CN111310346A - A method for judging the failure mode of carbon nanotubes in composite materials considering size parameters - Google Patents

Abstract

The invention discloses a method for judging the failure mode of carbon nanotubes in composite materials considering size parameters. For the three size variables of carbon nanotube diameter, length, and ratio of inner and outer diameters, the present invention takes the three variables as fixed values, and substitutes the basic mechanical properties of carbon nanotubes and composite materials into the formula, draws a coordinate diagram, and obtains the other two The critical size curve of each variable, when judging, substitute the specific size parameters of carbon nanotubes into the coordinate graph, and according to the relative positional relationship between the size parameters of carbon nanotubes and the critical size curve, the failure mode of carbon nanotubes in the composite material can be determined, Can be used to guide experiments and engineering practice.

Description

A method for judging the failure mode of carbon nanotubes in composite materials considering size parameters

technical field

The invention relates to the field of composite materials, in particular to a method for judging the failure mode of carbon nanotubes in composite materials considering size parameters.

Background technique

Carbon nanotubes (CNTs) are ideal reinforcement materials and have received extensive attention and applications in the field of composite materials in recent years. In fiber-reinforced composite materials, as a reinforcing and toughening material, the failure modes of carbon nanotubes are mainly pulling out and breaking. The fibers at the crack are anchored in the matrix on both sides of the crack and play a bridging role to prevent the expansion of the crack. At this time, the cohesion and friction between the fiber and the matrix resist the pull-out force of the carbon nanotubes. As the external load increases, the cracks expand further, and the pulling force on the fibers also increases. When the pulling force is greater than the bonding force, the fibers are debonded from the matrix and begin to be pulled out. On the other hand, in the process of fiber tension, if the tensile bearing capacity of the fiber itself is smaller than the bonding anchoring force, as the pull-out force increases, the pull-out force will first be greater than the tensile bearing capacity of the fiber, and the The fibers are pulled apart while the ends of the fibers remain anchored in the matrix. The failure process is as follows: the fiber at the crack is slightly stretched, then pulled off, and finally pulled out from the fracture.

It can be seen that when the failure mode of carbon nanotubes is the pull-out failure, the relative displacement of the carbon nanotubes and the matrix can increase the deformation capacity of the matrix, and the work of friction can also consume the energy of the external load and increase the toughness of the matrix. For the pull-out failure, the pull-off failure is more abrupt, and there is almost no relative displacement between the fiber and the matrix, so the deformation capacity of the matrix cannot be effectively improved. In recent years, in order to improve the performance of materials, carbon nanotubes have begun to develop in the direction of longer and thinner. The diameter and length of carbon nanotubes are the key factors to determine their tensile bearing capacity and anchoring force, respectively, and directly affect the failure mode of carbon nanotubes in the matrix. With the increasing application range of carbon nanotubes in composite materials, the relationship between the failure modes of carbon nanotubes in composite materials and their size characteristics should be proposed.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a method for judging the failure mode of carbon nanotubes in composite materials considering size parameters. The specific technical solutions are as follows:

Considering the hollowness of carbon nanotubes, define the ratio of inner and outer diameters λ=d/D (D and d are the outer and inner diameters of carbon tubes, respectively): a single carbon nanotube can be simplified into a hollow cylindrical tube, which is anchored in the cement matrix, A schematic diagram of the model of carbon nanotubes in the tension process is shown in Figure 1. During the process of pulling out the carbon tube, the frictional resistance F _f between the carbon tube and the substrate is:

F _f =πDxτ _i (1)

The tensile bearing capacity T of the carbon tube is:

Where: x is the anchoring length of the carbon tube in the matrix;

τ _i is the friction force between the carbon tube and the substrate;

σ is the tensile strength of the carbon tube itself.

Experiments show that most carbon nanotubes exist in the matrix by bending, and the bending model of carbon nanotubes in the matrix is shown in Figure 2(a). Taking the force analysis of carbon nanotubes at the outlet of the matrix, when the angle between the carbon nanotubes and the crack surface of the matrix is θ, as shown in Figure 2(b), the pull-out force F is decomposed, as follows:

F _f =F sinθ (3)

When the pull-out force F first reaches F _f /sinθ, the carbon tube is pulled out, and when F first reaches the tensile bearing capacity T of the carbon tube, the carbon tube is pulled off.

如需特殊考虑某根碳纳米管的破坏情况，可以根据电子显微镜观测得到特定的θ。It should be noted here that due to the random random distribution of carbon nanotubes, the value of θ is randomly distributed between 0 and 90°. For the macroscopic prediction of the overall failure law of a certain type of carbon nanotube, take θ=45°,

For special consideration of the destruction of a certain carbon nanotube, a specific θ can be obtained according to electron microscope observation.

Further, in order to compare the relationship between the frictional resistance and the tensile bearing capacity of carbon tubes, define the ratio of the two:

Among them, κ=τ _i /σ is the ratio of frictional resistance to the tensile strength of carbon nanotubes.

