Prediction method for elasticity modulus of carbon nanotube reinforced three-phase composite material
By decomposing the three-phase composite material system of carbon nanotubes/carbon fibers/epoxy resin, the relationship between elastic modulus of "effective fibers" and carbon nanotubes is established, and combined with the Halpin-Tsai equation and finite element model, the problem of lack of elastic modulus prediction methods in the existing technology is solved, and the accurate prediction of the macroscopic mechanical properties of three-phase composite materials is achieved.
Patent Information
- Application Number
- CN202510240155.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-03
- Publication Date
- 2025-06-27
AI Technical Summary
The prior art lacks a method for predicting the elastic modulus of carbon nanotube/carbon fiber/epoxy resin three-phase composite materials, and it is difficult to accurately predict its macroscopic mechanical properties.
By decomposing the three-phase composite system of carbon nanotube/carbon fiber/epoxy resin into two-phase matrix of carbon fiber, carbon nanotube and epoxy resin, the relationship between the elastic modulus of "effective fiber" and the elastic modulus of carbon nanotubes is established, and the elastic constant of the three-phase composite material is calculated based on the Halpin-Tsai semi-empirical equation and the finite element model.
A relatively accurate prediction of the macroscopic mechanical properties of carbon nanotube-enhanced three-phase composite materials was achieved, showing that the longitudinal elastic modulus of the composite materials increased by 4.9% after the addition of carbon nanotubes.
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Figure CN120217755A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of composite materials, and particularly relates to a method for predicting the elastic modulus of a carbon nanotube-reinforced three-phase composite material. Background Art
[0002] Adding nanomaterials such as carbon nanotubes and graphene to traditional composite materials can greatly improve the mechanical, electrical, and thermal properties of the structure. The high strength, high modulus, low density, and excellent thermal stability of carbon nanotubes make them one of the most ideal reinforcements for modern advanced composite materials. At present, most of the research on carbon nanotubes in the field of materials science focuses on the preparation and performance testing of carbon nanotubes, and in the field of mechanics, it mostly focuses on predicting the mechanical properties of carbon nanotube-reinforced three-phase composite materials using multi-scale modeling methods. At present, the research on applying carbon nanotubes to composite material structures to improve mechanical properties mainly relies on experimental research, and there is still a lack of a method for predicting the elastic modulus of carbon nanotube / carbon fiber / epoxy resin three-phase composite materials. Summary of the Invention
[0003] Object of the Invention: The object of the present invention is to provide a method for predicting the elastic modulus of a carbon nanotube-reinforced three-phase composite material, so as to accurately predict the macroscopic mechanical properties of the carbon nanotube-reinforced three-phase composite material starting from the microscopic structure of the material.
[0004] Technical Solution: A method for predicting the elastic modulus of a carbon nanotube-reinforced three-phase composite material includes the following steps:
[0005] S1. Decompose the carbon nanotube / carbon fiber / epoxy resin three-phase composite material system into carbon fiber, carbon nanotube, and epoxy resin two-phase matrices, and decompose the carbon nanotube and epoxy resin two-phase matrices into carbon nanotube / epoxy resin two-phase composite materials; then, equivalent the carbon nanotubes into "effective fibers" and establish the relationship between the elastic modulus of the "effective fibers" and the elastic modulus of the carbon nanotubes.
[0006] S2. According to the Halpin-Tsai semi-empirical equation of short fiber-reinforced composite materials, regard the carbon nanotubes as discontinuous short fibers randomly distributed in the epoxy resin matrix, and establish a mechanical model of the carbon nanotube / epoxy resin two-phase composite material.
[0007] S3. Take the carbon nanotube / epoxy resin two-phase composite material as the two-phase matrix and establish a representative volume element finite element model of the carbon nanotube / carbon fiber / epoxy resin three-phase composite material.
[0008] S4. Perform finite element mesh division on the representative volume element finite element model, apply boundary conditions and external loads, and calculate the displacements and reaction forces of the representative volume element under different loads.
[0009] S5. Calculate the average stress and average strain of the representative volume element based on the displacement and the magnitude of the reaction force obtained in step S4, and in combination with the geometric dimensions of the representative volume element.
[0010] S6. Based on the average stress and average strain of the representative volume element calculated in step S5, respectively form an average stress matrix and an average strain matrix from the average stress and average strain calculated under different loads, substitute them into the stress-strain equation of the three-phase composite material, and further solve for the stiffness matrix and compliance matrix of the composite material to obtain the elastic constants of the carbon nanotube / carbon fiber / epoxy three-phase composite material.
