Fiber stiffness

Transverse Dimensions or Fineness. Historically, the quantity used to describe the fineness or coarseness of a fiber was the diameter. Eor fibers that have irregular cross-sections or that taper along their lengths, the term diameter has no useful meaning. Eor cylindrical fibers, however, diameter is an accurate measurement of the transverse dimension. Though textile fibers can be purchased in a variety of cross-sectional shapes, diameter is stiU a useful descriptor of the transverse dimension. Eiber diameter is important in determining not only the ease with which fibers can be twisted in converting them to yams, but also fiber stiffness, ie, fabric stiffness, and, alternatively, fabric softness and drapeabiHty. 

For typical filament winding applications, the fiber reinforcement provides the stiffness and strength required to maintain structural integrity. Thus, material characterization for filament wound structures focuses on characterizing the fiber dominated stiffness and strength properties of the composite. The stiffness of fiber reinforced plastics (FRPs), in the fiber direction, is dominated by the fiber stiffness characteristics. The strength will be influenced by a number of factors, however, and not all of them are related to the fiber, including ... 

The middle layer (S2) forms the main portion of the cell wall. Its thickness in softwood tracheids varies between 1 (earlywood) and 5 (latewood) jiim and it may thus contain 30-40 lamellae or more than 150 lamellae. The thickness naturally varies with the cell types. The microfibrillar angle (Fig. 1 -16) varies between 10° (earlywood) and 20-30° (latewood). It decreases in a regular fashion with increasing fiber length. The characteristics of the S2 layer (thickness, microfibrillar angle, etc.) have a decisive influence on the fiber stiffness as well as on other papermaking properties. 

The sound velocity in a fiber, and the sonic modulus calculated therefrom, are related to molecular orientation (De Vries ). As shown by Moseley ), the sonic modulus is independent of the crystallinity at temperatures well below the T (which means that the inter- and intramolecular force constants controlling fiber stiffness are not measurably different for crystalline and amorphous regions at these temperatures). An orientation parameter a, calculated from the sonic modulus, is therefore taken as a measure for the average orientation of all molecules in the sample, regardless of the degree of crystallinity. The parameter is called the total orientation , as contrasted to crystalline and amorphous orientation, from X-ray data. 

Tensile properties that are related to fiber stiffness can be used to measure the T of almost all fibers. The elastic modulus, that is, the sl pe of the Hookean region of the fiber stress-strain curve, is a measure of the fiber stiffness and can be used for T determination since, by definition, a glass is stlffer than rubber (Figure 6). Since the transition from a glassy to a rubbery state Involves a reduction in stiffness, the temperature at which the modulus is abruptly lowered is taken as... 

Kraft T, Chalovich JM, Yu LC, Brenner B (1995) Parallel inhibition of active force and relaxed fiber stiffness by caldesmon fragments at physiological ionic strength and temperature conditions additional evidence that weak cross-bridge binding to actin is an essential intermediate for force generation. Biophys J 68 2404-2418 Krebs EG, Beavo JA (1979) Phosphorylation-dephosphorylation of enzymes. Annu Rev Biochem 48 923-959... 

The stiffness coefficient is directly proportional to fiber linear density. The data plotted in Figure 8-22 provide a correlation coefficient of 0.97 and an index of determination of 0.94 [74]. This demonstrates that 94% of the variation in stiffness (in this experiment) is accounted for by variation in linear density, and as theory predicts, stiffness increases with fiber diameter. Theory predicts a fourth-power dependence between fiber stiffness and diameter for a perfectly elastic system. 

As one might anticipate, hair fiber stiffness also varies with relative humidity it decreases with increasing relative humidity (see Figure 8-23). We might conclude that hair fiber stiffness generally parallels fiber-stretching properties with respect to treatments. This conclusion is probably correct however, further empirical tests should be made before this conclusion becomes accepted. 

Figure 8-22. Hair fiber stiffness index and linear density [74]. Reprinted with permission of the Journal of the Society of Cosmetic Chemists.

FIGURE 12.24 Dependency of fiber stiffness on cross section. (From Lulay, A. m Acrylic Fiber Technology and Applications, J.C. Masson, Ed., Marcel Dekker, New York, pp. 314 315,1995.)... 

As mentioned, the carbons resulting from the pyrolysis of stabilized PAN precursor fibers are non-graphitizable. As a result, further heating of PAN based carbon fibers at very high temperatures (>2500 C) and without any mechanical stretching only slightly improves the ordering of the carbon atoms and the fiber stiffness. 

For fibrous PU scaffolds, the mechanical environment is much more complex than 2D polyacrylamide since the scaffolds are porous, fibers are distributed within the constructs, and cells are attached to single fibers. As a result, the stiffness characteristics for both single fibers and scaffolds may have an impact on stan cell differentiation. We recently studied the effects of PU scaffold stiffness at small and large strains (before and after aUgmnent of fibers, respectively) and single fiber stiffness on cardiac differentiation of cardiosphere-derived cells (CDCs). The single fiber stiffness was... 

In (Pao and Ritman, 1978), the 3-layer analysis was adopted in the investigation of the transmural pressure distributions in the left ventricular wall before and after the coronary artery ligation. The stress-dependent E equation such as Eq. (3) enables the fiber stiffness to be adjusted from one element to another in accordance with the instantaneous stress level in each element calculated during the incremental-loading finite element analysis. 

Proc Symp on Appl Comput Methods, pp 477-486 Pao YC, Mayendra KK, Padiyar RR, Ritman EL (1980) Derivation of myocardial fiber stiffness equation based on theory of laminated composite. Trans ASME 103 202-259 Parmley WW, Tyberg JV (1976) Determination of myocardial oxygen demand. Prog Cardiol 5 19-36 Pierce WH (1981) Body forces and pressures in elastic models of the myocardium. Biophys J 34 35-39 Pollack OH, Krueger JW (1978) Myocardial sarcomere mechanics some parallels with skeletal muscle. In Baan Y, Noordegraaf A, Raines J (eds) Cardiovascular System Dynamics, Cambridge, pp 3-10... 

Cellulose is one of the most abundant natural polymers on earth and provides strength/stability to the plant cell walls [45]. The properties and economics of fiber production for various applications are influenced by the amount of cellulose in a fiber. In natural cellulosic fibers, stiff semicrystalline cellulose microfibrils have been found to be embedded in a pliable amorphous matrix (Figure 1.3) [45]. 

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