DRAW RATIO Subject

The similarity of Eqs. (13.155) and (13.152) can easily be understood, since drawing and elongation are, in principle, very similar if a yam with a draw ratio A0 and an initial modulus E0 (under the same conditions) were subjected to further elongation e, the total resulting draw ratio would be ... 

The effect of an orientation process on an isolated elliptic flaw is depicted in Figure 7A. Let < i and a2 be the permanent stretch (or draw) ratios (ratio of drawn to undrawn length) to which the master sheet is subjected in two orthogonal directions. If an elliptic flaw is originally at right angles to the ai direction (i.e.y p = ir/2) and a2 = 1, then R will increase with until a particular value of is reached at which R = 1. For larger values of i, R will then decrease but the major axis of the ellipse is now at ft = 0. The critical draw ratio at which the orientation P jumps from tt/2 to 0 and for which the ellipse is circular (R = 1) is described later. 

There is, however, a limit to the amount of stretch that can be given to a polymer because the phenomenon of necking can intervene and cause rupture of the fiber. In other words, in a polymeric fiber there is a limit to the modulus enhancement that can be obtained by subjecting it to an ever higher draw ratio. As we shall see in Chapter 4, this led to other means of obtaining high stiffness polymeric fibers such as aramid and polyethylene. 

Figure 11.9. First-order diffraction angle triangles) and calculated fringe spacing circles) vs. draw ratio for a grating inscribed on an ATE film subjected to extension closed symbols) and retraction open symbols). Source Zhao et al., 2002. Reprinted with permission.

In another study, Jose et al. [42] found that the strength and modulus of PP fiber were improved from 25 MPa and 1.0 GPa, respectively, to 125 MPa and 3.7 GPa, by the addition of 1 wt% MWCNTs. When the composite fiber was subjected to a draw ratio of 4, fhe sfrengfh was improved further to 420 MPa, but the modulus dropped slightly to 3.5 GPa. The modulus of drawn PP fibers increased by fhree times when 1 wt% of SWCNTs was added [6]. 

Before entering the air gap, the spinning solution is subjected to a so-called predraw, Xo> <)ue to the spinneret. Hence, the effective draw ratio pertaining to the affine model, X, is given by... 

In Section 24.1.3 we have discussed among others the time-temperature correspondence principle. An example of application of that principle is shown in Fig. 24.10. The results pertain to high density polyethylene (HOPE) subjected to different levels of predrawing [58]. The draw ratio is defined as... 

Figure 21.9. SEM photographs of the inner structure of oriented SiOj-g-PBA/PP (drawing ratio = 15, nano-SiOj content = 1 wt%). The specimens were first subjected to tension along the pre-drawing direction, unloaded prior to failure (at stress of 75 MPa), and then split parallel to the pre-drawing direction in liquid nitrogen, (a) Low magnification view, (b)(c) high magnification view...

During the cooling process the fiber is subjected to a draw-down force, which introduces the orientation. Additional orientation may be introduced later by stretching the fiber to a higher draw ratio. 

Recently special attention has been paid to the oriented polyolefins such as UHMWHDPE and LLDPE. These can be subjected to high drawing ratios resulting in materials with special properties as ultra-... 

The energy equation, Eq. 9.39, should be incorporated into the model to account for temperature variation along the filament axial length. Pearson and Shah (1974) solved the system of equations subjected to a linearized analysis and found that the critical draw ratio depends, besides on the power-law index, on the dimensionless number, S ... 

Introduced in 1972, the whoUy aromatic polyamide, poly i ra-phenylene teraphthalamide), termed aramid, was the subject of extensive evaluation as a tire cord in all types of tires (8,14). As of the late 1990s, however, only specialized appHcations have emerged for aramid tire cord that draw on their high strength-to-weight ratio to produce tires with lower weight (16). 

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