A method for obtaining a staged damage shear constitutive model of composite materials taking into account rate effects

Abstract

The present invention proposes a method for obtaining a staged damage shear constitutive model that accounts for the rate effect of composite materials. The method first conducts dynamic shear mechanical property tests of composite materials at multiple strain rates, recording the shear strain rate and shear stress-strain data for each test. A staged damage shear constitutive model with unknown parameters is proposed based on the characteristics of staged damage to the fiber and matrix within the composite material. A particle swarm optimization algorithm is used to obtain the parameter values ​​of the staged damage shear constitutive model corresponding to each test data point at the corresponding strain rate. A polynomial fitting method is used to obtain a functional relationship between the parameter values ​​of the staged damage shear constitutive model and the strain rate. The functional relationship between the parameter values ​​of the staged damage shear constitutive model and the strain rate is then substituted into the staged damage shear constitutive model with unknown parameters to obtain a staged damage shear constitutive model that accounts for the rate effect of the composite material. The present invention can characterize the shear constitutive relationship of composite materials under dynamic loads.

Description

Technical Field

[0001] The present invention belongs to the technical field of research on mechanical properties of composite materials, and particularly relates to a method for obtaining a staged damage shear constitutive model taking into account rate effects of composite materials. Background Art

[0002] Composite materials, characterized by high strength, high stiffness, and low density, are widely used in aerospace applications. However, aircraft structures are subject to long-term service in dynamic environments. Previous studies have shown that composite materials exhibit strain rate effects, and traditional shear constitutive models that do not consider strain rate effects have low accuracy in predicting structural dynamic response and assessing dynamic strength. Furthermore, the mechanical properties of the fibers and matrix within composite materials vary, and their damage process exhibits two damage stages. This staged damage characteristic of composite materials should be fully considered when constructing shear constitutive models for composite materials. Therefore, it is necessary to develop a staged damage shear constitutive model that accounts for the strain rate effects of composite materials.

[0003] Current research on dynamic shear constitutive models for composite materials has the following main problems: first, the strain rate effect of composite materials is ignored; second, the nonlinear effects of composite material damage caused by composite material damage are ignored; and third, the differences in damage accumulation between fibers and matrices within composite materials are ignored, and a single distribution model is used to characterize the damage accumulation characteristics of fibers and matrices within composite materials. These factors reduce the accuracy of composite shear constitutive models and, consequently, the accuracy of predicting the dynamic response of composite structures.

[0004] Therefore, a high-precision shear constitutive model that can simultaneously consider the strain rate effect and staged damage characteristics of composite materials is urgently needed in scientific research and engineering applications. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for obtaining a staged damage shear constitutive model of composite materials taking into account the rate effect of composite materials. The dynamic shear constitutive model of composite materials obtained by this method can effectively improve the dynamic response prediction and dynamic strength assessment accuracy of composite materials structures under dynamic loads.

[0006] The technical solutions for achieving the purpose of the present invention are:

[0007] A method for obtaining a staged damage shear constitutive model of a composite material taking into account rate effects comprises the following steps:

[0008] Complete dynamic shear mechanical properties tests of composite materials at multiple strain rate levels and record the shear strain rate and shear stress-strain data for each test;

[0009] Based on the characteristics of staged damage of fiber and matrix in composite materials, a staged damage shear constitutive model with unknown parameters is proposed.

[0010] Based on the shear stress-strain data at different strain rates measured in the experiment, the particle swarm optimization algorithm is used to obtain the parameter values ​​of the stage-type damage shear constitutive model corresponding to each test data at the corresponding strain rate. The functional relationship between the parameter values ​​of the stage-type damage shear constitutive model and the strain rate is obtained by polynomial fitting.

[0011] Finally, the functional relationship between the parameter values ​​of the staged damage shear constitutive model and the strain rate is substituted into the staged damage shear constitutive model containing unknown parameters to obtain the staged damage shear constitutive model that takes into account the rate effect of the composite material.

