Forming method for reducing curing deformation of composite laminated board through non-isothermal curing

Abstract

The invention discloses a forming method for reducing curing deformation of a composite material laminated board through non-isothermal curing. The forming method specifically comprises the following steps: step 1, determining a curing shrinkage generation area of a laminated composite material; step 2, constructing a first stage of a non-isothermal curing period, namely a rapid heating stage; step 3, constructing a second stage of the non-isothermal curing period, namely a slow heating stage; and step 4, constructing a third stage of the non-isothermal curing period, namely a cooling stage. The invention solves the problem that the existing curing molding process is easy to cause the deformation of the laminated composite material laminate.

Description

Technical Field

[0001] This invention belongs to the field of composite material processing and manufacturing technology, and relates to a molding method for reducing the curing deformation of composite laminates by non-isothermal curing. Background Technology

[0002] Laminated composites have found significant applications in aerospace and civil industries due to their excellent mechanical properties, such as high strength-to-weight ratio, corrosion resistance, and good fatigue resistance. However, the problems of residual stress and process-induced deformation (PID) during their manufacturing process are becoming increasingly prominent. The isothermal curing process suffers from asynchrony between resin shrinkage and thermal expansion during the curing stage, easily leading to warping and internal stress accumulation in laminated panels, thus affecting the mechanical properties and dimensional accuracy of the composite structure.

[0003] Studies have shown that residual stresses induced by these processes are released during demolding, leading to process-induced deformation (PID) and additional stress during assembly. Furthermore, these stresses are directly affected by the curing cycle experienced by the thermosetting prepreg. Therefore, adjusting the curing cycle to offset the thermal expansion effect with the curing shrinkage effect is an important means of reducing curing deformation. Summary of the Invention

[0004] The purpose of this invention is to provide a molding method for reducing the curing deformation of composite laminates through non-isothermal curing, thereby solving the problem that existing curing molding processes easily cause deformation of laminated composite materials.

[0005] The technical solution adopted in this invention is a molding method for reducing the curing deformation of composite laminates through non-isothermal curing, specifically including the following steps: Step 1: Determine the area where curing shrinkage of the laminated composite material occurs; Step 2: Construct the first stage of the non-isothermal curing cycle, namely the rapid heating stage; Step 3: Construct the second stage of the non-isothermal curing cycle, namely the slow heating stage; Step 4: Construct the third stage of the non-isothermal curing cycle, namely the cooling stage.

[0006] The invention is further characterized by: The specific process of step 1 is as follows: Step 1.1: Establish a curing kinetic model for the laminated composite material; Step 1.2: Establish a resin exothermic model for laminated composite materials; Step 1.3: Based on the model established in Steps 1.1 and 1.2, the curing curve of the laminated composite material is obtained by combining the heat preservation temperature and heat preservation time of the laminated composite material. Step 1.4: Determine the curing shrinkage region of the laminated composite material based on the curing curve of the laminated composite material obtained in Step 1.3.

[0007] The specific process of step 2 is as follows: Step 2.1: Establish the mapping relationship between heating parameters and deformation behavior, modeling the rapid heating stage as a linear heating process, with the heating rate defined as: (1) in: This indicates room temperature. Indicates the duration of the rapid warming phase. This refers to the temperature at the end of this phase. Step 2.2, generate heating parameters ( , For each set of sample data, a corresponding temperature cycle is constructed and the deformation is obtained. Step 2.3, determine the time parameters in Step 2.2. and target temperature The optimal solution.

[0008] The specific process of step 2.2 is as follows: Step 2.2.1: The Latin hypercube sampling method is used within the parameter range: , Generate N sets of sample points ( , ); Step 2.2.2: Obtain the temperature distribution of each group of sample points; Step 2.2.3: Based on the temperature distribution of each sample point, the curing degree distribution is obtained, and the modulus of the composite laminate is calculated. Based on the modulus, the stiffness matrix between strain and stress of the composite laminate is calculated. Step 2.2.4: Solve for the deformation of the composite laminate based on the stiffness matrix between strain and stress. Step 2.2.5: Since there is a one-to-one correspondence between the deformation amount and the degree of cure of the composite laminate, the degree of cure (DoC) is obtained based on the deformation amount. Samples with a DoC lower than 0.9 are discarded, ultimately forming a composite laminate containing... N Group( , A dataset containing (DoC, PID) sample points ( , )∈Dataset( , ).

