Calculation method for ultimate load of composite material laminated plate

Abstract

The invention discloses a method for calculating the limit load of a composite material laminated plate, the composite material laminated plate is composed of N single-layer plates, and the method comprises the following steps: S1, obtaining the material performance, the laying angle and the thickness of each single-layer plate; s2, calculating a stiffness matrix of each single-layer plate in the off-axis coordinate system; s3, calculating a regularization flexibility matrix of the laminated plate in the off-axis coordinate system; s4, calculating a regularization in-plane strain matrix of an external load matrix # imgabs0 # of the laminated plate in the off-axis coordinate system; s5, calculating a stress matrix of each single-layer plate in the positive axis coordinate system; s6, calculating the failure load and stress of each single-layer plate under the strength criterion; s7, judging the failure mode of the single-layer board according to the calculation result of the step S6; and S8, rigidity correction is carried out according to the failure mode judged in the S7, the corrected performance parameters are substituted into the step S2, the steps S2-S7 are executed again until fibers in the stress direction of all the single-layer plates fail, and the failure loads of all the single-layer plates are added to obtain the limit load of the laminated plate.

Description

Technical Field

[0001] The invention relates to a performance evaluation technology for automobile composite materials, and in particular to a method for calculating the ultimate load of a composite material laminate. Background Art

[0002] Composite materials are widely used in aviation and automobiles due to their high specific strength, high specific modulus, light weight and designability. Usually, when designing composite materials that meet certain mechanical properties, technicians in this field usually select materials and design plies based on experience, and then conduct tests after proofing. This method may lead to repeated adjustments to proofing tests, which takes a long time and wastes manpower and material resources. Therefore, it is necessary to be able to perform strength calculations in advance for design schemes. Composite laminates are the main form of composite material applications. Composite laminates are composed of several single-layer plates through a specific bonding method. The single-layer plates of composite materials are orthogonal anisotropic. Due to the different fiber arrangement modes of each single-layer plate, the strains generated under the action of external forces are different, so the final strength prediction of the laminate is a more complicated problem. At present, the performance evaluation of composite materials destroys the singleness. If a single material in the material composition is destroyed, the stiffness of the material is determined to be zero. However, composite materials are multiphase materials composed of resin matrix and fiber reinforcement. Single destruction zeroing is unreasonable for the material itself, and there is a lack of step-by-step analysis models and framework methods. Summary of the invention

[0003] In view of the above-mentioned problems existing in the prior art, the purpose of the present invention is to provide a method for calculating the ultimate load of composite laminate materials, which can provide the calculation of the step-by-step stiffness failure model of composite materials, provide a theoretical method for the strength performance verification of composite materials, and provide theoretical verification for the laying method.

[0004] In order to achieve the above purpose, the technical solution adopted by the present invention is: A method for calculating the ultimate load of an automobile composite laminate, wherein the composite laminate is composed of N single-layer plates. The method for calculating the ultimate load of the laminate comprises the following steps: S1. Obtain the material properties and ply angles of each single-layer board , thickness h; S2. Calculate the stiffness coefficient matrix of each single-layer plate in the eccentric coordinate system; S3, calculating the regularized flexibility matrix of the laminate in the eccentric coordinate system; S4. Calculate the external load matrix of the laminate in the eccentric coordinate system The regularized in-plane strain matrix of ; S5. Calculate the stress matrix of each single-layer plate in the positive axis coordinate system; S6. Calculate the failure load and stress of each single-layer plate under the strength criterion; S7, judging the failure mode of the single-layer board according to the calculation result of step S6, confirming whether the fibers in the force direction of all single-layer boards are failed; if so, the minimum failure load of step S6 is the limit load of the laminate, and the calculation is terminated; if not, executing step S8; S8, performing stiffness correction according to the failure mode determined in step S7: modifying the corresponding performance parameters E1, E2 of the resin matrix or fiber determined to have failed in step S7. 1、 G 12 Corrected to 0, re-execute steps S2-S7 until the fibers in the force direction of all single-layer boards fail, and the ultimate load of the laminate is obtained by adding the failure loads of each single-layer board.

