A method for predicting elastic properties of fiber composite materials

Abstract

The present invention discloses a method for predicting the elastic properties of fiber composite materials. The method associates the microscopic structural parameters of the fiber material with the macroscopic properties, reflects the stiffness coefficient of the fiber composite material in the stress direction through the equivalent RVE stiffness matrix, and judges the elastic properties of the fiber composite material based on this. The prediction method provided by the present invention uses uniformly defined curvature parameters and directional angle parameters to describe the ordered or disordered morphology of a large number of fibers, and uses the mean of the curvature distribution and the variance of the directional angle distribution to construct an aggregation function to quantitatively describe the fiber aggregation state and agglomerate content, which is suitable for predicting the elastic properties of composite materials under arbitrary curved fiber distribution states. Furthermore, the method uses a probability function to characterize the possibility of aggregation and entanglement of high-curvature fibers, which more realistically reflects the distribution state of curved fibers in the matrix, and improves the construction efficiency and practicality of the curved fiber composite material performance prediction model.

Description

Technical Field

[0001] The invention relates to a method for predicting elastic properties of a material, in particular to a method for predicting elastic properties of a fiber composite material, and belongs to the technical field of prediction of mechanical properties of composite materials. Background Art

[0002] Curved fiber composites were first proposed to replace straight fibers to improve the mechanical properties of perforated composite laminates. The subsequent introduction of the concept of variable stiffness composites has attracted attention and development in the structural optimization design of aircraft, high-speed trains and other fields. Compared with traditional straight fiber composites, curved fiber composites can change their stiffness distribution as required without changing the thickness of the laminate, and can also achieve continuous changes in the thickness of the laminate according to design requirements by only changing the fiber orientation angle, driving the laminate structure to develop in a lighter, stronger and more efficient form.

[0003] At present, most of the research on mechanical problems related to curved fiber composites at home and abroad is about the analysis of their macroscopic mechanical response and structural optimization design. The engineering community relies on commercial finite element software to predict the mechanical properties of new composite materials, but the simulation technology of commercial software is complicated to model, the solution is costly, and it is difficult to obtain universal laws. There are many methods for predicting the mechanical properties of new composite materials in the academic community, but a general mechanical model has not yet been established for curved fiber composites, and the existing methods do not pay enough attention to the agglomeration behavior of fibers under near-real conditions. Therefore, starting from the real micro-structural characteristics of curved fiber composites, exploring a more applicable mechanical property prediction method is one of the key basic work to promote curved fiber composites and their structural optimization design and engineering applications. Summary of the invention

[0004] In view of the deficiencies in the prior art, the purpose of the present invention is to provide a method for predicting the elastic properties of fiber composite materials. The method associates the microstructural parameters of the fiber material with the macroscopic properties, reflects the stiffness coefficient of the fiber composite material in the stress direction through the equivalent RVE stiffness matrix, and judges the elastic properties of the fiber composite material based on this.

[0005] To achieve the above technical objectives, the present invention provides a method for predicting the elastic properties of fiber composite materials, comprising the following steps: 1) obtaining fiber distribution characteristics based on a microscopic observation image of the fiber composite material and expressing the characteristics by parameters to obtain microscopic structural parameters;

[0006] 2) establishing an equivalent RVE model of the fiber composite material according to the microscopic observation image of the fiber composite material, wherein the equivalent RVE model consists of an equivalent reinforcement phase cl model and an equivalent matrix em model;

[0007] 3) Apply the mesoscopic structural parameters to the equivalent RVE model, and establish the stiffness matrix of the equivalent reinforcement phase and equivalent matrix through coordinate transformation and matrix calculation;

[0008] 4) The stiffness matrix of the equivalent reinforcement phase and the equivalent matrix is ​​used to obtain the stiffness matrix of the equivalent RVE through the mixing rule. Any element in the matrix is ​​the stiffness coefficient of the fiber composite material in the corresponding direction.

