A method for obtaining shear constitutive model for characterizing dual damage characteristics of composite materials

Abstract

The invention proposes a method for obtaining a shear constitutive model for characterizing the double damage characteristics of a composite material, and belongs to the technical field of research on mechanical properties of composite materials. Firstly, multiple shear tests of composite materials under the same loading conditions are completed, and the load-displacement data of each test are recorded, and then the measured shear stress-strain data of the composite material are calculated; then, two statistical distribution models are used to respectively characterize the probability distribution of the damage amount of the fiber and the matrix in the composite material in the loading strain domain, and the double damage shear constitutive model of the composite material is derived; finally, a genetic algorithm is used to obtain the double damage shear constitutive model parameter value corresponding to each measured composite material shear stress-strain data, and finally the shear constitutive model for characterizing the double damage characteristics of the composite material is obtained by taking the average of the same parameters; the composite material double damage shear constitutive model proposed by the invention can truly characterize the double damage characteristics of the composite material, and has high precision.

Description

Technical Field

[0001] The invention belongs to the technical field of research on mechanical properties of composite materials, and in particular relates to a method for obtaining a shear constitutive model for characterizing double damage characteristics of composite materials. Background Art

[0002] Fiber reinforced composite materials are composite materials made by winding, molding or pultrusion of fibers and matrix materials. Due to the differences in the mechanical properties and distribution patterns of fibers and matrix materials, during shear loading, the material may show the characteristics of two damage stages: body damage and fiber damage. The shear constitutive model of composite materials is the basis for calculating the structural response of composite materials. An accurate shear constitutive model will improve the response prediction accuracy of composite structures. Therefore, it is necessary to find a shear constitutive model that can characterize the dual damage characteristics of composite materials.

[0003] There are currently two types of commonly used shear constitutive models for composite materials. The first type: does not consider the damage within the composite material, and uses a linear constitutive model to characterize the shear stress-strain relationship of the material. This method has a certain accuracy only when the shear stress is small. When the shear stress is large, the error is very large. The second type: assumes that the damage of the fiber and matrix in the composite material has the same statistical characteristics, and derives a damage constitutive model for the composite material. Although this method is more accurate than the linear shear constitutive model, this constitutive model cannot characterize the "double hump" phenomenon of the shear stress-strain curve caused by the difference in damage to the fiber and matrix. Applying this constitutive model to the simulation calculation of composite structures will still result in large errors. Summary of the invention

[0004] The purpose of the present invention is to provide a method for obtaining a shear constitutive model that characterizes the dual damage characteristics of a composite material. Based on the differences in the damage accumulation characteristics of the fiber and matrix in the composite material, the obtained shear constitutive model can accurately characterize the constitutive relationship of the composite material and lay the foundation for high-fidelity response prediction of the composite material structure.

[0005] The technical solution to achieve the purpose of the present invention is:

[0006] A method for obtaining a shear constitutive model for characterizing dual damage characteristics of a composite material comprises the following steps:

[0007] Step 1, completing multiple composite shear tests under the same loading conditions, and recording the load-displacement data of each test, and then calculating the measured composite shear stress-strain data;

[0008] Step 2: Two statistical distribution models are used to characterize the probability distribution of the damage amount of the fiber and matrix in the composite material in the loading strain domain, and a double damage shear constitutive model of the composite material is derived;

[0009] Step 3: Use a genetic algorithm to obtain the double damage shear constitutive model parameter values ​​corresponding to each measured composite material shear stress-strain data, and finally obtain the shear constitutive model that characterizes the double damage characteristics of the composite material by taking the average of the same parameters.

[0010] Compared with the prior art, the present invention has the following significant advantages:

[0011] The present invention provides a method for accurately obtaining a shear constitutive model of a composite material. The method fully considers the differences in damage characteristics of fibers and matrices in the composite material, and adopts two Weibull distribution models to characterize the damage distribution of fibers and matrices respectively, and its physical meaning is clear. The present invention can more accurately characterize the "double hump" phenomenon of the shear stress-strain curve caused by the differences in damage of fibers and matrices, and lays a foundation for the analysis of damage failure mechanisms of composite materials and the simulation of composite material structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 Schematic diagram of the composite shear test specimen and its dimensions.

