System and method for synchronously measuring thermal expansion coefficient and chemical shrinkage coefficient of prepreg

Abstract

The invention provides a system and a method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepreg, and relates to the technical field of composite material attribute characterization, the system comprises: a heating table, which is used for placing a prepreg sample to be measured and providing an experiment temperature required by curing of the prepreg sample; the thermal infrared camera is used for measuring the surface temperature of the prepreg sample in the curing experiment process in real time; the lighting device is used for providing ambient brightness required by a curing experiment; the DIC image acquisition system is used for acquiring a high-resolution image of the prepreg sample in a curing experiment process in real time; and the data processing device is connected with the thermal infrared camera and the DIC image acquisition system, and is used for analyzing the image acquired by the DIC image acquisition system to obtain the strain of the prepreg sample and recording the strain and temperature data. The invention provides a non-contact measurement method based on an indirect volume measurement method, and the strain of the prepreg in the curing process is measured through a digital image correlation (DIC) method.

Description

Technical Field

[0001] The present invention relates to the technical field of composite material property characterization, and in particular to a system and method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs. Background Art

[0002] Continuous fiber-reinforced resin-based composites are widely used in the aerospace field due to their high specific strength and stiffness, excellent durability and fatigue resistance, and design flexibility. During the prepreg curing process, the resin cross-linking reaction causes the molecules to transform from a relatively free state to a mutually cross-linked three-dimensional network structure. The distance between the molecules decreases, resulting in a decrease in the total volume and chemical shrinkage. Simultaneously, due to the action of heat flow, the thermal motion of the resin molecules intensifies, the chemical bonds stretch due to heat, and the free volume increases, leading to thermal expansion. Thermal expansion and chemical shrinkage during the prepreg process are the main sources of internal stress in the manufacture of resin-based composites, leading to manufacturing defects such as wrinkles and warping in the final product. Therefore, accurately measuring the thermal expansion coefficient and chemical shrinkage coefficient of the prepreg is of great significance. However, since thermal expansion and chemical shrinkage occur simultaneously during the curing process, and the parameters vary not only with temperature but also with the degree of cure, this poses great difficulties in measuring the thermal expansion and chemical shrinkage coefficients.

[0003] In the prior art, there are two methods for measuring the coefficient of thermal expansion and the coefficient of chemical shrinkage: direct volume measurement and indirect volume measurement. Among them, the direct volume measurement method mainly includes the capillary method, the drainage method and the weight method. This method calculates the coefficient of thermal expansion and the coefficient of chemical shrinkage by directly measuring the volume change of the resin, but this method often lacks the output of the digital system and requires visual reading. The test results are affected by various factors and the measurement accuracy is low. The non-volume measurement method indirectly reflects the volume change of the resin by measuring the one-dimensional or two-dimensional dimensions of the resin through contact or non-contact sensors, such as DMA, laser beam, etc., but this method is not conducive to distinguishing between thermal expansion and chemical shrinkage during the curing process, and the test results are affected by the accuracy of the instrument; in addition, due to the anisotropy of prepregs, the above methods cannot measure the thermal expansion coefficient and chemical shrinkage coefficient of the prepreg in all directions. Summary of the Invention

[0004] In response to the problems mentioned in the above background technology, the present invention provides an experimental method and system that can simultaneously measure the thermal expansion and chemical shrinkage coefficients of prepreg in any direction.

[0005] Specifically, the first aspect of the present invention provides a system for synchronously measuring the thermal expansion and chemical shrinkage coefficients of prepregs, comprising: A heating table, which is used to place the prepreg sample to be tested and provide the experimental temperature required for its curing; Thermal infrared camera, which is used to measure the surface temperature of prepreg specimens in real time during the curing experiment; A lighting device, which is used to provide the ambient brightness required for the curing experiment; DIC image acquisition system, which is used to capture high-resolution images of prepreg samples in real time during the curing experiment; The data processing device is connected to the thermal infrared camera and the DIC image acquisition system, and is used to obtain the strain of the prepreg sample based on the image acquired by the DIC image acquisition system and record the strain and temperature data.

