Strength calculation method of composite laminates considering the effect of open-hole size

Abstract

The application discloses a kind of composite laminated plate strength calculation methods considering the size effect of opening, belong to the technical field of composite laminated plate.The present application is in view of the problem that existing prediction method relies on a large number of layer-specific test or complex numerical model, through a set of standard opening plate tensile test, combined with the basic mechanics parameters of unopened laminated plate, first calculate the characteristic length of standard plate and 0 ° layer strain energy release rate, and then establish the strain energy release rate conversion relationship between any orthogonal layer, finally realize the accurate prediction of the strength of any orthogonal layer, different aperture opening plate.This method greatly reduces the number of tests and cost, avoids the unconventional test such as fracture toughness, and is completed based on analytical formula throughout, high precision, simple operation, easy to apply and popularize in engineering practice.

Description

Technical Field

[0001] This invention belongs to the field of composite laminate technology, specifically relating to a method for calculating the strength of composite laminates that considers the effect of opening size. Background Technology

[0002] Composite laminates are widely used in aerospace, automotive engineering, and other fields due to their excellent mechanical properties. In practical engineering, it is necessary to drill holes in the laminates to connect them using mechanical methods such as bolts and rivets. Because drilling holes cuts the continuous fibers within the laminate, it has a significant impact on the laminate's strength. Furthermore, even if the ratio of hole diameter to laminate width remains consistent, the strength of laminates with different hole diameters will not be the same; this is known as the size effect.

[0003] Currently, methods for predicting the strength of perforated plates considering size effects mainly fall into three categories. The first is the classical method based on characteristic length theory. This method has a simple formula and good prediction accuracy, but the characteristic length varies with the ply structure. For different ply structures, the characteristic length needs to be inverted from the perforated plate test data corresponding to those ply structures, resulting in excessive experimental dependence. The second category is the calculation method based on strain energy release rate. This method assumes that the perforated plate will fail when the strain energy release rate of the laminate reaches a certain value. It can predict the tensile strength of perforated plates with arbitrary orthogonal ply structures, but it requires measuring the fracture toughness of the 0° layer through fracture toughness testing. However, there is no unified test standard for fracture toughness testing, and the test data has excessive dispersion. Furthermore, it requires calculation using a finite element model, which is inconvenient for engineering applications. The third category is the prediction method based on multi-scale numerical models such as cohesion models. However, this method is complex to model, and obtaining model parameters is difficult, making it unsuitable for direct application in engineering practice. Summary of the Invention

[0004] The technical problem to be solved by this invention is to overcome the shortcomings of the prior art and propose a method for calculating the strength of composite laminates that considers the effect of opening size. By deriving a formula, the relationship between characteristic length and fracture toughness is established, so as to achieve the goal of predicting the tensile strength of any orthogonal ply open plate based only on a batch of standard open plate tensile test data.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0006] First, this invention proposes a method for calculating the strength of composite laminates considering the effect of opening size, comprising the following steps:

[0007] S1. Obtain the tensile strength of a standard perforated plate through a tensile test;

[0008] S2. Obtain the elastic constant and tensile strength of a standard unperforated laminate;

[0009] S3. Calculate the characteristic length of the standard perforated plate according to the characteristic length theoretical formula;

[0010] S4. Based on the calculated characteristic length and the elastic constant and tensile strength of the standard unperforated laminate, calculate the strain energy release rate of the 0° layer;

[0011] S5. Based on the strain energy release rate of the 0° layer, calculate the strain energy release rate of any single layer in any orthogonal ply laminate.

[0012] S6. Based on the strain energy release rate of each single layer, calculate the overall strain energy release rate of the arbitrary orthogonal ply perforated plate;

[0013] S7. Calculate the strength of the arbitrary orthogonal ply perforated plate based on the characteristic length and the overall strain energy release rate.

[0014] Preferably, the standard perforated plate has a quasi-isotropic layup structure with a hole radius of 3 mm and a plate width of 36 mm; the unperforated standard laminate has the same layup structure and width as the standard perforated plate.

[0015] Preferably, in step S2, the elastic constant and tensile strength of the unperforated standard laminate are obtained through standard test or through calculation using a micromechanical model.

[0016] Preferably, in step S3, the theoretical formula for the feature length is as follows:

[0017] ;

[0018] ;

[0019] Where r is the hole radius, W is the laminate width, and a is the characteristic length. The tensile strength of a standard unperforated laminate. The tensile strength of a standard perforated plate. and Calculate according to the following formula:

[0020] ;

[0021] ;

[0022] in, , , , These are the elastic modulus in the x-direction, elastic modulus in the y-direction, in-plane shear modulus in the xy-plane, and principal Poisson's ratio in the xy-plane for a standard unperforated laminate, respectively.

