Fiber lengths

The effectiveness of short fibers in carrying applied force also depends on the critical length strength (Q defined by the following equation  

Micromechanical models such as Cox shear-lag and Halpin-Tsai are often used to predict the stiffness and strength of discontinuously short-fiber reinforced composites. Experimental results of tensile measurements are then compared or correlated with such theoretical models. The shear-lag analysis originally proposed by Cox considered a discontinuous fiber embedded in an elastic matrix with a perfectly bonded interface and loaded in tension along the fiber direction [25]. The analysis tabes into account the difference in strain displacements of the fiber and matrix along the interface. The stress transfer depends on the interfacial shear stress between the fiber and the matrix. The stress transfer from fiber ends is neglected in the analysis. The Cox model incorporates the aspect ratio (a = l/d where I is the fiber length and d the diameter) of the fiber into 

Sample Flexural modulus, GPa Flexural strength, MPa Elongation at break, % 

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It is difficult to determine the cross-sectional area of a fiber. Direct observation and measurement of a cross section under a microscope is the most accurate method (15). This is a destmctive test that does not allow subsequent study of fiber mechanical properties, and is slow and tedious. Also, it does not take into account any variations in the cross-sectional area along the fiber length. Measurement of fiber diameters from microscopic observations of longitudinal views is somewhat easier, but the eUipticity of the cross section in certain fibers can lead to serious errors. 

Fiber Length, mm Diameter, p.m Shape Diameter, p.m Length, cm Width, mm... 

Among the bast textile fibers, the density is close to 1.5 g/cm, or that of cellulose itself, and they are denser than polyester, as shown iu Table 5. Moisture regain (absorbency) is highest iu jute at 14%, whereas that of polyester is below 1%. The bast fibers are typically low iu elongation and recovery from stretch. Ramie fiber has a particularly high fiber length/width ratio. 

Glass fibers <3 fim are to be avoided because these are classed as respirable fibers which can enter and damage lung passages. Most glass fiber products have sufficient fiber lengths to prevent lung entry even if their diameters are <3 fim. 

Optimum mechanical piopeities of the fibers are developed provided the precursor novolak filaments ate less than 25 ]lni in diameter to ensure sufficient diffusion of the formaldehyde and catalyst into the fiber. The individual fibers are generally elliptical in cross section. Diameters range from 14 to 33 )J.m (0.2—1.0 tex or 2—10 den) and fiber lengths ate 1—100 mm. Tensile strength is 0.11—0.15 N /tex (1.3—1.8 g/den) and elongation is in the 30—60% range. Elastic recovery is as high as 96%. 

Flock is made by precision-cutting tow into 0.5—3-mm fiber lengths. 

Nonoxide fibers, such as carbides, nitrides, and carbons, are produced by high temperature chemical processes that often result in fiber lengths shorter than those of oxide fibers. Mechanical properties such as high elastic modulus and tensile strength of these materials make them excellent as reinforcements for plastics, glass, metals, and ceramics. Because these products oxidize at high temperatures, they are primarily suited for use in vacuum or inert atmospheres, but may also be used for relatively short exposures in oxidizing atmospheres above 1000°C. 

Because fiber frictional properties are so important in the conversion of staple yams to spun yams, ASTM D2612 has been designed to measure the cohesive force encountered in the drafting or fiber alignment of sHver and top under static conditions. This frictional force is affected by surface lubrication, linear density, surface configuration, fiber length, and fiber crimp. 

Asbestos fibers used in most industrial appHcations consist of aggregates of smaller units (fibrils). This is most evident with chrysotile which exhibits an inherent, weU-defined unit fiber. Typical diameters of fibers in bulk industrial samples may reach several tens of micrometers fiber lengths are on the order... 

Fig. 6. Fiber length distribution for (a) a long sample (group 4) and (b) a short sample (group 7) of chrysotile successive length classes separated by 50 p.m.

The fiber extraction (milling) process must be chosen so as to optimize recovery of the fibers in the ore, while minimizing reduction of fiber length. Since the asbestos fibers have a chemical composition similar to that of the host rock, the separation processes must rely on differences in the physical properties between the fibers and the host rock rather than on differences in their chemical properties (33). 

Currendy, the Bauer-McNett classification and the QS test are the most widely used fiber classification techniques. Whereas there are quaUtative relationships between QS and BMN, there is no quantitative correspondence. It is readily understood that these standard tests do not provide accurate definition of the fiber lengths the classification also redects the hydrodynamic behavior (volumes) of the fibers, which, because of thek complex shapes, is not readily predictable. 

Other classification techniques have been developed which provide some insight on fiber lengths, typically the Ro-Tap test, the Suter-Webb Comb, and the Wash test. 

The viscosity range of CN products can be adjusted in advance by choosing the starting cellulose with an appropriate degree of polymerization (DP). A study of the different celluloses examined the impact of various cellulose properties, such as morphological factors (percent crystallinity, fiber length, and distribution), chemical composition (DP, ash content), and hemiceUulose and lignin content, on the nitration behaviors of cellulose (55). 

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