[0006] As a further illustration of the present invention, the DIC image acquisition system is specifically a high-speed camera, the lens of which is located directly above the heating stage so that it can acquire high-resolution images of the prepreg sample.

[0007] As a further illustration of the present invention, the heating platform is a flat heating platform, and the prepreg sample to be tested is placed at the center of the flat heating platform; the thermal infrared camera is located above the side of the heating platform.

[0008] A second aspect of the present invention provides a method for simultaneously measuring the thermal expansion and chemical shrinkage coefficients of prepregs, comprising the following steps: The prepreg sample to be tested is speckle sprayed and then placed on a heating table; Set up any of the above-mentioned systems for synchronously measuring the thermal expansion and chemical shrinkage coefficients of prepregs, and complete the adjustment of the thermal infrared camera, lighting device and DIC image acquisition system; Start the heating stage and heat it according to the preset program. At the same time, use the thermal infrared camera and DIC image acquisition system to collect the surface temperature changes and high-resolution images of the prepreg sample in real time. The images collected by the DIC image acquisition system are analyzed using a data processing device to obtain the strain of the prepreg sample. Combined with the temperature measured by the thermal infrared camera, the thermal expansion and chemical shrinkage coefficients of the prepreg sample are calculated.

[0009] As a further illustration of the present invention, the DIC image acquisition system is specifically a high-speed camera, the lens of which is located directly above the heating stage.

[0010] As a further illustration of the present invention, when adjusting the lighting device and the DIC image acquisition system, the DIC image acquisition system is based on the ability to capture a complete and clear image of the prepreg sample. The DIC image acquisition system is then adjusted so that the lens focus is located at the center of the prepreg sample. The system is then calibrated using a calibration plate that comes with the DIC image acquisition system.

[0011] As a further illustration of the present invention, before starting the heating stage, it is necessary to set the operating parameters of the heating stage, including temperature and heating rate, to provide a high temperature environment required for curing the prepreg.

[0012] As a further illustration of the present invention, the data processing device is used to analyze the image acquired by the DIC image acquisition system to obtain the strain of the prepreg sample, and the thermal expansion and chemical shrinkage coefficients of the prepreg sample are calculated in combination with the temperature measured by the thermal infrared camera, specifically including: The data processing device obtains strain-time data of the prepreg sample during the experiment by analyzing the images collected by the DIC image acquisition system; Outputting temperature-time data based on the real-time temperature measured by the thermal infrared camera to obtain the heating stage and the heat preservation stage of the prepreg sample; wherein the heating stage corresponds to the thermal expansion stage, and the heat preservation stage corresponds to the chemical contraction stage; The thermal expansion coefficient of the prepreg sample is obtained based on the strain-temperature curve in the thermal expansion stage; the chemical shrinkage coefficient of the prepreg sample is obtained based on the strain-curing degree curve in the chemical shrinkage stage.

[0013] As a further illustration of the present invention, the calculation formula of the thermal expansion coefficient is as follows: ; Where, is the thermal expansion coefficient of the prepreg sample, and the subscripts 1 and 2 represent the fiber direction or the perpendicular fiber direction. is the strain in the thermal expansion stage, is the temperature change in this stage.

[0014] As a further illustration of the present invention, the calculation formula of the chemical shrinkage coefficient is as follows: ; Where, is the chemical shrinkage coefficient of the prepreg sample, and the subscripts 1 and 2 represent the fiber direction or the perpendicular fiber direction. is the strain in the chemical shrinkage stage, is the change in the degree of curing at this stage.

