Fibre volume fraction local

Based on the yam volume description, the fibrous stmcture of the yarn, or, more generally, the fibrous stmcture of the unit cell, is described as follows. Consider a point P and the fibres in the vicinity of this point. The fibrous assembly can be characterised by physical and mechanical parameters of the fibres near the point (which are not necessarily the same in all points of the fabric), fibre volume fraction Vf and direction /of them. If the point does not lie inside a yam, then Ff = 0 and/is not defined. For a point inside a yam, fibrous properties are easily calculated, providing that the fibrous stmcture of the yam/ply in the virgin state is known and its dependency of local compression of the yarn/ply, bending and twisting of the yam are given. Searching the cross-sections of the yams, cross-sections S, = S(si) and S,+i =5 (s,+i) (s is a... 

Local fibre volume fractions. Fibres are distributed nonuniformly within the yams. Experimental measurements show that distribution of fibres in a yam can vary and be up to 15% lower at the yam edges than in the middle zone [25—27]. In contrast, the local FVF in the overlap configurations may be up to 30% higher at the edges. Introduction of the local FVF variation within given iy-FVF constraints reduces o-FVF. This is why accounting for FVF variation is often treated as an unnecessary luxury. On the other hand, introduction of FVF variation may be useful for FEA to smooth down artificial stress concentrations imposed by the edges. 

First, elastic properties of each impregnated yam segment are calculated using homogenisation formulae (e.g. the aforementioned Chamis formulae) for the unidirectional array of fibres, using local fibre volume fraction at the segment, properties of the fibres and elastic properties of the matrix. The result is the stiffuess matrix C], expressed in the local 123 coordinate system. Then each yarn segment is represented by an ellipsoidal inclusion with axis... 

From equation (18.5), the stress caused by thermal mismatch in the matrix is proportional to the volume fraction of the fibres. Therefore, large thermal stresses in some local regions, where the distribution of carbon fibres is not uniform, will result in some cracks in the composite. 

Inter-yarn fibre and yam volume fractions. Within the meso-scale modelling paradigm, yams are considered as continuous soUd medium with effective properties that are primarily governed by the fibre volume firaction (FVF). The correct overall FVF (o-FVF) is an obligatory feature of any acceptable model as it has to match fabric areal density, resin content and specific composite weight. The o-FVF is determined as the product of the yam volume firaction (YVF) and the local intra-yam FVF (iy-FVF). The latter depends on yam compressibility, pressure used for preform consolidation and even matrix viscosity. 

Other phenomena have been observed during the forming process (Lin et al., 2007 Boisse et al., 2011 Mohammed et al., 2000), such as the variation of the volume fraction of fibres on the permeability of the resulted textile stmcture, the influence of the local orientation of multifilaments yams on the global rigidity of the fabric, and the localization of plies on the fabric surface. 

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