[0009] The specific process of step 2.2.2 is as follows: The heat conduction control equation is constructed as shown in the following formula (2). Based on the heat conduction control equation, the temperature distribution of each sample point is obtained: (2) in, , Indicates the in-plane thermal conductivity coefficient. Indicates the thermal conductivity coefficient in the thickness direction; Density of the composite material; This represents the specific heat capacity of the composite material.

[0010] The specific process of step 2.2.3 is as follows: The modulus of composite materials includes the elastic modulus of the resin. and fiber elastic modulus Fiber elastic modulus The elastic modulus of the resin is determined directly through the composite laminate. As shown in the following formulas (3) to (5): (3) (4) (5) in, This refers to the degree of curing at the gel point. The curing degree is the glass transition point. This refers to the elastic modulus of the resin. As an intermediate variable; Through the elastic modulus of resin and fiber elastic modulus The elastic modulus (E1, E2, E3) and shear modulus (G) of the three principal directions of the unidirectional layup of the composite material were obtained. 12 G 13 G 23 The calculation formula is as follows: (6) (7) (8) (9) in, , , This represents the elastic modulus of the composite material in the fiber direction and perpendicular to the fiber direction. , , This represents the shear modulus of the composite material in each planar direction; The elastic modulus of the resin; The shear modulus of the resin; The resin's Poisson's ratio; , , This represents the elastic modulus of the fiber in directions 1, 2, and 3. , , Let be the Poisson's ratio of the fiber in the three planar directions; , , This represents the shear modulus of the fiber in three planar directions; The fiber volume fraction is given; the stiffness matrix between strain and stress in the composite laminate is as follows: (10) (11) (12) (13) in, , , It is normal stress; , , Shear stress; , , Strain in the main direction; , , For shear strain; , , Let be the Poisson's ratio of the material in the three plane directions; Normalization factor; Tensile stiffness in the fiber direction; , Tensile stiffness perpendicular to the fiber direction; , , This is the coupling stiffness term; , , This represents the shear modulus of each principal plane.

[0011] The specific process of step 2.2.4 is as follows: the deformation of the composite laminate is calculated by using the stiffness matrix, thermal expansion coefficient and curing shrinkage coefficient of the composite laminate. The thermal expansion strain is calculated as shown in formula (14): (14) in, , , For the thermal expansion strain increments in different directions; , , These are the coefficients of thermal expansion in different directions; For temperature increment; The calculation of curing shrinkage strain is shown in formula (15): (15) in, , , For the solidification shrinkage strain increments in different directions; , , These represent the shrinkage coefficients in different directions; Curing rate; For time increments; The deformation of the composite laminate is obtained by combining the stiffness matrix obtained by formulas (6) to (13), the thermal expansion strain obtained by formula (14), and the curing shrinkage strain obtained by formula (15).

[0012] The specific process of step 2.3 is as follows: The NSGA-II genetic algorithm is used to search for the optimal solution. Based on the collected sample data, the objective function is to minimize the deformation amount PID; the constraint condition is that the degree of curing (DOC) ≥ 0.9; input: ( , Output: DoC, PID; The NSGA-II algorithm constructs the Pareto boundary through population evolution and non-dominated sorting mechanisms; Finally, the point that satisfies both DoC ≥ 0.9 and significantly suppresses PID is extracted as the optimal heating parameter. , ).