[0013] Figure 2 The shear stress-strain curve measured in the experiment and the shear constitutive model obtained in the patent of this invention to characterize the double damage characteristics of the composite material.

[0014] Figure 3 Schematic diagram of the two damage stages of the shear stress-strain curve of the composite material measured in the experiment DETAILED DESCRIPTION

[0015] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0016] A method for obtaining a shear constitutive model for characterizing dual damage characteristics of a composite material according to the present invention comprises the following steps:

[0017] Step 1: Complete multiple composite shear tests under the same loading conditions, record the load-displacement data of each test, and then calculate the measured composite shear stress-strain data; the specific steps are as follows:

[0018] 1) Design composite shear test pieces and complete multiple composite shear tests under the same loading conditions to obtain the load-displacement data output by the testing machine. In order to reduce the test error caused by accidental factors, at least 5 repeated tests should be completed;

[0019] 2) According to the shear loading load and shear loading displacement recorded in the test, the shear stress and shear strain of the composite material are calculated. The specific expressions are as follows:

[0020]

[0021] Where: F is the loading load recorded by the testing machine, is the measured shear stress in the shear region of the shear test piece, S s is the cross-sectional area of ​​the shear region, is the measured shear strain, d is the loading displacement recorded by the testing machine, and δ is the width of the shear area.

[0022] Step 2: Two statistical distribution models are used to characterize the probability distribution of the damage amount of the fiber and matrix in the composite material in the loading strain domain, and the double damage shear constitutive model of the composite material is derived; the specific steps are as follows:

[0023] 1) Two Weibull cumulative distribution models are used to characterize the two stages of shear damage evolution of composite materials, namely the first damage stage dominated by matrix damage and the second damage stage dominated by fiber damage. The cumulative damage amount D c1 and D c2 Respectively expressed as:

[0024]

[0025] Where γ is the shear strain of the composite material; a1 and b1 are the scale factor and shape factor of the Weibull cumulative damage distribution function in the first damage stage, respectively; a2 and b2 are the scale factor and shape factor of the Weibull cumulative damage distribution function in the second damage stage, respectively.

[0026] 2) Based on the damage mechanics theory, the double damage shear constitutive model of composite materials is derived, which is expressed as follows:

[0027]

[0028] Where τ is the shear stress of the composite material; G1 and G2 are the shear stiffness components at the first damage stage and the second damage stage, respectively.

[0029] Step 3: Use a genetic algorithm to obtain the double damage shear constitutive model parameter values ​​corresponding to each measured composite material shear stress-strain data, and finally obtain the shear constitutive model that characterizes the double damage characteristics of the composite material by taking the average of the same parameters.

[0030] The objective function of the measured composite material shear stress-strain data and the composite material double damage shear constitutive model is expressed as:

[0031]

[0032] Where n represents the number of sampling points of the measured composite shear stress-strain data; and τ(i) are the shear stress value of the i-th sampling point in the measured shear stress-strain data of the composite material and the shear stress value of the double damage shear constitutive model of the composite material at the same strain, respectively.

[0033] The parameter values ​​G1, G2, a1, a2, b1 and b2 of the double damage shear constitutive model of composite materials are optimized by genetic algorithm so that the objective function takes the minimum value.

[0034] The specific steps of obtaining the shear constitutive model that characterizes the dual damage characteristics of the composite material by taking the average of the same parameters are as follows:

[0035] 1) The measured composite shear stress-strain data obtained from repeated tests were used to obtain the corresponding parameter values ​​G1, G2, a1, a2, b1 and b2 using genetic algorithms;

[0036] 2) Calculate the arithmetic mean of these parameter values ​​respectively and And it is used as the characterization parameter value of the double damage shear constitutive model of the composite material;

[0037] 3) Substitute the characterization parameter values ​​into the double damage shear constitutive model of the composite material to obtain the shear constitutive model that characterizes the double damage characteristics of the composite material.