[0023] The dimensional parameters (r, W) and tensile strength of the standard perforated plate are used. Elastic constant of unperforated standard laminate , , , and tensile strength Substitution ,get The value; will be obtained Substitution of values The characteristic length a of the standard perforated plate is obtained.

[0024] Preferably, in step S4, the 0° layer strain energy release rate The calculation method is as follows:

[0025] ;

[0026] in, The elastic modulus in the x-direction of the 0° layer of a standard unperforated laminate. Let be the equivalent elastic modulus of the k-th layer of a standard unperforated laminate along the x-direction. The ratio of the tensile stress in the k-th layer along the x-direction to the tensile stress in the 0° layer along the x-direction is obtained through classical laminate theory, where n is the number of single layers in the laminate. The solution method is as follows:

[0027] ;

[0028] ;

[0029] in, , , , Let x be the equivalent elastic modulus along the x-direction, the equivalent elastic modulus along the y-direction, the principal Poisson's ratio in the xy-plane, and the secondary Poisson's ratio in the xy-plane of the k-th layer of the standard unperforated laminate. For the corresponding 0° layer parameters.

[0030] Preferably, in step S5, the strain energy release rate of any single layer in the arbitrary orthogonal ply laminate is... The calculation method is as follows:

[0031] ;

[0032] Preferably, in step S6, the overall strain energy release rate of the arbitrary orthogonal ply perforated plate is... The calculation method is as follows:

[0033] ;

[0034] Preferably, in step S7, the strength of the arbitrary orthogonal ply perforated plate... The calculation method is as follows:

[0035] ;

[0036] in, denoted as the equivalent elastic modulus in the x-direction of an unperforated laminate with an arbitrary orthogonal ply structure, obtained through experiments or micromechanical models; r and w are the hole radius and width of the arbitrary orthogonal ply laminate.

[0037] Furthermore, the present invention proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the computer program is executed, it implements the steps of the method described in the present invention.

[0038] Finally, the present invention proposes a computer-readable storage medium having a computer program stored thereon, characterized in that the computer program is configured to implement the steps of the method described in the present invention when invoked by a processor.

[0039] The strength calculation method for composite laminates considering the effect of opening size described in this invention has the following technical advantages compared with the prior art:

[0040] (1) The present invention only requires a set of standard perforated plate tensile test data to predict the strength of perforated plates with any orthogonal ply and different hole diameters, avoiding repeated perforation tests or fracture toughness tests for different plies, and greatly reducing test costs and cycle.

[0041] (2) While maintaining the simplicity and accuracy of characteristic length theoretical calculation, this invention achieves wide applicability to different orthogonal ply structures and can accurately reflect the effect of opening size.

[0042] (3) The present invention is based on analytical formulas to complete the calculation, without the need for complex numerical modeling experiments. The required parameters can be obtained through mature experiments or micromechanical models. The process is clear, the operation is strong, and it is easy to promote and use in engineering practice. Attached Figure Description

[0043] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0044] Figure 1 This invention relates to a flowchart of a method for calculating the strength of composite laminates that takes into account the effect of opening size.

[0045] Figure 2This is a comparison chart of the predicted strength results and experimental values ​​of the quasi-isotropic ply perforated plate involved in the embodiments of the present invention.

[0046] Figure 3 This is a comparison chart of the predicted strength results and experimental values ​​of the perforated plate with arbitrary orthogonal ply layup involved in the embodiments of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0048] Example 1: This example proposes a method for calculating the strength of composite laminates considering the effect of opening size, referring to... Figure 1 The specific steps are as follows:

[0049] S1. The tensile strength of the standard perforated plate is obtained by tensile test. The standard perforated plate has a quasi-isotropic ply structure with a hole radius of 3 mm and a plate width of 36 mm. The ply structure and width of the standard non-perforated laminate are the same as those of the standard perforated plate.

[0050] S2. Obtain the elastic constant and tensile strength of the standard unperforated laminate. The elastic constant and tensile strength of the standard unperforated laminate can be obtained through standard test, or the relevant parameters can be calculated using a micromechanical model.

[0051] S3. Calculate the characteristic length of the standard perforated plate according to the characteristic length theoretical formula;

[0052] S4. Based on the elastic constant and tensile strength of the standard unperforated laminate, calculate the strain energy release rate of the 0° layer;

[0053] S5. Based on the strain energy release rate of the 0° layer, calculate the strain energy release rate of any single layer in any orthogonal ply laminate.

