Study on influencing factors and optimization of carbon fiber wear resistance test

In order to accurately distinguish the wear resistance level of different carbon fibers including high strength fibers and high modulus fibers, and ensure minimal fluctuations in testing results, orthogonal tests are designed based on the testing method of carbon fiber wear resistance from the standard Q/ZHFC 4403-2014, and the influencing factors of wear resistance test is determined, and the corresponding test parameters were optimized by the error sum of squares. The results show that within a certain factor level, the traction tension, friction load, friction rod angle and the number of friction rods have a highly significant impact on the test results of fuzz mass, the traction speed has an impact on the test results, and the density of sponge sheet has no impact. When the traction tension is 25N, the friction load is 350g, the traction speed is 30m/min, and the sponge density is 2.28×10−2g/cm3, the angle of friction rod is 120°, the coefficient of variation of the fuzz mass test results is 2.9%~5.0%, which means the testing method with optimized parameters can accurately and quantitatively distinguish the wear resistance level of different brand carbon fibers.


Introduction
Carbon fiber composites have developed rapidly in recent years due to the good mechanical strength, stability, and long-term storage capabilities, and are widely used in fields such as aerospace, medical, electronics, and machinery.Due to the fact that carbon fiber is a brittle material, during production, processing, and application, mechanical friction can easily lead to the formation of fuzz or even clumps due to the fracture of some fibers.This results in poor fiber surface appearance and quality consistency, and ultimately affect the conversion rate and applying performance of carbon fiber [1,2].In recent years, significant progress has been made in the development of Chinese carbon fibers, which have reached or even surpassed imported carbon fibers in terms of tensile properties.However, compared to imported carbon fiber, the breakage and fuzzing after friction of domestic carbon fiber is more prominent, which affects the application of domestic carbon fiber and the performance of composite materials.Therefore, research institutions regard the wear resistance of carbon fiber as an important aspect of evaluating the processability and quality of carbon fiber.Wear resistance's accurate characterization will be helpful to evaluate and screen carbon fiber, optimize processing performance, and ultimately improve the quality of composite molding.Reasonable, quantitative, and accurate testing of the wear resistance of carbon fiber bundles can evaluate the damage situation of carbon fibers in application, which is of great significance for the development, production, and use of carbon fibers [3,4].
Carbon fiber manufacturers both domestically and internationally, including Jiangsu Hengshen, Henan Yongmei, Japan's Toray and Mitsubishi, as well as institutes such as Beihang University, Donghua University, and Beijing Institute of Aeronautical Materials, have conducted research on testing methods for the wear resistance of carbon fibers, mainly including two methods of measuring the ultimate friction number and fuzz number or mass of carbon fibers [5][6][7][8][9][10][11][12].At present, Chinese national standard GB/T 41956-2022 "Determination of fuzz mass for carbon fiber tow" for the measurement of carbon fiber tow fuzzing has been released for a relatively short time.Various institutions still mainly use the standard Q/ZHFC 4403-2014 "Test method for abrasion resistance of carbon fiber bundles" of AVIC Composite Co., Ltd.The principle of this test method is to weigh the mass of the fuzz produced by carbon fibers after friction under certain conditions.The application of this enterprise standard has achieved semi quantitative characterization of fiber wear resistance, but with the continuous increase of carbon fiber grades and quantities tested, it has been found that the data on carbon fiber filament quantity obtained by this method fluctuates greatly, and there are issues such as inaccurate differentiation of different carbon fibers [13,14].This article is focused on the Q/ZHFC 4403-2014 standard, the influencing factors of carbon fiber wear resistance testing are determined through orthogonal experiments, and the corresponding testing parameters are optimized to accurately distinguish the wear resistance level of high strength, high modulus Chinese and imported carbon fibers, and an optimized testing method for accurately distinguishing the wear resistance of carbon fibers of the same type or those of different types is provided.