[0015] Compared with the prior art, the present invention has the following beneficial technical effects: 1. The experimental system provided by the present invention is used to simultaneously measure the thermal expansion coefficient and chemical shrinkage coefficient of prepregs. A flat heating platform provides a high-temperature environment, providing a curing reaction site for the prepreg. A thermal infrared camera is used to collect the surface temperature of the prepreg. The DIC method is used to accurately measure the two-dimensional strain of the prepreg surface, thereby realizing the measurement of the thermal expansion coefficient and chemical shrinkage coefficient. The system is simple to operate and has high measurement accuracy. It can also meet the measurement requirements of the thermal expansion coefficient and chemical shrinkage coefficient of prepregs of different types.

[0016] 2. The experimental method provided by the present invention for simultaneously measuring the thermal expansion coefficient and chemical shrinkage coefficient of prepreg is based on a non-direct volume measurement method and a non-contact measurement method. The strain during the prepreg curing process is measured by the DIC method, which solves the problem of low measurement accuracy of the traditional direct volume measurement method and the problem that the existing technology cannot measure the thermal expansion coefficient and chemical shrinkage rate of the prepreg. In addition, this method can be directly used to measure the thermal expansion and chemical shrinkage coefficient of pure resin, and the process is exactly the same.

[0017] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings are used to provide further understanding of the present technical solution and constitute a part of the specification. Together with the embodiments of the present technical solution, they are used to explain the present technical solution and do not constitute a limitation to the present technical solution.

[0019] Figure 1 The present invention is a schematic diagram of an experimental system for measuring the thermal expansion coefficient and chemical shrinkage coefficient of prepreg.

[0020] Figure 2 It is a schematic diagram of the size of the prepreg sample provided by the present invention.

[0021] Figure 3 It is a schematic diagram of the effective area of the prepreg sample provided by the present invention.

[0022] Figure 4 The present invention provides a flow chart of an experimental method for measuring the thermal expansion coefficient and chemical shrinkage coefficient of prepreg.

[0023] Figure 5 This is an experimental curve diagram of the thermal expansion coefficient and chemical shrinkage coefficient of the prepreg obtained in an embodiment of the present invention.

[0024] Figure 6 These are the thermal expansion strain-temperature curve and the chemical shrinkage strain-curing degree curve of the prepreg obtained in the embodiment of the present invention.

[0025] Figure 7 This is a strain cloud diagram of the prepreg test collected in the embodiment of the present invention.

[0026] Reference numerals: Heating stage 100 ; prepreg sample 200 ; prepreg sample effective area 210 ; thermal infrared camera 300 ; DIC image acquisition system 400 ; lighting device 500 ; data processing device 600 . DETAILED DESCRIPTION

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0028] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0029] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not require further definition or explanation in subsequent drawings.

[0030] In the description of the present invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer" and the like indicate positions or locations based on the positions shown in the accompanying drawings, or the positions or locations in which the inventive product is typically placed when in use. These terms are intended solely to facilitate the description of the present invention and to simplify the description, and are not intended to indicate or imply that the devices or components referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. Furthermore, the terms "first," "second," and "third," etc., are used solely to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0031] Furthermore, terms such as "horizontal" and "vertical" do not necessarily mean that a component must be absolutely horizontal or overhanging, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but rather that it can be slightly tilted.

[0032] In the description of the present invention, it should also be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed connections, detachable connections, or integral connections; they may refer to mechanical connections or electrical connections; they may refer to direct connections or indirect connections through an intermediate medium; and they may refer to internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0033] like Figure 1 As shown, the present invention provides a system for synchronously measuring the thermal expansion and chemical shrinkage coefficients of prepregs, comprising: a heating stage 100, which is used to place a prepreg sample 200 to be measured and provide the experimental temperature required for its curing; a thermal infrared camera 300, which is used to measure the surface temperature of the prepreg sample 200 in real time during the curing experiment; an illumination device 500, which is used to provide the ambient brightness required for the curing experiment; a DIC image acquisition system 400, which is used to acquire high-resolution images of the prepreg sample 200 in real time during the curing experiment; and a data processing device 600, which is connected to the thermal infrared camera 300 and the DIC image acquisition system 400 and is used to process the images acquired by the DIC image acquisition system 400 during the experiment, obtain the strain of the prepreg sample 200 during the experiment, and record the strain and temperature data.