[0011] Furthermore, the relationship between the elastic modulus of the "effective fiber" and the elastic modulus of the carbon nanotube is:
[0012]
[0013] In the formula, E eff and E cnt represent the elastic moduli of the "effective fiber" and the carbon nanotube respectively, t is the wall thickness of the carbon nanotube, and d is the diameter of the carbon nanotube.
[0014] Furthermore, in step S2, the modified Halpin-Tsai equation for the carbon nanotube / epoxy two-phase composite material is:
[0015]
[0016] In the formula, E′ mnc is the elastic modulus of the modified carbon nanotube / epoxy two-phase matrix, E m is the elastic modulus of the epoxy resin matrix, and l is the length of a single carbon nanotube;
[0017] V cnt is the volume fraction of the carbon nanotube, and the expression is as follows:
[0018]
[0019] In the formula, w cnt represents the mass fraction of the carbon nanotube, and ρ cnt and ρ m represent the densities of the carbon nanotube and the epoxy resin matrix respectively.
[0020] Furthermore, in step S3, define the constitutive models of the carbon fiber and the two-phase matrix, set the volume fractions of the carbon fiber and the two-phase matrix, and the carbon fibers are non-intersecting and randomly distributed along the in-plane direction.
[0021] Further, in step S4, the boundary condition is that the six outer surfaces of the representative volume element are all constrained by periodic boundary conditions, and two corresponding outer surfaces are deformed in the same pattern; the load application method is to set up nodes on the outer surface of the representative volume element and couple them with the corresponding surfaces, and tensile and shear loads are applied to the coupled nodes.
[0022] Compared with the prior art, the remarkable effects of the present invention are as follows: by decomposing the carbon nanotube / carbon fiber / epoxy resin three-phase composite material system into two-phase matrices of carbon fiber / carbon nanotube and epoxy resin, and further decomposing the two-phase matrices into carbon nanotube / epoxy resin two-phase composite materials, starting from the microscopic structure of the material, the macroscopic mechanical properties of the carbon nanotube-reinforced three-phase composite material can be predicted more accurately; the prediction results of the present invention show that when the mass fraction of carbon nanotubes is 0%, that is, when no carbon nanotubes are added, the longitudinal (i.e., the carbon fiber direction) modulus E1 of the composite material is 116.6 GPa; after adding 5% mass fraction of carbon nanotubes, the longitudinal (i.e., the carbon fiber direction) modulus E1 of the three-phase composite material is 122.3 GPa; and after adding carbon nanotubes, the longitudinal (i.e., the carbon fiber direction) elastic modulus of the composite material is increased by 4.9%. Description of the Drawings
[0023] Figure 1 is a decomposition diagram of the carbon nanotube / carbon fiber / epoxy resin three-phase composite material system;
[0024] Figure 2 is a flow chart of the present invention;
[0025] Figure 3 is a schematic diagram of the "effective fiber" of carbon nanotubes, (a) is a schematic diagram of carbon nanotubes, and (b) is a schematic diagram of the "effective fiber";
[0026] Figure 4 is a schematic diagram of the mesh division of the representative volume element;
[0027] Figure 5 is a schematic diagram of the change of the longitudinal modulus of the composite material with the mass fraction of carbon nanotubes. Detailed Embodiments
[0028] The present invention will be further described in detail below with reference to the accompanying drawings of the specification and specific embodiments.
[0029] In one embodiment, the carbon nanotube / carbon fiber / epoxy resin three-phase composite material system is decomposed as Figure 1As shown, the carbon nanotube / carbon fiber / epoxy resin three-phase composite material system is decomposed into carbon fiber and carbon nanotube / epoxy resin two-phase matrix, and the carbon nanotube / epoxy resin two-phase matrix is decomposed into carbon nanotube / epoxy resin two-phase composite material. According to the material system decomposition diagram, a prediction method for the elastic modulus of carbon nanotube-reinforced three-phase composite material is provided, and the flow chart is as Figure 2 shown, including the following steps:
[0030] Step 1, according to the load transfer mechanism of carbon nanotubes embedded in the polymer matrix, assuming that the entire cross-section of the carbon nanotube has the same load-bearing capacity as the outermost layer, the carbon nanotube is equivalent to an "effective fiber", as Figure 3 shown, the effective fiber has the same deformation behavior and geometric dimensions as the carbon nanotube, and the relationship between the elastic modulus of the "effective fiber" and the elastic modulus of the carbon nanotube is:
[0031]
[0032] where, E eff 、E cnt respectively represent the elastic modulus of the "effective fiber" and the carbon nanotube, t is the wall thickness of the carbon nanotube, and d is the diameter of the carbon nanotube.
