Partitioned pressurization control method and system for compression molding of carbon fiber prepreg and molding process

Through partition pressurization control method and intelligent sensing monitoring, the problems of uneven pressure distribution and volatile components retention in traditional carbon fiber prepreg molding are solved, and efficient and accurate molding is achieved, which improves the mechanical properties and molding quality of composite materials.

CN120396388APending Publication Date: 2025-08-01CHENGDU ZHENGXI INTELLIGENT EQUIPMENT GROUP CO LTD

Patent Information

Application Number
CN202510913831.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-07-03
Publication Date
2025-08-01

AI Technical Summary

Technical Problem

Traditional carbon fiber prepreg molding technology has problems such as uneven pressure distribution, limited level of volatile components retention, pore formation and process control intelligence, and it is difficult to adapt to the molding needs of complex mold mold surfaces and asymmetric components, which affects the mechanical properties and molding efficiency of the product.

Method used

The partition pressurization control method is adopted, and through intelligent sensing, multi-channel hydraulic control and data-driven optimization algorithm, precise control of partition pressure and directional discharge of volatile components are achieved. Combined with PID algorithm and real-time monitoring of thermocouples, pressure and temperature are dynamically adjusted, and molding process parameters are optimized.

Benefits of technology

It realizes precise control of zoning pressure and efficient discharge of volatile components, improves the molding quality and efficiency of composite materials, and meets the molding needs of high-performance carbon fiber composite materials.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention relates to the technical field of compression molding of carbon fiber prepregs, in particular to a partitioned pressurization control method and system for compression molding of the carbon fiber prepregs and a molding process. S2, initial pressure calculation; s3, gradient pressurization control; s4, dynamic pressure adjustment; and S5, a global pressure maintaining stage: when the resin curing degree alpha reaches 0.6-0.8, switching to a full-screen pressure maintaining mode, and maintaining the pressure of each region to be 90%-95% of the current maximum pressure value until curing is completed. The invention provides a zoning pressurization control method and system for compression molding of carbon fiber prepreg and a molding process, and realizes the compression molding method and system with accurate zoning pressure regulation and control and directional discharge of volatile components. And by integrating intelligent sensing, multi-channel hydraulic control and a data driving optimization algorithm, the limitation of a traditional process is broken through, and a technical support is provided for efficient forming of the high-performance carbon fiber composite material.
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Description

Technical Field

[0001] The present invention relates to the technical field of compression molding of carbon fiber prepregs, and particularly to a method, system and molding process for zone pressure control in the compression molding of carbon fiber prepregs. Background Art

[0002] The compression molding technology of carbon fiber prepregs is widely used in fields such as aerospace, new energy vehicles, and high-end equipment manufacturing because it can prepare high-strength and lightweight composite components. This process places carbon fiber prepregs in a mold and realizes resin curing and fiber orientation arrangement under high temperature and high pressure conditions, thereby obtaining high-performance composite products. However, with the continuous improvement of industrial applications' requirements for component geometric complexity, molding accuracy, and performance consistency, traditional compression molding technology faces the following technical defects: 1. Uneven pressure distribution: Traditional compression molding processes usually adopt a global uniform pressure application method, which is difficult to meet the molding requirements of complex mold surfaces or asymmetric components. In areas with a high fiber volume fraction or large mold curvature changes, the resin flow resistance differences are significant, easily leading to local pressure deficiencies or overloads, causing defects such as pores, dry spots, or fiber wrinkles, seriously affecting the mechanical properties of the products; 2. Volatile retention and pore formation: During the heating and curing stage, if the residual volatiles (such as solvents and low molecular weight substances) in the resin cannot be effectively discharged, micropores will form inside the product. Although existing processes control the heating rate and use short-term pressure holding to assist in exhaust, the coordinated regulation of parameters such as mold opening and vacuum assistance is insufficient, making it difficult to achieve the directional and efficient discharge of volatiles; 3. Limited intelligent level of process control: Existing control systems mostly rely on empirical settings of process parameters and lack the ability to monitor and feedback regulate pressure, temperature, and resin flow state in real time. Especially in the scenario of multi-region coordinated pressure application, it is difficult to achieve precise dynamic matching of pressure gradients, restricting the molding efficiency and quality consistency.

[0003] In view of the above technical defects, the present invention provides a method, system and molding process for zone pressure control in the compression molding of carbon fiber prepregs, realizing a method and system for precise zone pressure regulation, directional discharge of volatiles, and compression molding. By integrating intelligent sensing, multi-channel hydraulic control, and data-driven optimization algorithms, the limitations of traditional processes are broken through, providing technical support for the efficient molding of high-performance carbon fiber composites. Summary of the Invention

[0004] A method for zone pressure control in the compression molding of carbon fiber prepregs includes the following steps: S1. Division of pressure application areas: According to the three-dimensional geometric model of the mold, at least 3 or more independent pressure application areas are divided through finite element rheological simulation; S2. Initial pressure calculation: Based on the prepreg ply angle θ (0° ≤ θ ≤ 90°) and resin viscosity μ (100 Pa·s ≤ μ ≤ 5000 Pa·s), calculate the initial pressure values for each region according to the formula: , where K is the material correction coefficient, calibrated through prepreg type and resin curing kinetics experiments, with a value range of 0.8 ≤ K ≤ 1.5; R i is the radial distance from the centroid of region i to the mold center; R0 is the characteristic radius of the mold, converting the mold projected area into an equivalent circular radius R eq , and take 0.6 - 0.8 times of its value as the characteristic radius R0 for zoned pressure control; S3. Gradient pressure control: During the molding closing stage, apply gradient pressure to each region so that the pressure in the edge region is 5% - 15% higher than that in the central region, and the pressure difference between adjacent regions does not exceed 6% - 8% of the total pressure value; S4. Dynamic pressure regulation: Real - time collect the pressure P i and temperature T i of each region through pressure sensors and thermocouples embedded in the mold surface, and dynamically regulate the pressure value based on the PID algorithm so that the deviation rate between the real - time pressure and the target pressure satisfies , and the response time ≤ 0.5 s; S5. Global pressure holding stage: When the resin curing degree α reaches 0.6 - 0.8, switch to the full - screen pressure holding mode, and keep the pressure of each region at 90% - 95% of the current maximum pressure value until curing is completed.