[0005] The material properties include: elastic modulus E1 in the fiber direction; elastic modulus E2 perpendicular to the fiber direction; the ratio of the strain perpendicular to the fiber direction to the strain acting in the fiber direction, i.e. Poisson's V 12 ; Shear modulus G in the fiber direction and in the plane perpendicular to the fiber direction 12 ; Compression strength along the fiber direction X c ; Tensile strength along the fiber direction X t ; Compressive strength perpendicular to the fiber direction Y t ; Tensile strength perpendicular to the fiber direction Y c ; Fiber in-plane shear strength S.

[0006] The ply angle Usually there are ±45°, ±90°, 0°, etc.

[0007] In step S2, based on the fact that the laminate is a continuous material composed of continuous, uniform, orthotropic single-layer plates, each single-layer plate constituting the laminate is usually analyzed as a two-dimensional plane, and the stiffness coefficient matrix formula for calculating any single-layer plate constituting the laminate is as follows: ; Where: k represents any k-th single-layer plate in the laminate, k=1,2,3...N; T represents the transpose of the matrix; represents the stiffness matrix of any k-th single-layer plate in the eccentric coordinate system; The transformation matrix representing the transformation of the normal axis coordinate system (1, 2) to the eccentric axis coordinate system (x, y) of any k-th single-layer board is as follows: = , definition: The two directions along the main axis of the material are the positive axis coordinate system, represented by (1,2), 1 represents the transverse direction (fiber direction), 2 represents the longitudinal direction (direction perpendicular to the fiber), and the material exhibits orthotropic material properties in the positive axis coordinate system; The coordinate system that reflects the overall performance of the laminate is the eccentric coordinate system, which is the coordinate system commonly used in composite material performance and is represented by (x, y); Therefore, in the formula is the ply angle of any k-th single-layer board, that is, the angle between the positive axis coordinate system (1, 2) and the eccentric axis coordinate system (x, y) where the k-th layer is located; θ is defined as positive when rotating counterclockwise and negative when rotating clockwise; It represents the stiffness coefficient matrix of any k-th single-layer plate in the positive axis coordinate system, and the formula is as follows: = ;

[0008] Where: E1, E2, V 12 , G 12 is the performance parameter corresponding to any k-th single-layer board.

[0009] In step S3, the regularized flexibility matrix of the laminate in the eccentric coordinate system (x, y) is The calculation formula is: = ; definition: ; ; ; Where: N represents the total number of layers of a single-layer board; h k is the thickness of any k-th single-layer board; H is the total thickness of the laminate; Z represents the variable in the thickness direction, Z k It represents the value of any k-th layer in the laminate on the Z axis in the coordinate system; represents the Z value of the mid-plane coordinate system of the kth layer of the laminate, ; is the in-plane stiffness matrix of the laminate; is the coupled stiffness matrix of the laminate; is the bending stiffness matrix.

[0010] In step S4, the laminate is subjected to an external load matrix in the eccentric coordinate system (x, y) The regularized in-plane strain matrix The formula is as follows: = .

[0011] The stress matrix formula of each single-layer plate in the positive axis coordinate system in step S5 is as follows: ; Where: is the stress of the single-layer plate in the 1 direction (fiber direction) in the (1, 2) coordinate system; is the stress of the single-layer plate in the 2-direction (perpendicular to the fiber direction) in the (1, 2) coordinate system; is the shear stress of the single-layer plate in the 12 direction (in-plane) in the (1, 2) coordinate system.

[0012] The step S6 calculates the failure load and stress of each single-layer board under the strength criterion, including: on the basis of step S5, calculating in combination with the failure load formula under the strength criterion, the failure load formula under the strength criterion is as follows: .