[0009] The prediction method provided by the present invention firstly describes the curve fiber distribution characteristics parameterizedly based on microscopic observation, and constructs the aggregation function and the agglomeration probability function. Then, an equivalent RVE model of a composite material composed of an equivalent reinforcing phase and an equivalent matrix is ​​established, and the volume content of the equivalent reinforcing phase is expressed by the aggregation function and the agglomeration probability function; the stiffness matrices of the equivalent reinforcing phase and the equivalent matrix are predicted and calculated based on the parallel and series models and the coordinate transformation relationship, and then the stiffness matrices under all curvature and angular values ​​are weighted and summed based on the distribution law to obtain the stiffness matrices of the equivalent reinforcing phase and the equivalent matrix respectively. Finally, the stiffness matrix of the equivalent RVE is obtained based on the mixing rule, which can be directly used to describe the elastic properties of the composite material. The accuracy of the prediction results of this method is affected by the parameterized expression of the fiber distribution characteristics in step 1). Further detailed and preferred parameter expressions are conducive to improving the prediction accuracy, but will cause an increase in the amount of calculation.

[0010] As a preferred solution, the microstructure parameters include: fiber volume fraction V f , fiber curvature values ​​λ1,λ2,...,λ i ,...,λ n and its distribution law Λ(λ), fiber curvature distribution law mean M λ , the fiber direction angles are θ1,θ2,...,θ i ,...,θ m Its distribution law Θ(θ), direction angle distribution law variance D θ , without considering the critical fiber volume fraction that will inevitably agglomerate when the fibers are compressed Among them, any fiber curvature λ i The equivalent straight line length L in the direction of the curved fiber extension is e The ratio of the actual length of the fiber to the actual length of the fiber f To characterize, its expression is λ i =L e / L f , the value range is 0<λ i ≤1; the curvature distribution law is expressed as a discrete or continuous distribution function Λ(λ), satisfying Any fiber direction angle θ jIt is characterized by the angle between the equivalent straight line length direction of the curve fiber and the x-axis of the macroscopic rectangular coordinate system, and its value range is 0≤θ j <π; the angular distribution law is expressed as a discrete or continuous distribution function Θ(θ), satisfying

[0011] M λ Characterizes the curvature of most fibers in the composite material, M λ →0, the more curved the fiber is, the λ →1 means the fiber is straighter overall; the variance D is calculated based on the distribution law of the direction angle θ The variance represents the consistency of the fiber direction in the composite material, D θ →0, the fiber direction is more consistent overall, D θ →+∞, the fiber direction is more chaotic overall.

[0012] As a preferred solution, the fiber composite material includes agglomerates and non-agglomerates.

[0013] As a preferred solution, the agglomerate includes agglomerated fibers and a matrix in corresponding regions.

[0014] As a preferred solution, the unagglomerated body includes unagglomerated fibers and a matrix in corresponding regions.

[0015] As a preferred solution, the equivalent RVE model of the agglomerate is an equivalent enhanced phase cl model.

[0016] As a preferred solution, the equivalent RVE model of the unagglomerated body is an equivalent matrix EM model.

[0017] As a preferred solution, the process of establishing the equivalent enhanced phase cl model includes:

[0018] ① In order to control the parameters, a fiber agglomeration probability function related to the fiber content is constructed, and the process is as follows:

[0019] Formula 1: This function satisfies: When 0≤g cl <1, when Time cl =1; and g cl =0 means no fiber agglomeration, 0<g cl <1 means the fibers may agglomerate, g cl =1 means that the fibers must be agglomerated;

[0020] ②M λ and D θIn order to control the parameters, a fiber aggregation function related to the fiber content is constructed, and the process is as follows:

[0021] Formula 2: ζ cl =ζ cl (V f ;M λ ,D θ ); 0≤ζ cl ≤1, and when M λ The larger the value, the θ The smaller the value, the cl The smaller the value;

[0022] ③ According to the fiber agglomeration probability function and aggregation degree function, the volume content of the equivalent reinforcement phase in the equivalent RVE of the composite material is determined. The process is as follows:

[0023] Formula 3: V cl =g cl ·ζ cl ;

[0024] In formulas 1 to 3: V f is the fiber volume fraction, dimension is 1; is the critical fiber volume fraction of agglomeration, dimension is 1; M λ is the mean of the curvature distribution, dimension is 1; D θ is the variance of the azimuth distribution, dimension is 1.