[0005] Furthermore, the division of the pressurized regions in step S1 determines the region sensitivity S according to the following steps: a. Parameter definition and measurement: Δh is the elevation difference along the resin flow path on the mold surface, measured by a 3D laser scanner; L is the characteristic length, taking 1.2 - 1.5 times the diameter of the largest inscribed circle in the mold projected area; is the change rate of curvature along the main resin flow path direction, extracting curvature data through the mold CAD model and calculating it using the cubic spline interpolation method; b. Sensitivity calculation: Calculate the region sensitivity according to the formula: , where S is dimensionless, and the units of Δh and L need to be unified to millimeters (mm); C. Sensitivity classification: When S > 0.5, it is determined as a highly sensitive pressurized region, and an additional 5% - 10% of the initial pressure needs to be added during zoned pressure application; When 0.3 ≤ S ≤ 0.5, it is determined as a moderately sensitive pressurized region, and the pressure regulation priority is secondary; When S < 0.3, it is determined as a low - sensitive pressurized region, and it is controlled according to the standard pressure range; d. Dynamic correction: During the molding process, Δh and data are updated in real time, and S is recalculated. If the sensitivity level changes, the adaptive adjustment of the pressure target value is triggered.

[0006] Furthermore, the application of the gradient pressure in step S3 needs to meet the following dynamic constraint conditions: , where is the pressure in the edge area, which is monitored in real time by a pressure sensor, and the value range is: 5 MPa ≤ ≤ 20 MPa; is the pressure in the central area, and the value range is: 4.5 MPa ≤ ≤ 18 MPa; is the pressure boost space, which is defined as the duration of the linear pressure boost stage from the initial pressure to the target pressure, and satisfies: 0.5 s ≤ ≤ 5 s; The calculation method of the pressure boost time is: , where is the target pressure, is the initial pressure, is the real-time viscosity of the resin; The pressure sensor is a fiber Bragg grating sensor, whose sampling frequency ≥ 100 HZ, and it is installed at the 1 / 3 position of the mold.

[0007] Furthermore, the control variable ΔP of the PID algorithm in step S4 is calculated by the following formula: , where , representing the real-time pressure deviation, K p , K i , K d are the proportional, integral, and differential coefficients respectively, and the value ranges satisfy: , and the value range of W is: 100 g / m 2 ≤ W ≤ 300 g / m 2 ; The integral term adopts the discretized cumulative calculation method, and the sampling time interval Δt ≤ 0.1 s. The differential term is approximated by backward difference, that is: .

[0008] Furthermore, the resin curing degree α in step S5 is calculated in real time through the following modified Arrhenius kinetic model: , where A is the frequency factor, which is calibrated through the differential scanning calorimetry experiment of isothermal DSC, and the unit is s -1 , E is the apparent activation energy, which is obtained by fitting the non-isothermal DSC curve, and the unit is kJ / mol. R is the ideal gas constant, is the real-time temperature, measured by a thermocouple embedded in the mold, with a sampling frequency ≥ 1 Hz. t is the current cumulative curing time, calculated starting from the resin gel point; and it satisfies the following constraint conditions: when the temperature T < T gel (resin gel temperature), the calculation of the degree of cure freezes, that is = 0; the applicable temperature range of the model is T gel ≤ T ≤ T degradation (resin degradation temperature); the calibration method of the frequency factor A and the activation energy E includes the following steps: (1) Through an isothermal DSC test, measure the degree of cure-time curve at a constant temperature T i , and fit to obtain A(T i ); (2) Through a non-isothermal DSC test, scan at a heating rate of β, and calculate E using the Kissinger equation: where T p is the curing exotherm peak temperature; (3) Perform a linear regression on multiple sets of A(T i ) and T i to obtain the global parameters A0 and E A in A = A0exp(-EA / RT); the measurement of the real-time temperature satisfies the following conditions: The thermocouple is installed at a depth of 1 / 3 of the mold surface and the distance from the resin flow front is ≤ 10 mm; the temperature data is processed by moving average filtering, and the window width is ≤ 5 s to suppress noise interference.

[0009] Further, it also includes a defect suppression step: when the pressure fluctuation in a certain area reaches the set threshold and the duration reaches the predetermined condition, trigger dynamic pressure compensation, which specifically includes the following steps: (S1) Pressure fluctuation detection: Real-time collect the pressure value P 实测 of the target area, with a sampling frequency ≥ 10 Hz, and calculate the pressure volatility ΔP 波动 : , when ΔP 波动 > 8% and lasts for ≥ 10 S, trigger the compensation action; (S2) Temperature-pressure coupling correction: According to the real-time temperature deviation, calculate the corrected pressure P 修正 according to the following formula: , where: T avg is the real-time average temperature of the trigger compensation area, measured by a thermocouple, with an accuracy of ±1°C, T set is the target temperature set by the process; K is the temperature-pressure coupling coefficient, with a value range of 0.1 ≤ k ≤ 0.3, calibrated through the rheological experiment of the prepreg; (S3) Compensation execution and feedback: Apply the corrected pressure P 修正Input molding control system, adjust the opening of the hydraulic proportional valve, response time ≤ 1 s; if the pressure fluctuation rate is still > 5% after compensation, trigger secondary compensation: pause the molding process and start mold cooling, and control the cooling rate to 2 °C - 5 °C / min; the calibration method of the temperature-pressure coupling coefficient k includes: under constant pressure conditions, measure the resin viscosity change rate corresponding to different temperature deviations (T avg −T set ), and fit a linear proportional relationship; the uniformity deviation of the cooling rate in the secondary compensation ≤ 10%; the pressure sensor is a piezoelectric sensor, installed in the contact area between the mold surface and the prepreg, and the surface is covered with a high-temperature resistant insulating layer; the pressure data needs to be processed by Kalman filtering to suppress high-frequency noise interference.