[0013] The judgment conditions for judging the failure mode of the single-layer board in step S7 include: (1) When , then bring in Make a judgment. If the inequality holds, it is judged that the fiber tensile failure occurs; if the inequality does not hold, it is judged that the fiber tensile failure does not occur. (2) When , then bring in Make a judgment. If the inequality holds, it is judged that the fiber compression has failed; if the inequality does not hold, it is judged that the fiber compression has not failed; (3) When , then bring in Make a judgment. If the inequality holds, it is judged that the matrix tensile fails; if the inequality does not hold, it is judged that the matrix tensile does not fail; (4) When , bring in If the inequality holds, it is judged that the matrix compression has failed; if the inequality does not hold, it is judged that the matrix tension has not failed.

[0014] Beneficial effects of the present invention: (1) Provide prediction of step-by-step failure stiffness degradation of composite materials; (2) This algorithm can be used to check the strength performance of composite materials and provide theoretical verification for composite material layup design. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Attached Figure 1 It is a calculation flow chart of the present invention; Attached Figure 2 It is a schematic diagram of the positive axis coordinate system and the eccentric axis coordinate system; Attached Figure 3 Schematic diagram of the laminate of Example 1. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution in the embodiment of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described below are only part of the embodiments of the present invention. For ordinary technicians in this field, without paying creative work, the modifications, equivalent replacements, etc. made according to these drawings and tables are all within the protection scope of the present invention.

[0017] See attached Figure 1 A method for calculating the strength of a composite material laminate of an automobile, wherein the composite material laminate is composed of N single-layer plates, and the strength calculation of the laminate comprises the following steps: S1. Obtain the material properties and ply angles of each single-layer board , thickness h; S2. Calculate the stiffness coefficient matrix of each single-layer plate in the eccentric coordinate system; S3, calculating the regularized flexibility matrix of the laminate in the eccentric coordinate system; S4. Calculate the external load matrix of the laminate in the eccentric coordinate system The regularized in-plane strain matrix of ; S5. Calculate the stress matrix of each single-layer plate in the positive axis coordinate system; S6. Calculate the failure load and stress of each single-layer plate under the strength criterion; S7, judging the failure mode of the single-layer board according to the calculation result of step S6, confirming whether the fibers in the force direction of all single-layer boards are failed; if so, the minimum failure load of step S6 is the limit load of the laminate, and the calculation is terminated; if not, only step S8 is executed; S8, perform stiffness correction according to the failure mode determined in S7: modify the performance parameters E1, E2, G corresponding to the resin matrix and / or fiber determined to have failed in S7. 12 Correct it to 0, and re-execute steps S2-S7 until the fibers in the force direction of all single-layer boards fail. The ultimate strength of the laminate is obtained by adding the destructive loads of each single-layer board.

[0018] The material properties include: elastic modulus E1 in the fiber direction; elastic modulus E2 perpendicular to the fiber direction; the ratio of the strain perpendicular to the fiber direction to the strain acting in the fiber direction, i.e. Poisson's V 12 ; Shear modulus G in the fiber direction and in the plane perpendicular to the fiber direction 12 ; Compression strength along the fiber direction X c ; Tensile strength along the fiber direction X t ; Compressive strength perpendicular to the fiber direction Y t ; Tensile strength perpendicular to the fiber direction Y c ; Fiber in-plane shear strength S.

[0019] The ply angle Usually there are ±45°, ±90°, 0°, etc.

[0020] In step S2, based on the fact that the laminate is a continuous material composed of continuous, uniform, orthotropic single-layer plates, each single-layer plate constituting the laminate is usually analyzed as a two-dimensional plane, and the stiffness coefficient matrix formula for calculating any single-layer plate constituting the laminate is as follows: ; Where: k represents any k-th single-layer plate in the laminate, k=1,2,3...N; T represents the transpose of the matrix; represents the stiffness matrix of any k-th single-layer plate in the eccentric coordinate system; The transformation matrix representing the transformation of the normal axis coordinate system (1, 2) to the eccentric axis coordinate system (x, y) of any k-th single-layer board is as follows: ; definition: See attached Figure 2 , the two directions along the main axis of the material are the positive axis coordinate system, represented by (1,2), 1 represents the transverse direction (fiber direction), 2 represents the longitudinal direction (direction perpendicular to the fiber), and the material exhibits orthotropic material properties in the positive axis coordinate system; The coordinate system that reflects the overall performance of the laminate is the eccentric coordinate system, which is the coordinate system commonly used in composite material performance and is represented by (x, y); Therefore, in the formula is the ply angle of any k-th single-layer board, that is, the angle between the positive axis coordinate system (1, 2) and the eccentric axis coordinate system (x, y) where the k-th layer is located; θ is defined as positive when rotating counterclockwise and negative when rotating clockwise; It represents the stiffness matrix of any k-th single-layer plate in the positive axis coordinate system, and the formula is as follows: ;

