Two-dimensional numerical simulation method capable of predicting mechanical properties of chopped aramid fiber reinforced rubber composite material

Abstract

The invention discloses a two-dimensional numerical simulation method capable of predicting mechanical properties of a chopped aramid fiber reinforced rubber composite material. According to the simulation method, a finite element numerical model is adopted, the finite element numerical model is a two-dimensional square model, a main body of the finite element numerical model is a rubber matrix, chopped aramid fibers are randomly distributed in the model, and the contact relation between the rubber and the chopped aramid fibers is simulated by adopting an embedded unit technology. Grids of the rubber matrix and the chopped aramid fiber in the embedded unit model are mutually independent and are in regular shapes, and simulating uniaxial stretching of the chopped aramid fiber reinforced rubber composite material based on selected model boundary conditions to obtain a stress-strain curve of the chopped aramid fiber reinforced rubber composite material. The method can be applied to the composite material containing fibers with the large length-diameter ratio, and the regular grid form delays the non-convergence phenomenon of non-linear numerical calculation, so that the mechanical property of the rubber composite material can be obtained within a large strain range.

Description

Technical Field

[0001] This invention relates to the field of rubber composite materials, particularly the application of rubber composite materials in tires, and specifically to a two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid reinforced rubber composite materials. Background Technology

[0002] Due to the hyperelastic properties of the rubber matrix, the large aspect ratio of aramid fibers, and their anisotropy, classical theoretical analysis models and traditional numerical methods cannot be used to predict the mechanical properties of chopped aramid-reinforced rubber composites. Therefore, the mechanism of mechanical property research in chopped aramid-reinforced rubber composites remains a challenge. In the finite element method, the mechanical behavior of non-homogeneous materials can be described using representative volume elements. Combining theoretical analysis and experimental results, reliable finite element numerical calculation results can usually be obtained if a suitable representative volume element model is found. However, due to the large aspect ratio of aramid short fibers, it is difficult to obtain high mesh quality using traditional solid elements, and numerical calculations are not easy to converge under large deformation conditions. Therefore, numerical simulation of large deformation of chopped aramid-reinforced rubber composites has always faced many technical difficulties. Summary of the Invention

[0003] In view of the shortcomings of the prior art, the present invention provides a two-dimensional numerical simulation method for predicting the mechanical properties of short-cut aramid reinforced rubber composites at the microscale. The model used in this method can be applied to composites containing fibers with a large aspect ratio (the ratio of fiber length to fiber diameter), and the mechanical properties of rubber composites can be obtained over a large strain range.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites is proposed. The simulation method employs a finite element model, which is a two-dimensional square model. The main body of the finite element model is the rubber matrix, and the chopped aramid fibers are randomly distributed within the model. The side length L of the model is related to the length l of the chopped aramid fibers. f The ratio L / l f For a value ≥18, the contact relationship between rubber and chopped aramid fibers is simulated using embedded element technology. The chopped aramid fibers and the matrix are assumed to have ideal adhesion at the interface. In the embedded element model, the meshes of the rubber matrix and the chopped aramid fibers are independent of each other and both have regular shapes. Based on the selected model boundary conditions, the uniaxial tension of the chopped aramid reinforced rubber composite material is simulated, and the stress-strain curve of the chopped aramid reinforced rubber composite material is obtained.

[0006] Furthermore, the chopped aramid fibers in the finite element numerical model are straight.

[0007] Furthermore, plane stress continuous elements are used to simulate the rubber matrix, and linear hybrid beam elements are used to simulate the bending characteristics of chopped aramid fibers.

[0008] Furthermore, it is assumed that the rubber matrix material is homogeneous and that the constitutive behavior of the rubber material can be described by a hyperelastic constitutive model.

[0009] Furthermore, assuming the chopped aramid fiber material is homogeneous and the longitudinal elastic modulus E of the aramid is... f With the initial elastic modulus E of rubber m The ratio of E f / E m ≥20.

[0010] Furthermore, the volume fraction V of chopped aramid fibers in chopped aramid reinforced rubber composites f ≤8%.

[0011] Furthermore, the number of grids N per unit area of ​​the rubber matrix m ≥1, the number of grids per unit length of chopped aramid fiber N n ≥5.

[0012] Furthermore, periodic boundary conditions are preferred for the model's boundary conditions. In addition, equidisplacement boundary conditions and mixed boundary conditions can also be used.

[0013] This invention employs a two-dimensional finite element numerical model to predict the mechanical properties of aramid short fiber reinforced rubber composites. This model can be applied to composites containing fibers with a large aspect ratio (the ratio of fiber length to fiber diameter), and the regular mesh shape delays the occurrence of nonlinear numerical calculation non-convergence. Therefore, the mechanical properties of rubber composites can be obtained over a large strain range. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the structure of a two-dimensional numerical model for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to the present invention.

[0015] Figure 2 This is a mesh diagram of a two-dimensional numerical model for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to the present invention.