[0010] A pressurization control system for implementing any one of the above methods, comprising: A. Differentiated mold: A plurality of piezoelectric pressure sensors and multiple groups of thermocouples are evenly distributed on the surface of the mold cavity. Among them, the pressure sensors are embedded in a matrix form, covering the resin flow front and the interlayer interface of each independent pressurization area; the thermocouples are arranged at intervals along the resin main flow path, the spacing within the group ≤ 50 mm, and each group contains at least 3 temperature measurement points; The hydraulic press is rigidly connected to the partitioned mold, providing the main pressure output required for molding, with a pressure output range of 5 - 100 MPa, accuracy ≤ ±0.5% FS, the piston stroke speed of the hydraulic press is adjustable, the adjustment range is 0.1 ~ 10 mm / s, and it is equipped with a displacement feedback sensor, resolution ≤ 1 μm; Multi-channel servo hydraulic station: Each hydraulic channel is independently controlled, equipped with a proportional valve, its response time < 30 ms, and the pressure adjustment accuracy ≤ ±0.5% FS; the output pressure range of the hydraulic station covers 5 ~ 30 MPa, supporting the gradient pressure superposition mode; B. Control terminal: Built-in process parameter optimization module, based on the BP neural network to achieve the following functions: real-time fusion of pressure and temperature data, predicting the resin flow front position and cure degree distribution; dynamically generating the pressure target value P 目标 and the pressure rise rate R ramp , and closed-loop control the opening of the proportional valve through the PID algorithm; supporting multi-objective optimization, including minimizing porosity, shortening the molding cycle and reducing energy consumption; C. Data cross-architecture: The pressure sensor and the thermocouple are connected to the control terminal through the CAN bus, and the data sampling frequency ≥ 100 Hz; real-time Ethernet communication is used between the control terminal and the servo hydraulic station, and the instruction delay < 1 ms.

[0011] Furthermore, the flow rate Q of the proportional valve and the opening command V satisfy the following relational expression: , where Cu is the valve flow coefficient, and its value range is calibrated through experiments; is the pressure difference before and after the valve, satisfying 0.5 MPa ≤ ΔP ≤ 10 MPa, ρ is the density of hydraulic oil, and the nominal value is taken as 850 - 900 kg / m³ 3 ; Vmax is the maximum opening voltage of the proportional valve, fixed at 10 V, and the opening command V satisfies 0 ≤ V ≤ Vmax; and the following constraint conditions are satisfied: when the hydraulic oil temperature T > 60 °C, C u needs to be dynamically corrected according to ; the flow linearity error of the proportional valve ≤ 1.5% FS; the calibration method of the valve flow coefficient C u includes: under a constant pressure difference ΔP = 5 MPa, measuring the flow rate Q corresponding to different opening commands V, and fitting a non-linear regression model; during the calibration process, the hydraulic oil temperature is controlled at 40 ± 2 °C, and the viscosity range is 32 - 46 cSt; the proportional valve is integrated with a pressure difference compensation module, when it detects that the fluctuation of ΔP exceeds ±5%, it automatically adjusts the opening command V to stabilize the flow rate; the compensation response time ≤ 50 ms, and the flow rate deviation after compensation ≤ 1%.

[0012] Furthermore, the optimization module trains the neural network through the following objective function: , where is the real-time pressure value of the i-th region, measured by a piezoelectric pressure sensor; is the optimal pressure value obtained by experimental calibration, determined through the rheological properties test of prepreg and the experiment of minimizing porosity; is the actual curing time, defined as the time from the start of molding to the resin curing degree α ≥ 0.95; is the target curing time set by the process; λ is the weight coefficient, and its value range is 0.6 ≤ λ ≤ 1.2, and its value satisfies a linear relationship with the prepreg gram weight W (unit: g / m²) as λ = 0.6 + 0.002W; and the following conditions are satisfied: 1. The training data set contains historical process parameters, real-time sensor data, and post-detection data (porosity, interlaminar shear strength) with a quantity ≥ 10,000 groups; 2. The neural network training adopts the Levenberg-Marquardt algorithm, and the number of hidden layer nodes is adaptively adjusted according to the number of mold partitions; 3. The optimization result of the objective function needs to pass cross-validation, and the test set error ≤ 3%.

[0013] A zone pressing process for the molding of carbon fiber prepreg by molding, applying any one of the above-mentioned zone pressing control methods for the molding of carbon fiber prepreg, characterized in that it includes a. Prepreg laying stage: the adjacent laying angle difference Δθ ≥ 45°, and the single-layer fiber volume fraction V f is controlled at 55% ≤ V f≤62%; The ply orientation is topologically optimized according to the mold geometry to ensure that the deviation between the fiber orientation and the principal stress direction is ≤10°; In the molding heating stage: the heating rate R heat ≤3°C / min, and it is maintained at t volatile within the temperature range T hold =80 - 120°C for t δ ≥10 min to fully discharge the volatiles; During the discharge of volatiles, the micro-opening of the mold 成型 ≤0.1 mm, and vacuum-assisted exhaust is applied with a vacuum degree ≤ -90 kPa; In the post-curing stage: at 80% of the stress level of the molding pressure P relax maintain for t post ≥30 min to eliminate the interfacial residual stress; During post-curing, the temperature is kept constant at T cure =T f +10°C, where Tcure is the resin curing peak temperature; The fiber volume fraction V is checked by the following formula: where N is the number of plies, determined by optical scanning or X-ray detection with an error ≤1, m is the mass of a single-layer prepreg, measured by a high-precision balance; Q f is the fiber density, with a value of 1.75 - 1.85 g / cm 3 calibrated according to the fiber type; A is the ply area, extracted from the mold CAD model with an accuracy ≤0.5%; h is the theoretical single-layer thickness, calculated as h = m / (Q f ×A); The stress holding time t relax in the post-curing stage is determined by the following formula: where θ is the resin creep coefficient, calibrated by dynamic mechanical analysis (DMA) experiment, with the unit s; E is the resin elastic modulus, with a value of 3.0 - 4.5 GPa; E matrix is the fiber elastic modulus, with a value of 230 - 300 GPa; σ fiber is the initial interfacial stress, measured by a residual stress tester; initial is the allowable residual stress threshold, set to ≤10 MPa. σ final Compared with the existing technology, the advantages of the present invention are as follows:

