Fibres curve-fitting

In most simple applications of models all that is really being achieved is curve fitting. This applies to the Takayanagi models (which are one dimensional and assume uniformity of stress and strain within each element) as well as to simple fibre models such as the shear lag. 

Fig. 38. Curves fitted to plateau creep data on the basis of the two-process model with no constraint on parameters ( ) Rigidex 50, X = 20 (X) 006.60, X = 20 (A) y-irradiated Rigidex 50, X = 20 (O) H020, >. = 20 (o) Hostalen GUR, solution-spun fibre...

The determination of the composition of ethylene-propylene copolymers at a temp, of200C by means of an IR fibre-optic sensor based on sapphire fibres was studied. LDPE and PP were also investigated. Data are presented on spectra of LDPE and PP at 200C obtained using the sensor, CH3/CH2 ratio after curve fitting versus C2 content, ratio of absorbance at 2950 and 2852/cm versus C2 content and calibration graph of multivariate calibration. 31 refs. 

Fig. 8 Tensile curves of cellulose II fibres measured at an RH of 65% (1) Fibre B, (2) Cor-denka EHM yarn, (3) Cordenka 700 tyre yarn, (4) Cordenka 660 tyre yarn and (5) Enka viscose textile yarn [26]. The solid circles represent the strength corrected for the reduced cross section at fracture. The dotted curve is the hyperbola fitted to the end points of the tensile curves 1,3 and 5. The dashed curve is the fracture envelope calculated with Eqs. 9,23 and 24 using a critical shear stress rb=0.22 GPa... 

Fig. 13.102 shows this theoretical relation between the tensile strength and the initial modulus of PpPTA fibres for five values of ft varying from 0.10 to 0.12 rad (i.e. from 5.7 0 to 6.9 °) and for yd = 1.8 GPa and ech = 240 GPa (see Table 13.18). A rapid increase in strength of PpPTA is observed in the modulus range from 40 to 80 GPa and there the best fit agrees with j> = 0.115. For higher moduli the tensile strength levels off. This is also the case with the theoretical curves, but not until a modulus of 110 GPa (not shown here). 

Ahn et al. have developed fibre-based composite electrode structures suitable for oxygen reduction in fuel cell cathodes (containing high electrochemically active surface areas and high void volumes) [22], The impedance data obtained at -450 mV (vs. SCE), in the linear region of the polarization curves, are shown in Figure 6.22. Ohmic, kinetic, and mass transfer resistances were determined by fitting the impedance spectra with an appropriate equivalent circuit model. 

Fig. 12. (A) m -V relationship for fibres perfused with high Cs in 1/4 Na-SW. . , O, fibres perfused with high Cs and bathed in 1/4 Na-SW made with chloride -t-. X, O. V, fibres perfused with high Cs in 1/4 Na-SW made with iscthionate, with 15 mM CaCl2 (the calcium activity in this solution was identical to that of the 1 /4 Na-SW made with chloride). (B) Voltage dependence of the steady-state distribution of charges. C, , O, , , A, V, fibres internally perfused with high Cs" (the different symbols represent separate experiments) O, , fibres internally perfused with low Cs and all experimental points shifted toward more negative values by 9 mV. All experiments were carried out in an Na- and K-free saline made with iscthionate in place of chloride. Curve was computed by the least-squares fit with the experimental points (sec text). (Adapted from Keynes and Rojas [38].)...

Aromatic ether amide or aramid fibres are organic, man made fibres which are available in various forms for use in composites. They are characterised by having reasonably high tensile strength, a medium modulus and a very low density. Their composites fit well into a gap in the range of stress/strain curves left by the family of carbon fibres at one extreme and glass fibres at the other. 

Scattered intensity from microtubules aligned with their long axis parallel to the X-ray beam (panel a). This is equivalent to the equatorial data obtained from a fibre diffraction pattern but one is certain that neither systematic errors due to mathematical procedures used for correction of the angular spread of the molecules are seen nor intensity due to overlap from diffraction arcs of the layer lines. Panel b shows the best fits = 0.05) to the data using the fitting procedure described in the text. The dotted line indicates the maximum extend of the experimental data at present. The tine indicated with cylinder is the contribution of two J) functions describing the basic cylinder. The modulated curve is the real fit taking into account the modulations on the cylinder suiface. 

Figure8.6 Raman spectrum in the region 1080-1 lS0cm for an experimental high-m ulus gel-spun polyethylene fibre (after [S9]). The Raman band has been fitted to two Gaussian curves, (a) Fibre undeformed (b) at a strain of 4.06%...

Figure 8.12 shows the distribution of strain along a single Kevlar 149 fibre in a model single-fibre epoxy composite [38] calculated from the point-to-point variation of the shift of the 1610cm aramid Raman band. Measurements were taken at 20 pm intervals along the fibre for different levels of matrix strain e ranging from 0% to 2.0% in intervals of 0.4%, and the curves drawn are best fits to the experimental data. It can be seen that in the unstrained case (e = 0%) there is no strain in the fibre. As increases the strain in the fibre increases from... 

Figure 8.13 Derived variation of fibre strain with distance along the Kevlar 149 fibre in a single-fibre composite tensile specimen at different indicated levels of matrix strain e . The curves are fitted using Equation (3) (after [38])...

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