[0034] In some achievable embodiments, the DIC image acquisition system is preferably a high-speed camera, the lens of which is located directly above the heating stage 100 so as to be able to capture a complete image of the prepreg sample 200 .

[0035] In some feasible embodiments, the above-mentioned heating platform 100 is preferably a flat heating platform, and the prepreg sample 200 to be tested is placed at the center of the flat heating platform. The flat heating platform provides a place for the curing reaction of the prepreg sample to be tested, and can realize functions such as heating, heat preservation, and adjustment of heating power.

[0036] In some feasible embodiments, the thermal infrared camera 300 is preferably located above and to the side of the heating stage 100 so as to be able to collect the surface temperature of the prepreg sample.

[0037] In some implementations, the data processing device 600 is specifically a computer with built-in DIC data analysis software.

[0038] like Figure 4 As shown, the size is Taking the unidirectional tape composite material prepreg as an example, the measurement method of the system for synchronously measuring the thermal expansion and chemical shrinkage coefficient of the prepreg includes the following steps: Step 1: The prepreg sample 200 to be tested is subjected to speckle spraying and then placed on the heating platform 100 .

[0039] Specifically, prepregs with different curing degrees are prepared by hot pressing and then cut into sizes of Prepreg specimens (such as Figure 2 As shown), the sample is then speckled and sprayed to ensure that the speckles are uniform and clear. To ensure the accuracy of the experimental data, the center of the prepreg sample 200 is selected as the sample effective area 210 (as shown). Figure 3 shown).

[0040] Step 2: Set up the above-mentioned system for synchronously measuring the thermal expansion and chemical shrinkage coefficients of prepregs, and complete the adjustment of the thermal infrared camera 300, the lighting device 500 and the DIC image acquisition system 400.

[0041] In some implementations, the DIC image acquisition system is specifically a high-speed camera, with its lens positioned directly above the heating stage. When adjusting the lighting device and the DIC image acquisition system, the DIC image acquisition system is designed to capture a complete and clear image of the prepreg sample 200. The high-speed camera is then adjusted so that its lens focus is centered on the prepreg sample 200. The system is then calibrated using the calibration plate provided with the DIC image acquisition system. After calibration, the positions of the prepreg sample and the DIC image acquisition system must remain unchanged.

[0042] Step 3: Start the heating stage 100 to heat according to a preset program, and simultaneously use the thermal infrared camera 300 and the DIC image acquisition system 400 to collect the surface temperature change and high-resolution image of the prepreg sample 200 in real time.

[0043] It should be noted that before starting the heating stage, the operating parameters of the heating stage 100, including the temperature and the heating rate, need to be set to provide the high temperature environment required for curing the prepreg.

[0044] Step 4: Use a data processing device to analyze the images collected by the DIC image acquisition system to obtain the strain of the prepreg sample. Combined with the temperature measured by the thermal infrared camera, the thermal expansion and chemical shrinkage coefficients of the prepreg sample are calculated.

[0045] The above step 4 specifically includes the following process: Step 401: The data processing device 600 analyzes the high-resolution image acquired by the DIC image acquisition system 400 and outputs the strain data of the prepreg sample 200 during the experiment.

[0046] Step 402: Based on the real-time temperature measured by the thermal infrared camera 300, the heating stage and the insulation stage of the prepreg sample 200 are obtained; wherein the heating stage corresponds to the thermal expansion stage, and the insulation stage corresponds to the chemical contraction stage.