[0013] The beneficial effect of this invention is that, by constructing a non-isothermal curing cycle, the curing shrinkage stage is shifted to the thermal expansion-dominated stage without altering the original material system. This allows the material to utilize thermal expansion strain to offset chemical shrinkage strain as much as possible during curing, thereby reducing curing deformation of laminated composite materials. This invention aims to reduce process-induced deformation of laminated composite materials. Based on methods related to heat transfer, curing kinetics, and composite material lamination mechanics, it uses a genetic algorithm to control the heating rate, delaying modulus development and the appearance of the glass transition point. This effectively offsets the curing shrinkage effect against the thermal expansion effect, thereby reducing curing deformation and improving the dimensional accuracy of the manufactured parts. Attached Figure Description

[0014] Figure 1 A simplified two-step curing cycle profile for AS4 / 3501 laminated composites; Figure 2(a) shows the curing period and deformation under isothermal curing cycle; Figure 2(b) shows the curing period and deformation under non-isothermal conditions; Figure 3(a) shows the deformation distribution of the part under the isothermal curing cycle; Figure 3(b) shows the deformation distribution of the part under a non-isothermal period; Figure 4 To optimize the before-and-after deformation comparison image. Detailed Implementation

[0015] The following detailed description is provided in conjunction with specific implementation methods.

[0016] Example 1 The molding method of the present invention for reducing the curing deformation of composite laminates by non-isothermal curing includes a first heating stage (S1), a second slow heating stage (S2), and a cooling stage (S3). By controlling the heating rate and the time point of the transition temperature between stages, the modulus growth stage is delayed to the stage with stronger thermal expansion, thereby effectively offsetting the shrinkage effect.

[0017] Example 2 The molding method for reducing curing deformation of composite laminates through non-isothermal curing according to the present invention is implemented according to the following steps: Step 1: Determine the area where curing shrinkage of the laminated composite material occurs; Step 2: Construct the first stage (S1) of the non-isothermal curing cycle—the rapid heating stage. The main goal is to quickly heat the material from room temperature to the intermediate temperature range, thereby shortening the residence time of the material in the low-reaction state during the initial curing stage. To ensure optimal temperature control, this invention further uses simulation training and optimization algorithms to scientifically determine the heating time t and the final heating temperature T of this stage. Step 3, construct the second stage (S2) – the slow heating stage, by obtaining the parameters of stage S1 from step 2. , () then as the starting point of this stage, will () , ) as the termination point, where The insulation temperature of the laminated composite material, This refers to the end time of the insulation stage of the laminated composite material. The specific termination temperature and time should be selected reasonably according to the actual situation. During this stage, the resin gradually transitions from a liquid or gel state to a glassy state, and the material changes from being dominated by thermal expansion to being dominated by volume shrinkage. Therefore, the curing shrinkage stage, i.e., the gel point (from point G to the glass transition point (point V)), is limited to be completed within this temperature range, and the curing shrinkage is offset by thermal expansion.

[0018] Step 4, construct the third stage (S3) - the cooling stage. Starting from the end point of S2, the material temperature is gradually reduced to room temperature by controlling the mold and heating system. The cooling rate is consistent with the cooling rate recommended by the manufacturer (for example, the cooling rate of AS4 / 3501 laminated composite material is 2.22 ℃ / min), reducing the thermal gradient stress during the cooling process.

[0019] Example 3 The specific process of step 1 is as follows: Step 1.1: Establish a curing kinetic model. For AS4 / 3501 laminate material, a two-segment kinetic expression is used to model the resin curing rate. Degree of Curing It is a process variable describing the gradual transformation of thermosetting resin from a liquid state to a three-dimensional cross-linked structure. Its rate of change directly determines the material reaction process and the time position of modulus growth. The curing kinetic model expressions are shown in equations (1) and (2): (1) (2) in, Indicates degree of curing. Indicates the curing rate of the laminated composite material. Pre-exponential factor, As the apparent activation energy, is the molar gas constant; the thermochemical mechanical properties of AS4 / 3501 laminate material are listed in Table 1.

[0020] Step 1.2: Establish a resin exothermic model. During the curing process of thermosetting resins, the chemical reaction is accompanied by a large amount of exothermic reaction. For the AS4 / 3501 prepreg system, the heat generation rate (Q, in units of...) is... This can be represented as: (3) in, For the density of the composite material, The total heat released per unit mass of the reaction. The curing rate has been determined in step 1.1; the parameters for the AS4 / 3501 prepreg system are given in Table 1.

