Mapping method for microhardness and macroscopic strength of polyacrylonitrile-based carbon fiber

Abstract

The invention relates to a polyacrylonitrile-based carbon fiber microhardness and macroscopic strength mapping method, which comprises the following steps: carrying out a nanoindentation indentation test along the center of the cross section direction of a carbon fiber to obtain the microhardness of the carbon fiber; performing a macroscopic tensile property test on the carbon fiber tow to obtain the macroscopic tensile strength of the carbon fiber; determining six main parameters, namely P (load), E (elastic modulus), v (Poisson's ratio), sigma (strength), h (deformation) and theta (equivalent half-cone angle of a pressure head), influencing the press-in and stretching processes of the carbon fiber; from the perspective of dimensional analysis, a mathematical model of microhardness and macroscopic strength is established, and variables influencing the relationship between the microhardness and the macroscopic strength are evaluated; and finally, performing least square fitting on the hardness / strength expression according to the macroscopic tensile strength and microcosmic hardness test data of the carbon fiber to obtain a microcosmic hardness-macroscopic strength mapping relationship. The method solves the problem that the connection between the microhardness and the macroscopic strength of the carbon fiber cannot be established, and provides a means for the performance test of the carbon fiber in the product state.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical property analysis and failure analysis of composite materials, and relates to a mapping method of microhardness and macro strength of polyacrylonitrile-based carbon fiber, which is used to study the relationship between the microperformance and macroperformance of carbon fiber. Background Art

[0002] Carbon fiber is a material with low density, high specific strength, high specific modulus, strong heat resistance and good chemical stability. It has been widely used in the aerospace field. At present, both domestic and imported carbon fibers have been widely used, and their mechanical properties have become a must-check item before use. Currently, common mechanical property test items include tensile strength (σ), elastic modulus (E) and elongation at break (ε). However, the above mechanical property tests are all macroscopic performance tests, which are only suitable for re-inspection of raw materials, and the mechanical properties of carbon fibers prepared into products cannot be effectively tested.

[0003] From the perspective of practical engineering applications, there are many occasions where the mechanical properties of carbon fiber in the product state need to be tested, such as checking whether there is a problem of raw material mixing when the macroscopic performance of the product is unqualified, the change of mechanical properties of the product after the flight test environment and before the flight test, the performance evaluation of the product after different rounds of impregnation and cracking, and the analysis of the performance differences of carbon fiber in different parts of the product. However, macroscopic mechanical performance testing cannot test the performance of carbon fiber in the product state, so it is necessary to rely on microscopic in-situ methods to test product performance.

[0004] Nanoindentation technology is an excellent in-situ mechanical property testing method for micro-nano-scale composite materials. Based on the analysis of load-displacement curves, it can realize the performance testing of bulk materials such as metal materials, ceramic materials, polymer materials, and low-dimensional materials such as films, fibers, and particles. It is very suitable for the performance testing of carbon fiber. Compared with traditional methods, it has the advantages of high resolution, in-situ testing, and controllable measuring points. It can easily obtain mechanical property data such as hardness and modulus of specified micro-areas of materials. However, on the one hand, the above-mentioned studies are relatively isolated and scattered, lacking systematicity. On the other hand, they only give nanoindentation test results and lack comparison with macroscopic mechanical properties. Therefore, the nanoindentation test method is still a long way from practical engineering application. Summary of the invention

[0005] The technical problem solved by the present invention is: to overcome the shortcomings of the prior art, to propose a mapping method for the microhardness and macrostrength of polyacrylonitrile-based carbon fiber, to solve the problem that the microhardness and macrostrength of carbon fiber cannot be linked, and to provide a means for testing the performance of carbon fiber in a product state.

[0006] The solution of the present invention is:

[0007] A method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber, comprising:

[0008] The polyacrylonitrile-based carbon fiber product was prepared into a metallographic specimen, and a nano-indentation test was performed along the center of the carbon fiber cross section to obtain the micro-hardness of the carbon fiber, with a loading load of 0.5mN to 10mN.