[0025] As a preferred solution, the process of establishing the stiffness matrix of the equivalent enhanced phase cl model includes:

[0026] ① Determine the single curvature (λ=λ i ) elastic constant of the equivalent reinforcement phase in one direction (θ=0), and the single curvature (λ=λ i ) Off-axis unidirectional (θ=θ j ) Stiffness matrix Q of the equivalent reinforcement phase cl (λ i ,θ j ), the main process is:

[0027] Formula 4:

[0028] Formula 5:

[0029] Formula 6:

[0030] Formula 7:

[0031] Formula 8:

[0032] Formula 9:

[0033]

[0034]

[0035]

[0036]

[0037] Formula 10:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] ② Substitute all values ​​of curvature and direction angle into the single curvature eccentric unidirectional equivalent reinforcement phase stiffness matrix and perform weighted summation to obtain the equivalent reinforcement phase stiffness matrix under the fiber distribution characteristics. The main process is:

[0045] Formula 11:

[0046] In formulas 4 to 11: i is any curvature parameter, dimension is 1; θ j is any direction angle parameter, dimension is 1; E f1 、E m , G f and G m They are respectively the longitudinal elastic modulus of the fiber, the elastic modulus of the matrix, the fiber shear modulus and the matrix shear modulus, and the quantities are all MT -2 L -1 ;μ f and μ m They are the fiber Poisson's ratio and the matrix Poisson's ratio, both with a dimension of 1. Among them, the parameters with a subscript f are the corresponding physical parameters of the fiber material, and the parameters with a subscript m are the corresponding physical parameters of the reinforcement phase material; the parameters with a subscript 1 are limited to the parameters obtained along the longitudinal direction of the fiber, and the parameters with a subscript 2 are limited to the parameters obtained along the transverse direction of the fiber.

[0047] As a preferred solution, the process of establishing the equivalent matrix EM model is as follows:

[0048] The process of determining the volume content of the equivalent matrix in the equivalent RVE of the composite material is as follows:

[0049] Formula 12:

[0050] In formula 12: V f is the fiber volume fraction, is the critical fiber volume fraction for agglomeration, V cl is the equivalent reinforcement phase volume fraction, and the dimensions of the above parameters are all 1.

[0051] As a preferred solution, the process of establishing the stiffness matrix of the equivalent matrix EM model is as follows:

[0052] ① Determine the single curvature (λ=λ i ) unidirectional (θ=0) equivalent matrix elastic constant, and use coordinate transformation to obtain a single curvature (λ=λ i ) Off-axis unidirectional (θ=θ j ) The stiffness matrix Q of the equivalent matrix em (λ i ,θ j ), the main process is:

[0053] Formula 13:

[0054] Formula 14:

[0055] Formula 15:

[0056] Formula 16:

[0057] Formula 17:

[0058] Formula 18:

[0059]

[0060]

[0061]

[0062]

[0063] Formula 19:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] ② Substitute all values ​​of curvature and direction angle into the single curvature eccentric unidirectional equivalent matrix stiffness matrix and perform weighted summation to obtain the equivalent matrix stiffness matrix under the fiber distribution characteristics. The main process is:

[0071] Formula 20:

[0072] In formulas 12 to 20: V f is the fiber volume fraction, is the critical fiber volume fraction for agglomeration, V cl is the equivalent reinforcement phase volume fraction, λ i is any curvature parameter, θ j is any direction angle parameter, the dimension of the above physical quantities is 1; E f1 、E f2 、E m , G f and G m They are the longitudinal elastic modulus of the fiber, the transverse elastic modulus of the fiber, the elastic modulus of the matrix, the fiber shear modulus and the matrix shear modulus, and all are MT -2 L -1 ; η2 and η 12 is a statistical empirical parameter with a dimension of 1; μ f and μ m are respectively the fiber Poisson's ratio and the matrix Poisson's ratio, both of which have a dimension of 1. Further preferably, the η2 and η 12 is a statistical empirical parameter, η2=0.56, η 12 =0.5.