[0012] Compared with the prior art, the present invention has the following significant advantages:

[0013] This invention provides a method for accurately obtaining a dynamic shear constitutive model for composite materials. This method considers both the strain rate effects of the initial stiffness and damage characteristics caused by the rate dependence of crack propagation within the composite material, as well as the staged damage characteristics caused by the differential damage between the fiber and matrix within the composite material. A method for obtaining a staged damage shear constitutive model for composite materials that accounts for the rate effect is proposed. The resulting dynamic shear constitutive model for composite materials has clear physical meaning and high accuracy, effectively improving the accuracy of dynamic response prediction and dynamic strength assessment of composite structures under dynamic loads. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Typical in-plane shear stress-strain curves of C / C composite materials at different strain rates measured in the experiment.

[0015] Figure 2 The in-plane damage shear constitutive structure of the C / C composite material obtained in the patent of this invention under various strain rates and the in-plane shear stress-strain curve measured by the experiment are shown. DETAILED DESCRIPTION

[0016] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0017] A method for obtaining a staged damage shear constitutive model of a composite material taking into account the rate effect of the composite material according to the present invention comprises:

[0018] Complete dynamic shear mechanical properties tests of composite materials at multiple orders of magnitude of strain rates, and record the shear strain rate and shear stress-strain data for each test.

[0019] Completing the dynamic shear mechanical properties test of composite materials at multiple orders of magnitude of strain rates means completing the in-plane shear mechanical properties test of composite materials or the interlaminar shear mechanical properties test of composite materials at no less than 3 different orders of magnitude of strain rates. The distance between each two adjacent strain rates should be no less than 10 times, and the number of effective tests at the same strain rate should be no less than 5 times.

[0020] Based on the characteristics of staged damage of fibers and matrices in composite materials, a staged damage shear constitutive model with unknown parameters is proposed, which is expressed as follows:

[0021]

[0022] Where σ and ε are the shear stress and shear strain, respectively; E1, λ1, and k1 are the initial stiffness, scale factor, and shape factor of the matrix damage stage, respectively; and E2, λ2, and k2 are the initial stiffness, scale factor, and shape factor of the fiber damage stage, respectively. The parameters E1, λ1, k1, E2, λ2, and k2 are all functions related to the shear strain rate.

[0023] Based on the shear stress-strain data at different strain rates measured in the experiment, the particle swarm optimization algorithm is used to obtain the parameter values ​​of the stage-type damage shear constitutive model corresponding to each test data at the corresponding strain rate; and the functional relationship between the parameter values ​​of the stage-type damage shear constitutive model and the strain rate is obtained by polynomial fitting. The specific steps are as follows:

[0024] 1) The parameter values ​​and shear strain rate of the composite material stage damage shear constitutive model are dimensionless and can be expressed as:

[0025]

[0026] Where c p represents the parameters of the stage-type damage shear constitutive model, c p =E1, λ1, k1, E2, λ2, k2; and are the dimensionless stage-damage shear constitutive model parameter values ​​and the dimensionless shear strain rate, respectively; and are the parameter values ​​of the stage damage shear constitutive model and the dimension of the shear strain rate,

[0027] 2) The functional relationship between the parameter values ​​of the stage-type damage shear constitutive model and the logarithmic strain rate is fitted using a quadratic polynomial, which can be expressed as:

[0028]

[0029] Where, and are the quadratic term coefficient, linear term coefficient and constant term coefficient of the quadratic function of the staged damage shear constitutive model parameters.

[0030] Finally, the functional relationship between the parameter values ​​of the staged damage shear constitutive model and the strain rate is substituted into the staged damage shear constitutive model with unknown parameters to obtain the staged damage shear constitutive model that takes into account the rate effect of the composite material. It is expressed as follows:

[0031]

[0032] in are the dimensions of E1 and E2 respectively, and are the quadratic coefficients of the quadratic functions of parameters E1, λ1, k1, E2, λ2 and k2, respectively. and are the linear coefficients of the quadratic functions of parameters E1, λ1, k1, E2, λ2 and k2, respectively. and are the constant term coefficients of the quadratic function of parameters E1, λ1, k1, E2, λ2 and k2 respectively.

