Design method for matrix crack density evolution of resin-based composites under fatigue load

Abstract

This invention belongs to the field of composite material fatigue damage characterization technology, and relates to a design method for the evolution of matrix crack density in resin-based composite materials under fatigue loading. Fatigue tests at different load levels are conducted to observe and record the matrix crack density ρ and its corresponding cycle number N of fiber-reinforced resin-based composite materials. A matrix density evolution model for fiber-reinforced resin-based composite materials is established. Based on the experimental matrix crack density data, the parameters of the matrix density evolution model are fitted using the nonlinear least squares method. The coefficient of determination is used to quantitatively evaluate the model's evolution fitting accuracy. This method can accurately describe the evolution process of matrix crack density in FRP materials under ultra-high cycle fatigue loading, is convenient and fast to calculate, and has strong engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of composite material fatigue damage characterization technology, and relates to a method for designing the matrix crack density evolution of resin-based composite materials under fatigue load. Background Technology

[0002] Fiber-reinforced plastics (FRP) are widely used in aerospace, transportation, and energy fields due to their high specific strength, high specific modulus, and good corrosion resistance. However, FRP materials are prone to damage forms such as matrix cracking, interfacial debonding, and interlaminar delamination under fatigue loading. In particular, the initiation and propagation of matrix cracks are key early characteristics of fatigue damage evolution. Therefore, studying the characteristic evolution of FRP matrix cracks is crucial. Accurately predicting the matrix crack density of resin-based composites under service conditions is a key technology for simulating the fatigue performance of resin-based composites.

[0003] Existing research indicates that the matrix crack density exhibits a nonlinear evolution trend with increasing load cycle number, typically divided into three stages: initial crack initiation, stable crack propagation, and crack saturation. Although some models attempt to describe this process, such as the single-parameter power function model proposed by Wormby et al., this model assumes the crack exists from the onset of fatigue and fails to reflect the delayed crack initiation characteristics. Therefore, a physical model that reflects the evolutionary characteristics of these three stages is needed.

[0004] Currently, there is a lack of a unified, predictable, and clearly defined empirical model for the evolution of matrix crack density in FRP materials during fatigue, especially under ultra-high cycle fatigue loading, where the applicability and accuracy of the model still need further verification. Therefore, there is an urgent need for a model that can accurately describe the evolution of matrix crack density in FRP materials under different load levels to support fatigue life prediction and structural reliability assessment. Summary of the Invention

[0005] Purpose of the invention The purpose of this invention is to provide a method for designing the matrix crack density evolution of resin-based composite materials under fatigue loads. This method can accurately describe the evolution process of matrix crack density in FRP materials under ultra-high cycle fatigue loads, and is convenient, fast, and highly applicable to engineering.

[0006] Technical solution A method for designing the matrix crack density evolution of resin-based composite materials under fatigue loading includes the following steps: S1. Conduct fatigue tests at different load levels, observe and record the matrix crack density ρ and its corresponding cycle number N of the fiber-reinforced resin matrix composite. S2, Establish a matrix density evolution model for fiber-reinforced resin matrix composites; S3. Based on the experimental matrix crack density data, the parameters of the matrix density evolution model of fiber-reinforced resin matrix composites were fitted using the nonlinear least squares method. S4, using the coefficient of determination The evolutionary fitting accuracy of the model is quantitatively evaluated.

[0007] Further, in step S2, the matrix density evolution model expression is:

[0008] In the formula, The matrix crack density when the cycle number is N; The crack density is the saturated matrix. This represents the cycle number corresponding to the initiation of cracks in the matrix. is the cycle number corresponding to the damage feature; m is the Weibull shape parameter.

[0009] Furthermore, before conducting the fatigue test in step S1, the test piece is subjected to X-ray microcomputed tomography to ensure that there is no internal damage to the test piece before the test.

[0010] Furthermore, before conducting the fatigue test in step S1, a uniaxial tensile test must be performed on the test specimen to determine its tensile strength. The fatigue load in step S1 must not exceed the tensile strength of the test specimen, and the fatigue load can be controlled at 80% or less of the tensile strength.

[0011] Further, in step S3, the model parameters , , , m were obtained by fitting fatigue test data using the nonlinear least squares method, and the fitting objective function was:

[0012] In the formula, S is the sum of squared residuals, which is minimized during the fitting process; Let be the matrix crack density at the i-th test data point; Let i be the cycle number for the i-th test data point; The crack density is the saturated matrix. This represents the cycle number corresponding to the initiation of cracks in the matrix. is the cycle number corresponding to the damage feature; m is the Weibull shape parameter.