Experimental Materials
The carbon fibers used in this study include domestic high-strength carbon fiber T-1, imported highstrength carbon fiber T-2, domestic high modulus carbon fiber M-1, M-2, and imported high modulus carbon fiber M-3.The above carbon fibers are all 12K specifications, and except for M-3 fibers with grooves on the surface, all other fibers have smooth and grooveless surfaces.Scanning electron microscopy observation of fiber bundles after friction shows that T-1 presents a small amount of filaments, while T-2 presents almost no filaments; M-1 and M-2 presents a small amount of filaments, while M-3 presents a large amount of filaments, as shown in Figure 1 (T-1 in the upper left is a photo before friction).A fiber wear resistance testing device is built in this study based on the testing methods of Q/ZHFC 4403-2014 and GB/T 41956-2022.The principle of the testing device is shown in Figure 2. The fiber rack can meet the requirements of different specifications of carbon fibers, and the fiber cylinder can be tightened, as well as braked in the forward direction.The surface of the friction rod is chrome plated to prevent rust or scratches on the surface.19 friction rods form a 120° angle with each other and can be disassembled and combined to achieve rod to rod angles of 60°, 90°, and 120°, as well as rod quantity adjustment.The fuzz collector is equipped with sponge sheets, which can achieve load adjustment of 0-300g, and the collection method is the same as the above standards.The tension test roller is set behind the yarn collection mechanism and does not participate in fiber friction.It monitors the fiber traction tension in real-time, and the tension test roller can be calibrated and corrected to achieve accurate tension control.The counting roller moves with the fibers, and the fiber's traveling distance is obtained by measuring the number of revolutions of the roller.The fiber rewinding roller achieves fiber traction and speed control, and can move back and forth along the axial direction of the rewinding roller to prevent fiber accumulation [11][12][13][14].During the test, the carbon fiber is fixed on the fiber rack, and testing parameters such as the angle and number of friction rods, traction tension, and traction speed are set to conduct the test.The difference in mass of the weighing sponge before and after the test is the amount of carbon fiber fibers.

Orthogonal experimental analysis method
Through a preliminary analysis of the wear resistance testing process of carbon fibers, six influencing factors were selected for research, including traction tension, traction rate, sponge density, friction load, friction rods angle, and number of friction rods.They were analyzed to determine whether and to what extent they had an impact on the fuzz mass.Due to the limited length of the fiber sample, the structure of the device and the difficulty in adjusting the testing environment, other factors will remain unchanged, including the fiber's traveling distance, friction rod radius, friction rod surface roughness, and environmental temperature and humidity.This study involves six influencing factors, with three different levels selected for each factor, forming a six factor three level system experiment (see Table 1 for details).It should be noted that in order to avoid serious damage to sponge sheets or fibers, the traction tension should be selected at three levels below 40N, the traction speed should be selected at three levels below 50m/min, and the friction load should be selected at three levels below 350g.Sponge sheets are selected from three common types of polyurethane sponges with different densities in the market, and all other parameters are consistent except for density.By adjusting the yarn routing, the friction rods angle can be selected between 60°, 90°, and 120 °, and the number of friction rods can be selected between 2, 6, and 10 [15][16][17][18][19][20][21].In an orthogonal table which row number is mn, Number of tests (rows)=∑ (subscript columns) (number of levels per column -1)+1 (1) For the six factors and three levels system, the number of experiments should not be less than 13, without considering the interaction between various factors, and an L18 (36) orthogonal table should be used.The six factors are randomly arranged in the six columns of L18 (36), in any order.The levels combination of each factor in each row is the experimental conditions for each group, with a total of 18 groups of experiments.The experimental data is analyzed by the analysis of variance method, which can distinguish the differences between experimental results caused by changes in factor levels and the fluctuations in errors [22].Assuming there is no interaction between the six factors, each of the 18 data can be decomposed into: And so on, In the above equation, μ is the overall average of all data, and A 1 , A 2 , A 3 represent the effects of factor A at different levels, while the other 5 factors are the same.e i represents the error of experiment No i, which is independent of each other and follow a normal distribution N(0,σ 2 ) .In order to conduct variance analysis on the data, the sum of squares of variation S and corresponding degrees of freedom are introduced.The sum of squares of total variation S T can be decomposed into the sum of squares of variation S i and the sum of squares of error S e for each factor, which is: e =  e1 +  e2 (7) Equation ( 5) represents the sum of squares of variations within the entire experiment group, truly reflecting the magnitude of the experimental error.In the analysis of variance with repeated experiments, S e includes model errors such as high-order interactions, namely the sum of squares of errors for the first type, S e1 , and the sum of squares of errors for the second type, S e2 .The calculation of the sum of squares of variation and degrees of freedom is often complex, and the accumulated error in calculation is also large.The following practical equations can also be used for the calculation:  2, it can be seen that test results vary at different levels of factors.For the same carbon fiber sample, the average value of the highest group of tests is 13.3mg, while the lowest group is only 1.3mg.When the test result of a certain factor level is greater than 4mg, the coefficient of variation is below 15%, which means the data stability is good; When the test result is below 3mg, due to the small amount of fuzz, the data fluctuates greatly, with a coefficient of variation between 30% and 50%.It can be seen that this method can be used as a quantitative or semi quantitative evaluation method for fiber wear resistance, but there are differences in the test results and stability of the fuzz mass at various factor levels.Appropriate test parameters need to be selected to ensure minimal fluctuations in testing results.Perform variance analysis of orthogonal experiments on the data in Table 2, where the experiment number n=18, the number of replicates of the same experiment r=5, the number of levels p=3, and the number of factors q=6.The sum of squared variations for each factor can be obtained by calculation, as shown in Table 3.
For factor A, when the ratio F A is greater than the critical value F α , it indicates that the influence of the factor is significant.Check the F table based on degree of freedom, F A , f e and specified significance level α, the critical value F α (f A， f e ) can be obtained.And comparing F α And F e , the significance judgment can be made.Based on the above calculation method and the judgment rules of Table F, Table 4 is obtained.4, it can be seen that within the level of factors studied in this article, traction tension, friction load, friction rod angle, and number of friction rods have a highly significant influence on the test results of fuzz mass.Traction speed has an influence on the test results, while sponge density has no influence.Adjusting the level of other five factors except for sponge density will result in different test results.