[0033] Example

[0034] A method for obtaining an in-plane staged damage shear constitutive model of a C / C composite material taking into account the rate effect of the C / C composite material in this embodiment includes the following steps:

[0035] Step 1: Use the C43.504 electronic universal material testing machine produced by MTS to complete the in-plane shear test of C / C composite materials at shear strain rates of 0.001 / s and 5 / s. Use the HTM5020 high-speed testing machine produced by Zwick formula to complete the in-plane shear test of C / C composite materials at a shear strain rate of 1000 / s. Record the shear strain rate and shear stress-strain data of each test, and repeat 5 valid tests at each loading strain rate.

[0036] Step 2: Based on the characteristics of fiber and matrix staged damage in C / C composites ( Figure 1 (As shown in

[15] ), an in-plane staged damage shear constitutive model with unknown parameters is proposed, which is expressed as follows:

[0037]

[0038] Where σ and ε are the in-plane shear stress and in-plane shear strain, respectively; E1, λ1, and k1 are the initial stiffness, scale factor, and shape factor of the matrix damage stage, respectively; and E2, λ2, and k2 are the initial stiffness, scale factor, and shape factor of the fiber damage stage, respectively. The parameters E1, λ1, k1, E2, λ2, and k2 are all functions related to the in-plane shear strain rate.

[0039] Step 3: Based on the in-plane shear stress-strain data at different strain rates measured in the experiment, the particle swarm optimization algorithm is used to obtain the parameter values ​​of the in-plane staged damage shear constitutive model corresponding to each experimental data at the corresponding strain rate, namely, the values ​​of E1, λ1, k1, E2, λ2, and k2, as shown in Table 1.

[0040] Table 1 Parameters of the in-plane staged damage shear constitutive model for C / C composites

[0041]

[0042] The parameter values ​​(E1, λ1, k1, E2, λ2 and k2) and the in-plane shear strain rate of the in-plane staged damage shear constitutive model of C / C composites are analyzed. Non-dimensionalized, it can be expressed as:

[0043]

[0044] Where c p represents the parameters of the in-plane staged damage shear constitutive model, c p =E1, λ1, k1, E2, λ2, k2; and are the dimensionless in-plane staged damage shear constitutive model parameter values ​​and the dimensionless in-plane shear strain rate, respectively; and are the parameter values ​​of the in-plane staged damage shear constitutive model and the dimensions of the in-plane shear strain rate,

[0045] The functional relationship between the parameter values ​​of the in-plane staged damage shear constitutive model and the logarithmic strain rate is fitted using a quadratic polynomial, which can be expressed as:

[0046]

[0047] Where, and are the quadratic term coefficient, linear term coefficient and constant term coefficient of the quadratic function of the in-plane staged damage shear constitutive model parameters.

[0048] The quadratic function coefficients obtained by fitting are shown in Table 2.

[0049] Table 2 Strain rate-dependent quadratic function fitting results of the in-plane staged damage shear constitutive model parameters

[0050]

[0051] Step 4: Substitute the functional relationship between the parameter values ​​of the in-plane staged damage shear constitutive model and the strain rate into the in-plane staged damage shear constitutive model with unknown parameters to obtain the in-plane staged damage shear constitutive model that takes into account the rate effect of C / C composite materials. The expression is as follows:

[0052]

[0053] The parameter values ​​are given in Table 2. The in-plane shear stress-strain data of C / C composite materials tested at various loading strain rates and the in-plane damage shear constitutive model of C / C composite materials obtained by this method are shown in Figure 2 As shown, Figure 2 (a) shows the in-plane shear stress-strain data of C / C composite materials measured at a strain rate of 0.001 / s and the in-plane damage shear constitutive model of C / C composite materials obtained by this method. Figure 2 (b) shows the in-plane shear stress-strain data of C / C composite materials measured at a strain rate of 5 / s and the in-plane damage shear constitutive model of C / C composite materials obtained by this method. Figure 2 (c) Shown are the in-plane shear stress-strain data of the C / C composite material tested at a strain rate of 1000 / s and the in-plane damaged shear constitutive structure of the C / C composite material obtained by this method.

