Fibre length distribution

The microstructure of all mouldings was characterised by determining fibre content (weight and volume fraction), average fibre dimensions (diameter and length), fibre length distribution and fibre orientation distribution. 

Characterising glass fibres in an injected moulded polypropylene plate (a) Fibre length distribution (Mine, R J. et aL, Compos. Sci. Tech., 62, 1445, 2002) (b) theoretical angular distribution (Mine, R J. et al., Compos. Sci. Tech., 64, 1081, 2004) Elsevier. 

Correct compounding Figure 6.5 Glass fibre length distribution in reinforced polymer... 

Pulp quality data (automated, on-line analysis of grab samples using Pulp Expert system) fibre length distribution freeness consistency brightness. 

Hine, P.J., Lusti, H.R. and Gusev, A.A. (2002) Numerical simulation of the effects of volume fraction, aspect ratio and fibre length distribution on the elastic and thermoelastic properties of short fibre composites. Comp. Sci. Tech., 62, 1445. 

The SEM analysis of the fibrous structure was done to determine the fibre length distribution for each process condition. Also SEM images of the specimen surfaces were investigated. 

FIGURE 12.1 Length distribution of short Hbers after mixing. (From Ashida, M., Short Fibre-Polymer Composites, De, S.K. and White, J.R. (Eds.), Woodhead Publishing Ltd., Cambridge, U.K., 1996. With permission.)... 

Fig. 21 Schematic visualisation of interchain bonding in a domain of a polymer fibre. The lines represent the chains with a length distribution and the dashed lines depict the interchain secondary bonds. Chain ends prevent the formation of these bonds in their immediate surroundings... 

For the transformation of the macrocomposite model to a molecular composite model for the ultimate strength of the fibre the following assumptions are made (1) the rods in the macrocomposite are replaced by the parallel-oriented polymer chains or by larger entities like bundles of chains forming fibrils and (2) the function of the matrix in the composite, in particular the rod-matrix interface, is taken over by the intermolecular bonds between the chains or fibrils. In order to evaluate the effect of the chain length distribution on the ultimate strength the monodisperse distribution, the Flory distribution, the half-Gauss and the uniform distribution are considered. 

It is assumed that all chains are oriented parallel to the fibre axis and that equal parts of the fibre contain equal numbers of starting points of chains of arbitrary length u. Thus the starting points are distributed homogeneously along the length of the fibre. The length distribution of the chains is determined by the distribution function /( ) with... 

The number of chains of length u which cross a certain fibre cross section is determined by the crossing length distribution h(u) defined in Sect. 3.1.1. The tensile stress in a chain passing through a fibre cross section is calculated in Sect. 3.1.2. The force S per unit area in a cross section can be found from... 

Fig. 49 Effect of the width of a uniform chain length distribution on fibre strength. The width of the block w is centred at the end of the value of the molecular weight, expressed as the length of the monomeric unit. For example, for the point on the curve zw=100 m.u. and 12.5wz"1=20, it means that the total block width w=160 m.u. hence, the range of the distribution, which is centred at zw=100 m.u., is from z=20 up to z=180. Note that for a uniform distribution zw=zn...

In the previous sections the theoretical relations describing the strength of a polymer fibre as a function of the intrinsic parameters, such as the chain modulus, the modulus for shear between adjacent chains, the orientation distribution and the chain length distribution, have been discussed. In this section the dependence of the strength on the time and the temperature will be investigated. 

Figure 4.1 Sheet structures arising from (a) the random distribution of 970 straight fibres of uniform length, (b) a photomicrograph of a 2.5gmr2 sheet of paper in which the mean fibre length and density correspond to that...

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