[0009] The tensile performance test, linear density test and bulk density test of polyacrylonitrile-based carbon fiber multifilament were carried out to obtain the macroscopic tensile strength σ and elastic modulus E of the material, and the loading speed was 1 mm / min to 5 mm / min;

[0010] From the perspective of dimensional analysis, the maximum load P during the pressing process is obtained according to the Π theorem: max , contact depth h c Expressions of elastic modulus E, Poisson's ratio ν, strength σ, deformation h, and equivalent semi-cone angle θ of the indenter of carbon fiber materials;

[0011] Obtain the contact area A with the contact depth h under a specific indenter shape c Expression of

[0012] According to the definition of hardness, the expression of microhardness H with elastic modulus E, Poisson's ratio ν, strength σ, deformation h, and indenter equivalent semi-cone angle θ is obtained;

[0013] According to the test data of carbon fiber microhardness obtained by carbon fiber macro tensile strength and nano indentation test, the expression of the ratio of micro hardness to macro strength is fitted by least squares to obtain the mapping relationship between micro hardness and macro strength.

[0014] Preferably, the surface roughness Ra of the metallographic sample is better than 0.1 μm.

[0015] Preferably, when the tensile performance test, linear density test and bulk density test are performed on the polyacrylonitrile-based carbon fiber multifilament, reinforcing sheets are attached to both ends of the multifilament after being dipped in glue for testing, and the specifications of the multifilament range from 1K to 48K.

[0016] Preferably, C0, σ / E, ν, and θ are all constant values ​​after the carbon fiber loading direction, fiber type, and indenter type are determined, wherein C0 is a fitting parameter.

[0017] Preferably, for different types of carbon fibers, the σ / E parameter is stabilized at 0.018±0.002.

[0018] Preferably, the maximum load during the pressing process P max , contact depth h c The elastic modulus E, Poisson's ratio ν, strength σ, deformation h, and equivalent semi-cone angle of the indenter of carbon fiber material The expression is:

[0019] P max =Eh 2 Π α (Π1,ν,θ)

[0020]

[0021] P is the load during the loading process, Π α It is a dimensionless quantity determined by P, E, and h.

[0022] Preferably, the microhardness H of the carbon fiber satisfies:

[0023]

[0024] A is the contact area.

[0025] Preferably, the specific indenter shape refers to a Berkovich indenter or a conical indenter.

[0026] Preferably, the contact area A increases with the contact depth h c The expression is:

[0027]

[0028] Where C0 is the fitting parameter.

[0029] Preferably, the contact depth h c The expression of the deformation h is:

[0030] h c =hΠ β (Π1,ν,θ)

[0031]

[0032] Π β For h c , h is a dimensionless quantity determined by.

[0033] Preferably, the mapping relationship between microhardness and macro strength is:

[0034]

[0035] P is the load during the loading process, Π α , Π β It is a dimensionless quantity determined by different parameters during the nanoindentation process.

[0036] The beneficial effects of the present invention compared with the prior art are:

[0037] According to the microstructure of the carbon fiber material, the present invention makes a reasonable assumption on the deformation behavior of the carbon fiber during loading, obtains the hardness / strength expression from the perspective of dimensional analysis according to the Π theorem and the Oliver and Pharr theory, fits the hardness / strength expression according to the hardness test data obtained by the macroscopic tensile strength of the carbon fiber and the nanoindentation test, and obtains the hardness-strength mapping relationship, which has great value and significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the typical tensile load-displacement curve of carbon fiber multifilament;

[0039] Figure 2 This is the cross-sectional morphology of polyacrylonitrile-based carbon fiber;

[0040] Figure 3 The load-depth curve of T800 carbon fiber under different loading directions;

[0041] Figure 4 The load-depth curve of T300 carbon fiber obtained by testing with a glass indenter and a cube corner indenter;

[0042] Figure 5 is the statistical relationship between carbon fiber strength and modulus;

[0043] Figure 6 is the relationship between the macroscopic tensile strength of carbon fiber and the hardness obtained by nanoindentation test;

[0044] Figure 7 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0045] The present invention will be further described below in conjunction with the accompanying drawings.