Standard parameter testing of high-strength fibers
According to the testing parameters in Q/ZHFC 4403-2014, wear resistance tests are conducted on 8 batches of domestic high-strength carbon fiber T-1, while comparative tests were conducted on imported high-strength carbon fiber T-2.The influential testing parameters in the above standard are determined to be: traction tension 2N, friction load 250g, friction rod angle 120°, 6 friction rods, and traction speed 15m/min.Medium density sponge sheets were selected for this test, and the test results are shown in Figure 3. Comparing Table 2 and Figure 3, it can be seen that the data's coefficient of variation (12.0%~38.2%)by testing parameters in the standard is significantly higher than the lowest level of data's coefficient of variation (11.4%) in Table 2.The overall fuzz mass of T-2 is similar to that in the literature, while the test result fluctuates greatly, ranging from 1.2mg to 5.0mg, which is not consistent with practical application [19].In summary, it can be seen that there is still room for optimization of the testing parameters in the standard for high-strength carbon fiber.

Standard parameter testing for high modulus carbon fiber
According to the testing parameters in the standard, wear resistance test is conducted on domestic high modulus carbon fibers M-1, M-2, and imported high modulus carbon fiber M-3.The settings of the five testing parameters are the same as high-strength carbon fiber, and the test results are shown in Figure 4.

Figure 4. Comparison test of medium and high modulus carbon fiber fuzz mass
From Figure 4, it can be seen that the coefficient of variation of each group of data in the wear resistance test of high modulus carbon fibers is between 1.3% and 14.2%, and there is still a significant difference in the coefficient of variation of different groups of data, indicating that there is room for optimization of the test parameters in the standard.To verify whether the testing parameters in the standard can reflect the differences in wear resistance between different types of carbon fibers, a substantial difference analysis of inter-group data with a confidence level of 95% is conducted for the data in Figure 4.The analysis results are shown in Table 5, where "Yes" indicates substantial differences and "No" indicates no substantial differences.Table 5 shows that there are substantial differences between most of the data groups in the table, indicating that using the test parameters in the standard can distinguish the wear resistance differences of the three types of high modulus carbon fibers in the table.4 and Table 5, it can be seen that both the fuzz mass of M-1 and M-2 are greater than M-3, and there are substantial differences in most groups.It is worth mentioning that due to the dry spray wet spinning process used to prepare M-1 and M-2, their surfaces are smooth and tidy, while M-3 is prepared using wet spinning process, with a large number of grooves on their surfaces.In addition, other performance of these carbon fibers is equivalent.Under these conditions, the fuzz mass of M-1 and M-2 should be smaller, and the phenomenon of composite processing experiment also indicates that the fuzz amount of M-3 is greater than that of M-1 and M-2.The above analysis indicates that although the standard test can distinguish the difference of various high modulus carbon fibers, the wear resistance tesing results do not match the phenomenon of composite processing, which means optimization is needed.