[0014] Compared with the existing technology, the advantages of the present invention are as follows: The present invention provides a method, system and forming process for zoned pressure control in the compression molding of carbon fiber prepregs, realizing a method and system for precise zoned pressure regulation, directional volatiles discharge and compression molding. By integrating intelligent sensing, multi-channel hydraulic control and data-driven optimization algorithms, the limitations of traditional processes are broken through, providing technical support for the efficient forming of high-performance carbon fiber composites. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flowchart of a method for zoned pressure control in the compression molding of carbon fiber prepregs in the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0016] Example 1, please refer to the drawings in the specification Figure 1 As shown in, a method for zoned pressure control in the compression molding of carbon fiber prepregs includes the following steps: S1. Division of pressurized areas: According to the three-dimensional geometric model of the mold, at least 3 or more independent pressurized areas are divided through finite element rheological simulation; the rheological simulation uses the Cross-WLF viscosity model, and the resin flow front pressure threshold is set to not less than 1.2 MPa; S2. Calculation of initial pressure: According to the prepreg ply angle θ (0° ≤ θ ≤ 90°) and resin viscosity μ (100 Pa·s ≤ μ ≤ 5000 Pa·s), calculate the initial pressure value of each area according to the formula: , where K is the material correction coefficient, calibrated through prepreg type and resin curing kinetics experiments, and the value range is 0.8 ≤ K ≤ 1.5; R i is the radial distance from the centroid of area i to the center of the mold; R0 is the characteristic radius of the mold, converting the projected area of the mold into an equivalent circular radius R eq , and 0.6 to 0.8 times of its value is taken as the characteristic radius R0 for zoned pressure control; In this embodiment, according to the three-dimensional graph of mold 3, finite element rheological simulation technology is used to divide the mold into zones. According to the simulation results (pressure gradient, flow front distribution), the mold is divided into pressurized area one, pressurized area two, and pressurized area three, and each area corresponds to an independent hydraulic control unit. Initial pressure calculation: For each pressurized area, calculate the initial pressurization value, and the specific method is as follows: Parameter acquisition: Ply angle θ: Obtain the prepreg ply angle through laser scanning or image analysis, and the value range is 0° (unidirectional ply) to 90° (orthogonal ply); Resin viscosity: Measure the viscosity of the resin at the initial curing temperature using a rotational rheometer, and the value range is 1000 Pa·s to 5000 Pa·s; Pressure formula: Initial pressure value of each areaPi Calculated by the following formula: , where K is the material correction coefficient, calibrated through the prepreg curing kinetics experiment. Place the prepreg in an autoclave, monitor the relationship between the resin curing degree and pressure, and fit to obtain K (value range: 0.8 - 1.5). R I is the radial distance from the centroid of region i to the mold center (unit: mm); R o is the mold characteristic radius, taking 0.6 - 0.8 times the radius of the equivalent circle of the mold projection area. The calculation method is: , where S is the projection area of the mold. During the molding process, collect the actual pressure values of each region through a pressure sensor. If the deviation between the actual pressure of a certain region and the target value exceeds ±5%, adjust the opening of the hydraulic valve until the pressure is stable. When the resin flow front reaches the mold edge, trigger the pressure decay mode, and reduce the pressure to the final value according to an exponential curve. In this embodiment, the directions of the arrows in pressing area 1, pressing area 2, and pressing area 3 indicate the resin flow direction. It can be seen that the resin flow direction becomes more divergent downward.

[0017] S3. Gradient pressure control: During the molding closing stage, apply gradient pressure to each region, making the pressure in the edge region 5% - 15% higher than that in the central region, and the pressure difference between adjacent regions not exceeding 6% - 8% of the total pressure value; S4. Dynamic pressure regulation: Real - time collect the pressure P i and temperature T i of each region through the pressure sensors and thermocouples embedded in the mold surface, and dynamically regulate the pressure value based on the PID algorithm, so that the deviation rate between the real - time pressure and the target pressure satisfies , and the response time ≤ 0.5 s; S5. Global pressure holding stage: When the resin curing degree α reaches 0.6 - 0.8, switch to the full - screen pressure holding mode, and keep the pressure of each region at 90% - 95% of the current maximum pressure value until curing is completed.

[0018] Example 2. On the basis of the above example, the division of the pressing regions in step S1 determines the region sensitivity S according to the following steps: a. Parameter definition and measurement: Δh is the height difference along the resin flow path on the mold surface, measured by a 3D laser scanner with an accuracy ≤ 0.1 mm; L is the characteristic length, taking 1.2 - 1.5 times the diameter of the largest inscribed circle in the mold projection area; is the change rate of curvature along the resin main flow path direction, extracted from the mold CAD model curvature data and calculated using the cubic spline interpolation method; b. Sensitivity calculation: Calculate the regional sensitivity according to the formula: , where S is dimensionless, and the units of Δh and L need to be unified to millimeters (mm); C. Sensitivity grading: When S > 0.5, it is determined as a highly sensitive pressurized area, and an additional 5% - 10% of the initial pressure needs to be added during zonal pressurization; When 0.3 ≤ S ≤ 0.5, it is determined as a moderately sensitive pressurized area, and the pressure adjustment priority is secondary; When S < 0.3, it is determined as a low - sensitive pressurized area, and it is controlled according to the standard pressure range; d. Dynamic correction: During the molding process, Δh and data are updated in real - time, and S is recalculated. If the sensitivity level changes, it triggers the adaptive adjustment of the pressure target value.

[0019] Example 3, based on the above - mentioned Example 1, in step S3, the application of the gradient pressure needs to meet the following dynamic constraint conditions: , where, is the pressure of the edge area, which is monitored in real - time by a pressure sensor, and its value range is: 5 MPa ≤ ≤ 20 MPa; is the pressure of the central area, and its value range is: 4.5 MPa ≤ ≤ 18 MPa; is the pressure - rising space, defined as the duration of the linear pressure - rising stage from the initial pressure to the target pressure, and it satisfies: 0.5S ≤ ≤ 5S; The pressure - rising time is calculated as: , where, is the target pressure, is the initial pressure, is the real - time viscosity of the resin; The pressure sensor is a fiber - optic Bragg grating sensor, its sampling frequency ≥ 100 HZ, and it is installed at the 1 / 3 position of the mold.

[0020] Example 4, based on the above - mentioned Example 1, in step S4, the control variable ΔP of the PID algorithm is calculated by the following formula: , where, , represents the real - time pressure deviation, K p , K i , K d are the proportional, integral, and differential coefficients respectively, and their value ranges satisfy: , and the value range of W is: 100 g / m 2 ≤ W ≤ 300 g / m 2 ; The integral term Using the discretized cumulative calculation method, the sampling time interval Δt ≤ 0.1 s, and the differential term is approximated by backward difference, i.e.: .