When γ<1, the carbon tube is pulled out, and as the carbon tube is pulled out, the anchoring length x decreases gradually, the friction resistance F also decreases, and γ continues to decrease; when γ>1, the carbon tube is directly pulled off .

Further, consider the relationship between the carbon nanotube length L and the failure mode. For the anchoring length x of the carbon tube in the matrix in formula (4), it varies between (0, L/2) with the distribution of cracks (it should be noted that when x>L/2, the other end of the anchoring x'<L/ 2. Consider the end that is more prone to failure). Take the average value x=L/4.

In summary, the critical dimension of the pull-out/pull-off failure of carbon nanotubes is:

Using equation (6) to predict the failure mode of carbon nanotubes:

There are three parameters related to the geometric size of carbon nanotubes in the formula, the outer diameter D, the ratio of inner and outer diameters λ, and the length L. When the inner and outer diameter ratio λ of carbon nanotubes is the set value, through the calculation of formula (5), the critical relationship line with the length L as the abscissa and the outer diameter D as the ordinate is obtained. When the corresponding point of the length L and the outer diameter D of the nanotube falls below the critical relationship line, the failure mode of the carbon nanotube is pulling off, and when it falls above the critical relationship line, the failure mode of the carbon nanotube is pulling out. . When the outer diameter D of the carbon nanotube is the set value, through the calculation of formula (5), the inner and outer diameter ratio λ is the abscissa, and the length L is the critical relationship line of the ordinate. When the carbon nanotube with the corresponding outer diameter D is used When the corresponding point of the length L of the tube and the ratio of the inner and outer diameters λ falls below the critical relationship line, the failure mode of the carbon nanotube is pulling out, and when it falls above the critical relationship line, the failure mode of the carbon nanotube is pulling off. . When the length L of the carbon nanotube is the set value, through the calculation of formula (5), the ratio of the inner and outer diameters λ is the abscissa, and the outer diameter D is the critical relationship line of the ordinate. When the corresponding point of the outer diameter D and the ratio λ of the inner and outer diameters falls below the critical relationship line, the failure mode of the carbon nanotube is pulling off, and when it falls above the critical relationship line, the failure mode of the carbon nanotube is pulling out .

For example, taking σ=50GPa and τ _i =20MPa, then κ=0.4×10 ^-3 , and the graph shows the relationship between the failure mode of carbon nanotubes and three geometric parameters (Fig. 3, Fig. 4, Fig. 5). Substitute the geometric parameters of carbon nanotubes into the figure to obtain corresponding points, and the failure mode of such carbon nanotubes can be judged according to the positions of the points.

The invention proposes a method for judging the destruction mode of carbon nanotubes in composite materials by analyzing the material properties of carbon nanotubes themselves. The failure mode of nanotubes in composite materials can effectively predict the failure of composite materials and be used to guide experiments and engineering practices.

Description of drawings

Figure 1 is a schematic diagram of the hollow tube/fiber being pulled out from the matrix;

Figure 2(a) is the bending model of carbon nanotubes in the matrix;

Figure 2(b) is the force analysis diagram of carbon nanotubes at the outlet of the substrate;

Figure 3 is the relationship between the critical diameter D and the critical length L when the carbon nanotubes are pulled out/pulled off;

Figure 4 shows the relationship between the critical length L and the critical inner and outer diameter ratio λ when the carbon nanotubes are pulled out/pulled off;

Figure 5 shows the relationship between the critical outer diameter D and the critical inner and outer diameter ratio λ when the carbon nanotubes are pulled out/pulled off;

Fig. 6(a) and Fig. 6(b) are respectively the judgment diagram and the microscope observation picture of the destruction of carbon nanotubes in Example 1;

Figure 7 (a) and Figure 7 (b) are respectively the judgment diagram and the microscope observation picture of the destruction of carbon nanotubes in Example 2;

FIG. 8( a ) and FIG. 8( b ) are the judgment diagram and the microscope observation picture of the damage of the carbon nanotubes in Example 3, respectively.

Detailed ways

The technical solutions in the embodiments of the present invention will be described clearly and completely below. It should be understood that the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention. The unspecified implementation conditions are generally those in routine experiments.

Consider carbon nanotube-reinforced cementitious composites. The examples will be tested with different kinds of multi-walled carbon nanotubes. The multi-walled carbon nanotubes are first dispersed in an aqueous solution, and then the cement-based material is mixed with the carbon nanotube aqueous solution. After stirring evenly, forming a mold, and curing for 28 d, the test block after compression and bending was tested, and the test block after the test was knocked out to observe the damage of carbon nanotubes at the damaged surface.

Example 1: Prediction of the failure mode of a multi-walled carbon nanotube.

