Fibre orientation angle

The variation of the loading curve shape with fibre orientation (angle a) is less regular in Im/s fracture tests and the identification of the point of fracture initiation from the load diagram was often problematic. Load-point displacements at fracture initiation in 1 m/s tests appear to be larger than in low rate tests. This apparent result is not unexpected, in view of the damping technique used in the impact tests which increases the compliance of the test system initially. 

Figure 4.8 VIPASA definition of the VAT panel. 6i is the fibre orientation angle in each strip for a VAT ply.

FIBRE ORIENTATION ANGLE = 45° FIBRE ORIENTATION ANGLE = 90°... 

Individual fibres are aligned in nonwoven structures in various directions. These fibre alignments are inherited from fibre alignments in both fibrous web forms and fibre relocation in the nonwoven bonding process. This characteristic can be described by fibre orientation angles in two or three dimensions (Fig. 6.1). 

In a 2D fabric plane, fibre orientation is defined by the fibre orientation angle, which is defined as the relative directional positions of individual fibres in the structure of a... 

Figure 6.1 Fibre orientation angle in 3D nonwoven fabrics.

In order to simplify the discussion and to keep the derivation of the formulae tractable, the major part of this analysis is limited to a polymer fibre with a single orientation angle 0. This angle is assumed to be a kind of average angle and a characteristic parameter of the orientation distribution of the chain axes. 

The presented explanation for the existence of the fracture envelope will be used in formulating a fracture criterion for polymer fibres. Let us suppose a hypothetical polymer fibre with chains having a single orientation angle in the unloaded state. The shape of the fracture envelope is now calculated by taking into account the shear deformation of the chains only. For this case the work per unit volume up to fracture is given by... 

This simple fracture model has a major shortcoming. The exclusion of chain stretching in the model leads for small initial orientation angles to strength values that become infinite. It follows from Eq. 27 that the shear stress is a continuous function of the fibre stress and it increases asymptotically to the value of 2gtan . So for initial orientation angles... 

For a polymer fibre with a single orientation angle the modulus, E, or the slope at each point of the tensile curve, is a function of the tensile stress and given by... 

Equation 32 gives the total strain energy stored in a domain of a fibre with an orientation angle 0 in the unloaded state after the stress has been increased from 0 to o. The first term on the right-hand side is the strain energy of the chain extension, and the second term is the shear strain energy. The continu-... 

Figures 26 and 27 present the modulus and strength as a function of the orientation parameter sin2 for the PpPTA, PBO and PIPD-HT fibres, assuming a fibre with a single orientation angle. As the precise value of g for the PBO fibre is not known, we have taken the same value as for PpPTA. This enables us to demonstrate the effect of the chain modulus on the modulus and the strength of the fibres, in particular at medium values of the orientation parameter and for highly oriented fibres. For example, at an orientation parameter value of sin2 =0.028 the modulus and strength for a PpPTA fibre are =84 and crb=3.9 GPa, for PBO =104 and ab=5.2 GPa, and for PIPD-HT =241 and crb=8.6 GPa.

During the creep of PET and PpPTA fibres it has been observed that the sonic compliance decreases linearly with the creep strain, implying that the orientation distribution contracts [ 56,57]. Thus, the rotation of the chain axes during creep is caused by viscoelastic shear deformation. Hence, for a creep stress larger than the yield stress, Oy,the orientation angle is a decreasing function of the time. Consequently, we can write for the viscoelastic extension of the fibre... 

According to the simple Eq. 115 and the full Eq. 140, the lifetime of a fibre measured at a constant load decreases with increasing orientation parameter. The dependence of the slope of the curve, log( b) vs ob, on the initial orientation distribution has been calculated for PpPTA fibres using Eq. 140. Figure 70 shows that at constant load for increasing orientation angle the lifetime curves become steeper, while at the same time the lifetime decreases. This effect has been observed for nylon 66 yarns as shown in Fig. 71, where the lifetime data... 

Fig. 70 Calculated lifetime curves of PpPTA fibres for three orientation angles using Eq. 140 with the parameters T=294 K, g= 1.8 GPa, /0= 13.3-1 O 20 J, I0=0.653-1020 T0=121 K,...

The presented derivations of the load rate and the lifetime relationships applying the shear failure criterion are based on a single orientation angle for the characterisation of the orientation distribution. Therefore these relations give only an approximation of the lifetime of polymer fibres. Yet, they demonstrate quite accurately the effect of the intrinsic structural parameters on the time and the temperature dependence of the fibre strength. 

Generally it is found that PPT fibres are highly oriented and that those variants with the lowest values of orientation angle exhibit the highest tensile modulus. Indeed the average crystallite orientations derived from azimuthal peak widths at half maximum intensities of the 200 reflections in Kevlar 49 and Kevlar 29 are found to be nine and eleven degrees respectively. 

FIG. 13.90 Typical sonic modulus vs. strain curves of PET, cellulose II and PpPTA fibres. The differences in initial moduli per polymer are due to differences in orientation angles. From Northolt and Baltussen (2002). Courtesy John Wiley Sons, Inc. 

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