[0046] The present invention mainly analyzes the relationship between the microhardness and macrostrength of carbon fiber, and establishes a microhardness-macrostrength mapping method with high accuracy, wide application range, convenience and flexibility, thereby laying a foundation for the re-inspection and detection of carbon fiber materials.

[0047] like Figure 7 As shown, the present invention first prepares the polyacrylonitrile-based carbon fiber product into a metallographic specimen, performs a nanoindentation test along the center of the carbon fiber cross section, obtains the microhardness of the carbon fiber according to the Oliver and Pharr theory, and the loading load is 0.5mN to 10mN; secondly, the tensile performance of the polyacrylonitrile-based carbon fiber multifilament is tested to obtain the macroscopic tensile strength and elastic modulus of the material, and the loading speed is 1mm / min to 5mm / min; then, from the perspective of dimensional analysis, the maximum load P during the indentation process is obtained according to the Π theorem. max , contact depth h cThe expressions of carbon fiber material parameters E (elastic modulus), ν (Poisson's ratio), σ (strength), h (deformation), and θ (equivalent semi-cone angle of the indenter); According to the Oliver and Pharr theory, the contact area A changes with the contact depth h under a specific indenter shape. c , and simplified it according to the shape of the Berkovich indenter; then, according to the definition of hardness, the expression of microhardness with E (elastic modulus), ν (Poisson's ratio), σ (strength), h (deformation), and θ (equivalent semi-cone angle of the indenter) parameters was obtained and simplified; finally, according to the expression of the ratio of microhardness to macrostrength, based on the evaluation results of the values ​​of C0, σ / E, ν, and θ, the macrotensile strength of carbon fiber and the hardness test data obtained by nanoindentation test were fitted to obtain the mapping relationship between microhardness and macrostrength.

[0048] In the present invention, the surface roughness Ra of the metallographic sample is better than 0.1μm. After the multifilament is dipped in glue, reinforcing sheets are attached to both ends for testing, and the specifications of the multifilament range from 1K to 48K. It is assumed that the deformation behavior of the carbon fiber cross-sectional nanoindentation test and the carbon fiber multifilament tensile performance test material satisfies the linear elastic material model. The elastic modulus E and the deformation h are taken as two independent dimensions, and the expressions of the maximum load and the contact depth are analyzed based on the Π theorem without considering the specific functional relationship. The contact area is proportional to the contact depth h c The expression is also applicable to the shape of the cubic corner indenter, and only the fitting parameter C0 changes. According to the definition of hardness, the Π theorem, and the Oliver and Pharr theory, this ratio is an expression of C0, σ / E, ν, and θ, which is independent of the deformation h. The tensile strength of carbon fiber ranges from 3000MPa to 8000MPa, the hardness range obtained by nanoindentation test is 5GPa to 12GPa, and there are no less than 10 test data on the macroscopic tensile strength of carbon fiber and the hardness obtained by nanoindentation test. The parameters C0, σ / E, ν, and θ that affect the expression are all fixed values ​​after the carbon fiber loading direction, fiber type, and indenter type are determined. For different types of carbon fibers, the σ / E parameter is stable at 0.018±0.002.

[0049] The specific implementation process of the present invention is as follows:

[0050] First, the loading process of carbon fiber is analyzed theoretically. The rebound of carbon fiber is very obvious, and the load-displacement curves of carbon fiber during loading and unloading are close; in the final stage of unloading, the rebound of carbon fiber is very obvious, and the rebound rate exceeds 95%. Therefore, the nanoindentation loading process of carbon fiber can be regarded as an elastic process, and its typical load-displacement curve is as follows: Figure 1 As shown. Figure 1It can be seen that the stretching process of carbon fiber multifilament is almost a straight line, indicating that the stretching process of carbon fiber is almost an elastic process and the plastic deformation is very small, which also facilitates subsequent modeling and analysis.