The parameters of the multi-walled carbon nanotube are: D=25nm, d=20nm, length L=30μm, σ=50GPa, τ _i =20MPa, then λ=0.8, κ=0.4×10 ⁻³ .

Substitute λ=0.8 into Equation (5), by changing the diameter D, and using Equation (5) to calculate the different corresponding critical values of the length L, the relationship between the damage mode of carbon nanotubes and the geometric parameters is plotted, as shown in Figure 6(a) ).

Substitute the point (30, 25) corresponding to the carbon nanotube into Fig. 6(a), it is found that the point is below the relationship line, and it is predicted that the carbon nanotube will be fractured. Observing the carbon nanotubes with an electron microscope is verified, as shown in Figure 6(b), and it is found that the fracture marks of the carbon nanotubes are obvious, indicating that the carbon nanotubes are indeed broken, and the judgment method proposed by the present invention is accurate.

Example 2: Prediction of the failure mode of a multi-walled carbon nanotube.

The parameters of the multi-walled carbon nanotube are: D=30nm, d=20nm, length L=60μm, σ=50GPa, τ _i =20MPa, then λ=0.67, κ=0.4×10 ⁻³ .

Substitute D=30nm into Equation (5), by changing the inner and outer diameter ratio λ, and using Equation (5) to calculate the different corresponding critical values of the length L, the relationship between the damage mode of carbon nanotubes and the geometric parameters is plotted, as shown in Figure 7 (a).

Substitute the corresponding point (0.67, 60) of the carbon nanotube into Fig. 7(a), it is found that the point is above the relationship line, and it is predicted that the carbon nanotube will be fractured. Observing the carbon nanotubes with an electron microscope is verified, as shown in Figure 7(b), and it is found that the fracture marks of the carbon nanotubes are obvious, indicating that they are indeed broken, and the judgment method proposed by the present invention is accurate.

Example 3: Prediction of the failure mode of a multi-walled carbon nanotube.

The parameters of the multi-walled carbon nanotube are: D=50nm, d=15nm, length L=30μm, σ=50GPa, τ _i =20MPa, then λ=0.3, κ=0.4×10 ⁻³ .

Substitute L=30μm into formula (5), change the diameter D, and use formula (5) to calculate the different corresponding critical values of the ratio of inner and outer diameters λ, and plot the relationship between the damage mode of carbon nanotubes and geometric parameters, as shown in Figure 8 (a).

Substitute the point (0.3, 50) corresponding to the carbon nanotube into Fig. 8(a) to determine, and it is found that the point is above the relationship line, and it is predicted that the carbon nanotube will be pulled out and damaged. Observing the carbon nanotubes with an electron microscope is verified, as shown in Figure 8(b), it is found that the ends of the carbon nanotubes are complete and smooth, and there is no fracture mark, indicating that the carbon nanotubes are pulled out, and the judgment method proposed by the present invention is accurate.

The present invention has been described in detail above. The above embodiments are only preferred embodiments of the present invention, which are used to help understand the method and the core idea of the present invention. The content of the invention and its implementation are not intended to limit the protection scope of the invention. Any modification, equivalent change or improvement made according to the spirit of the present invention shall be included within the protection scope of the present invention.

Claims (1)

1. the judging method of the failure mode of carbon nanotubes considering size parameter in composite material, it is characterized in that according to the following formula as the critical size calculation formula of carbon nanotube failure mode transformation,

where D ^* is the critical outer diameter of the carbon nanotube, λ is the ratio of the inner and outer diameters of the carbon nanotube, L is the length of the carbon nanotube, κ=τ _i /σ, and τ _i is the friction between the carbon nanotube and the substrate force, σ is the tensile strength of the carbon nanotube itself. Taking the inner and outer diameter ratio λ of carbon nanotubes as the set value, through the calculation of formula (5), the critical relationship line with the length L as the abscissa and the outer diameter D as the ordinate is obtained. When the corresponding point of the length L and the outer diameter D of the tube falls below the critical relationship line, the failure mode of the carbon nanotube is pulling off, and when it falls above the critical relationship line, the failure mode of the carbon nanotube is pulling out; or: When the outer diameter D of carbon nanotubes is set as the set value, through the calculation of formula (5), the critical relationship line of inner and outer diameter ratio λ as abscissa and length L as ordinate is obtained. When the corresponding point of the length L of the tube and the ratio of the inner and outer diameters λ falls below the critical relationship line, the failure mode of the carbon nanotube is pulling out, and when it falls above the critical relationship line, the failure mode of the carbon nanotube is pulling off. ;or: Taking the length L of the carbon nanotube as the set value, through the calculation of formula (5), the critical relationship line of the inner and outer diameter ratio λ as the abscissa and the outer diameter D as the ordinate is obtained. When the corresponding point of outer diameter D and inner diameter ratio λ falls below the critical relationship line, the failure mode of the carbon nanotube is pulling off, and when it falls above the critical relationship line, the failure mode of the carbon nanotube is pulling out.

Images