Characterization method for mechanical properties of carbon fiber reinforced epoxy resin-based composite material

By using common distribution and Copula function models, the problem of characterizing multiple mechanical performance parameters of carbon fiber reinforced epoxy resin-based composites was solved, a refined description of material properties was achieved, and the reliability design of aerospace equipment was supported.

CN120636645APending Publication Date: 2025-09-12BEIJING INST OF STRUCTURE & ENVIRONMENT ENG
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Patent Information

Application Number
CN202510804175.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-06-17
Publication Date
2025-09-12

AI Technical Summary

Technical Problem

Existing technologies make it difficult to effectively characterize the multiple mechanical performance parameters of carbon fiber reinforced epoxy resin-based composites, resulting in difficulty in achieving refined design in the structural reliability design of aerospace equipment.

Method used

Common distribution and Copula function models are used to characterize the multiple mechanical properties of carbon fiber reinforced epoxy resin matrix composites. The joint distribution of normal, Weibull and Copula functions is constructed by likelihood estimation method to characterize the discreteness and correlation of the material.

Benefits of technology

The effective characterization of multiple mechanical performance parameters of carbon fiber reinforced epoxy resin-based composite materials has been achieved, supporting the refined design of the reliability of aerospace equipment structures.

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Abstract

The invention provides a method for characterizing mechanical properties of a carbon fiber reinforced epoxy resin-based composite material, which comprises the following steps of: characterizing discreteness of single mechanical property parameters of the carbon fiber reinforced epoxy resin-based composite material by adopting normal distribution, logarithmic normal distribution and Weibull distribution, and characterizing correlation of multiple mechanical property parameters of the material by utilizing a Copula function; multivariable joint distribution is constructed, and the mechanical property of the material is represented. The method gets rid of the limitation on the edge distribution type and the Copula distribution type when the joint distribution is used as the overall construction in the traditional multi-dimensional distribution, and creates conditions for the flexible construction of the multivariate joint distribution model.
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Description

Technical Field

[0001] The invention belongs to the field of composite material design, and in particular relates to a method for characterizing the mechanical properties of a carbon fiber reinforced epoxy resin-based composite material. Background Art

[0002] Carbon fiber reinforced epoxy resin-based composites, as one of the most important advanced materials for aerospace equipment, are attracting increasing attention. Tensile strength, stiffness, and flexural strength and stiffness are the fundamental mechanical properties of carbon fiber reinforced epoxy resin-based composites, and their characterization is fundamental to the reliability design of aerospace equipment structures. Numerous studies have been conducted domestically and internationally on the characterization of the mechanical properties of carbon fiber reinforced epoxy resin-based composites. These studies have all employed common distribution models, such as normal, lognormal, and Weibull, to fit the material's strength and stiffness data. The Kolmogorov-Smirnov test and maximum likelihood test were used to evaluate the statistical distribution model fit, and the optimal fitting distribution model was selected to characterize the strength and stiffness of carbon fiber reinforced epoxy resin-based composites. Due to the characteristics of carbon fiber reinforced epoxy resin-based composites, their mechanical properties, such as strength and stiffness, exhibit correlations. Current methods for characterizing a single mechanical property parameter are insufficient for the precise reliability design of aerospace equipment structures. Summary of the Invention

[0003] Aiming at the problem of characterizing multiple mechanical performance parameters of carbon fiber reinforced epoxy resin-based composite materials, the present invention proposes a method for characterizing the mechanical properties of carbon fiber reinforced epoxy resin-based composite materials. Common distribution and Copula function models are used to characterize the discreteness and correlation of multiple mechanical performance parameters such as stiffness and strength of carbon fiber reinforced epoxy resin-based composite materials, providing support for the refined design of aerospace equipment structural reliability.

[0004] The method comprises the following steps:

[0005] Step 1: Arrange the tensile or flexural strength test data of carbon fiber reinforced epoxy resin composite materials, as shown in the following table.

[0006] Test piece serial number 1 2 …… 4 …… n Intensity data <![CDATA[S1]]> <![CDATA[S2]]> …… <![CDATA[S i ]]> …… <![CDATA[S n ]]> Stiffness data <![CDATA[E1]]> <![CDATA[E2]]> …… <![CDATA[E i ]]> …… <![CDATA[E n ]]>

[0007] Step 2: Use the material strength data to estimate the normal N using the likelihood estimation method S (S|μ S ,σ S ), Weibull distribution W S (S|η S ,m S ) Model parameter μ S , σ S , η S 、m S, calculate the normal distribution N S (S|μ S ,σ S ) Weibull distribution W S (S|η S ,m S ) likelihood value, and select the distribution with the larger likelihood value as the material strength distribution model F S (S|θ S ), characterizing the discreteness of material strength data.

[0008] Step 3: Use the material stiffness data to estimate the normal N using the likelihood estimation method E (E|μ E ,σ E ), Weibull distribution W E (E|η E ,m E ) Model parameter μ E , σ E , η E 、m E , calculate the normal distribution N E (E|μ E ,σ E ) Weibull distribution N E (E|μ E ,σ E ) and select the distribution with the larger likelihood value as the material stiffness distribution model F E (E|θ E ), characterizing the discreteness of material stiffness data.