[0021] Where: E1, E2, V 12 , G 12 is the performance parameter corresponding to any k-th single-layer board.

[0022] In step S3, the regularized flexibility matrix of the laminate in the eccentric coordinate system (x, y) is The calculation formula is: = ; definition: ; ; ; Where: N represents the total number of layers of a single-layer board; h k is the thickness of any k-th single-layer board; H is the total thickness of the laminate; Z represents the variable in the thickness direction, Z k It represents the value of any k-th layer in the laminate on the Z axis in the coordinate system; represents the Z value of the mid-plane coordinate system of the kth layer of the laminate, ; is the in-plane stiffness matrix of the laminate; is the coupled stiffness matrix of the laminate; is the bending stiffness matrix.

[0023] In step S4, the laminate is subjected to an external load matrix in the eccentric coordinate system (x, y) The regularized in-plane strain matrix The formula is as follows: = ; Where: , is the in-plane load decomposed from the external load F in the eccentric coordinate system of the single-layer plate.

[0024] The stress matrix formula of each single-layer plate in the positive axis coordinate system in step S5 is as follows: ; Where: is the stress of the single-layer plate in direction 1 (fiber direction) in the (1, 2) coordinate system; is the stress of the single-layer plate in the 2-direction (perpendicular to the fiber direction) in the (1, 2) coordinate system; is the shear stress of the single-layer plate in the 12 direction (in-plane) in the (1, 2) coordinate system.

[0025] The step S6 calculates the failure load and stress of each single-layer board under the strength criterion, including: on the basis of step S5, calculating in combination with the failure load formula under the strength criterion, the failure load formula under the strength criterion is as follows: .

[0026] The judgment and correction conditions of the single-layer board failure mode in step S7 include: (1) When , then bring in Make a judgment. If the inequality holds, it is judged that the fiber tensile failure occurs; if the inequality does not hold, it is judged that the fiber tensile failure does not occur. (2) When , then bring in Make a judgment. If the inequality holds, it is judged that the fiber compression has failed; if the inequality does not hold, it is judged that the fiber compression has not failed; (3) When , bring in Make a judgment. If the inequality holds, it is judged that the matrix tensile fails; if the inequality does not hold, it is judged that the matrix tensile does not fail; (4) When , bring in If the inequality holds, it is judged that the matrix compression has failed; if the inequality does not hold, it is judged that the matrix tension has not failed.

[0027] Example 1 In this embodiment, each single-layer board is made of 12K. In this example, 12KT700-UD carbon / epoxy unidirectional tape prepreg is used. =132Gpa =8.6 Gpa, =0.3, =4.4Gpa, =2.340Gpa, Xc=1.320 Gpa, =0.056 Gpa, =0.149 Gpa, =0.075 Gpa, H=8t, calculate the ultimate load F at which the laminate will fail.

[0028] For ply design, please refer to the attached Figure 3, is a three-layer symmetrical orthogonal laminate. The principal axis coordinate system (1, 2) of the first and third layers coincides with the eccentric axis coordinate system (x, y). is 0°, thickness h1=h3= 2t (the thickness of the unidirectional tape prepreg is recorded as t, and the first and third layers of the single-layer board are both made of two layers of unidirectional tape prepreg); the angle between the second layer material coordinate system (1 / 2) and the eccentric coordinate system (x / y) is 90°, and the second layer of the single-layer board The angle is 90° and the thickness is h2=4t (the second single-layer board is made of 4 layers of unidirectional tape prepreg).