[0021] In this embodiment, based on the partitioned pressure control method for the compression molding of carbon fiber prepreg described in Embodiment 1, this embodiment further optimizes the dynamic pressure adjustment process in step S3, and introduces a PID control algorithm to achieve higher-precision pressure regulation. The implementation details of the algorithm are as follows: Discretization of the integral term: Convert the continuous integral into a discrete accumulation, with the sampling time interval Δt < 0.1 s. The formula is: ; Approximation of the differential term: Calculate the differential term using the backward difference method to avoid noise interference. The formula is: ; Control execution: Adjust the opening degree of the hydraulic valve in the corresponding area according to ΔP to quickly converge the measured pressure to the target value; if the absolute value of the deviation continuously exceeds 5%, trigger the adaptive adjustment logic to dynamically update Kp, Ki, and Kd; Effect verification: Taking a certain aviation composite skin mold as an example (the areal density of the prepreg W = 200 g / m 2 ), K P = 1.2 - 0.004 × 200 = 0.4, K i = 0.1 - 0.0005 × 200 = 0.0, K d = 0.5 - 0.002 × 200 = 0.1 (when the calculated value of K i is negative, take K i = 0.01 to ensure the integral effect); Control effect: The pressure overshoot is reduced from 12% of the traditional PID to 3%; The resin filling time is shortened by 15%, and the finished product thickness tolerance is controlled within ±0.05 mm, meeting the AS9100 aerospace standard.

[0022] Embodiment 5, based on Embodiment 1, in step S5, the resin cure degree α is calculated in real time through the following modified Arrhenius kinetic model: , where A is the frequency factor, calibrated through the differential scanning calorimetry experiment of isothermal DSC, with the unit s -1 , E is the apparent activation energy, obtained through non-isothermal DSC curve fitting, with the unit kJ / mol, R is the ideal gas constant, is the real-time temperature, measured by the thermocouple embedded in the mold, with the sampling frequency ≥ 1 Hz, t is the current cumulative curing time, calculated from the resin gel point; and the following constraint conditions are satisfied: when the temperature T < T gelWhen the degree of cure calculation freezes at the resin gel temperature, i.e., = 0; the applicable temperature range of the model is T gel ≤ T ≤ T degradation (resin degradation temperature); the calibration method of the frequency factor A and the activation energy E includes the following steps: (1) Through an isothermal DSC test, measure the degree of cure - time curve at a constant temperature T i and fit to obtain A(T i ); (2) Through a non - isothermal DSC test, scan at a heating rate of β and calculate E using the Kissinger equation: where T p is the temperature of the curing exothermic peak; (3) Perform linear regression on multiple groups of A(T i ) and T i to obtain the global parameters A0 and E A in A = A0exp(-EA / RT); the measurement of the real - time temperature meets the following conditions: Install the thermocouple at a depth of 1 / 3 of the mold surface and the distance from the resin flow front ≤ 10 mm; the temperature data is processed by moving average filtering with a window width ≤ 5 s to suppress noise interference.

[0023] Example 6, on the basis of the above example, further includes a defect suppression step: When the pressure fluctuation in a certain area reaches the set threshold and the duration reaches the predetermined condition, trigger dynamic pressure compensation, which specifically includes the following steps: (S1) Pressure fluctuation detection: Real - time collect the pressure value P 实测 of the target area with a sampling frequency ≥ 10 Hz, and calculate the pressure volatility ΔP 波动 : , when ΔP 波动 > 8% and lasts for ≥ 10 S, trigger the compensation action; (S2) Temperature - pressure coupling correction: According to the real - time temperature deviation, calculate the corrected pressure P 修正 according to the following formula: [[ID=F41]] , where: T avg is the real - time average temperature of the trigger compensation area, measured by the thermocouple with an accuracy of ±1 °C, T set is the target temperature set by the process; K is the temperature - pressure coupling coefficient, with a value range of 0.1 ≤ k ≤ 0.3, calibrated through the pre - impregnated material rheological experiment; (S3) Compensation execution and feedback: Apply the corrected pressure P 修正Input molding control system, which adjusts the opening degree of the hydraulic proportional valve, and the response time ≤ 1 s; if the pressure fluctuation rate is still > 5% after compensation, then secondary compensation is triggered: pause the molding process and start mold cooling, and the cooling rate is controlled at 2 °C to 5 °C / min; the calibration method of the temperature-pressure coupling coefficient k includes: under constant pressure conditions, measure the resin viscosity change rate corresponding to different temperature deviations (T avg −T set ), and fit a linear proportional relationship; the uniformity deviation of the cooling rate in the secondary compensation ≤ 10%; the pressure sensor is a piezoelectric sensor, which is installed in the contact area between the mold surface and the prepreg, and the surface is covered with a high-temperature resistant insulating layer; the pressure data needs to be processed by Kalman filtering to suppress high-frequency noise interference.

[0024] Example 7, A pressurization control system for implementing any one of the above methods, including: A. Distinguish the mold: A plurality of piezoelectric pressure sensors and multiple groups of thermocouples are evenly distributed on the surface of the mold cavity. Among them, the pressure sensors are embedded in a matrix form, covering the resin flow front and the interlayer interface of each independent pressurization area; the thermocouples are arranged at intervals along the resin main flow path, the spacing within the group ≤ 50 mm, and each group contains at least 3 temperature measurement points; The hydraulic press is rigidly connected to the partitioned mold, providing the main pressure output required for molding, with a pressure output range of 5 - 100 MPa, an accuracy ≤ ±0.5% FS, the piston stroke speed of the hydraulic press is adjustable, with an adjustment range of 0.1~10 mm / s, and is equipped with a displacement feedback sensor, with a resolution ≤ 1 μm; Multi-channel servo hydraulic station: Each hydraulic channel is independently controlled, equipped with a proportional valve, whose response time < 30 ms, and the pressure adjustment accuracy ≤ ±0.5% FS; the output pressure range of the hydraulic station covers 5~30 MPa, supporting the gradient pressure superposition mode; B. Control terminal: Built-in process parameter optimization module, which realizes the following functions based on the BP neural network: real-time fusion of pressure and temperature data, prediction of the resin flow front position and curing degree distribution; dynamically generate the pressure target value P 目标 and the pressure increase rate R ramp , and closed-loop control the opening degree of the proportional valve through the PID algorithm; support multi-objective optimization, including minimizing porosity, shortening the molding cycle and reducing energy consumption; C. Data cross-architecture: The pressure sensor and the thermocouple are connected to the control terminal through the CAN bus, and the data sampling frequency ≥ 100 Hz; real-time Ethernet communication is used between the control terminal and the servo hydraulic station, and the instruction delay < 1 ms.

