A method for testing and constructing a constitutive model of a carbon fiber composite laminate

Abstract

The present application relates to the technical field of testing, in particular to a kind of carbon fiber composite material layer plate constitutive model test construction method, comprising: S1 utilizes test system and measures different angle carbon fiber tensile test data;S2 for 0 degree carbon fiber layer plate tensile test data, calculate and take the average of two tests 0 degree direction elastic modulus, calculate and obtain the poisson's ratio, and take the average of two tests 0 degree to 90 degree direction poisson's ratio;S3 for 90 degree carbon fiber layer plate tensile test data, calculate and take the average of two tests 90 degree direction elastic modulus, calculate and obtain the poisson's ratio, and take the average of two tests 90 degree to 0 degree direction poisson's ratio;S4 for 45 degree carbon fiber layer plate tensile test data, calculate shear modulus and average 0 degree to 90 degree direction shear modulus;S5 finally according to the calculated composite material layer plate constitutive model;To test and construct a kind of carbon fiber composite material layer plate constitutive model.

Description

Technical Field

[0001] This invention relates to the field of testing technology, and in particular to a method for constructing a constitutive model for carbon fiber composite laminates. Background Technology

[0002] Carbon fiber composites are inorganic high-performance fibers with a carbon content exceeding 90%, transformed from organic fibers through a series of heat treatments. They are a new type of material with excellent mechanical properties, possessing the inherent characteristics of carbon materials while also exhibiting the softness and processability of textile fibers, making them a new generation of reinforcing fibers. A constitutive model, also known as the mechanical constitutive equation of a material or the stress-strain model of a material, is a mathematical expression describing the mechanical properties of a material.

[0003] The mechanical properties of carbon fiber composite laminates need to be studied, therefore a constitutive model for carbon fiber composite laminates is required. Summary of the Invention

[0004] The purpose of this invention is to provide a method for testing and constructing a constitutive model of a carbon fiber composite laminate, which aims to test and construct a constitutive model of a carbon fiber composite laminate.

[0005] To achieve the above objectives, this invention provides a method for constructing and testing a constitutive model of a carbon fiber composite laminate, comprising the following steps:

[0006] S1 used a testing system to measure carbon fiber tensile test data at different angles;

[0007] S2 calculates the elastic modulus in the 0-degree direction based on the tensile test data of the 0-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 0-degree direction. Then, it calculates the Poisson's ratio and takes the average of two tests to obtain the Poisson's ratio in the 0-degree to 90-degree direction.

[0008] S3 calculates the elastic modulus in the 90-degree direction based on the tensile test data of the 90-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 90-degree direction. Then, it calculates the Poisson's ratio and takes the average of two tests to obtain the Poisson's ratio in the 90-degree to 0-degree direction.

[0009] S4 calculates the shear modulus based on the tensile test data of 45-degree carbon fiber laminates and averages the shear modulus from 0 to 90 degrees.

[0010] S5 ultimately obtained the constitutive model of the composite laminate based on calculations.

[0011] The testing system includes a base, a left L-plate, a right L-plate, a left ball joint, a left clamp, a displacement sensor, a hydraulic servo linear cylinder, a force sensor, a right ball joint, a right clamp, an extensometer, a first strain gauge, a second strain gauge, a third strain gauge, a fourth strain gauge, a fifth strain gauge, and a sixth strain gauge.

[0012] The left L-plate is fixedly mounted on the base; the right L-plate is fixedly mounted on the base; the left ball joint is mounted on one side of the left L-plate; the left clamp is mounted on one side of the left ball joint; the displacement sensor is mounted on one side of the right L-plate; the hydraulic servo linear cylinder is mounted on one side of the displacement sensor; the force sensor is mounted on one side of the hydraulic servo linear cylinder; the right ball joint is mounted on one side of the force sensor; the right clamp is mounted on one side of the right ball joint; the extensometer is placed on the side of the base; the first strain gauge, the second strain gauge, the third strain gauge, the fourth strain gauge, the fifth strain gauge, and the sixth strain gauge are all placed on the side of the base.

[0013] The specific steps for obtaining carbon fiber tensile test data at different angles using the testing system include:

[0014] S11 was made into a material specimen using 0-degree carbon fiber material;

[0015] S12. The first strain gauge and the second strain gauge are pasted in the middle of the front side of the material specimen, and the first strain gauge and the second strain gauge are perpendicular to each other. The pasting position is marked as the first position.