[0029] The matrix subjected to external load .

[0030] In this embodiment, a method for calculating the ultimate load of a composite laminate includes: S1. Obtain the material properties and ply angles of each single-layer board , thickness h; S2. Calculate the stiffness matrix of each single-layer plate in the eccentric coordinate system ; because, ; ; ; ; ; therefore, ; .

[0031] S3. Calculate the regularized flexibility matrix of the laminate in the eccentric coordinate system = ; because, ; ; ;

[0032] so, .

[0033] S4. Calculate the regularized in-plane strain matrix of the laminate under external load in the eccentric coordinate system ; .

[0034] S5. Calculate the stress matrix of each single-layer plate in the positive axis coordinate system: ; ; The same can be said .

[0035] S6. Based on the stress matrix formula in step 6, the stress and failure load are calculated in combination with the failure load formula under the strength criterion; the failure load formula under the strength criterion is as follows: ;

[0036] Find: (1) Ultimate load value for failure of the first and third single-layer plates: ; (2) The ultimate load value for the failure of the second single-layer plate: ; (3) ; (4) .

[0037] S7. According to the calculation result of step S6, the failure mode judgment condition of the single-layer board is judged as follows: (1) , bring in judge, It is not true, that is, the fiber stretching does not fail; (2) , bring in judge, Established, that is, the resin matrix tensile failure; (3) , bring in judge, It is not true, that is, the fiber stretching does not fail; (4) , bring in judge, It is not true, that is, the resin matrix does not fail in tension; In summary, the 1st and 3rd layers of the laminate are tensilely damaged, and the fibers in the stress direction (Ny direction) of the 2nd layer have not failed, so step S8 needs to be performed; S8. Perform stiffness correction according to the failure mode determined in S7: Correct the performance parameters corresponding to the resin matrix or fiber determined to be failed in S7 to 0, i.e., the tensile failure of the resin matrix of the 1st and 3rd layers, and the corresponding E2 and G 12 Correct it to 0, then go to step S2 and re-execute steps S2-S7; after correction: ; ; Furthermore, ; Furthermore, ; Furthermore, ; ; ; ; Furthermore, ; ; ; .

[0038] In summary, after judgment, the fibers in the force direction of the second single-layer board have failed. The ultimate load of the laminate is obtained by adding the failure loads of each single-layer board: F= ==1.713Gpa.

[0039] The comparison with the actual experimental results is shown in Table 1. Table 1.

[0040] It can be seen from Table 1 that the error between the calculated value of the present invention and the actual experimental value of the laminate is within 10%, and the calculation method of the present invention has guiding significance for the performance design of composite materials.

Claims

1. A method for calculating the ultimate load of a composite laminate, wherein the composite laminate is composed of N single-layer plates, characterized in that: Includes steps: S1. Obtain the material properties and ply angles of each single-layer board , thickness h; S2, calculate the stiffness matrix of each single-layer plate in the eccentric coordinate system; S3, calculating the regularized flexibility matrix of the laminate in the eccentric coordinate system; S4. Calculate the external load matrix of the laminate in the eccentric coordinate system The regularized in-plane strain matrix of ; S5. Calculate the stress matrix of each single-layer plate in the positive axis coordinate system; S6. Calculate the failure load and stress of each single-layer plate under the strength criterion; S7, judging the failure mode of the single-layer board according to the calculation result of step S6, confirming whether the fibers in the force direction of all single-layer boards have failed; if so, the minimum failure load of step S6 is the limit load of the laminate, and the calculation is terminated; if not, executing step S8; S8, performing stiffness correction according to the failure mode determined in S7: modifying the performance parameters corresponding to the resin matrix and / or fiber determined to have failed in S7 , , Corrected to 0, re-execute steps S2-S7 until the fibers in the force direction of all single-layer boards fail, and the ultimate load of the laminate is obtained by adding the failure loads of each single-layer board; The material properties include: elastic modulus E1 in the fiber direction; elastic modulus E2 perpendicular to the fiber direction; the ratio of the strain perpendicular to the fiber direction to the strain acting in the fiber direction, i.e. Poisson's V 12 ; Shear modulus G in the fiber direction and in the plane perpendicular to the fiber direction 12 ; Compression strength along the fiber direction X c ; Tensile strength along the fiber direction X t ; Compressive strength perpendicular to the fiber direction Y t ; Tensile strength perpendicular to the fiber direction Y c ; Fiber in-plane shear strength S.