[0054] Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other implementations obtained by ordinary technicians in this field without making any creative work are within the scope of protection of the present invention.

Claims

1. A method for obtaining a staged damage shear constitutive model of a composite material taking into account the rate effect, characterized in that: The following steps are involved: Complete dynamic shear mechanical properties tests of composite materials at multiple strain rate levels and record the shear strain rate and shear stress-strain data for each test; Based on the characteristics of staged damage of fiber and matrix in composite materials, a staged damage shear constitutive model with unknown parameters is proposed. Based on the shear stress-strain data at different strain rates measured in the experiment, the particle swarm optimization algorithm is used to obtain the parameter values ​​of the stage-type damage shear constitutive model corresponding to each test data at the corresponding strain rate. The functional relationship between the parameter values ​​of the stage-type damage shear constitutive model and the strain rate is obtained by polynomial fitting. Finally, the functional relationship between the parameter values ​​of the staged damage shear constitutive model and the strain rate is substituted into the staged damage shear constitutive model with unknown parameters to obtain the staged damage shear constitutive model that takes into account the rate effect of the composite material. The obtained staged damage shear constitutive expression taking into account the rate effect of the composite material is as follows: where σ and ε are shear stress and shear strain, respectively. is the dimensionless shear strain rate, E1, λ1 and k1 are the initial stiffness, scale factor and shape factor of the matrix damage stage, E2, λ2 and k2 are the initial stiffness, scale factor and shape factor of the fiber damage stage, are the dimensions of E1 and E2 respectively, and are the quadratic coefficients of the quadratic functions of parameters E1, λ1, k1, E2, λ2 and k2, respectively. and are the linear coefficients of the quadratic functions of parameters E1, λ1, k1, E2, λ2 and k2, respectively. and are the constant term coefficients of the quadratic function of parameters E1, λ1, k1, E2, λ2 and k2 respectively.

2. The method for obtaining a staged damage shear constitutive model taking into account the rate effect of composite materials according to claim 1, characterized in that: The specific expression of the staged damage shear constitutive model with unknown parameters is as follows: where σ and ε are the shear stress and shear strain, respectively; E1, λ1, and k1 are the initial stiffness, scale factor, and shape factor of the matrix damage stage, respectively; and E2, λ2, and k2 are the initial stiffness, scale factor, and shape factor of the fiber damage stage, respectively.

3. The method for obtaining a staged damage shear constitutive model taking into account the rate effect of composite materials according to claim 1, characterized in that: The functional relationship between the parameter values ​​of the staged damage shear constitutive model and the strain rate is obtained by the polynomial fitting method. The specific steps are as follows: 1) The parameter values ​​and shear strain rate of the composite material stage damage shear constitutive model are dimensionless and expressed as: Where c p represents the parameters of the stage-type damage shear constitutive model, c p =E1, λ1, k1, E2, λ2, k2; and are the dimensionless stage-damage shear constitutive model parameter values ​​and the dimensionless shear strain rate, respectively; and are the parameter values ​​of the stage damage shear constitutive model and the dimension of the shear strain rate, 2) The quadratic polynomial is used to fit the functional relationship between the parameter values ​​of the stage damage shear constitutive model and the logarithmic strain rate, which is expressed as: Where, and are the quadratic term coefficient, linear term coefficient and constant term coefficient of the quadratic function of the staged damage shear constitutive model parameters.

4. The method for obtaining a staged damage shear constitutive model taking into account the rate effect of composite materials according to claim 1, characterized in that: Completing the dynamic shear mechanical properties test of composite materials at multiple orders of magnitude of strain rates means completing the in-plane shear mechanical properties test of composite materials or the interlaminar shear mechanical properties test of composite materials at no less than 3 different orders of magnitude of strain rates, with the strain rate difference between each two adjacent strain rates being no less than 10 times, and the number of effective tests at the same strain rate should be no less than 5 times.

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