[0021] Step 1.3: Based on the curing kinetics model, the curing curve is obtained by combining the holding temperature and holding time. The curing process of composite materials generally goes through three stages: liquid, viscoelastic gel, and glassy (solid). The change in modulus of the material mainly occurs in the stage from gel to glass. In this stage, the resin system undergoes a rapid transformation from a low-viscosity liquid to a high-modulus solid, with a sudden increase in modulus, significant chemical shrinkage, and the system is most sensitive to deformation. Figure 1The given curing curves show that the gel point and glass transition point of the AS4 / 3501 prepreg system are G point (α≈0.57) and V point (α≈1), respectively. Therefore, a non-isothermal curing cycle model is constructed so that G point and V point appear in the heating stage, thereby offsetting the curing shrinkage through thermal expansion.

[0022] Example 4 Step 2 specifically includes the following steps: Step 2.1, establish the mapping relationship between heating parameters and deformation behavior, model the rapid heating stage as a linear heating process, and define its heating rate as: (4) in, This represents room temperature, usually taken as 25℃. Indicates the duration of the rapid warming phase. This refers to the temperature at the end of this stage (unit: °C). This heating rate directly affects the temporal position of the modulus growth region (GV) during the curing process, thus influencing the formation mechanism of process-induced deformation (PID). Since the relationship between heating parameters and deformation is difficult to express directly analytically, it is necessary to extract the input parameters through simulation. , The mapping between the deformation response and the deformation response.

[0023] Step 2.2: Generate sample data and obtain deformation. For each group of samples, construct a corresponding temperature cycle and obtain the deformation. This invention is based on ABAQUS software, and the modeling material is AS4 / 3501-4-layer plywood with a layup of [0 / 90 / 90 / 0]. The thickness-direction temperature gradient, curing degree distribution, and modulus development history are considered. Each set of heating parameters corresponds to a complete analysis process, specifically divided into two stages: thermal analysis and static analysis. After the simulation results are extracted, a data set containing... N Group( , The dataset (DoC, PID) contains sample points ( , )∈Dataset( , This serves as input for subsequent optimization.

[0024] Step 2.3, determine the time parameters in Step 2.2. and target temperature Optimal Solution; The NSGA-II genetic algorithm is used to search for the optimal solution. Based on the collected sample data, this invention aims to minimize the process-induced deformation while ensuring the integrity of the curing reaction, and constructs a curing cycle parameter optimization problem. Its objective function is: minimize the deformation PID; the constraint condition is that the degree of curing (DOC) ≥ 0.9; input: ( , Output: DoC, PID.

[0025] In objective optimization problems, there is often no unique optimal solution, but rather a set of mutually exclusive solutions, known as the Pareto Optimal Set. In the heating cycle optimization constructed in this invention, each solution in this set represents a balance between reducing process-induced deformation and ensuring complete curing. The NSGA-II algorithm automatically identifies these optimal solution points through population evolution and non-dominated sorting mechanisms, forming the Pareto boundary. Finally, points that satisfy DoC ≥ 0.9 and significantly suppress PID are extracted from this solution set as optimal heating parameters, achieving process optimization of the heating strategy.

[0026] The optimized process is as follows: (1) Use the 80 sets of data obtained in step 2.2 as the initial population; (2) In each generation, crossover and mutation are used to generate new individuals; (3) Calculate the deformation and degree of curing by calling the interpolation function; (4) Discard solutions that do not meet the requirement of curing degree ≥ 0.9; (5) Use non-dominated sorting and crowding distance to select the next generation; (6) Extract the Pareto boundary solution after repeating the iteration for 100 generations.

[0027] Finally, the minimum PID that satisfies process feasibility is selected from the boundary solutions. , ) is used as the optimal parameter, and one set of optimal solutions is =10 min, =133 ℃, corresponding to a maximum deformation reduction of approximately 10%. This parameter set is the recommended setting value for the non-isothermal curing rapid heating section, and is being imported into the next slow heating section (S2) curing cycle generation.