[0051] Secondly, the carbon fiber nanoindentation process is analyzed. From the perspective of dimensional analysis, P (load), E (elastic modulus), ν (Poisson's ratio), σ (tensile strength), h (indentation depth), and θ (equivalent semi-cone angle) are the six main parameters that affect the indentation and stretching process.

[0052] The hardness of carbon fiber material can be calculated using formula (1):

[0053]

[0054] Among them, P max is the maximum load during the loading process, and A is the contact area.

[0055] Since carbon fiber is mainly composed of graphite lamellae in different directions, and the direction of the graphite lamellae is roughly parallel to the axial direction, Paris et al. studied PAN-based (polyacrylonitrile) and intermediate phase Pitch-based (asphalt-based) carbon fiber monofilaments and found that there are azimuthal differences in the mechanical properties of carbon fiber, which is caused by the difference in the preferential sampling of graphite microcrystals. Therefore, unlike the usually neatly arranged lattices (plus dislocations) inside metal materials, the special lamellae structure of carbon fiber makes the mechanical properties of carbon fiber in different directions different, and the mechanical response under different types of loads is also different. The microscopic morphology of the cross-section of carbon fiber can be seen. Figure 2 .

[0056] Figure 3 The load-depth curve of T800 carbon fiber under different loading directions is shown when the loading load is 2mN and the indenter type is Bokovich indenter. It can be seen from the figure that the maximum indentation depth of the carbon fiber in the cross-sectional test direction is h. max The minimum slope of the curve in the unloading stage is the largest; and in the longitudinal section test direction, the maximum indentation depth of the carbon fiber is h max The maximum value is obtained, and the slope of the curve is the smallest during the unloading stage. Under the 45° test direction, the load-depth curve test results are centered.

[0057] From the above analysis results, it can be seen that there are obvious differences in the mechanical responses of carbon fiber materials under different loading directions. This is also one of the characteristics that carbon fiber (anisotropic material) is significantly different from metal (generally isotropic material). In order to eliminate the influence of the anisotropy of carbon fiber materials, only the loading test in the direction of the carbon fiber cross section is considered, and it is assumed that the deformation behavior of the material in this direction satisfies the linear elastic material model. The Π theorem in dimensional analysis is used to give the relationship between hardness and material strength from a theoretical level. The basic idea is to only consider the dimensional relationship between different parameters, without delving into the specific functional relationship between the parameters. According to the above assumptions and models, the load P during the loading process is only related to the material strength σ, elastic modulus E, indentation depth h, Poisson's ratio ν, and indenter semi-cone angle. Taking the elastic modulus E and the indentation depth h as two independent dimensions, we can get:

[0058]

[0059] According to the Π theorem, we can get:

[0060] Π α =Π α (Π1,ν,θ)(3)

[0061] In the formula,

[0062] According to formula (3), we can get formula (4):

[0063] P max =Eh 2 Π α (Π1,ν,θ)(4)

[0064] In the formula,

[0065] Through fitting analysis of experimental results, Oliver and Pharr proposed a general form of the area function, as shown in formula (5):

[0066]

[0067] In the formula, h c is the contact depth, C i is the fitting parameter.

[0068] For the Berkovich indenter or conical indenter, the contact area A is as shown in formula (6):

[0069]

[0070] Similarly, according to the Π theorem, we can get:

[0071] Πβ =Π β (Π1,ν,θ)(7)

[0072] In the formula, According to formula (7), we can get formula (8):

[0073] h c =hΠ β (Π1,ν,θ)(8)

[0074] Combining equations (1), (4), (6), and (8), we can obtain equation (9):

[0075]

[0076] By analyzing formula (9), we can see that there is a correlation between microhardness and macro strength. Although the specific functional relationship is relatively complex, it can be seen that the ratio of microhardness to macro strength is related to C0, σ / E, ν, And other parameters.

[0077] Among them, C0 is the fitting parameter in the area function. For the Berkovich indenter or conical indenter, C0 is 24.5. In the theoretical research of nanoindentation and the practical application of nanoindentation technology, researchers have used indenters of various shapes, including regular tetrahedral Vickers indenters, triangular pyramidal Berkovich indenters, spherical indenters and other special shapes. Even for indenters of other shapes, C0 is a fixed value.