[0038] Example:

[0039] A method for obtaining an interlaminar shear constitutive model for characterizing double damage characteristics of a carbon fiber reinforced composite material in this embodiment includes the following steps:

[0040] Step 1: Design the carbon fiber reinforced composite interlaminar shear test specimen, whose geometry and dimensions are as follows: Figure 1 An electronic universal material testing machine was used to complete five interlaminar shear tests of carbon fiber reinforced composite materials with a loading rate of 0.001 mm / s, and the load-displacement data of each test was recorded, and then the measured interlaminar shear stress and interlaminar shear strain of the carbon fiber reinforced composite materials were calculated. The specific expressions are as follows:

[0041]

[0042] Where: F is the loading load recorded by the testing machine; is the measured interlaminar shear stress in the shear region of the carbon fiber reinforced composite interlaminar shear test specimen; S s is the cross-sectional area of ​​the shear region of the carbon fiber reinforced composite interlaminar shear test specimen, S s =16mm×5mm×2=160mm 2 ; is the measured interlaminar shear strain; d is the loading displacement recorded by the testing machine; δ is the width of the shear area, δ = 1 mm.

[0043] The calculated measured interlaminar shear stress-strain curve of carbon fiber reinforced composite materials is as follows: Figure 2 shown.

[0044] Step 2: The interlaminar shear stress-strain curve of carbon fiber reinforced composite materials shows a "double hump" phenomenon with two damage stages, such as Figure 3 As shown in the figure, two Weibull cumulative distribution models are used to characterize the two stages of interlaminar shear damage evolution of carbon fiber reinforced composite materials, namely the first damage stage dominated by matrix damage and the second damage stage dominated by fiber damage. The cumulative damage amount D c1 and D c2 Respectively expressed as:

[0045]

[0046] Wherein, γ is the interlaminar shear strain of carbon fiber reinforced composite materials; a1 and b1 are the scale factor and shape factor of the Weibull cumulative damage distribution function in the first damage stage, respectively; a2 and b2 are the scale factor and shape factor of the Weibull cumulative damage distribution function in the second damage stage, respectively.

[0047] Based on the damage mechanics theory, the double-damaged interlaminar shear constitutive model of carbon fiber reinforced composite materials is derived and expressed as follows:

[0048]

[0049] Where τ is the interlaminar shear stress of carbon fiber reinforced composite materials; G1 and G2 are the interlaminar shear stiffness components at the first damage stage and the second damage stage, respectively.

[0050] Step 3: Construct the objective function of the measured carbon fiber reinforced composite material interlaminar shear stress-strain data and the carbon fiber reinforced composite material double-damage interlaminar shear constitutive model, which is expressed as:

[0051]

[0052] Where n represents the number of sampling points of measured interlaminar shear stress-strain data of carbon fiber reinforced composite materials; and τ(i) are the shear stress value of the i-th sampling point in the measured interlaminar shear stress-strain data of carbon fiber reinforced composite materials and the shear stress value of the double-damaged interlaminar shear constitutive model of carbon fiber reinforced composite materials at the same strain, respectively.

[0053] The genetic algorithm is used to obtain the parameter values ​​(G1, G2, a1, a2, b1 and b2) of the double-damage interlaminar shear constitutive model corresponding to each measured carbon fiber reinforced composite interlaminar shear stress-strain data, so that the objective function takes the minimum value. The optimized parameter results are shown in Table 1.

[0054] Table 1 Parameter values ​​of double-damaged interlaminar shear constitutive model of carbon fiber reinforced composites

[0055]

[0056]

[0057] Calculate the arithmetic mean of each parameter in Table 1 respectively. and Substituting it into the double-damage interlaminar shear constitutive model of carbon fiber reinforced composite materials, the interlaminar shear constitutive model that characterizes the double-damage characteristics of the carbon fiber reinforced composite materials can be obtained, such as Figure 2 shown.