[0028] Example 5 Step 2.2.1: The Latin hypercube sampling method is used within the parameter range: , Generated in N = 80 sample points ( , ),in i It refers to any single sample point, ensuring uniform coverage of data points in space and preventing sample concentration or blank areas. Step 2.2.2, obtain the temperature distribution of each sample point: solve formula (1) to obtain the curing rate of the laminated composite material. Curing rate of laminated composite materials Input formula (3) to obtain the heat generation rate Q of the composite material, and load Q into the heat conduction control equation, as shown in formula (5); (5) in, , Indicates the in-plane thermal conductivity coefficient. Indicates the thermal conductivity in the thickness direction; Density of the composite material; Specific heat capacity of composite materials; In actual calculations, the curing process is divided into many extremely small time intervals. Each The temperature change can be expressed as an integral form as shown in formula (6): (6) because Extremely small and If the changes are not significant, then formula (6) can be approximated as formula (7): (7) In each small time step Given the temperature at the previous moment First, calculate the heat generation rate Q, and then substitute it into the heat conduction equation (5). By solving the time integral using equations (6) and (7), the change in temperature over time can be obtained. and the temperature at the next moment Based on this, iterative calculations are performed, continuously updating the temperature until the entire process is complete. This process is executed simultaneously at various locations within the meshed composite material model. Each element has multiple integration points for accurately calculating the temperature changes within that element; nodes are the connection points between elements, used to record and transmit calculation results. In the calculation, the initial temperature is first applied at the integration points... Calculate the temperature change Then, the temperature results at the integration points are transferred to the nodes of the elements; finally, the node temperatures of all elements are summed to obtain the overall temperature distribution of the composite material.

[0029] Step 2.2.3: Based on the temperature distribution, the degree of cure distribution is obtained, and the modulus of the composite material is calculated. There is a one-to-one correspondence between the degree of cure and the modulus at each location on the composite material. The modulus value of the composite material at each location can be determined through the degree of cure distribution. The composite material modulus includes the resin's elastic modulus. and fiber elastic modulus (fiber elastic modulus) The known quantities include: , , (This refers to the elastic modulus of the fiber in directions 1, 2, and 3), where the elastic modulus of the resin is calculated using the CHILE model. The model sets a transition point before which the resin's elastic modulus changes. Extremely low (one-thousandth of the initial value), then increases linearly to the final modulus. .

[0030] (8) (9) (10) in, This refers to the degree of curing at the gel point. The curing degree is the glass transition point. This refers to the elastic modulus of the resin. The parameters are intermediate variables; the mechanical parameters of the resin and fiber in the AS4 / 3501 prepreg system are listed in Table 2.