[0078] Figure 4 The load-depth curves of T300 carbon fiber obtained by testing with a Bosch indenter and a cubic indenter are shown. As can be seen from the figure, the two curves almost overlap, so different indenters have no significant effect on the test results. Table 1 shows the test results of nanoindentation mechanical properties of T300 carbon fiber using a Bosch indenter and a cubic indenter. It can be seen that the results obtained using a Bosch indenter and a cubic indenter are highly consistent, and the key results obtained by the test do not change due to changes in the indenter type.

[0079] Table 1 Test results of mechanical properties of T300 carbon fiber by nanoindentation using a glass indenter and a cubic indenter

[0080]

[0081] The parameter ν is the Poisson's ratio. When the type of carbon fiber is fixed, the Poisson's ratio in the cross-sectional direction is also fixed, and is generally selected as 0.013. Some researchers have also used values ​​that are quite different, such as Ai et al. who selected a Poisson's ratio of 0.26. However, no matter what value is selected, it is generally believed that the Poisson's ratio in a fixed direction of the carbon fiber should be a relatively fixed value.

[0082] Parameter θ is the shape parameter of the indenter, which mainly refers to the semi-cone angle of the indenter. When the indenter type is fixed, the value of the semi-cone angle of the indenter is also fixed. For example, the equivalent semi-cone angle of the Berkovich indenter is 70.32°, and the equivalent semi-cone angle of the cubic corner indenter is 42.28°. Although the different shapes of the indenters will lead to differences in the indentation shape and the residual indentation shape, as long as the same indenter is maintained during the test, the stability of parameter θ can be guaranteed.

[0083] Finally, σ / E is analyzed. In the carbon fiber macro-mechanical properties test, a large amount of statistical analysis was conducted on the strength and modulus of different types of carbon fibers, T300, T700, and T800 (100 points each). The statistical results are shown in Figure 5 .from Figure 5 It can be seen that, in general, greater carbon fiber strength corresponds to greater carbon fiber modulus. Linear fitting of the mechanical properties test results of T300, T700 and T800 carbon fibers shows that the σ / E fitting values ​​obtained by the three are close, all 0.018±0.002. Therefore, σ / E can also be regarded as a constant.

[0084] When the parameter values ​​on the right side of equation (9) are fixed, the strength and hardness of the carbon fiber material can be expressed as a simple functional relationship. By transforming equation (9), the relationship between strength and hardness can be obtained as shown in equation (10):

[0085] lnσ=alnH-b(10)

[0086] Among them, a and b are fitting parameters. The T300 and T800 carbon fibers of different strengths in the retest were prepared into metallographic specimens, and the carbon fibers were subjected to nanoindentation hardness tests. According to the macroscopic tensile strength of the carbon fibers and the hardness test data obtained by the nanoindentation test, the equation (10) was fitted, and the relationship between the two can be obtained: lnσ=1.54lnH-1.80, as shown in Figure 6 As shown. Figure 6 It can be seen that the model prediction and the experimental data have a good fitting accuracy, and the error between the model prediction value and the experimental data does not exceed 20%.

[0087] From formula (9), we can see that the premise for formula (2) to be valid is that the test conditions (including material type, test direction, indenter type, strength-modulus ratio, Poisson's ratio, etc.) must be consistent, which is actually impossible to achieve completely. Therefore, formula (10) can only give a semi-quantitative prediction result. However, the semi-quantitative prediction result alone is of great significance in engineering practice, and the above fitting relationship can establish a more accurate correlation as the amount of data increases, and perform envelope analysis, thereby laying a good foundation for the further engineering application of nanoindentation technology.