[0073] As a preferred solution, the process of establishing the equivalent RVE stiffness matrix is:

[0074] Formula 21:

[0075] Compared with the existing fiber composite elastic properties prediction methods, it has the following advantages:

[0076] 1) In the technical solution provided by the present invention, uniformly defined curvature parameters and direction angle parameters are used to describe the curved fiber morphology characteristics, which is suitable for simulating the non-linearity and angular offset characteristics of fibers under real conditions. When the curvature is 1 and the direction angle is 0, it can degenerate into the ideal form of a classic unidirectional straight fiber. When continuous or random values ​​are taken within a certain range, the ordered or disordered forms of a large number of fibers can be described, which is simple and easy to use.

[0077] 2) In the technical solution provided by the present invention, the aggregation function is constructed using the mean of the curvature distribution and the variance of the angular distribution, and the agglomeration probability function is constructed based on experimental statistical data. This can quantitatively describe different fiber aggregation states and agglomerate contents. It is more reasonable than the Uemura-Yamawaki empirical formula that only defines the contact coefficient when considering fiber contact, and can be applied to the prediction model of composite materials under any fiber distribution state.

[0078] 3) In the technical solution provided by the present invention, the entire prediction process only needs to input the fiber volume fraction, curvature, orientation angle statistical data obtained by microscopic observation and the basic physical properties of the fiber and matrix materials. The formula calculation process can be implemented by numerical calculation software such as Matlab. The prediction process for different component materials or different fiber distribution conditions does not need to be remodeled or reprogrammed. Compared with the finite element software simulation calculation method commonly used in experimental tests or engineering, it is more universal and convenient. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 Schematic diagram of the definition of curvature parameters and orientation angle parameters for curved fibers;

[0080] Figure 2 It is a schematic diagram of the equivalent RVE two-dimensional geometric model of the curved fiber composite material;

[0081] Figure 3 A flow chart of a method for predicting elastic properties of a fiber composite material in any direction provided by the present invention;

[0082] Figure 4 Comparison of the stiffness coefficient of the unidirectional linear carbon fiber composite material predicted and calculated by Example 1 of the present invention with the predicted value by the hybrid law and the experimental test value;

[0083] Figure 5 The cross-distribution nearly linear carbon fiber composite material stiffness coefficient predicted and calculated in Example 2 of the present invention;

[0084] Figure 6 This is the Weibull distribution curve glass fiber composite material stiffness coefficient predicted and calculated in Example 3 of the present invention. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are 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 creative work are within the scope of protection of the present invention.

[0086] Example 1

[0087] Prediction, calculation and comparison of stiffness coefficient of unidirectional linear carbon fiber composite materials. The component material parameters are as follows: E f1 =201.0GPa, E f2 =13.5GPa, G f =95GPa,μ f =0.22; E m =4.30GPa, G m =1.59GPa,μ m =0.35. Curvature range λ a ≤λ≤λ b , the direction angle range θ a ≤θ≤θ b The curvature value is continuous and uniformly distributed, and the constructed probability density function is where λ a =0.999,λ b =1.0; the direction angle is Bernoulli distribution, and the constructed probability density function is where θ a =0,θ b =0.001, p = 1 / 2. Ignoring the fiber aggregation effect, let ζ cl ≈0.

[0088] The calculated stiffness coefficients at different fiber contents and their predicted values ​​with the mixed law, V f =0.66 when the experimental test value is compared. Figure 4 As shown in the figure. The relative errors of the predicted results and experimental values ​​of the proposed fiber composite stiffness coefficient prediction method are ΔQ 11 =-0.16%, ΔQ 12 =-0.24%, ΔQ 22 =0.85%, ΔQ 66 =-0.20%, the error is small and within the acceptable range, and is closer to the experimental value than the commonly used mixed law prediction calculation method, which shows the accuracy of the prediction results.