[0031] Resin elastic modulus and fiber elastic modulus The elastic modulus (E1, E2, E3) and shear modulus (G) of the three principal directions of the unidirectional layup of the composite material were obtained. 12 G 13 G 23 The fiber-direction modulus E1 and Poisson's ratio remain unchanged, while other moduli E2, E3, and G remain unchanged. 12 G 13 and G 23 Calculated based on resin changes and micromechanical formulas: (11) (12) (13) (14) in, , , The elastic modulus of the composite material in directions 1 (fiber direction), 2, and 3 (perpendicular to the fiber). , , This represents the shear modulus of the composite material in each planar direction; The elastic modulus of the resin; The shear modulus of the resin; The resin's Poisson's ratio; , , The elastic modulus of the fiber in directions 1, 2, and 3; , , is the Poisson's ratio of the fiber in each planar direction; , , This represents the shear modulus of the fiber in each planar direction; This represents the fiber volume fraction (50%). Next, these moduli are used to calculate the stiffness matrix between strain and stress. For fiber composites, the stress-strain relationship (stiffness matrix) is: (15) (16) (17) (18) in, , , These are normal stresses, acting on the material in directions 1 (fiber direction), 2, and 3 (perpendicular to the fiber), respectively. , , This is shear stress, acting on the corresponding plane; , , Strain in the main direction; , , For shear strain; , , Let be the Poisson's ratio of the material in each planar direction; Normalization factor; Tensile stiffness in the fiber direction; , Tensile stiffness perpendicular to the fiber direction; , , This is the coupled stiffness term, which reflects the effect of tension in one direction on stress in the other two directions. , , Represents the shear modulus of each principal plane; Step 2.2.4, Obtain the deformation amount; To calculate the deformation amount of the composite material, three core parameters are required simultaneously: the material's stiffness matrix, the coefficient of thermal expansion, and the curing shrinkage coefficient; The stiffness matrix describes the material's resistance to external loads in different directions; Temperature changes cause the material to expand thermally, while the curing reaction causes volume shrinkage; These three parameters together determine the stress response and deformation trend of the material during the curing process. The thermal expansion strain calculation is shown in formula (19), which reflects the volume expansion behavior of the material. For anisotropic materials like composite materials, the coefficient of thermal expansion is different in different directions, and should be calculated separately to apply it to different directions; (19) in, , , For the thermal expansion strain increments in different directions; , , These are the coefficients of thermal expansion in different directions; The temperature increment; the calculation of curing shrinkage strain is shown in formula (20). The shrinkage behavior of the material in the reaction of the resin is similar to that of thermal expansion. For anisotropic materials such as composite materials, the shrinkage coefficients in different directions are also different. They should be calculated separately to act on different directions. (20) in, , , For the solidification shrinkage strain increments in different directions; , , These represent the shrinkage coefficients in different directions; Curing rate; The time increment is used because there are usually molds or other structural constraints during the molding process. These free deformations caused by temperature and curing reaction cannot be completely released. Combining the stiffness matrix, thermal expansion strain and curing shrinkage strain obtained by formulas (11)-(18), the finite element software will automatically convert these free strains into additional stress through the stiffness matrix during the solution process, and use the structural mechanics equilibrium equation to calculate the displacement of each node, and finally obtain the overall deformation of the composite material in the whole curing process. The resin elastic modulus, thermal expansion and curing shrinkage characteristics of the material are different under different curing degrees, so the deformation also changes with the curing degree. There is a one-to-one correspondence between the two. In order to ensure the feasibility of the process, samples with a curing degree DoC of less than 0.9 are removed.

[0032] The key to implementing the entire non-isothermal curing cycle lies in the continuity and stability between the three curing stages. In actual operation, it is essential to ensure that the temperature transition point from S1 to S2 is stable and without sudden increases or decreases, ensuring that the modulus development range fully overlaps with the thermal expansion dominance zone, and avoiding local strain overload caused by discontinuous heating or thermal lag. Similarly, the cooling transition from S2 to S3 must also ensure linear stability, so that the rigid structure after vitrification maintains its geometric shape under stable cooling conditions.

[0033] By constructing a non-isothermal curing cycle model for the heating / cooling process described above, the non-isothermal curing cycle can shift the modulus growth later without changing the original material system. It moves the moment of modulus surge from the early high-stress unstable segment to the later thermal expansion-dominated segment, allowing the material to use thermal strain to offset chemical shrinkage strain as much as possible during the curing process. This has high operability and universality in actual industrial production.

[0034] Example 6 For the AS4 / 3501 laminate composite material, the isothermal curing at 177°C and the deformation are shown in Figure 2(a). This figure shows the curing period and deformation under the isothermal curing cycle, and it can be seen that the modulus development (GV) occurs during the isothermal holding stage. For the non-isothermal curing cycle of the present invention, as shown in Figure 2(b), this figure shows the curing period and deformation under the non-isothermal curing cycle, and it can be seen that the modulus development (GV) occurs during the non-isothermal stage. Therefore, the non-isothermal curing cycle leads to the interaction between the thermal effect and the CSH effect during the second stage. After the second stage (marked by point V), the thermal effect dominates before the end of the cooling stage. Compared with the isothermal curing cycle, the G and V points in the non-isothermal curing cycle appear in the later stage of the curing process, allowing the resin to be fully compressed during the early curing process, subsequently enabling better bonding between components, and ultimately effectively reducing process-induced deformation (PID) through the thermal effect in the later stage of curing.