[0016] S13. The third strain gauge, the fourth strain gauge, the fifth strain gauge, and the sixth strain gauge are respectively attached at symmetrical positions in the middle of the reverse side of the material specimen; the third strain gauge and the fourth strain gauge are perpendicular to each other, and the attachment position is marked as the second position; the fifth strain gauge and the sixth strain gauge are perpendicular to each other, and the attachment position is marked as the third position;

[0017] S14 The material specimen is clamped by the left clamp and the right clamp respectively, and an extensometer is installed on the material specimen. The specimen is stretched at speeds of 2 mm / min and 4 mm / min respectively. The tensile test data of the carbon fiber material at 0 degrees is measured and the stress-strain curve is plotted.

[0018] S15 involves repeating steps S12-S14 to obtain tensile test data for material specimens made of 45-degree carbon fiber and 90-degree carbon fiber, and then plotting stress-strain curves accordingly.

[0019] The present invention provides a method for constructing a constitutive model of a carbon fiber composite laminate, comprising the following steps:

[0020] S1 uses a testing system to measure tensile test data of carbon fibers at different angles; S2 calculates the elastic modulus in the 0-degree direction based on the tensile test data of the 0-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 0-degree direction. Then, Poisson's ratio is calculated based on the calculation, and the average of two tests is taken to obtain the Poisson's ratio in the 0-90 degree direction; S3 calculates the elastic modulus in the 90-degree direction based on the tensile test data of the 90-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 90-degree direction. Then, Poisson's ratio is calculated based on the calculation, and the average of two tests is taken to obtain the Poisson's ratio in the 90-degree to 0 degree direction; S4 calculates the shear modulus based on the tensile test data of the 45-degree carbon fiber laminate, and averages it to obtain the shear modulus in the 0-90 degree direction; S5 finally obtains the constitutive model of the composite laminate based on the calculation. Thus, a constitutive model of a carbon fiber composite laminate is constructed. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0022] Figure 1 This is a flowchart of a constitutive model testing and construction method for carbon fiber composite laminates according to the present invention.

[0023] Figure 2 This is a flowchart of the present invention for obtaining carbon fiber tensile test data at different angles using a testing system.

[0024] Figure 3 This is a schematic diagram of the test system of the present invention.

[0025] Figure 4 This is a schematic diagram of the material specimen of the present invention.

[0026] Figure 5 This is a schematic diagram of the third, fourth, fifth, and sixth strain gauges of the present invention being attached to the material specimen.

[0027] Figure 6 This is a schematic diagram of the first and second strain gauges of the present invention being attached to the material specimen.

[0028] Figure 7 This is a schematic diagram of the extensometer of the present invention installed on a material specimen.

[0029] Figure 8 This is the stress-strain curve of 0° carbon fiber.

[0030] Figure 9 It is the stress-strain curve of 45° carbon fiber.

[0031] Figure 10 It is the stress-strain curve of 90° carbon fiber.

[0032] 1-Base, 2-Left L-plate, 3-Right L-plate, 4-Left ball joint, 5-Left clamp, 6-Displacement sensor, 7-Hydraulic servo linear cylinder, 8-Force sensor, 9-Right ball joint, 10-Right clamp, 11-Extensometer, 12-First strain gauge, 13-Second strain gauge, 14-Third strain gauge, 15-Fourth strain gauge, 16-Fifth strain gauge, 17-Sixth strain gauge, 18-Material specimen. Detailed Implementation

[0033] Please see Figures 1-10 ,in, Figure 1 This is a flowchart of a constitutive model testing and construction method for carbon fiber composite laminates according to the present invention. Figure 2 This is a flowchart of the present invention for obtaining carbon fiber tensile test data at different angles using a testing system. Figure 3 This is a schematic diagram of the test system of the present invention. Figure 4 This is a schematic diagram of the material specimen of the present invention. Figure 5 This is a schematic diagram of the third, fourth, fifth, and sixth strain gauges of the present invention being attached to the material specimen. Figure 6 This is a schematic diagram of the first and second strain gauges of the present invention being attached to the material specimen. Figure 7 This is a schematic diagram of the extensometer of the present invention installed on a material specimen. Figure 8 This is the stress-strain curve of 0° carbon fiber. Figure 9 It is the stress-strain curve of 45° carbon fiber. Figure 10 It is the stress-strain curve of 90° carbon fiber.