[0088] The present invention relates to a mapping method of the microhardness of polyacrylonitrile-based carbon fiber and the macroscopic tensile strength of the fiber bundle obtained by nanoindentation technology testing. First, a nanoindentation test is performed along the center of the carbon fiber cross section to obtain the microhardness of the carbon fiber; secondly, a macroscopic tensile performance test is performed on the carbon fiber bundle to obtain the macroscopic tensile strength of the carbon fiber; then, the six main parameters affecting the carbon fiber indentation and stretching process are determined, including P (load), E (elastic modulus), ν (Poisson's ratio), σ (strength), h (deformation), (equivalent semi-cone angle of the indenter); from the perspective of dimensional analysis, a mathematical model of microhardness and macro strength is established at the theoretical level, and the variables that affect the relationship between the two (C0, σ / E, ν, Finally, the hardness / strength expression was evaluated based on the carbon fiber macro tensile strength and micro hardness test data obtained by nano indentation test. The least squares fitting is performed to obtain the mapping relationship between microhardness and macro strength. According to the microstructure of polyacrylonitrile-based carbon fiber, the present invention makes a reasonable assumption about the deformation behavior of carbon fiber during loading, and can predict the strength of carbon fiber within the tensile strength range of 3000MPa to 8000MPa based on the microhardness test results, which has the characteristics of wide application range and high accuracy.

[0089] Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.

Claims

1. A method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber, characterized in that: include: The polyacrylonitrile-based carbon fiber product was prepared into a metallographic specimen, and a nano-indentation test was performed along the center of the carbon fiber cross section to obtain the micro-hardness of the carbon fiber, with a loading load of 0.5mN to 10mN. The tensile performance test, linear density test and bulk density test of polyacrylonitrile-based carbon fiber multifilament were carried out to obtain the macroscopic tensile strength σ and elastic modulus E of the material, and the loading speed was 1 mm / min to 5 mm / min; From the perspective of dimensional analysis, the maximum load P during the pressing process is obtained according to the Π theorem: max , contact depth h c Expressions of elastic modulus E, Poisson's ratio ν, strength σ, deformation h, and equivalent semi-cone angle θ of the indenter of carbon fiber materials; Obtain the contact area A with the contact depth h under a specific indenter shape c Expression of According to the definition of hardness, the expression of microhardness H with elastic modulus E, Poisson's ratio ν, strength σ, deformation h, and indenter equivalent semi-cone angle θ is obtained; According to the test data of carbon fiber microhardness obtained by carbon fiber macro tensile strength and nano indentation test, the expression of the ratio of micro hardness to macro strength is fitted by least squares to obtain the mapping relationship between micro hardness and macro strength.

2. A method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: The surface roughness Ra of the metallographic specimen is better than 0.1μm.

3. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: When conducting tensile performance test, linear density test and bulk density test on polyacrylonitrile-based carbon fiber multifilament, reinforcing sheets are attached to both ends of the multifilament after being dipped in glue for testing. The specifications of the multifilament range from 1K to 48K.

4. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: C0, σ / E, ν, and θ are all constants after the carbon fiber loading direction, fiber type, and indenter type are determined, among which C0 is a fitting parameter.

5. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: For different types of carbon fibers, the σ / E parameter is stable at 0.018±0.

002.

6. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: Maximum load P during pressing max , contact depth h c The expressions of elastic modulus E, Poisson's ratio ν, strength σ, deformation h, and equivalent semi-cone angle θ of the indenter are as follows: P max =Eh 2 P α (Π1,ν,θ) P is the load during the loading process, Π α It is a dimensionless quantity determined by P, E, and h.

7. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: The microhardness H of carbon fiber satisfies: A is the contact area.

8. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: The specific indenter shape refers to a Berkovich indenter or a conical indenter.

9. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 7, characterized in that: Contact area A versus contact depth h c The expression is: Where C0 is the fitting parameter.

10. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: Contact depth h c The expression of the deformation h is: h c =hΠ β (Π1,ν,θ) Π β For h c , h is a dimensionless quantity determined by.

11. The method for mapping microhardness and macro strength of polyacrylonitrile-based carbon fiber according to claim 1, characterized in that: The mapping relationship between microhardness and macro strength is: P is the load during the loading process, Π α , Π β It is a dimensionless quantity determined by different parameters during the nanoindentation process.

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