[0054] S6. Based on the strain energy release rate of each single layer, calculate the overall strain energy release rate of the arbitrary orthogonal ply perforated plate;

[0055] S7. Calculate the strength of the arbitrary orthogonal ply perforated plate based on the characteristic length and the overall strain energy release rate.

[0056] Specifically, the feature length is calculated in step S3 as follows:

[0057] (1);

[0058] (2);

[0059] Where r is the hole radius, W is the laminate width, and a is the characteristic length. The tensile strength of a standard unperforated laminate. For standard perforated laminate tensile strength, and Calculate according to equations (3) and (4).

[0060] (3);

[0061] (4)

[0062] In equation (3) , , , These are the elastic modulus in the X direction, elastic modulus in the Y direction, in-plane shear modulus in the XY plane, and principal Poisson's ratio in the XY plane of the standard unperforated laminate obtained in step S2, respectively.

[0063] The standard perforated plate's dimensional parameters (r, W) and tensile strength are used to determine the dimensions (r, W) and tensile strength. The elastic constant of the standard laminate without openings , , , and tensile strength Substituting into equation (1), we can obtain The value will be obtained. Substituting the value into equation (2) yields the characteristic length a of the standard perforated plate.

[0064] Specifically, in step S4, the 0° layer strain energy release rate The calculation method is as follows:

[0065] (5)

[0066] in The modulus of elasticity in the x-direction of the 0° layer of a standard unperforated laminate (the fiber direction of the 0° layer is the x-direction of the laminate). Let be the equivalent elastic modulus of the k-th layer of a standard unperforated laminate along the x-direction. The ratio of the tensile stress in the k-th layer along the x-direction to the tensile stress in the 0° layer along the x-direction can be obtained through classical laminate theory, where n is the number of single layers in the laminate. It can be obtained by the following formula:

[0067] (6)

[0068] (7)

[0069] in , , , Let be the equivalent elastic modulus of the k-th layer of the standard unperforated laminate along the x-direction, the equivalent elastic modulus along the y-direction, the principal Poisson's ratio in the xy-plane, and the secondary Poisson's ratio in the xy-plane.

[0070] The parameters for the 0° layer can be obtained by replacing the corresponding parameters in equations (6) and (7) with the parameters for the 0° layer.

[0071] Specifically, in step S5, the strain energy release rate of the k-th layer in any orthogonal laminate is... The calculation method is as follows:

[0072] (8)

[0073] Specifically, the method for calculating the strain energy release rate of the arbitrary orthogonal ply laminate in step S6 is as follows:

[0074] (9)

[0075] Specifically, the tensile strength of the orthogonally ply perforated laminate in step S7 The calculation method is as follows:

[0076] (10)

[0077] in The equivalent elastic modulus in the x-direction of an orthogonal ply laminate without openings can be obtained through experiments or micromechanical models, where r and w are the hole radius and width of the orthogonal ply laminate, respectively, and M and ... The values ​​of r and w can be obtained by substituting them into equations (3) and (4) for any orthogonal ply perforated plate.

[0078] Figure 2 The strength prediction performance of T300 / 7901 [0 / 45 / -45 / 90]2s perforated laminate was demonstrated. Specifically, the characteristic length was calculated from the strength of a standard perforated plate with a hole radius of 3mm. This calculated characteristic length was then substituted into the strength prediction formulas for perforated plates with hole radii of 1.5mm and 4.5mm to calculate the corresponding perforated plate strengths. The prediction accuracies were 9.6% and 1.5%, respectively, meeting engineering accuracy requirements. Since the standard perforated plate used to calculate the characteristic length and the perforated plates with other hole radii used for prediction verification all have the same layup structure, i.e., [0 / 45 / -45 / 90]2s, the applicability of the traditional characteristic length theory in predicting the strength of perforated plates considering size effects is proven.

[0079] Figure 3The strength prediction results for T300 / 7901 [0 / ±30 / ±60 / 90]2s laminates are demonstrated. Specifically, the strength prediction results are obtained by using the standard perforated plate strength of quasi-isotropic layups (i.e., Figure 2 The characteristic length was calculated using data points with r=3mm. Then, the calculation method provided by this invention was used to calculate the tensile strength of perforated plates with different hole radii for different ply structures (the ply structure used to calculate the characteristic length is [0 / 45 / -45 / 90]2s, and the ply structure used for strength prediction verification is [0 / ±30 / ±60 / 90]2s). For hole radii of 1.5mm, 3mm, and 4.5mm, the prediction errors of this invention were 0.63%, 8.7%, and 3.4%, respectively, proving the effectiveness of the method of this invention in predicting the tensile strength of perforated plates with different hole diameters for arbitrary ply structures using the tensile strength of standard perforated plates.