[0034] This invention provides a method for constructing a constitutive model of carbon fiber composite laminates, the specific steps of which include:

[0035] S1 used a testing system to measure carbon fiber tensile test data at different angles;

[0036] S11 was made into material specimen 18 using 0-degree carbon fiber material;

[0037] Material specimen 18 has a slender middle gauge length and wider clamping ends to ensure that plastic deformation occurs first at the center of the specimen during tensile testing, ensuring that the fracture occurs within the gauge length and thus providing accurate test data. The total length of the specimen is 180 mm, the width of the clamping ends is 30 mm, the gauge length is 55 mm, and the width within the gauge length is 10 mm. Considering that friction alone may not be sufficient to provide the force required for tensile fracture, holes are drilled in the specimen, and bolts pass through the small holes to provide additional axial force, such as... Figure 4 As shown.

[0038] S12. The first strain gauge 12 and the second strain gauge 13 are pasted at the middle position of the front side of the material specimen 18, and the first strain gauge 12 and the second strain gauge 13 are perpendicular to each other. The pasting position is marked as the first position.

[0039] like Figure 6 As shown.

[0040] S13 The third strain gauge 14, the fourth strain gauge 15, the fifth strain gauge 16 and the sixth strain gauge 17 are respectively attached at symmetrical positions in the middle of the reverse side of the material specimen 18; the third strain gauge 14 and the fourth strain gauge 15 are perpendicular to each other, and the attachment position is marked as the second position; the fifth strain gauge 16 and the sixth strain gauge 17 are perpendicular to each other, and the attachment position is marked as the third position;

[0041] like Figure 5 As shown.

[0042] S14 The material specimen 18 is clamped by the left clamp 5 and the right clamp 10 respectively, and an extensometer 11 is installed on the material specimen 18. The specimen is stretched at speeds of 2 mm / min and 4 mm / min respectively. The tensile test data of the 0-degree carbon fiber material is measured and the stress-strain curve is plotted.

[0043] like Figure 3 , Figure 7 As shown; during installation, the intersection of the upper, lower, left and right symmetrical planes of the material specimen 18 is on the axis of the hydraulic servo linear cylinder, ensuring that the specimen is not subjected to tensile, compressive, bending and torsional loads in the initial installation state. After installing the extensometer 11, connect all signals to the same data acquisition system for synchronous acquisition; stretch at speeds of 2 mm / min and 4 mm / min respectively, calculate the stress and strain of the gauge length of the material according to formulas (1)-(4), and then plot the stress-strain curve.

[0044] Material tensile engineering stress Engineering strain The calculation formulas are shown in equations (1) and (2):

[0045]

[0046] In the formula, F represents the tensile force on the material along the tensile direction, i.e., the tensile force of the hydraulic servo linear cylinder, and b and d are the gauge length width and thickness of the specimen, respectively. Gauge length of the specimen The elongation within the body is the elongation of extensometer 11. The actual stress and strain are calculated according to equations (3) and (4).

[0047] (3) (4)

[0048] S15 Repeat steps S12-S14 sequentially for material specimen 18 made of 45-degree carbon fiber material and material specimen 18 made of 90-degree carbon fiber material to obtain tensile test data of 45-degree carbon fiber material and 90-degree carbon fiber material, and plot stress-strain curves accordingly.

[0049] like Figures 8-10 As shown.

[0050] S2 calculates the elastic modulus in the 0-degree direction based on the tensile test data of the 0-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 0-degree direction. Then, it calculates the Poisson's ratio and takes the average of two tests to obtain the Poisson's ratio in the 0-degree to 90-degree direction.

[0051] S3 calculates the elastic modulus in the 90-degree direction based on the tensile test data of the 90-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 90-degree direction. Then, it calculates the Poisson's ratio and takes the average of two tests to obtain the Poisson's ratio in the 90-degree to 0-degree direction.

[0052] S4 calculates the shear modulus based on the tensile test data of 45-degree carbon fiber laminates and averages the shear modulus from 0 to 90 degrees.

[0053] S5 ultimately obtained the constitutive model of the composite laminate based on calculations.

[0054] Elastic modulus E, Poisson's ratio The calculation formulas are shown in equations (5) and (6):

[0055]

[0056] In the formula, The values ​​are the strain values ​​at three locations along the tensile direction of the material specimen 18 and the strain values ​​at three locations perpendicular to the tensile direction.

[0057]

[0058]

[0059] The strain along the tensile direction is represented by the strain at the first, second, and third positions. The strain is the strain perpendicular to the stretching direction at the first, second, and third positions.