[0089] Example 2

[0090] Prediction and calculation of stiffness coefficient of cross-distributed near-linear carbon fiber composite material. The component material parameters are as follows: E f1 =201.0GPa, E f2 =13.5GPa, G f =95GPa,μ f =0.22; E m =4.30GPa, G m =1.59GPa,μ m =0.35. Curvature range λ a ≤λ≤λ b , the direction angle range θ a ≤θ≤θ b The curvature value is continuous and uniformly distributed, and the constructed probability density function is where λ a =0.9,λ b =1.0; the direction angle is Bernoulli distribution, and the constructed probability density function is where θ a =0,θ b =π / 6, π / 4, π / 3, π / 2, p = 1 / 2. Mean curvature M λ =(λ b +λ a ) / 2, angular variance The constructed aggregation function is in is the aggregation degree of the constructed unidirectional straight fiber composite material. The constructed agglomeration probability function is in

[0091] The calculated stiffness coefficients at different crossing angles and different fiber contents are as follows: Figure 5 shown.

[0092] Example 3

[0093] Weibull distribution curve glass fiber composite stiffness coefficient prediction calculation. The component material parameters are as follows: E f1 =E f2 =73GPa, G f =30GPa,μ f =0.22; E m =3.5GPa, G m =1.28GPa,μ m =0.37. The curvature range is 0<λ≤1, and the direction angle range is 0<θ≤π. The distribution law obeys the Weibull function Where α is the shape parameter and β is the scale parameter. The curvature distribution is constructed as Λ=f(λ;2.4,0.4) and the azimuth distribution is constructed as Θ=f(θ;2.5,1.5). The mean curvature M λ =β·Γ(1+1 / α), angular variance D θ =β 2 ·[Γ(1+2 / α)-Γ(1+1 / α) 2 ],in Constructing the aggregation function in is the aggregation degree of the constructed unidirectional straight fiber composite material. Construct agglomeration probability function in

[0094] The calculated stiffness coefficients at different fiber contents are as follows: Figure 6 shown.

Claims

1. A method for predicting elastic properties of fiber composite materials, characterized in that: The following steps are involved: 1) Obtain fiber distribution characteristics based on microscopic observation images of fiber composite materials and express parameters to obtain microscopic structural parameters; 2) establishing an equivalent RVE model of the fiber composite material according to the microscopic observation image of the fiber composite material, wherein the equivalent RVE model consists of an equivalent reinforcement phase cl model and an equivalent matrix em model; 3) Apply the mesoscopic structural parameters to the equivalent RVE model, and establish the stiffness matrix of the equivalent reinforcement phase and equivalent matrix through coordinate transformation and matrix calculation; 4) The stiffness matrix of the equivalent reinforcement phase and the equivalent matrix is ​​used to obtain the stiffness matrix of the equivalent RVE by the mixing rule. Any element in the matrix is ​​the stiffness coefficient of the fiber composite material in the corresponding direction; The fiber composite material includes agglomerates and unagglomerated bodies; the agglomerates include agglomerated fibers and a matrix in corresponding regions; and the unagglomerated bodies include unagglomerated fibers and a matrix in corresponding regions. The equivalent RVE model of the agglomerate is the equivalent reinforcement phase cl model; the equivalent RVE model of the non-agglomerated body is the equivalent matrix em model. The establishment process of the equivalent enhanced phase cl model includes: ① In order to control the parameters, a fiber agglomeration probability function related to the fiber content is constructed, and the process is as follows: Formula 1: ②M λ and D θ In order to control the parameters, a fiber aggregation function related to the fiber content is constructed, and the process is as follows: Formula 2: g cl =ζ cl (V f ;M λ ,D θ ); ③ According to the fiber agglomeration probability function and aggregation degree function, the volume content of the equivalent reinforcement phase in the equivalent RVE of the composite material is determined. The process is as follows: Formula 3: V cl =g cl ·ζ cl ; In formulas 1 to 3: V f is the fiber volume fraction, dimension is 1; is the critical fiber volume fraction of agglomeration, dimension is 1; M λ is the mean of the curvature distribution, dimension is 1; D θ is the variance of the azimuth distribution, with a dimension of 1.