[0013] Furthermore, in step S4, the coefficient of determination The expression is:

[0014] In the formula, Let be the matrix crack density corresponding to the i-th test data point; This represents the matrix crack density prediction value of the model in S2 at the corresponding cycle number; is the average crack density of the test matrix; n is the total number of data points.

[0015] Furthermore, when the coefficient of determination R 2 When the value is ≥0.90, the model is deemed to have passed validation and can be used to predict the evolution trend of matrix crack density in composite materials.

[0016] Furthermore, after the model parameters are fitted and the evaluation in step S4 is passed, a new fatigue load is selected and the fatigue test in step S1 is performed again to verify the accuracy of the model.

[0017] Technical effect This invention enables rapid and accurate prediction of the matrix crack density evolution of fiber-reinforced resin matrix composites under fatigue loading. The matrix crack density evolution model parameters proposed in this invention have clear physical meanings and provide excellent description of the FRP matrix crack density evolution curves under high-cycle and ultra-high-cycle fatigue loading. The model is simple to calculate, and the fitted evolution curves are accurate and reliable, effectively characterizing the matrix crack density development of fiber-reinforced resin matrix composites under ultra-high-cycle fatigue loading, thus providing a basis for the fatigue-resistant design of fiber-reinforced resin matrix composites. Attached Figure Description

[0018] Figure 1 This is a graph showing the evolution trend of matrix crack density in this invention. Figure 2 This is a flowchart illustrating an embodiment of the present invention; Figure 3 This is a schematic diagram of the matrix crack morphology in an embodiment of the present invention; Figure 4a This is the crack density evolution curve of the composite material D2 layup matrix in the embodiment of the present invention; Figure 4b This is the crack density evolution curve of the composite material D3 layup matrix in the embodiments of the present invention; Figure 4c This is the crack density evolution curve of the composite material D4 layup matrix in an embodiment of the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be described in more detail below. In the examples, the same or similar reference numerals denote the same or similar components or elements having the same or similar functions throughout. The described embodiments are some, but not all, of the embodiments of this invention. The embodiments described below with reference to reference are exemplary and intended to explain this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. The embodiments of this invention will be described in detail below.

[0020] Figure 2 This is a flowchart illustrating the matrix crack density evolution model of fiber-reinforced resin matrix composites under fatigue load, according to an embodiment of the present invention. See also... Figure 2 This invention provides a method for designing the matrix crack density evolution of resin-based composite materials under fatigue loading. The model includes the following steps: S1. Conduct fatigue tests at different load levels, observe and record the matrix crack density ρ and its corresponding cycle number N of the fiber-reinforced resin matrix composite. S2, Establish a matrix density evolution model for fiber-reinforced resin matrix composites; S3. Based on the experimental matrix crack density data, the parameters of the matrix density evolution model of fiber-reinforced resin matrix composites were fitted using the nonlinear least squares method. S4, using the coefficient of determination The evolutionary fitting accuracy of the model is quantitatively evaluated.

[0021] Specifically, the fiber-reinforced resin matrix composite matrix crack density evolution model under fatigue load of the present invention includes the following steps: Step 1: Conduct fatigue tests at different load levels, observe and record the matrix crack density ρ and its corresponding cycle number N of the fiber-reinforced resin matrix composite. Figure 3 This is a schematic diagram of the matrix crack morphology in an embodiment of the present invention. In this example, the fatigue test loading process is force-controlled, with a loading frequency of 8Hz and a stress ratio of R=0.1.

[0022] Step 2: Establish a matrix density evolution model for fiber-reinforced resin matrix composites and describe it using equation (1), where... The matrix crack density when the cycle number is N; The crack density is the saturated matrix. This represents the cycle number corresponding to the initiation of cracks in the matrix. is the cycle number corresponding to the damage feature; m is the Weibull shape parameter.

[0023] (1) Step 3: Based on the experimental matrix crack density data, the parameters of the matrix density evolution model of fiber-reinforced resin matrix composites are evaluated using the nonlinear least squares method. , , The fitting is performed on m, and the fitting objective function is shown in equation (2), where S is the sum of squared residuals, which is minimized during the fitting process; Let be the matrix crack density at the i-th test data point; Let i be the cycle number for the i-th test data point; The crack density is the saturated matrix. This represents the cycle number corresponding to the initiation of cracks in the matrix. is the cycle number corresponding to the damage feature; m is the Weibull shape parameter.

[0024] (2) Step 4: Use the coefficient of determination The evolutionary fitting accuracy of the model is quantitatively evaluated, and the expression for the coefficient of determination is given in equation (3). Where... Let be the matrix crack density corresponding to the i-th test data point; The matrix crack density prediction value of the model described in claim 1 at the corresponding number of cycles; is the average crack density of the test matrix; n is the total number of data points.