[0060] In-plane shear modulus of material The calculation is shown in equation (7):

[0061]

[0062] Due to the different angles, the stress-strain curves of carbon fiber tensile tests are different. The stress-strain curves of 0° and 90° carbon fiber tensile tests exhibit linear elasticity characteristics, with stress and strain showing a linear relationship. As the strain and stress of the stretched material of the specimen gradually increase, the stress drops to 0 immediately after reaching the peak value, exhibiting the characteristics of brittle fracture. The shear stress-strain curve of 45° carbon fiber is initially linear, but becomes nonlinear after exceeding a certain value. This is related to the shear nonlinearity of carbon fiber materials. When the shear stress does not reach the shear stress corresponding to matrix cracking, the shear stress and shear strain show a linear relationship.

[0063] The elastic modulus of carbon fiber materials differs along the fiber direction and perpendicular to the fiber direction. Carbon fiber is composed of multiple layers of fibers stacked in different directions, which makes carbon fiber anisotropic and non-uniform. Its constitutive relationship is very complex and difficult to obtain accurately.

[0064] In the macroscopic mechanical analysis of composite laminates, multi-layer shell element modeling method is often used. The thickness of the shell element is smaller than the dimensions in other directions. The stress change in the thickness direction is ignored, and the 3D orthotropic material is simplified to a 2D orthotropic material. The fiber direction is the 0° direction, and the direction perpendicular to the fiber direction is the 90° direction. Its constitutive relationship is shown in Equation (8).

[0065] (8)

[0066] In the formula, The stress is in the fiber direction, i.e., the tensile direction of the carbon fiber at 0°. The stress is perpendicular to the fiber direction, i.e., at 90° to the tensile direction of the carbon fiber. For shear stress, The strain is in the fiber direction, i.e., the tensile direction of the carbon fiber at 0°. The strain is perpendicular to the fiber direction, i.e., 90° to the tensile direction of the carbon fiber. For shear strain, The linear stiffness in the 0° direction is calculated using equation (9). The linear stiffness in the 90° direction is calculated using equation (12). The linear stiffness in the direction from 0° to 90° is calculated using equation (10). The linear stiffness in the 90° to 0° direction is calculated using equation (11). The shear modulus is calculated according to formula (7).

[0067] (9)

[0068] (10)

[0069] (11)

[0070] (12)

[0071] Based on the tensile test data of the 0° carbon fiber laminate, the elastic modulus in the 0° direction was calculated according to equation (5), and the average value of the two tests was taken. Then, according to equation (6), the Poisson's ratio is obtained, and the average of the two experiments is taken to obtain the result. .

[0072] Based on the tensile test data of the 90° carbon fiber laminate, the elastic modulus in the 90° direction was calculated according to equation (5), and the average value of the two tests was taken. Then, according to equation (6), the Poisson's ratio is obtained, and the average of the two experiments is taken to obtain the result. .

[0073] Based on the tensile test data of 45° carbon fiber laminate, select Figure 9 The linear segment is taken and the shear modulus is calculated according to formula (7) and averaged to obtain the result. .

[0074] The constitutive model of the composite laminate was finally obtained.

[0075]

[0076] Furthermore, the testing system includes a base 1, a left L-plate 2, a right L-plate 3, a left ball joint 4, a left clamp 5, a displacement sensor 6, a hydraulic servo linear cylinder 7, a force sensor 8, a right ball joint 9, a right clamp 10, an extensometer 11, a first strain gauge 12, a second strain gauge 13, a third strain gauge 14, a fourth strain gauge 15, a fifth strain gauge 16, and a sixth strain gauge 17;

[0077] The left L-plate 2 is fixedly mounted on the base 1; the right L-plate 3 is fixedly mounted on the base 1; the left ball joint 4 is mounted on one side of the left L-plate 2; the left clamp 5 is mounted on one side of the left ball joint 4; the displacement sensor 6 is mounted on one side of the right L-plate 3; the hydraulic servo linear cylinder 7 is mounted on one side of the displacement sensor 6; the force sensor 8 is mounted on one side of the hydraulic servo linear cylinder 7; the right ball joint 9 is mounted on one side of the force sensor 8; the right clamp 10 is mounted on one side of the right ball joint 9; the extensometer 11 is placed on the side of the base 1; the first strain gauge 12, the second strain gauge 13, the third strain gauge 14, the fourth strain gauge 15, the fifth strain gauge 16, and the sixth strain gauge 17 are all placed on the side of the base 1.