2. The method for predicting elastic properties of fiber composite materials according to claim 1, characterized in that: The microstructure parameters include: fiber volume fraction V f , fiber curvature values ​​λ1,λ2,...,λ i ,...,λ n and its distribution law Λ(λ), fiber curvature distribution law mean M λ , the fiber direction angles are θ1,θ2,...,θ i ,...,θ m Its distribution law Θ(θ), direction angle distribution law variance D θ , without considering the critical fiber volume fraction that will inevitably agglomerate when the fibers are compressed 3. The method for predicting elastic properties of fiber composite materials according to claim 1, characterized in that: The process of establishing the stiffness matrix of the equivalent enhanced phase cl model includes: ① Determine the single curvature (λ=λ i ) elastic constants of the equivalent reinforcement phase in one direction (θ=0), and the single curvature (λ=λ i ) Off-axis unidirectional (θ=θ j ) Stiffness matrix Q of the equivalent reinforcement phase cl (λ i ,θ j ), the main process is: Formula 4: Formula 5: Formula 6: Formula 7: Formula 8: Formula 9: Formula 10: ② Substitute all values ​​of curvature and direction angle into the single curvature eccentric unidirectional equivalent reinforcement phase stiffness matrix and perform weighted summation to obtain the equivalent reinforcement phase stiffness matrix under the fiber distribution characteristics. The main process is: Formula 11: In formulas 4 to 11: i is any curvature parameter, dimension is 1; θ j is any direction angle parameter, dimension is 1; E f1 、E m , G f and G m They are respectively the longitudinal elastic modulus of the fiber, the elastic modulus of the matrix, the fiber shear modulus and the matrix shear modulus, and the quantities are all MT - 2 L -1 ;μ f and μ m are the fiber Poisson's ratio and matrix Poisson's ratio, respectively, both with a dimension of 1.

4. The method for predicting elastic properties of fiber composite materials according to claim 1, characterized in that: The establishment process of the equivalent matrix EM model is as follows: The process of determining the volume content of the equivalent matrix in the equivalent RVE of the composite material is as follows: Formula 12: In formula 12: V f is the fiber volume fraction, is the critical fiber volume fraction for agglomeration, V cl is the equivalent reinforcement phase volume fraction, and the dimensions of the above parameters are all 1.

5. The method for predicting elastic properties of fiber composite materials according to claim 1, characterized in that: The process of establishing the stiffness matrix of the equivalent matrix EM model is as follows: ① Determine the single curvature (λ=λ i ) unidirectional (θ=0) equivalent matrix elastic constant, and the single curvature (λ=λ i ) Off-axis unidirectional (θ=θ j ) The stiffness matrix Q of the equivalent matrix em (λ i ,θ j ), the main process is: Formula 13: Formula 14: Formula 15: Formula 16: Formula 17: Formula 18: Formula 19: ② Substitute all values ​​of curvature and direction angle into the single curvature eccentric unidirectional equivalent matrix stiffness matrix and perform weighted summation to obtain the equivalent matrix stiffness matrix under the fiber distribution characteristics. The main process is: Formula 20: In formulas 12 to 20: V f is the fiber volume fraction, V f c is the critical fiber volume fraction for agglomeration, V cl is the equivalent reinforcement phase volume fraction, λ i is any curvature parameter, θ j is any direction angle parameter, the dimension of the above physical quantities is 1; E f1 、E f2 、E m , G f and G m They are the longitudinal elastic modulus of the fiber, the transverse elastic modulus of the fiber, the elastic modulus of the matrix, the fiber shear modulus and the matrix shear modulus, and all are MT -2 L -1 ; η2 and η 12 is a statistical empirical parameter with a dimension of 1; μ f and μ m are the fiber Poisson's ratio and matrix Poisson's ratio, respectively, both with a dimension of 1.

6. The method for predicting elastic properties of fiber composite materials according to claim 1, characterized in that: The establishment process of the equivalent RVE stiffness matrix is: Formula 21:

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