[0009] Step 4: Use the material's strength data, stiffness data, and strength distribution model F S (S|θ S ), stiffness distribution model F E (E|θ E ), use the likelihood estimation method to estimate the Gaussian Copula, t Copula, Archimid Copula function parameters τ G , τ t , τ A Calculate the likelihood values ​​of Gaussian Copula, t Copula, and Archimid Copula functions, and select the function with the larger likelihood value as the joint distribution function F(F) of material strength and stiffness. S (S|θ S ),F E (E|θ E )|α), characterizes the correlation of material stiffness data.

[0010] The beneficial effects of the present invention are as follows:

[0011] This method employs discrete and correlated methods to characterize the multiple mechanical properties of carbon fiber-reinforced epoxy resin composites. It uses normal, lognormal, and Weibull distributions to characterize the discreteness of individual mechanical property parameters of carbon fiber-reinforced epoxy resin composites. It also utilizes Copula functions to characterize the correlations among multiple mechanical property parameters, constructing a multivariate joint distribution to characterize the mechanical properties of the material. This method overcomes the limitations of traditional multidimensional distributions, which use a joint distribution as a whole, on marginal and Copula distribution types, and facilitates the flexible construction of multivariate joint distribution models. DETAILED DESCRIPTION

[0012] In order to help those skilled in the art better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention are clearly and completely described below. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0013] This embodiment provides a method for characterizing the mechanical properties of a carbon fiber reinforced epoxy resin-based composite material, the method comprising the following steps:

[0014] Step 1: Arrange the tensile or flexural strength test data of carbon fiber reinforced epoxy resin composite materials as shown in the following table:

[0015] Test piece serial number 1 2 …… 4 …… n Intensity data <![CDATA[S1]]> <![CDATA[S2]]> …… <![CDATA[S i ]]> …… <![CDATA[S n ]]> Stiffness data <![CDATA[E1]]> <![CDATA[E2]]> …… <![CDATA[E i ]]> …… <![CDATA[E n ]]>

[0016] Step 2: Use the material strength data to estimate the normal N using the likelihood estimation method S (S|μ S ,σ S ), Weibull distribution W S (S|η S ,m S ) Model parameter μ S , σ S , η S 、m S , calculate the normal distribution N S (S|μ S ,σ S ) Weibull distribution W S (S|η S ,m S ) likelihood value, and select the distribution with the larger likelihood value as the material strength distribution model F S (S|θ S ), characterizing the discreteness of material strength data.

[0017] Step 3: Use the material stiffness data to estimate the normal N using the likelihood estimation method E (E|μ E ,σ E ), Weibull distribution W E (E|η E ,m E ) Model parameter μ E , σ E , η E 、m E , calculate the normal distribution N E (E|μ E ,σ E ) Weibull distribution N E (E|μ E ,σ E ) and select the distribution with the larger likelihood value as the material stiffness distribution model F E (E|θ E ), characterizing the discreteness of material stiffness data.

[0018] Step 4: Use the material's strength data, stiffness data, and strength distribution model F S (S|θ S ), stiffness distribution model F E (E|θ E ), use the likelihood estimation method to estimate the Gaussian Copula, t Copula, Archimid Copula function parameters τ G , τ t , τ A Calculate the likelihood values ​​of Gaussian Copula, t Copula, and Archimid Copula functions, and select the function with the larger likelihood value as the joint distribution function F(F) of material strength and stiffness. S (S|θ S ),F E (E|θ E )|α), characterizes the correlation of material stiffness data.

[0019] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for characterizing the mechanical properties of carbon fiber reinforced epoxy resin-based composite materials, characterized in that: The steps include: Step 1: Arrange the tensile or bending test data of carbon fiber reinforced epoxy resin matrix composite materials; the test data includes strength data and stiffness data; Step 2: Construct material strength distribution model F S (S|θ S ), characterizes the discreteness of material strength data; Step 3: Construct material stiffness distribution model F E (E|θ E ), characterizing the discreteness of material stiffness data; Step 4: Use the material's strength data, stiffness data, and strength distribution model F S (S|θ S ), stiffness distribution model F E (E|θ E ), use the likelihood estimation method to estimate the GaussianCopula, tCopula, Archimid Copula function parameter τ G , τ t , τ A Calculate the likelihood values ​​of Gaussian Copula, t Copula, and Archimed Copula functions, and select the function with the larger likelihood value as the joint distribution function F(F) of material strength and stiffness. S (S|θ S ),F E (E|θ E )|α), characterizes the correlation of material stiffness data.

2. The method for characterizing the mechanical properties of carbon fiber reinforced epoxy resin-based composite materials according to claim 1, characterized in that: The construction of the material strength distribution model is specifically as follows: using the material strength data to estimate the normal distribution N using the likelihood estimation method S (S|μ S ,σ S ), Weibull distribution W S (S|η S ,m S ) Model parameter μ S , σ S , η S 、m S , calculate the normal distribution N S (S|μ S ,σ S ) Weibull distribution W S (S|η S ,m S ) likelihood value, and select the distribution with the larger likelihood value as the material strength distribution model F S (S|θ S ).

3. The method for characterizing the mechanical properties of carbon fiber reinforced epoxy resin-based composite materials according to claim 1, characterized in that: The construction of the material stiffness distribution model is specifically as follows: using the material stiffness data to estimate the normal distribution N using the likelihood estimation method E (E|μ E ,σ E ), Weibull distribution W E (E|η E ,m E ) Model parameter μ E , σ E , η E 、m E , calculate the normal distribution N E (E|μ E ,σ E ) Weibull distribution N E (E|μ E ,σ E ) likelihood value, and select the distribution with the larger likelihood value as the material stiffness distribution model F E (E|θ E ).