[0035] Figures 3(a) and 3(b) show the deformation contour plots of the AS4 / 3501 laminate composite material under isothermal curing at 177°C and non-isothermal curing using the present invention. Combining Figures 2(a) and 2(b), for the isothermal curing cycle, the CSH effect (deformation dominated by curing shrinkage) dominates between points G and V. However, for the non-isothermal curing cycle, the thermal expansion caused by temperature changes leads to the thermal effect offsetting the CSH effect. Figure 4 To optimize the deformation comparison diagram before and after, the simulation results of the maximum deformation displacement of the laminate under the two curing cycles were further compared. The results show that the maximum displacement of the part in the non-isothermal curing cycle is significantly lower than that in the isothermal curing cycle, and the deformation control effect is excellent. This verifies the effect of non-isothermal curing proposed in this invention on suppressing process-induced deformation.

[0036] Through the above steps, the present invention can effectively reduce the PID of laminated composite parts during the curing process, achieving a 10% reduction in deformation.

[0037] Table 1

[0038] Note: , Indicates the in-plane thermal conductivity coefficient. Indicates the thermal conductivity in the thickness direction Table 2

[0039] Note: This refers to the degree of curing at the gel point. The curing degree is the glass transition point. The resin's Poisson's ratio; , , The elastic modulus of the fiber in directions 1, 2, and 3; , , is the Poisson's ratio of the fiber in each planar direction; , , This represents the shear modulus of the fiber in each planar direction; This represents the fiber volume fraction (50%).

Claims

1. A molding method for reducing curing deformation of composite laminates through non-isothermal curing, characterized in that: Specifically, the steps include the following: Step 1: Determine the area where curing shrinkage of the laminated composite material occurs; Step 2, construct the first stage of the non-isothermal curing cycle; Step 3, construct the second stage of the non-isothermal curing cycle; Step 4: Construct the third stage of the non-isothermal curing cycle.

2. The molding method for reducing curing deformation of composite laminates by non-isothermal curing according to claim 1, characterized in that: The specific process of step 1 is as follows: Step 1.1: Establish a curing kinetic model for the laminated composite material; Step 1.2: Establish a resin exothermic model for laminated composite materials; Step 1.3: Based on the model established in Steps 1.1 and 1.2, the curing curve of the laminated composite material is obtained by combining the heat preservation temperature and heat preservation time of the laminated composite material. Step 1.4: Determine the curing shrinkage region of the laminated composite material based on the curing curve of the laminated composite material obtained in Step 1.

3.

3. The molding method for reducing curing deformation of composite laminates by non-isothermal curing according to claim 2, characterized in that: The specific process of step 2 is as follows: Step 2.1: Establish the mapping relationship between heating parameters and deformation behavior, modeling the rapid heating stage as a linear heating process, with the heating rate defined as: （1） in: This indicates room temperature. Indicates the duration of the rapid warming phase. This refers to the temperature at the end of this phase. Step 2.2, generate heating parameters ( , For each set of sample data, a corresponding temperature cycle is constructed and the deformation is obtained. Step 2.3, determine the time parameters in Step 2.

2. and target temperature The optimal solution.

4. The molding method for reducing curing deformation of composite laminates by non-isothermal curing according to claim 3, characterized in that: The specific process of step 2.2 is as follows: Step 2.2.1: The Latin hypercube sampling method is used within the parameter range: , Generate N sets of sample points ( , ); Step 2.2.2: Obtain the temperature distribution of each group of sample points; Step 2.2.3: Based on the temperature distribution of each sample point, the curing degree distribution is obtained, and the modulus of the composite laminate is calculated. Based on the modulus, the stiffness matrix between strain and stress of the composite laminate is calculated. Step 2.2.4: Solve for the deformation of the composite laminate based on the stiffness matrix between strain and stress. Step 2.2.5: Since there is a one-to-one correspondence between the deformation amount and the degree of cure of the composite laminate, the degree of cure (DoC) is obtained based on the deformation amount. Samples with a DoC lower than 0.9 are discarded, ultimately forming a composite laminate containing... N Group( , A dataset containing (DoC, PID) sample points ( , )∈Dataset( , ).