[0078] In this embodiment, the left clamp 5, in conjunction with the right clamp 10, holds the material specimen 18. The hydraulic servo linear cylinder 7 provides tension, the force sensor 8 measures the tension, and the extensometer 11 measures the elongation at the time gauge end of the material. The first strain gauge 12 and the second strain gauge 13 are attached to the center of the front side of the material specimen 18, and the first strain gauge 12 and the second strain gauge 13 are perpendicular to each other. The third strain gauge 14, the fourth strain gauge 15, the fifth strain gauge 16, and the sixth strain gauge 17 are attached to the symmetrical center of the back side of the material specimen 18, respectively. The third strain gauge 14 and the fourth strain gauge 15 are perpendicular to each other; the fifth strain gauge 16 and the sixth strain gauge 17 are perpendicular to each other.

[0079] The above-disclosed embodiments are merely one or more preferred embodiments of this application and should not be construed as limiting the scope of this application. Those skilled in the art can understand that implementing all or part of the above embodiments and making equivalent changes in accordance with the claims of this application still fall within the scope of this application.

Claims

1. A method for constructing and testing a constitutive model of a carbon fiber composite laminate, characterized in that, The specific steps include: S1 used a testing system to measure carbon fiber tensile test data at different angles; S2 calculates the elastic modulus in the 0-degree direction based on the tensile test data of the 0-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 0-degree direction. Then, it calculates the Poisson's ratio and takes the average of two tests to obtain the Poisson's ratio in the 0-degree to 90-degree direction. S3 calculates the elastic modulus in the 90-degree direction based on the tensile test data of the 90-degree carbon fiber laminate, and takes the average of two tests to obtain the elastic modulus in the 90-degree direction. Then, it calculates the Poisson's ratio and takes the average of two tests to obtain the Poisson's ratio in the 90-degree to 0-degree direction. S4 calculates the shear modulus based on the tensile test data of 45-degree carbon fiber laminates and averages the shear modulus from 0 to 90 degrees. S5 ultimately obtained the constitutive model of the composite laminate based on calculations; The testing system includes a base, a left L-plate, a right L-plate, a left ball joint, a left clamp, a displacement sensor, a hydraulic servo linear cylinder, a force sensor, a right ball joint, a right clamp, an extensometer, a first strain gauge, a second strain gauge, a third strain gauge, a fourth strain gauge, a fifth strain gauge, and a sixth strain gauge. The left L-plate is fixedly mounted on the base; the right L-plate is fixedly mounted on the base; the left ball joint is mounted on one side of the left L-plate; the left clamp is mounted on one side of the left ball joint; the displacement sensor is mounted on one side of the right L-plate; the hydraulic servo linear cylinder is mounted on one side of the displacement sensor; the force sensor is mounted on one side of the hydraulic servo linear cylinder; the right ball joint is mounted on one side of the force sensor; the right clamp is mounted on one side of the right ball joint; the extensometer is placed on the side of the base; the first strain gauge, the second strain gauge, the third strain gauge, the fourth strain gauge, the fifth strain gauge, and the sixth strain gauge are all placed on the side of the base; The specific steps for obtaining carbon fiber tensile test data at different angles using the testing system include: S11 was made into a material specimen using 0-degree carbon fiber material; S12. The first strain gauge and the second strain gauge are pasted in the middle of the front side of the material specimen, and the first strain gauge and the second strain gauge are perpendicular to each other. The pasting position is marked as the first position. S13. The third strain gauge, the fourth strain gauge, the fifth strain gauge, and the sixth strain gauge are respectively attached at symmetrical positions in the middle of the reverse side of the material specimen; the third strain gauge and the fourth strain gauge are perpendicular to each other, and the attachment position is marked as the second position; the fifth strain gauge and the sixth strain gauge are perpendicular to each other, and the attachment position is marked as the third position; S14 The material specimen is clamped by the left clamp and the right clamp respectively, and an extensometer is installed on the material specimen. The specimen is stretched at speeds of 2 mm / min and 4 mm / min respectively. The tensile test data of the carbon fiber material at 0 degrees is measured and the stress-strain curve is plotted. S15 Repeat steps S12-S14 to obtain tensile test data for material specimens made of 45-degree carbon fiber and material specimens made of 90-degree carbon fiber, and plot stress-strain curves accordingly. Among them, the middle gauge length of the material specimen is slender and the clamping parts at both ends are relatively wide to ensure that the central position of the specimen undergoes plastic deformation first during the tensile process, and to ensure that the fracture occurs within the gauge length, thus providing