[0025] Example 8, On the basis of the above example, the flow rate Q of the proportional valve and the opening instruction V satisfy the following relationship: , Among them, C u is the valve flow coefficient, and its value range is calibrated through experiments; is the pressure difference before and after the valve, satisfying 0.5 MPa ≤ ΔP ≤ 10 MPa, ρ is the density of the hydraulic oil, and the nominal value is taken as 850 - 900 kg / m³ 3 ; Vmax is the maximum opening voltage of the proportional valve, fixed at 10 V, and the opening command V satisfies 0 ≤ V ≤ Vmax; and the following constraint conditions are satisfied: when the hydraulic oil temperature T > 60 °C, C u needs to be dynamically corrected according to ; the flow linearity error of the proportional valve ≤ 1.5% FS; the calibration method of the valve flow coefficient C u includes: measuring the flow rate Q corresponding to different opening commands V under a constant pressure difference ΔP = 5 MPa, and fitting a non - linear regression model; during the calibration process, the hydraulic oil temperature is controlled at 40 ± 2 °C, and the viscosity range is 32 - 46 cSt; the proportional valve is integrated with a pressure difference compensation module, when it is detected that the ΔP fluctuation exceeds ± 5%, the opening command V is automatically adjusted to stabilize the flow rate; the compensation response time ≤ 50 ms, and the flow rate deviation after compensation ≤ 1%.

[0026] Example 9, on the basis of the above - mentioned example, the optimization module trains the neural network through the following objective function: , where is the real - time pressure value of the i - th area, measured by a piezoelectric pressure sensor; is the optimal pressure value calibrated through experiments, determined by the pre - impregnated material rheological property test and the porosity minimization experiment; is the actual curing time, defined as the time from the start of molding to the resin curing degree α ≥ 0.95; is the target curing time set by the process; λ is the weight coefficient, and its value range is 0.6 ≤ λ ≤ 1.2, and its value satisfies a linear relationship with the pre - impregnated material gram weight W (unit: g / m²) as λ = 0.6 + 0.002W; and the following conditions are satisfied: 1. The training data set contains historical process parameters, real - time sensor data, and post - detection data (porosity, interlaminar shear strength) with a quantity ≥ 10,000 groups; 2. The neural network training adopts the Levenberg - Marquardt algorithm, and the number of hidden layer nodes is adaptively adjusted according to the number of mold partitions; 3. The optimization result of the objective function needs to pass cross - validation, and the test set error ≤ 3%.

[0027] Example 10, a carbon fiber pre - impregnated material molding process by compression molding, applying the method described in any one of the above, includes a. The pre - impregnated material laying stage: the adjacent layer laying angle difference Δθ ≥ 45 °, and the single - layer fiber volume fraction V f is controlled within 55% ≤ V f≤62%; The ply orientation is topologically optimized according to the mold geometric features to ensure that the deviation between the fiber orientation and the principal stress direction is ≤10°; During the compression molding heating stage: the heating rate R heat ≤3 °C / min, and it is maintained at t volatile within the temperature range T hold =80 - 120 °C for t δ ≥10 min to fully discharge the volatiles; During the volatiles discharge period, the mold micro-opening 成型 ≤0.1 mm, and vacuum-assisted exhaust is applied with a vacuum degree ≤ -90 kPa; During the post-curing stage: it is maintained at t relax for ≥30 min at 80% of the forming pressure P post to eliminate the interfacial residual stress; The temperature is kept constant at T cure =Tcure + 10 °C during the post-curing, where Tcure is the resin curing peak temperature; The fiber volume fraction V f is checked by the following formula: where N is the number of plies, determined by optical scanning or X-ray detection with an error ≤1, m is the mass of a single-layer prepreg measured by a high-precision balance; Q f is the fiber density, with a value of 1.75 - 1.85 g / cm 3 calibrated according to the fiber type; A is the ply area extracted from the mold CAD model with an accuracy ≤0.5%; h is the theoretical single-layer thickness calculated as h = m / (Q f ×A); The stress holding time t relax during the post-curing stage is determined by the following formula: where θ is the resin creep coefficient calibrated by dynamic mechanical analysis (DMA) experiment in units of s; E matrix is the resin elastic modulus with a value of 3.0 - 4.5 GPa; E fiber is the fiber elastic modulus with a value of 230 - 300 GPa; σ initial is the initial interfacial stress measured by a residual stress tester; σ final is the allowable residual stress threshold set to ≤10 MPa.

[0028] As described above, it is only the preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent substitutions or changes, shall be covered by the protection scope of the present invention.

Claims

1. A partitioned pressure control method for compression molding of carbon fiber prepreg, characterized in that, Including the following steps: S1. Pressurization area division: According to the three-dimensional geometric model of the mold, at least three or more independent pressurization areas are divided through finite element rheological simulation; S2. Initial pressure calculation: According to the prepreg ply angle θ (0° ≤ θ ≤ 90°) and resin viscosity μ (100 Pa·s ≤ μ ≤ 5000 Pa·s), calculate the initial pressure values of each region according to the formula: , where K is the material correction coefficient, calibrated through prepreg type and resin curing kinetics experiments, with a value range of 0.8 ≤ K ≤ 1.5; R i is the radial distance from the centroid of region i to the center of the mold; R0 is the characteristic radius of the mold, converting the projected area of the mold into an equivalent circular radius R eq , and take 0.6 to 0.8 times its value as the characteristic radius R0 for zonal pressure control; S3. Gradient pressurization control: In the mold closing stage, gradient pressure is applied to each area, so that the pressure in the edge area is 5% - 15% higher than that in the central area, and the pressure difference between adjacent areas does not exceed 6% - 8% of the total pressure value; S4. Dynamic pressure regulation: The pressure sensors and thermocouples embedded in the die surface are used to collect the pressure P of each area in real time i and temperature T i . Based on the PID algorithm, the pressure value is dynamically adjusted to make the deviation rate between the real-time pressure and the target pressure meet , and the response time ≤ 0.5 s; S5. Global pressure holding stage: When the resin curing degree α reaches 0.6 - 0.8, switch to the full-screen pressure holding mode, and keep the pressure in each area at 90% - 95% of the current maximum pressure value until curing is completed.

