1.3 Measurement and characterization of aspect ratio
The aspect ratio of short fiber determines the transfer and distribution of stress in material, and its distribution regularity can be obtained by measuring the radius and the length of fibers in the NASC products. Some samples of NASC were prepared. Using organic solvents, such as gasoline or toluene, to dissolve the matrix rubber, the short fibers different in size are left and dried. Considering the fiber radius is about micron, a digital camera with high-resolution is used to take pictures of fibers, and the length and radius of each short fiber are obtained by numerically analyzing the pictures. Then the distribution of aspect ratios can be obtained by counting the aspect ratios of 500 to 1000 fibers. The typical histograms of aspect ratios of aramid fibers can be seen in Fig. 10.
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Fiber length Fiber length (a) Fiber content 5% (b) Fiber content 10% Fig. 10. Aspect ratio distribution of aramid fibers with the initial length of 4-6 mm |
If the aspect ratio varies in a relatively small range, it can be characterized by the mean aspect ratio. If it distributes dispersedly, however, the characterization with a distribution function is appropriate. Furthermore, a histogram can also be used to express the distribution of aspect ratios without considering the dispersity of aspect ratios.
The log-normal density function is usually used to characterize the aspect ratios, as Eq. (7) expresses.
ratio and lmod/d the maximum probability density of the aspect ratio. The arithmetical mean of aspect ratios can be calculated by Eq. (8).
1 m
l »/d = – !(„/d ) (8)
m n=l
where ls/d is the average value of aspect ratios, m is the number of short fibers and ln/d is the aspect ratio of the number n short fiber. The arithmetical mean aspect ratio can also be calculated by Eq. (9) if the histogram of aspect ratios is known.
‘»/d=У Pi (lJd)/X Pi (9)
where li/ d is the aspect ratio of fibers in the interval i, and pi is the ratio of the number of fibers whose aspect ratios are in the interval i to the total number of fibers.