[0025] (3) When R 2 When the value is ≥0.90, the model is deemed valid and can be used to predict the matrix crack density evolution trend of composite materials. In this example, the goodness-of-fit R of the composite material's D2, D3, and D4 layups is calculated based on equation (3). 2 The values ​​are 0.9621, 0.9851, and 0.9746, respectively, all greater than 0.90. Figure 4 shows the matrix crack density evolution curves of composite material layups D2, D3, and D4 in the embodiments of the present invention.

[0026] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0027] Furthermore, unless otherwise defined, the technical or scientific terms used in this application description shall have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "upper," "lower," "left," "right," "center," "vertical," "horizontal," "inner," and "outer," etc., used in this application description to indicate relative direction or positional relationship are used only to indicate relative orientation or positional relationship, and do not imply that the device or component must have a specific orientation, or be constructed and operated in a specific orientation. When the absolute position of the described object changes, its relative positional relationship may also change accordingly, and therefore should not be construed as a limitation on this application. The terms "first," "second," "third," and similar terms used in this application description are used only for descriptive purposes to distinguish different components, and should not be construed as indicating or implying relative importance. The terms "a," "one," or "the," etc., used in this application description should not be construed as an absolute limitation on quantity, but should be construed as indicating the existence of at least one. The terms "including," "comprising," etc., used in this application description mean that the element or object preceding the word covers the element or object listed after the word and its equivalents, without excluding other elements or objects.

[0028] Furthermore, it should be noted that, unless otherwise explicitly specified and limited, terms such as “installation,” “connection,” and “linkage” used in the description of this application should be interpreted broadly. For example, a connection can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; or it can be a connection within two components. Those skilled in the art can understand its specific meaning in this application according to the specific circumstances.

[0029] The above description is merely a specific embodiment of the present invention and is not intended to limit the present invention. Within the spirit and principles of the present invention, any person skilled in the art may use the above-disclosed technical content to make changes or modifications to equivalent embodiments and apply them to other fields. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention, as well as any modifications, equivalent substitutions, improvements, etc., should be included within the protection scope of the present invention.

Claims

1. A method for designing the evolution of matrix crack density in resin-based composite materials under fatigue loading, characterized in that, Includes the following steps: S1. Conduct fatigue tests at different load levels, observe and record the matrix crack density ρ and its corresponding cycle number N of the fiber-reinforced resin matrix composite. S2, Establish a matrix density evolution model for fiber-reinforced resin matrix composites; S3. Based on the experimental matrix crack density data, the parameters of the matrix density evolution model of fiber-reinforced resin matrix composites were fitted using the nonlinear least squares method. S4, using the coefficient of determination The evolutionary fitting accuracy of the model is quantitatively evaluated.

2. The method as described in claim 1, characterized in that, In step S2, the matrix density evolution model expression is: In the formula, The matrix crack density when the cycle number is N; The crack density is the saturated matrix. This represents the cycle number corresponding to the initiation of cracks in the matrix. is the cycle number corresponding to the damage feature; m is the Weibull shape parameter.

3. The method of claim 1, wherein, Before conducting the fatigue test in step S1, the test piece is subjected to X-ray microcomputed tomography to ensure that there is no internal damage to the test piece before the test.

4. The method of claim 1, wherein, Before conducting the fatigue test in step S1, a uniaxial tensile test must be performed on the test piece to determine its tensile strength.

5. The method of claim 4, wherein, The fatigue load in step S1 must not exceed the tensile strength of the test specimen, and the fatigue load can be controlled at 80% or less of the tensile strength.

6. The method of claim 1, wherein, In step S3, the model parameters 、 、 , m are obtained by fitting the fatigue test data using a non-linear least squares method, with the objective function being: In the formula, S is the sum of squared residuals, which is minimized during the fitting process; Let be the matrix crack density at the i-th test data point; Let i be the cycle number for the i-th test data point; The crack density is the saturated matrix. This represents the cycle number corresponding to the initiation of cracks in the matrix. is the cycle number corresponding to the damage feature; m is the Weibull shape parameter.

7. The method of claim 1, wherein, In step S4, the coefficient of determination The expression is: In the formula, Let be the matrix crack density corresponding to the i-th test data point; This represents the matrix crack density prediction value of the model in S2 at the corresponding cycle number; is the average crack density of the test matrix; n is the total number of data points.

8. The method of claim 1, wherein, When the determination coefficient R 2 ≥ 0.90, the model passes the verification and can be used to predict the matrix crack density evolution trend of the composite material.

9. The method of claim 1, wherein, After the model parameters are fitted and the evaluation in step S4 is passed, a new fatigue load is selected and the fatigue test in step S1 is performed again to verify the accuracy of the model.

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