2. The partitioned pressure control method for molding a carbon fiber prepreg by compression molding according to claim 1, characterized in that: In step S1, the division of the pressurization area determines the area sensitivity S according to the following steps: a. Parameter definition and measurement: Δh is the height difference of the mold surface along the resin flow path, measured by a 3D laser scanner; L is the characteristic length, taking 1.2 - 1.5 times the diameter of the largest inscribed circle in the mold projection area; is the change rate of curvature along the resin main flow path. The curvature data is extracted from the mold CAD model and calculated using the cubic spline interpolation method; b. Sensitivity calculation: Calculate the regional sensitivity according to the formula: , where S is dimensionless, and the units of Δh and L need to be unified as millimeters (mm); C. Sensitivity classification: When S > 0.5, it is determined as a highly sensitive pressurization area, and an additional 5% - 10% of the initial pressure needs to be added during zoned pressurization; When 0.3 ≤ S ≤ 0.5, it is determined as a medium-sensitive pressurization area, and the pressure adjustment priority is secondary; When S < 0.3, it is determined as a low-sensitive pressurization area, and it is controlled according to the standard pressure range; d. Dynamic correction: During the molding process, update Δh and data in real time, recalculate S, and if the sensitivity level changes, trigger the adaptive adjustment of the pressure target value.

3. A zoning pressure control method for compression molding of carbon fiber prepregs according to claim 1, characterized in that: The application of the gradient pressure in step S3 needs to satisfy the following dynamic constraint conditions: , where is the pressure in the edge region, which is monitored in real time by a pressure sensor, and its value range is: 5 MPa ≤ ≤ 20 MPa; is the pressure in the central region, and its value range is: 4.5 MPa ≤ ≤ 18 MPa; is the pressure boost space, which is defined as the duration of the linear pressure boost stage from the initial pressure to the target pressure, and satisfies: 0.5 s ≤ ≤ 5 s; The pressure boost time is calculated as: , where is the target pressure, is the initial pressure, is the real-time viscosity of the resin; The pressure sensor is a fiber Bragg grating sensor, whose sampling frequency ≥ 100 HZ, and it is installed at the 1 / 3 position of the mold.

4. A zoning pressure control method for molding a carbon fiber prepreg by compression molding according to claim 1, characterized in that: In step S4, the control quantity ΔP of the PID algorithm is calculated by the following formula: , Among them, , representing the real-time pressure deviation, K p , K i , K d are the proportional, integral, and differential coefficients respectively, and their value ranges satisfy: , and the value range of W is: 100 g / m 2 ≤W≤300 g / m 2 ; the integral term adopts a discretized cumulative calculation method, the sampling time interval Δt ≤ 0.1 s, and the differential term is approximated by backward difference, that is: .

5. A zoning pressure control method for compression molding of carbon fiber prepreg according to claim 1, characterized in that: In the step S5, the resin curing degree α is calculated in real time through the following modified Arrhenius kinetic model: , where A is the frequency factor, calibrated through the differential scanning calorimetry experiment of isothermal DSC, with the unit s -1 , E is the apparent activation energy, obtained through non-isothermal DSC curve fitting, with the unit kJ / mol, R is the ideal gas constant, is the real-time temperature, measured through the thermocouple embedded in the mold, with the sampling frequency ≥ 1 Hz, t is the current cumulative curing time, calculated starting from the resin gel point; and the following constraint conditions are satisfied: when the temperature T < T gel (resin gel temperature), the curing degree calculation freezes, that is = 0; the applicable temperature range of the model is T gel ≤ T ≤ T degradation (resin degradation temperature); the calibration method of the frequency factor A and the activation energy E includes the following steps: (1) Through the isothermal DSC experiment, measure the curing degree-time curve at a constant temperature T i , and fit to obtain A(T i ); (2) Through the non-isothermal DSC experiment, scan at a heating rate β, and calculate E using the Kissinger equation: where T p is the curing exothermic peak temperature; (3) Conduct linear regression on multiple groups of A(T i ) and T i to obtain the global parameters A0 and E A in A = A0exp(-EA / RT); the measurement of the real-time temperature satisfies the following conditions: Install the thermocouple at a depth of 1 / 3 of the mold surface, and the distance from the resin flow front ≤ 10 mm; the temperature data is processed by moving average filtering, with the window width ≤ 5 s, to suppress noise interference.

6. A zoning pressure control method for compression molding of carbon fiber prepreg according to claim 1, characterized in that: It also includes a defect suppression step: When the pressure fluctuation in a certain area reaches the set threshold and the duration reaches the predetermined condition, dynamic pressure compensation is triggered, which specifically includes the following steps: (S1), Pressure fluctuation detection: Real-time collect the pressure value P of the target area 实测 , with a sampling frequency ≥ 10Hz, calculate the pressure volatility ΔP 波动 : , when ΔP 波动 > 8% and lasts ≥ 10S, trigger the compensation action; (S2), Temperature-pressure coupling correction: Calculate the corrected pressure P according to the real-time temperature deviation using the following formula 修正 : , Where: T avg is the real-time average temperature of the trigger compensation area, measured by a thermocouple with an accuracy of ±1°C, T set is the target temperature set by the process; K is the temperature-pressure coupling coefficient, with a value range of 0.1 ≤ k ≤ 0.3, calibrated through the rheological experiment of prepreg; (S3), Compensation Execution and Feedback: Input the corrected pressure P 修正 into the molding control system, adjust the opening of the hydraulic proportional valve, and the response time ≤ 1 s; if the pressure fluctuation rate after compensation is still > 5%, then trigger secondary compensation: pause the molding process and start mold cooling, and control the cooling rate to be 2°C to 5°C / min; the calibration method of the temperature-pressure coupling coefficient k includes: under constant pressure conditions, measure the resin viscosity change rate corresponding to different temperature deviations (T avg - T set ), and fit a linear proportional relationship; the uniformity deviation of the cooling rate in the secondary compensation ≤ 10%; the pressure sensor is a piezoelectric sensor, installed in the contact area between the mold surface and the prepreg, and the surface is covered with a high-temperature resistant insulating layer; the pressure data needs to be processed by Kalman filtering to suppress high-frequency noise interference.