accurate data for the test; during installation, the intersection of the upper, lower, left and right symmetrical planes of the material specimen is on the axis of the hydraulic servo linear cylinder, ensuring that the specimen is not subjected to tensile, compressive, bending and torsional loads in the initial installation state; after installing the extensometer, connect all signals to the same data acquisition system for synchronous acquisition; perform tensile testing at speeds of 2 mm / min and 4 mm / min respectively, calculate the stress and strain of the gauge length of the material according to formula (1)-(4), and then draw the stress-strain curve; Material tensile engineering stress σ g Engineering strain ε g The calculation formula is shown in formula (1) and formula (2): ； In the formula, F is the tensile force on the material along the tensile direction, i.e. the tensile force of the hydraulic servo linear cylinder, b and d are the gauge width and thickness of the specimen, respectively, ΔL is the elongation within the gauge length L0 of the specimen, i.e. the elongation of the extensometer; the actual stress and strain are calculated according to formula (3) and formula (4). (3) (4) The formulas for calculating the elastic modulus E and Poisson's ratio μ are shown in equations (5) and (6); ； In the formula, ε1 and ε2 are the strain along the tensile direction of the material specimen and the average strain at three positions perpendicular to the tensile direction, respectively. where ε S1 , ε S3 , and ε S5 are the strains in the stretching direction at the first position, the second position, and the third position, respectively, and ε S2 , ε S4 , and ε S6 are the strains perpendicular to the stretching direction at the first position, the second position, and the third position, respectively. In-plane shear modulus G of material 12 The calculation is shown in equation (7): ； Due to the different angles, the stress-strain curves of carbon fiber tensile tests are different. The stress-strain curves of 0° and 90° carbon fiber tensile tests exhibit linear elasticity characteristics, with stress and strain showing a linear relationship. As the strain and stress of the stretched material of the specimen gradually increase, the stress drops to 0 immediately after reaching the peak value, exhibiting the characteristics of brittle fracture. The shear stress-strain curve of 45° carbon fiber is initially linear, but becomes nonlinear after exceeding a certain value. This is related to the shear nonlinearity of carbon fiber materials. When the shear stress does not reach the shear stress corresponding to matrix cracking, the shear stress and shear strain show a linear relationship. The elastic modulus of carbon fiber materials differs along the fiber direction and perpendicular to the fiber direction. Carbon fiber is composed of multiple layers of fibers stacked in different directions, which makes carbon fiber anisotropic and non-uniform. Its constitutive relationship is very complex and difficult to obtain accurately. In the macroscopic mechanical analysis of composite laminates, multi-layer shell element modeling method is often used. The thickness of the shell element is smaller than the dimensions in other directions. The stress change in the thickness direction is ignored. The 3D orthogonal anisotropy is simplified to a 2D orthogonal anisotropy material. The fiber direction is the 0° direction and the direction perpendicular to the fiber direction is the 90° direction. Its constitutive relationship is shown in Equation (8). In the formula, σ 0-0 The stress in the fiber direction, i.e., the tensile direction of the carbon fiber at 0°, is σ. 90-90 The stress is perpendicular to the fiber direction, i.e., at 90° to the tensile direction of the carbon fiber. For shear stress, ε 0-0 ε represents the strain in the fiber direction, i.e., the tensile direction of the carbon fiber at 0°. 90-90 γ represents the strain perpendicular to the fiber direction, i.e., at 90° to the tensile direction of the carbon fiber. 0-90 For shear strain, C 0-0 The linear stiffness in the 0° direction is calculated using equation (9), C. 90-90 For the linear stiffness in the 90° direction, calculate using equation (12), C 0-90 The linear stiffness in the direction from 0° to 90° is calculated using equation (10), C 90-0 The linear stiffness in the direction from 90° to 0° is calculated using equation (11); G 0-90 The shear modulus is calculated according to formula (7); Based on the tensile test data of the 0° carbon fiber laminate, the elastic modulus in the 0° direction was calculated according to Equation (5), and the average value of the two tests was taken to obtain E. 0-0 Then, according to equation (6), the Poisson's ratio is obtained, and the average of the two experiments is taken to obtain μ. 0-90 ; Based on the tensile test data of 90° carbon fiber laminate, the elastic modulus in the 90° direction was calculated according to Equation (5), and the average value of the two tests was taken to obtain E. 90-90 Then, according to equation (6), the Poisson's ratio is obtained, and the average of the two experiments is taken to obtain μ. 90-0 ; Based on the tensile test data of 45° carbon fiber laminate, the shear modulus was calculated according to formula (7) and the average value of G was obtained. 0-90 ; The final constitutive model of the composite laminate is obtained as follows: 。

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