermal expansion effect of the fiber is ignored, i.e., the change of the fiber density in the whole curing process is ignored, and then the density of the composite material is calculated using the mixing rate formula: In S3, the density of the composite material is calculated using the mixing rate formula: p = p f V f + p m (1 - V f ) (19) wherein p m represents the resin density, p f represents the fiber density, p represents the composite density, V f represents the fiber volume fraction; In S3, the specific heat capacity of the composite material is calculated by the mixing law: Wherein, C f is the fiber specific heat, C m is the resin specific heat, V m is the resin volume fraction; The thermal conductivity of the composite material along the fiber direction is obtained by the mixing law: K L = K f V f + K m (1 - V f ) (21) The thermal conductivity perpendicular to the fiber direction is calculated according to the Springer-Tsai model by the following formula: In the formulae, 9. The method of claim 5, wherein the winding or ply angle optimization method of the curing deformation of the composite material is characterized in that: In S3, the thermal expansion coefficients of the unidirectional composite material along the fiber direction and perpendicular to the fiber direction are: α2=(α 2f +n 12 a 1f )V f +(a m +n m a m )(1-V f )-[n 12f V f +n m (1-V f )]·α1(24) α2 ＝ α3 (25) wherein α 1f is the coefficient of thermal expansion parallel to the fiber direction, α 2f is the coefficient of thermal expansion perpendicular to the fiber direction, E 1f is the modulus of elasticity parallel to the fiber direction, E m denotes the modulus of elasticity of the resin, v m denotes the Poisson's ratio of the resin, v 12f denotes the in-plane Poisson's ratio of the fiber 12, V f denotes the fiber volume fraction.

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