[0080] Example 2: This example proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, when the computer program is executed, it implements the steps of the method described in this invention.

[0081] Example 3: This example proposes a computer-readable storage medium storing a computer program thereon, characterized in that the computer program is configured to implement the steps of the method described in this invention when invoked by a processor.

[0082] It should be noted that the processing flow of embodiments 2-3 corresponds to the specific steps of the method provided in embodiment 1 of the present invention, and has the corresponding functional modules and beneficial effects of the method. Technical details not described in detail in this embodiment can be found in the method provided in embodiment 1 of the present invention.

[0083] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0084] The specific implementation schemes described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific implementation schemes of the present invention and are not intended to limit the scope of the present invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the present invention should fall within the scope of protection of the present invention.

Claims

1. A method for calculating the strength of composite laminates considering the effect of opening size, characterized in that, Includes the following steps: S1. Obtain the tensile strength of a standard perforated plate through a tensile test; S2. Obtain the elastic constant and tensile strength of a standard unperforated laminate; S3. Calculate the characteristic length of the standard perforated plate according to the characteristic length theoretical formula; S4. Based on the calculated characteristic length and the elastic constant and tensile strength of the standard unperforated laminate, calculate the 0° layer strain energy release rate; S5. Based on the strain energy release rate of the 0° layer, calculate the strain energy release rate of any single layer in any orthogonal ply laminate. S6. Based on the strain energy release rate of each single layer, calculate the overall strain energy release rate of the arbitrary orthogonal ply perforated plate; S7. Calculate the strength of the arbitrary orthogonal ply perforated plate based on the characteristic length and the overall strain energy release rate.

2. The method according to claim 1, characterized in that, The standard perforated plate has a quasi-isotropic layup structure with a hole radius of 3 mm and a plate width of 36 mm; the unperforated standard laminate has the same layup structure and width as the standard perforated plate.

3. The method according to claim 1, characterized in that, In step S2, the elastic constant and tensile strength of the unperforated standard laminate are obtained through standard test or through calculation using a micromechanical model.

4. The method according to claim 1, characterized in that, In step S3, the theoretical formula for the feature length is as follows: ； ； Where r is the hole radius, W is the laminate width, and a is the characteristic length. The tensile strength of a standard unperforated laminate. The tensile strength of a standard perforated plate. and Calculate according to the following formula: ； ； in, , , , These are the elastic modulus in the x-direction, elastic modulus in the y-direction, in-plane shear modulus in the xy-plane, and principal Poisson's ratio in the xy-plane for a standard unperforated laminate, respectively. The dimensional parameters (r, W) and tensile strength of the standard perforated plate are used. Elastic constant of unperforated standard laminate , , , and tensile strength Substitution ,get The value; will be obtained Substitute value The characteristic length a of the standard perforated plate is obtained.

5. The method according to claim 1, characterized in that, In step S4, the 0° layer strain energy release rate The calculation method is as follows: ； in, The elastic modulus in the x-direction of the 0° layer of a standard unperforated laminate. Let be the equivalent elastic modulus of the k-th layer of a standard unperforated laminate along the x-direction. The ratio of the tensile stress in the k-th layer along the x-direction to the tensile stress in the 0° layer along the x-direction is obtained by classical laminate theory, and n is the number of single layers in the laminate. The solution method is as follows: ； ； in, , , , Let x be the equivalent elastic modulus along the x-direction, the equivalent elastic modulus along the y-direction, the principal Poisson's ratio in the xy-plane, and the secondary Poisson's ratio in the xy-plane of the k-th layer of the standard unperforated laminate. For the corresponding 0° layer parameters.

6. The method according to claim 5, characterized in that, In step S5, the strain energy release rate of any single layer in the arbitrary orthogonal ply laminate is... The calculation method is as follows: 。 7. The method according to claim 6, characterized in that, In step S6, the overall strain energy release rate of the arbitrary orthogonal ply perforated plate The calculation method is as follows: 。 8. The method according to claim 7, characterized in that, In step S7, the strength of the arbitrary orthogonal ply perforated plate The calculation method is as follows: ； in, denoted as the equivalent elastic modulus in the x-direction of an unperforated laminate with an arbitrary orthogonal ply structure, obtained through experiments or micromechanical models; r and w are the hole radius and width of the arbitrary orthogonal ply laminate.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed, it implements the steps of the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, The computer program is configured to implement the steps of the method according to any one of claims 1 to 8 when invoked by a processor.

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