[0058] Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

Claims

1. A method for obtaining a shear constitutive model for characterizing dual damage characteristics of a composite material, characterized in that: The following steps are involved: Step 1, completing multiple composite shear tests under the same loading conditions, and recording the load-displacement data of each test, and then calculating the measured composite shear stress-strain data; Step 2: Two statistical distribution models are used to characterize the probability distribution of the damage amount of the fiber and matrix in the composite material in the loading strain domain, and the double damage shear constitutive model of the composite material is derived; specifically, the following steps are included: 1) Two Weibull cumulative distribution models are used to characterize the two stages of shear damage evolution of composite materials, namely the first damage stage dominated by matrix damage and the second damage stage dominated by fiber damage. The cumulative damage amount D c1 and D c2 Respectively expressed as: Where γ is the shear strain of the composite material; a1 and b1 are the scale factor and shape factor of the Weibull cumulative damage distribution function in the first damage stage, respectively; a2 and b2 are the scale factor and shape factor of the Weibull cumulative damage distribution function in the second damage stage, respectively; 2) Based on the damage mechanics theory, the double damage shear constitutive model of composite materials is derived, which is expressed as follows: Where τ is the shear stress of the composite material; G1 and G2 are the shear stiffness components at the first damage stage and the second damage stage, respectively; Step 3: Use a genetic algorithm to obtain the double damage shear constitutive model parameter values ​​corresponding to each measured composite material shear stress-strain data, and finally obtain the shear constitutive model that characterizes the double damage characteristics of the composite material by taking the average of the same parameters.

2. The method for obtaining a shear constitutive model for characterizing dual damage characteristics of a composite material according to claim 1, characterized in that: Step 1 specifically includes the following steps: 1) Design composite shear test pieces and complete multiple composite shear tests under the same loading conditions to obtain load-displacement data output by the testing machine; 2) According to the shear loading load and shear loading displacement recorded in the test, the shear stress and shear strain of the composite material are calculated. The specific expressions are as follows: Where: F is the loading load recorded by the testing machine, is the measured shear stress in the shear region of the shear test piece, S s is the cross-sectional area of ​​the shear region, is the measured shear strain, d is the loading displacement recorded by the testing machine, and δ is the width of the shear area.

3. The method for obtaining a shear constitutive model for characterizing dual damage characteristics of a composite material according to claim 1, characterized in that: In step 3, a genetic algorithm is used to obtain the double damage shear constitutive model parameter values ​​corresponding to each measured composite material shear stress-strain data, which specifically includes the following steps: (1) The objective function of the measured composite shear stress-strain data and the composite double-damage shear constitutive model is expressed as: Where n represents the number of sampling points of the measured composite shear stress-strain data; and τ(i) are the shear stress value of the i-th sampling point in the measured shear stress-strain data of the composite material and the shear stress value of the double-damage shear constitutive model of the composite material at the same strain, respectively; (2) The parameter values ​​G1, G2, a1, a2, b1 and b2 of the double damage shear constitutive model of composite materials are optimized by genetic algorithm so that the objective function takes the minimum value.

4. The method for obtaining a shear constitutive model for characterizing dual damage characteristics of a composite material according to claim 1, characterized in that: In step 3, the shear constitutive model characterizing the dual damage characteristics of the composite material is obtained by taking the average of the same parameters. The specific steps are as follows: 1) The measured composite shear stress-strain data obtained from repeated tests were used to obtain the corresponding parameter values ​​G1, G2, a1, a2, b1 and b2 using genetic algorithms; 2) Calculate the arithmetic mean of these parameter values ​​respectively and And it is used as the characterization parameter value of the double damage shear constitutive model of the composite material; 3) Substitute the characterization parameter values ​​into the double damage shear constitutive model of the composite material to obtain the shear constitutive model that characterizes the double damage characteristics of the composite material.

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