2. The method for calculating the ultimate load of a composite laminate according to claim 1, characterized in that: The stiffness matrix formula of each single-layer plate in the eccentric coordinate system in step S2 is: , Where: k represents any k-th single-layer plate in the laminate, k=1,2,3...N; T represents the transpose of the matrix; represents the stiffness matrix of any k-th single-layer plate in the eccentric coordinate system (x, y); The transformation matrix representing the transformation of the normal axis coordinate system (1, 2) to the eccentric axis coordinate system (x, y) of any k-th single-layer board is as follows: = ， Where: is the ply angle of any k-th single-layer board, that is, the angle between the positive axis coordinate system (1, 2) and the eccentric axis coordinate system (x, y) where the k-th single-layer board is located, and Counterclockwise rotation is positive, clockwise rotation is negative; It represents the stiffness matrix of any k-th single-layer plate in the positive axis coordinate system, and the formula is as follows: = 。 3. The method for calculating the ultimate load of a composite laminate according to claim 2, characterized in that: In step S3, the regularized flexibility matrix of the laminate in the eccentric coordinate system (x, y) is The calculation formula is: = , definition: ； L= ； ； Where: N represents the total number of layers of a single-layer board; h k is the thickness of any k-th single-layer board; H is the total thickness of the laminate; Z represents the variable in the thickness direction, Z k Represents the value of any k-th layer in the laminate on the Z axis in the coordinate system; represents the Z value of the mid-plane coordinate system of the kth layer of the laminate, ; is the in-plane stiffness matrix of the laminate; is the coupled stiffness matrix of the laminate; is the bending stiffness matrix.

4. The method for calculating the ultimate load of a composite laminate according to claim 3, characterized in that: In step S4, the laminate is subjected to an external load matrix in the eccentric coordinate system (x, y): The regularized in-plane strain matrix , the formula is as follows: = 。 5. The method for calculating the ultimate load of a composite laminate according to claim 4, characterized in that: The stress matrix formula of the positive axis coordinate system of each single-layer plate under external loading in step S5 is as follows: ， Where: is the stress of the single-layer plate in direction 1 (fiber direction) in the (1, 2) coordinate system; is the stress in the 2-direction (perpendicular to the fiber direction) of the single-layer plate in the (1, 2) coordinate system, is the shear stress of the single-layer plate in the 12 direction (in-plane) in the (1, 2) coordinate system.

6. A method for calculating the ultimate load of a composite laminate according to claim 5, characterized in that The step S6 calculates the failure load and stress of each single-layer board under the strength criterion, including: based on the stress matrix formula of step 6, the failure load formula under the strength criterion is combined for calculation, and the failure load formula under the strength criterion is as follows: =1.

7. A method for calculating the ultimate load of a composite laminate according to claim 6, characterized in that: The judgment conditions for judging the failure mode of the single-layer board in step S7 include: (1) When 0, then bring in Make a judgment. If the inequality holds, it is judged that the fiber tensile failure occurs; if the inequality does not hold, it is judged that the fiber tensile failure does not occur. (2) When , then bring in 1. If the inequality holds, it is judged that the fiber compression has failed. If the inequality does not hold, it is judged that the fiber compression has not failed. (3) When , then bring in Make a judgment. If the inequality holds, it is judged that the matrix tensile fails; if the inequality does not hold, it is judged that the matrix tensile does not fail; (4) , bring in If the inequality holds, it is judged that the matrix compression has failed. If the inequality does not hold, it is judged that the matrix tension has not failed.

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