[0016] Figure 3 These are the stress-strain curves obtained from numerical and experimental results. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0018] The rubber matrix component of the chopped aramid reinforced rubber composite consists of natural rubber and styrene-butadiene rubber (SBR), with 80 parts of natural rubber and 20 parts of SBR. Chopped aramid fibers with a length of 1.5 mm and a volume content of 0.486% are incorporated into the rubber matrix. The rubber compounding process involves two stages of mixing, conducted on a Banbury mixer and a two-roll mill, respectively. Each stage of mixing is allowed to stand for at least 8 hours before vulcanization on a flat vulcanizing machine at 143℃ for 45 minutes. The vulcanized chopped aramid reinforced rubber specimens are cut into standard I-shaped dumbbell-shaped uniaxial tensile specimens, and uniaxial tensile tests are performed using a tensile testing machine to obtain the stress-strain curves (experimental results).

[0019] Based on the experimental materials described above, this embodiment establishes a two-dimensional square model at a microscale (e.g., Figure 1 As shown in the figure, the dimensions are represented as L×L. Short-cut aramid fibers are randomly distributed within the model. The side length of the model is L=30mm, and the fiber length is l. f =1.5mm, model side length L and fiber length l f The ratio L / l f =20. The finite element numerical model is based on a rubber matrix, with chopped aramid fibers randomly distributed within the model. Embedded element technology is used to simulate the contact relationship between the rubber and fibers. In the embedded element model, the meshes of the rubber and fibers are independent and have regular shapes. The constitutive behavior of the rubber material is described using the Ogden N3 hyperelastic constitutive model, where the material parameters are: μ1 = -8.116 MPa, α1 = 1.975, μ2 = 5.725 MPa, α2 = 2.388, μ3 = 5.467 MPa, α3 = -4.495, and the initial elastic modulus of the rubber is E. m＝ 8.43 MPa. The mechanical properties of chopped aramid fibers are as follows: E 11 =70000MPa, E 22 =1500MPa, E 33 =1500MPa, v 12 =v 13 =0.13, v 23 =0.135, G 12 =G 13 =1.3MPa, G 23 =1.1 MPa, where the longitudinal elastic modulus E of the aramid is... f = 70000MPa. The above μ1, α1, μ2, α2, μ3, and α3 are parameters of the Ogden N3 hyperelastic constitutive model; E 11 E 22 E 33 The elastic modulus of chopped aramid fibers in all directions; v 12 v 13 v23 G is the Poisson's ratio of chopped aramid fibers. 12 G 13 G 23 The shear modulus of chopped aramid fiber is given. The rubber matrix is ​​simulated using a plane stress continuous element CPS8R, and the bending characteristics of the fiber are simulated using a linear hybrid beam element B21H. The mesh size N per unit area of ​​the rubber matrix is ​​given. m =5, N is the number of grids per unit length of aramid material. n =20. Uniaxial tension of the chopped aramid reinforced rubber material was simulated using periodic boundary conditions, yielding the stress-strain curve (numerical results) of the chopped aramid reinforced rubber material in this embodiment. Comparing the numerical results with the experimental results, the stress-strain curves obtained from both are very close (e.g., Figure 3 As shown in the figure, within a 30% strain range, under the same strain, the maximum error in stress values ​​between the two is less than 6.25%.

Claims

1. A two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites, characterized in that: The simulation method employs a finite element numerical model, which is a two-dimensional square model. The main body of the finite element numerical model is a rubber matrix, with chopped aramid fibers randomly distributed within the model. The side length L of the model is proportional to the length l of the chopped aramid fibers. f The ratio L / l f For a value of ≥18, the contact relationship between rubber and chopped aramid fibers is simulated using embedded element technology. In the embedded element model, the meshes of the rubber matrix and the chopped aramid fibers are independent of each other and both have regular shapes. Based on the selected model boundary conditions, the uniaxial tension of the chopped aramid reinforced rubber composite material is simulated, and the stress-strain curve of the chopped aramid reinforced rubber composite material is obtained.

2. The two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to claim 1, characterized in that: The chopped aramid fibers in the finite element numerical model are straight.

3. The two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to claim 1, characterized in that: Planar stress continuous elements are used to simulate the rubber matrix, and linear hybrid beam elements are used to simulate the bending characteristics of chopped aramid fibers.

4. The two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to claim 1, characterized in that: The longitudinal elastic modulus E of the chopped aramid fiber f With the initial elastic modulus E of rubber m The ratio of E f / E m ≥20.

5. The two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to claim 1, characterized in that: The volume percentage V of the chopped aramid fibers in the chopped aramid reinforced rubber composite material f ≤8%.

6. The two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to claim 1, characterized in that: The number of grids per unit area of ​​the rubber matrix, N m ≥1, the number of meshes N per unit length of the chopped aramid fiber n ≥5.

7. The two-dimensional numerical simulation method for predicting the mechanical properties of chopped aramid-reinforced rubber composites according to claim 1, characterized in that: The boundary conditions of the model are periodic boundary conditions, equal displacement boundary conditions, or mixed boundary conditions.

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