[0047] Taking unidirectional tape composite prepreg as an example, Figure 5 The fiber direction strain-time curve of the prepreg sample 200 during the experiment is shown. The flat heating table heats the prepreg sample, and the prepreg sample gradually solidifies after being heated, accompanied by thermal expansion and chemical contraction. Figure 5 As shown in the figure, the thermal expansion coefficient and chemical shrinkage coefficient measurement experimental process is divided into two stages: Thermal Expansion (CTE) Stage: During this stage, the temperature rises rapidly. The temperature set during this stage is lower than the fastest curing point. The prepreg sample does not undergo a curing reaction, but instead undergoes thermal expansion as the temperature rises. This is a purely physical change. Therefore, during this stage, the prepreg sample is considered to have only undergone thermal expansion, and this curve can be used to determine the prepreg's coefficient of thermal expansion.

[0048] Chemical Shrinkage (CSC) Stage: During this stage, the heating phase ceases and the heat preservation phase begins. Temperature data collected by the thermal infrared camera indicates that the surface temperature of the prepreg specimen has stabilized. Curing reactions are occurring during this stage, and chemical shrinkage occurs as the curing reaction proceeds. Therefore, during this stage, the prepreg specimen is considered to have only undergone chemical shrinkage, and the chemical shrinkage coefficient of the prepreg can be obtained from this curve.

[0049] Step 403: Based on the strain-time curve and the temperature-time curve of the thermal expansion stage, the strain-temperature curve of the thermal expansion stage is obtained, and the thermal expansion coefficient of the prepreg sample 200 is calculated; based on the strain-time curve and the temperature-time curve of the chemical shrinkage stage, combined with the curing kinetics equation of the prepreg sample 200, the strain-curing degree relationship curve of the chemical shrinkage stage is obtained, and the chemical shrinkage coefficient of the prepreg sample 200 is calculated.

[0050] In the thermal expansion (CTE) stage, the thermal expansion strain of the prepreg sample 200 changes linearly with the increase of temperature; in the chemical shrinkage (CSC) stage, the chemical shrinkage strain of the prepreg sample 200 changes linearly with the increase of curing degree, such as Figure 6 Therefore, specifically, the calculation formula for the thermal expansion coefficient is as follows: ; Where, is the thermal expansion coefficient of the prepreg sample 200, and the subscripts 1 and 2 represent the fiber direction or the perpendicular fiber direction. is the strain in the thermal expansion stage, is the temperature change in this stage.

[0051] The calculation formula of chemical shrinkage coefficient is as follows: ; Where, is the chemical shrinkage coefficient of the prepreg sample 200, and the subscripts 1 and 2 represent the fiber direction or the perpendicular fiber direction. is the strain in the chemical shrinkage stage, is the change in the degree of curing at this stage.

[0052] Taking the carbon fiber unidirectional tape prepreg with a curing degree of 0.7 as an example, Figure 7 The strain images of the prepreg specimens collected by the DIC image acquisition system during the experiment are shown. The strain, time, and temperature data are derived through the data processing system, and the thermal expansion strain-temperature curve and the chemical shrinkage strain-curing degree curve are calculated by combining the above formulas. In the CTE stage, the strain in the first direction per unit temperature is 4.30313*10e-7, and the strain in the second direction is 7.41029*10e-5, that is, the thermal expansion coefficients of the prepreg in the first and second directions are 4.30313*10e-7 and 7.41029*10e-5 respectively. In the CSC stage, the strain in the first direction per unit curing degree is -1.66084*10e-4, and the strain in the second direction is -0.01092, that is, the chemical shrinkage coefficients of the prepreg in the first and second directions are -1.66084*10e-4 and -0.01092 respectively.

[0053] Obviously, those skilled in the art may make various changes and modifications to this technical solution without departing from the spirit and scope of this technical solution. Thus, if these modifications and variations of this technical solution fall within the scope of the claims of this technical solution and their equivalents, this technical solution is intended to include these modifications and variations.

