Force-elongation curve

Typical force-elongation curves of some manufactured and natural staple fibers and textile-type manufactured filaments are shown in Figs 12.1 and 12.2. Table 12.1 gives the values of some of the physical and tensile properties of textile fibers. 

Fig. 12.1. Force-elongation curves of natural and manufactured staple fibers at standard conditions of 70°F and 65 percent humidity.

The tensile test shows a steady course of the tensile force-elongation curve, where a linear relationship exists only at low tensile forces. There are only small deviations from a linear course at approximately half-rupture. The tensile strength increases with increasing density. The degree of heat-sealing has an effect here also. 

The raw data from a tensile test (Fig. 11-20) are obtained in terms of force and corresponding elongation for a test specimen of given dimensions. The area under such a force-elongation curve can be equated to the impact strength of an isotropic polymer specimen if the tensile test is performed at impact speeds. Show that this area is proportional to the work necessary to rupture the sample. 

The viscoelastic character of stratum corneum is further demonstrated by the dependence of elastic modulus on strain rate (Figure 32). Even the dry corneum 10 wt % H2O) showed significant viscoelastic behavior over the narrow range of strain rates studied. In the case of hydrated membranes, there is also a change in shape of the force-elongation curve (6, 85). 

The initial portion of the virgin force-elongation curve is approximately linear, and the crystals support compressional forces. 

However, when the applied force is expressed in terms of the linear density of the fiber at the commencement of the test and the elongation is expressed in terms of the percentage elongation of the fiber, the true story emerges, as shown in Fig. 17 where the force/ elongation curve is transferred from Fig. 16. 

Figure 19 Force elongation curve illustrating work factor.

A is the area under the force-elongation curve in cm S is the full-scale load in gf R is the cross-head speed in cm/min G is the (corrected) effective specimen length in cm IV is the chart width in cm L is the chart speed in cm/min... 

The force-elongation curves of the radial and spiral threads prepared from... 

Fig. 4.41 Force-elongation curves of the radial and spiral threads prepared from an Argiope bruennuichii spider with a weight of 0.949 g. Stretching velocity 3.3 X10 m/s.

Here, F is the force applied to the dragline, S is the cross sectional area of the double filament, L is the initial length of the dragline, and AL is the elongation of the dragline when the F is applied. The F and AL are determined from the force-elongation curve within the elastic limit point and the S from the electron scanning microscopy. 

Due to the low strains involved in the calculation of initial modulus and the likelihood of eurvatuie of the force-elongation curve, the reported values will be subject to some degree of error. With judicious selection of the calculation parameters these errors ean be reduced, but differences will always exist between the values calculated by the different methods. The standard deviation for a series of specimens cut from a single sample should not exceed 5% for a given calculation method. Different ealeulation methods may provide values that are discrepant by 50% or more. 

The same trend is shown by the terms (64) and (65). While term (64) adds a constant to f(A - A ) S Eq. (65) adds a negative term with a minimum value for A = 0.8. However, due to the restrictions (68) and (69), the absolute value of this term is too small to account for the observed deviations from ideal behaviour. For values of x > 0.6, the trend of the force elongation curve remains the same while the magnitude of the theoretical deviations from ideal behaviour will be shown to increase. 

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