[0033] Step 2, according to the Halpin-Tsai semi-empirical equation of short fiber-reinforced composite materials, regarding the carbon nanotubes as discontinuous short fibers randomly distributed in the epoxy resin matrix, a mechanical model of carbon nanotube / epoxy resin two-phase composite material is established. According to the Halpin-Tsai equation, the elastic modulus of the carbon nanotubes regarded as short fibers can be expressed as:
[0034]
[0035] In the formula, E mnc represents the elastic modulus of the carbon nanotube / epoxy resin two-phase composite material regarded as short fibers, V eff represents the volume fraction of the "effective fiber", E eff 、E m respectively represent the elastic modulus of the "effective fiber" and the epoxy resin matrix; ξ depends on the geometric shape and boundary conditions of the "effective fiber", and in the case of low fiber volume fraction, the parameter ξ can be simplified to 2l / d.
[0036] According to the relationship between the elastic modulus of the "effective fiber" and the elastic modulus of the carbon nanotube, the Halpin-Tsai equation can be further expressed as:
[0037]
[0038] In the formula, E′ mncis the elastic modulus of the modified carbon nanotube / epoxy resin two-phase composite, E m is the elastic modulus of the epoxy resin matrix, l is the length of a single carbon nanotube, and V cnt is the volume fraction of the carbon nanotubes.
[0039] The relationship between the volume fraction and mass fraction of the carbon nanotubes can be expressed as:
[0040]
[0041] where w cnt represents the mass fraction of the carbon nanotubes, ρ cnt , ρ m represent the densities of the carbon nanotubes and the epoxy resin matrix, respectively.
[0042] Step 3: Taking the carbon nanotube / epoxy resin two-phase composite as the two-phase matrix, establish a finite element model of the representative volume element of the carbon nanotube / carbon fiber / epoxy resin three-phase composite.
[0043] Among them, the detailed steps for modeling the finite element model of the representative volume element include: defining the constitutive models (tensile modulus, shear modulus, and Poisson's ratio) of the carbon fiber and the two-phase matrix, determining the structural size of the representative volume element as 30μm×30μm×30μm, setting the volume fractions of the carbon fiber and the two-phase matrix to 50% each, and arranging the carbon fibers non-intersecting and randomly distributed along the in-plane direction.
[0044] Step 4: Conduct a finite element simulation analysis on the representative volume element of the carbon nanotube / carbon fiber / epoxy resin three-phase composite, apply boundary conditions and displacement external loads, and calculate the displacements and reaction forces of the representative volume element under different loads.
[0045] In one embodiment, when meshing the finite element model of the representative volume element, set the mesh type to tetrahedral mesh and the size to 0.00012mm. At the same time, the outer surfaces of the RVE (Representative Volume Element) are all subjected to periodic boundary conditions. The boundary conditions are that the six outer surfaces of the representative volume element are all subjected to periodic boundary conditions, and two corresponding outer surfaces deform in the same mode; the load application method is to set up nodes on the outer surface of the representative volume element and couple them with the corresponding surfaces, and apply tensile loads and shear loads to the coupled nodes.
[0046] Among them, for the contact interface between the two-phase matrix material and the carbon fiber material, the mesh needs to be divided in a co-node manner to avoid the phenomenon of finite element analysis interruption caused by fiber slippage. The mesh division of the representative volume element in this embodiment is as shown in Figure 4 shown.
[0047] Step 5: Calculate the average stress of the representative volume element according to the displacements and reaction forces under different loads, and in combination with the geometric dimensions of the representative volume element. And the average strain are:
[0048]
[0049] In the formula, represents the displacement in the i direction of the boundary surface perpendicular to the j direction in the representative volume element, represents the reaction force in the i direction of the surface perpendicular to the j direction in the representative volume element, L i 、L j are the dimensions of the representative volume element in the i direction and j direction respectively, and V is the volume of the representative volume element.
[0050] Step 6: According to the average stress and average strain of the representative volume element calculated in Step 5, form the average stress matrix and average strain matrix respectively from the six average stresses and average strains calculated under different loads, and substitute them into the stress-strain equation of the three-phase composite material (orthotropic material) to further solve the stiffness matrix and compliance matrix of the three-phase composite material, and obtain the elastic constants of the carbon nanotube / carbon fiber / epoxy resin three-phase composite material.
[0051] In one embodiment, the stress-strain equation of the three-phase composite material is:
[0052]
[0053] In the formula, ε 11 、ε 22 、ε 33 、γ 12 、γ 13 、γ 23 are the six average strain components, σ 11 、σ 22 、σ 33 、σ 12 、σ 13 、σ 23 are the six average stress components, E1, E2, E3 are the elastic moduli of the three main directions of the three-phase composite material, G 12 、G 13 、G 23 are the three shear moduli of the three-phase composite material, ν ij (i,j = 1,2,3) are the Poisson's ratios of the three-phase composite material.