7. A pressurization control system for implementing the method according to any one of claims 1-6, characterized in that Including: A. Distinguishing the mold: A plurality of piezoelectric pressure sensors and multiple groups of thermocouples are evenly distributed on the surface of the mold cavity. Among them, the pressure sensors are embedded in a matrix form, covering the resin flow front and the interlayer interface of each independent pressurization area; the thermocouples are arranged at intervals along the resin main flow path, the spacing within the group ≤ 50 mm, and each group contains at least 3 temperature measurement points; The hydraulic press is rigidly connected to the zoned mold, providing the main pressure output required for molding, with a pressure output range of 5 - 100 MPa, an accuracy ≤ ±0.5% FS, the piston stroke speed of the hydraulic press is adjustable, with an adjustment range of 0.1 - 10 mm / s, and it is equipped with a displacement feedback sensor with a resolution ≤ 1 μm; Multi-channel servo hydraulic station: Each hydraulic channel is independently controlled, equipped with a proportional valve, with a response time < 30 ms and a pressure adjustment accuracy ≤ ±0.5% FS; the output pressure range of the hydraulic station covers 5 - 30 MPa, supporting the gradient pressure superposition mode; B. Control Terminal: It is built with a process parameter optimization module, which realizes the following functions based on the BP neural network: real-time fusion of pressure and temperature data to predict the resin flow front position and cure degree distribution; dynamically generate the pressure target value P for each region 目标 and the pressure rise rate R ramp , and closed-loop control the proportional valve opening through the PID algorithm; support multi-objective optimization, including minimizing porosity, shortening the molding cycle, and reducing energy consumption; C. Data cross-architecture: The pressure sensors and thermocouples are connected to the control terminal through the CAN bus, with a data sampling frequency ≥ 100 Hz; real-time Ethernet communication is used between the control terminal and the servo hydraulic station, and the instruction delay < 1 ms.

8. The pressure control system according to claim 7, characterized in that: The flow rate Q of the proportional valve and the opening command V satisfy the following relational formula: , Among them, C u is the valve flow coefficient, and the value range is calibrated through experiments; is the pressure difference before and after the valve, satisfying 0.5 MPa ≤ ΔP ≤ 10 MPa, ρ is the density of hydraulic oil, and the nominal value is taken as 850 - 900 kg / m3 3 ; Vmax is the maximum opening voltage of the proportional valve, fixed at 10 V, and the opening command V satisfies 0 ≤ V ≤ Vmax; and the following constraint conditions are satisfied: when the hydraulic oil temperature T > 60 °C, C u needs to be dynamically corrected according to ; the flow linearity error of the proportional valve ≤ 1.5% FS; the calibration method of the valve flow coefficient C u includes: measuring the flow rate Q corresponding to different opening commands V under a constant pressure difference ΔP = 5 MPa, and fitting a non - linear regression model; during the calibration process, the hydraulic oil temperature is controlled at 40 ± 2 °C, and the viscosity range is 32 - 46 cSt; the proportional valve is integrated with a pressure difference compensation module, when it is detected that the ΔP fluctuation exceeds ± 5%, the opening command V is automatically adjusted to stabilize the flow rate; the compensation response time ≤ 50 ms, and the flow rate deviation after compensation ≤ 1%.

9. The pressure control system according to claim 7, wherein: The optimization module trains the neural network through the following objective function: , where is the real-time pressure value of the i-th region, measured by a piezoelectric pressure sensor; is the optimal pressure value calibrated through experiments, determined by the pre-preg rheological property test and the porosity minimization experiment; is the actual curing time, defined as the time from the start of molding to the resin curing degree α≥0.95; is the target curing time set by the process; λ is the weight coefficient, with a value range of 0.6≤λ≤1.2, and its value satisfies a linear relationship with the pre-preg gram weight W (unit: g / m²) as λ = 0.6 + 0.002W; and the following conditions are met:

1. The training data set contains historical process parameters, real-time sensor data, and post-detection data (porosity, interlaminar shear strength) with a quantity ≥10,000 groups; 2. The neural network training uses the Levenberg-Marquardt algorithm, and the number of hidden layer nodes is adaptively adjusted according to the number of mold partitions; 3. The optimization result of the objective function needs to pass cross-validation, and the test set error ≤3%.

10. A zone pressurization process for molding carbon fiber prepregs by compression molding, applying the zone pressurization control method for molding carbon fiber prepregs by compression molding according to any one of claims 1-6, characterized in that, Including a, prepreg layup stage: the difference in adjacent layup angles Δθ ≥ 45°, and the single-layer fiber volume fraction V f is controlled within 55% ≤ V f ≤ 62%; the layup direction is topologically optimized according to the mold geometric features to ensure that the deviation of the fiber orientation from the principal stress direction ≤ 10°; molding heating stage: the heating rate R heat ≤ 3°C / min, and it is maintained at t volatile for t ≥ 10 min within the temperature range T hold = 80 - 120°C to fully discharge volatiles; during the discharge of volatiles, the mold micro-opening δ ≤ 0.1 mm, and vacuum-assisted exhaust is applied with a vacuum degree ≤ -90 kPa; post-curing stage: maintained at t 成型 for t ≥ 30 min at 80% of the forming pressure P relax to eliminate interfacial residual stress; the temperature is kept constant at T post = T cure + 10°C during post-curing, where Tcure is the resin curing peak temperature; the fiber volume fraction V f is verified by the following formula: , Among them, N is the number of plies, determined by optical scanning or X-ray detection, with an error ≤ 1, m is the mass of a single-layer prepreg, measured by a high-precision balance; Q f is the fiber density, with a value of 1.75 - 1.85 g / cm 3 , calibrated according to the fiber type; A is the ply area, extracted from the die CAD model, with a precision ≤ 0.5%; h is the theoretical single-layer thickness, calculated as h = m / (Q f ×A); the stress holding time t relax in the post-curing stage is determined by the following formula: , where θ is the resin creep coefficient, calibrated by dynamic mechanical analysis (DMA) experiment, with the unit of s; E matrix is the resin elastic modulus, with a value range of 3.0 - 4.5 GPa; E fiber is the fiber elastic modulus, with a value of 230 - 300 GPa; σ initial is the initial interface stress, measured by a residual stress tester; σ final is the allowable residual stress threshold, set to ≤10 MPa.

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