Parameters optimization and validation
To improve the stability and discrimination of wear resistance testing methods, and accurately distinguish the differences in wear resistance between different types of carbon fibers, the testing parameters in the standard is optimized.After optimization, the intra-group data fluctuation of the test results should be reduced, while the inter-group differences of the test results should be reflected.It is also necessary to accurately reflect the differences in fuzz mass between different types of carbon fibers with different process application phenomenon.To achieve the above goals, optimization was carried out for six influencing factors, and the three levels of each factor in Table 2 are divided into three groups.The sum of squares of errors for the second type Se 2 of the test results at each factor level is calculated separately, according to equations 8 to 13.Smaller Se 2 indicates that the repeated test error is smaller, and the test stability is higher at that factor level.The specific calculation results are shown in Table 6, Se 2 -1 represents the sum of squares of errors for the second type Se 2 for a certain factor at level 1.For example, the sum of squares of errors for the second type Se 2 for factor A at level 2, i.e.Se 2 -2, is 15.6, which is smaller than both level 1 and level 3.It can be seen that when the traction tension(factor A) is level 2, the friction load(factor B) is level 3, the traction speed(factor C) is level 2, the sponge density(factor D) is level 3, the friction rod angle(factor E) is level 3, and the number of friction rods(factor F) is level 2, the test result Se 2 is the smallest.When the traction tension is 25N, the friction load is 350g, the traction speed is 30m/min, and the sponge density is 2.28×10 -2 g/cm 3 , the friction rod angle is 120°, and the number of friction rods is 6, the repeated test error of the test results would be smallest, and the coefficient of variation of the test results would be smallest.difference of the average value and data coefficient of variation between different groups of the same carbon fiber is also smaller.Finally, the overall stability of the test is significantly improved.7, it can be seen that for imported high-strength carbon fiber T-2, there is no substantial difference in data between Group A and Group B, there is a substantial difference in data between Group A and Group C, and between Group B and Group C. The comparison between the three groups of data reflects a slight fluctuation in the wear resistance of T-2, which matches the changes in the amount of fuzz during composite processing.In addition, the fuzz mass of T-2 carbon fiber is significantly lower than that of T-1, while the fuzz mass of M-3 is slightly higher than that of M-2 carbon fiber, which matches the phenomenon of composite processing completely.It can be seen that the test method with optimized parameters can accurately reflect the level of carbon fibers' wear resistance and distinguish different carbon fibers.

Conclusion
(1)The six factor three level orthogonal experiment shows that within the factor level studied herein, the traction tension, friction load, friction rod angle, and number of friction rods have a highly significant influence on the test results of carbon fiber wear resistance.The traction speed has an influence on the test results, while the sponge density has no effect.
(2)The test results obtained by using the standard parameters in Q/ZHFC 4403-2014 is similar to literature, while the coefficient of variation is relatively large, and the relative level of the fuzz mass of different high modulus carbon fibers does not match the phenomenon of composite processing.
(3)The test parameters with the lowest error level determined through the analysis of the sum of squares of errors.After optimizing the parameters, the coefficient of variation of the test results for the fuzz mass is 2.9%~5.0%,which can accurately and quantitatively distinguish the wear resistance level of different types of carbon fibers.

Figure 1 .
Figure 1.SEM of fiber bundle before and after friction

Figure 2 .
Figure 2. Schematic diagram of wear resistance test device

10thFigure 3 .
Figure 3.Comparison test of fuzz mass of high-strength carbon fibers

Figure 5 .
Figure 5. Fuzz mass test after parameters optimization Substantial difference analysis on the test data of carbon fibers of the same type is conducted in Figure 5. From Table7, it can be seen that for imported high-strength carbon fiber T-2, there is no substantial difference in data between Group A and Group B, there is a substantial difference in data between Group A and Group C, and between Group B and Group C. The comparison between the three groups of data reflects a slight fluctuation in the wear resistance of T-2, which matches the changes in the amount of fuzz during composite processing.In addition, the fuzz mass of T-2 carbon fiber is significantly lower than that of T-1, while the fuzz mass of M-3 is slightly higher than that of M-2 carbon fiber, which matches the phenomenon of composite processing completely.It can be seen that the test method with optimized parameters can accurately reflect the level of carbon fibers' wear resistance and distinguish different carbon fibers.Table7.Substantial difference analysis of fuzz mass after optimization

Table 1 .
Six factors and three levels system /(g• cm-3) C 1.01×10 -2 1.69×10 -2 2.28×10 -2 (21) =  e1 +  e2(21)In which, x ij represents the j-th test of the i-th test number, and the same test number is repeated r times.Analysis of testing influencing factors According to the L18 (36) orthogonal table, 18 groups of tests are conducted on imported highstrength carbon fiber T-2 with good wear resistance in the applying process.Five valid data are tested on each group of samples, and all other factors except for six factors in Table1remained unchanged.The test results are shown in Table2.From Table

Table 2 .
Orthogonal test results of fuzz mass

Table 3 .
Calculation of orthogonal test results without interaction Perform F-test by the sum of squared variations S for various factors and other parameters in Table3.The calculated value of statistic F is:

Table 4 .
Test variance analysis without interaction

Table 5 .
Analysis of substantial differences in high modulus carbon fiber fuzz mass Group M-1A M-1B M-1C M-1D M-2A M-

Table 6 .
Analysis of Se 2 of repeated tests without interactionWear resistance testing according to the above optimized testing parameters is conducted to verify the level of test error.The test results are shown in Figure5.From Figure5, it can be seen that after the optimization of testing parameters, the coefficient of variation of test data for various types of carbon fibers ranges from 2.9% to 5.0%.The fluctuation of test data is significantly reduced, and the 10th Global Conference on Polymer and Composite Materials (PCM 2023) Journal of Physics: Conference Series 2652 (2023) 012006 IOP Publishing doi:10.1088/1742-6596/2652/1/012006