Claims

1. A system for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs, characterized in that: include: A heating table, which is used to place the prepreg sample to be tested and provide the experimental temperature required for its curing; Thermal infrared camera, which is used to measure the surface temperature of prepreg specimens in real time during the curing experiment; A lighting device, which is used to provide the ambient brightness required for the curing experiment; DIC image acquisition system, which is used to capture high-resolution images of prepreg samples in real time during the curing experiment; The data processing device is connected to the thermal infrared camera and the DIC image acquisition system, and is used to obtain the strain of the prepreg sample based on the image acquired by the DIC image acquisition system and record the strain and temperature data.

2. The system for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 1, characterized in that: The DIC image acquisition system is specifically a high-speed camera, the lens of which is located directly above the heating stage so that it can capture a complete image of the prepreg sample.

3. The system for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 1, characterized in that: The heating platform is a flat heating platform, and the prepreg sample to be tested is placed at the center of the flat heating platform; The thermal infrared camera is located above and to the side of the heating stage.

4. A method for synchronously measuring the thermal expansion and chemical shrinkage coefficients of prepregs, characterized in that: The process includes the following: The prepreg sample to be tested is speckle sprayed and then placed on a heating table; Set up a system for synchronously measuring the thermal expansion and chemical shrinkage coefficients of prepregs according to any one of claims 1 to 3, and complete the adjustment of the thermal infrared camera, lighting device and DIC image acquisition system; Start the heating stage and heat it according to the preset program. At the same time, use the thermal infrared camera and DIC image acquisition system to collect the surface temperature changes and high-resolution images of the prepreg sample in real time. The images collected by the DIC image acquisition system are analyzed using a data processing device to obtain the strain of the prepreg sample. Combined with the temperature measured by the thermal infrared camera, the thermal expansion and chemical shrinkage coefficients of the prepreg sample are calculated.

5. The method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 4, characterized in that: The DIC image acquisition system is specifically a high-speed camera, and its lens is located directly above the heating stage.

6. The method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 5, characterized in that: When adjusting the lighting device and the DIC image acquisition system, the DIC image acquisition system should be able to capture a complete and clear image of the prepreg sample. Then adjust the DIC image acquisition system so that its lens focus is located at the center of the prepreg sample. Then use the calibration plate that comes with the DIC image acquisition system to calibrate the system.

7. The method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 4, wherein: Before starting the heating table, it is necessary to set the working parameters of the heating table, including temperature and heating rate, to provide the high temperature environment required for prepreg curing.

8. The method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 4, wherein: The data processing device is used to analyze the image acquired by the DIC image acquisition system to obtain the strain of the prepreg sample, and the thermal expansion and chemical shrinkage coefficients of the prepreg sample are calculated in combination with the temperature measured by the thermal infrared camera, specifically including: The data processing device obtains strain-time data of the prepreg sample during the experiment by analyzing the images collected by the DIC image acquisition system; Outputting temperature-time data based on the real-time temperature measured by the thermal infrared camera to obtain the heating stage and the heat preservation stage of the prepreg sample; wherein the heating stage corresponds to the thermal expansion stage, and the heat preservation stage corresponds to the chemical contraction stage; The thermal expansion coefficient of the prepreg sample is obtained based on the strain-temperature curve in the thermal expansion stage; the chemical shrinkage coefficient of the prepreg sample is obtained based on the strain-curing degree curve in the chemical shrinkage stage.

9. The method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 8, wherein: The calculation formula of the thermal expansion coefficient is as follows: ； Where, is the thermal expansion coefficient of the prepreg sample, and the subscripts 1 and 2 represent the fiber direction or the perpendicular fiber direction. is the strain in the thermal expansion stage, is the temperature change in this stage.

10. The method for synchronously measuring thermal expansion and chemical shrinkage coefficients of prepregs according to claim 8, characterized in that: The calculation formula of the chemical shrinkage coefficient is as follows: ； Where, is the chemical shrinkage coefficient of the prepreg sample, and the subscripts 1 and 2 represent the fiber direction or the perpendicular fiber direction. is the strain in the chemical shrinkage stage, is the change in the degree of curing at this stage.

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