[0054] Such as Figure 5It can be seen that when the mass fraction of carbon nanotubes is 0%, the tensile modulus E1 of the composite material is 116.6 GPa. When 5% mass fraction of carbon nanotubes is added, the longitudinal modulus E1 of the composite material is 122.3 GPa.
[0055] It should be understood that although the steps of the prediction method of the present invention do not have to be executed in sequence. Unless there is a clear description in the present invention, there is no strict order limit for the execution of these steps, and these steps can be executed in other orders. Moreover, at least some of the steps may include multiple sub-steps or multiple stages, and these sub-steps or stages do not necessarily have to be executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages does not have to be sequential, but can be executed alternately or alternately with at least a part of other steps or sub-steps or stages of other steps.
[0056] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.
[0057] The above-described embodiments only represent several implementation manners of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can be made, and these all belong to the protection scope of the present invention.
Claims
1. A method for predicting the elastic modulus of a carbon nanotube reinforced three-phase composite material, characterized in that: The steps include: S1, decomposing the carbon nanotube / carbon fiber / epoxy resin three-phase composite material system into a two-phase matrix of carbon fiber, carbon nanotube and epoxy resin, and decomposing the two-phase matrix of carbon nanotube and epoxy resin into a two-phase composite material of carbon nanotube / epoxy resin; then, the carbon nanotube is equivalent to "effective fiber", and the relationship between the elastic modulus of "effective fiber" and the elastic modulus of carbon nanotube is established; S2, based on the Halpin-Tsai semi-empirical equation of short fiber reinforced composites, carbon nanotubes are regarded as discontinuous short fibers randomly distributed in the epoxy resin matrix, and a mechanical model of carbon nanotube / epoxy resin two-phase composites is established; S3, taking the carbon nanotube / epoxy resin two-phase composite as the two-phase matrix, a representative volume unit finite element model of the carbon nanotube / carbon fiber / epoxy resin three-phase composite was established; S4, performing finite element meshing on the representative volume unit finite element model, applying boundary conditions and external loads, and calculating the displacement and support reaction force of the representative volume unit under different loads; S5, calculating the average stress and average strain of the representative volume unit according to the displacement and the magnitude of the support reaction force calculated in step S4 and the geometric dimensions of the representative volume unit; S6, according to step S5, the average stress and average strain of the representative volume unit are calculated, and the average stress and average strain calculated under different loads are respectively composed into an average stress matrix and an average strain matrix, which are substituted into the stress-strain equation of the three-phase composite material, and the stiffness matrix and flexibility matrix of the composite material are further solved to obtain the elastic constants of the carbon nanotube / carbon fiber / epoxy resin three-phase composite material.
2. The method for predicting the elastic modulus of the carbon nanotube reinforced three-phase composite material according to claim 1, characterized in that: The relationship between the elastic modulus of "effective fiber" and the elastic modulus of carbon nanotubes is: In the formula, E eff 、E cnt represent the elastic modulus of "effective fiber" and carbon nanotube respectively, t is the wall thickness of carbon nanotube, and d is the diameter of carbon nanotube.
3. The method for predicting the elastic modulus of the carbon nanotube reinforced three-phase composite material according to claim 2, characterized in that: In step S2, the modified Halpin-Tsai equation of the carbon nanotube / epoxy resin two-phase composite material is: In the formula, E′ mnc is the elastic modulus of the modified carbon nanotube / epoxy resin two-phase matrix, E m is the elastic modulus of the epoxy resin matrix, l is the length of a single carbon nanotube; V cnt is the volume fraction of carbon nanotubes, and the expression is as follows: In the formula, w cnt represents the mass fraction of carbon nanotubes, ρ cnt , m represent the density of carbon nanotubes and epoxy resin matrix, respectively.
4. The method for predicting the elastic modulus of the carbon nanotube reinforced three-phase composite material according to claim 2, characterized in that: In step S3, the constitutive model of the carbon fiber and the two-phase matrix is defined, and the volume fractions of the carbon fiber and the two-phase matrix are set. The carbon fibers do not intersect each other and are randomly distributed along the span direction.
5. The method for predicting the elastic modulus of the carbon nanotube reinforced three-phase composite material according to claim 2, characterized in that: In step S4, the boundary condition is that the six outer surfaces of the representative volume unit are all constrained by periodic boundary conditions, and the two corresponding outer surfaces deform in the same mode; the load application method is to establish nodes on the outer surfaces of the representative volume unit and couple them with the corresponding surfaces, and apply tensile loads and shear loads to the coupled nodes.