5. The molding method for reducing curing deformation of composite laminates by non-isothermal curing according to claim 4, characterized in that: The specific process of step 2.2.2 is as follows: The heat conduction control equation is constructed as shown in the following formula (2). Based on the heat conduction control equation, the temperature distribution of each sample point is obtained: （2） in, , Indicates the in-plane thermal conductivity coefficient. Indicates the thermal conductivity in the thickness direction; Density of the composite material; This represents the specific heat capacity of the composite material.

6. The molding method for reducing curing deformation of composite laminates by non-isothermal curing according to claim 5, characterized in that: The specific process of step 2.2.3 is as follows: The modulus of composite materials includes the elastic modulus of the resin. and fiber elastic modulus Fiber elastic modulus The elastic modulus of the resin is determined directly through the composite laminate. As shown in the following formulas (3) to (5): （3） （4） （5） in, This refers to the degree of curing at the gel point. The curing degree is the glass transition point. This refers to the elastic modulus of the resin. As an intermediate variable; Through the elastic modulus of resin and fiber elastic modulus The elastic modulus (E1, E2, E3) and shear modulus (G) of the three principal directions of the unidirectional layup of the composite material were obtained. 12 G 13 G 23 The calculation formula is as follows: （6） （7） （8） （9） in, , , This represents the elastic modulus of the composite material in the fiber direction and perpendicular to the fiber direction. , , This represents the shear modulus of the composite material in each planar direction; The elastic modulus of the resin; The shear modulus of the resin; The resin's Poisson's ratio; , , This represents the elastic modulus of the fiber in directions 1, 2, and 3. , , Let be the Poisson's ratio of the fiber in the three planar directions; , , This represents the shear modulus of the fiber in three planar directions; The fiber volume fraction is given; the stiffness matrix between strain and stress in the composite laminate is as follows: （10） （11） （12） （13） in, , , It is normal stress; , , Shear stress; , , Strain in the main direction; , , For shear strain; , , Let be the Poisson's ratio of the material in the three plane directions; Normalization factor; Tensile stiffness in the fiber direction; , Tensile stiffness perpendicular to the fiber direction; , , This is the coupling stiffness term; , , This represents the shear modulus of each principal plane.

7. The molding method for reducing curing deformation of composite laminates by non-isothermal curing according to claim 6, characterized in that: The specific process of step 2.2.4 is as follows: the deformation of the composite laminate is calculated by using the stiffness matrix, thermal expansion coefficient and curing shrinkage coefficient of the composite laminate. The thermal expansion strain is calculated as shown in formula (14): （14） in, , , For the thermal expansion strain increments in different directions; , , These are the coefficients of thermal expansion in different directions; For temperature increment; The calculation of curing shrinkage strain is shown in formula (15): （15） in, , , For the solidification shrinkage strain increments in different directions; , , These represent the shrinkage coefficients in different directions; Curing rate; For time increments; The deformation of the composite laminate is obtained by combining the stiffness matrix obtained by formulas (6) to (13), the thermal expansion strain obtained by formula (14), and the curing shrinkage strain obtained by formula (15).

8. The molding method for reducing curing deformation of composite laminates by non-isothermal curing according to claim 7, characterized in that: The specific process of step 2.3 is as follows: the NSGA-II genetic algorithm is used to search for the optimal solution. Based on the collected sample data, the objective function is to minimize the deformation amount PID; the constraint condition is that the degree of curing DOC ≥ 0.

9. enter:( , Output: DoC, PID; The NSGA-II algorithm constructs the Pareto boundary through population evolution and non-dominated sorting mechanisms; Finally, the point that satisfies both DoC ≥ 0.9 and significantly suppresses PID is extracted as the optimal heating parameter. , ).

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