80 3-D textile reinforcements in composite materials W R 3.4 Lenticular yarn cross-section.W is width of yarn,t is yarn thickness,R is radius of curvature. The most detailed geometric analysis would consider the path of each WV IL:OE single fibre in the unit cell.The greatest practical problem,however,is caused by the fact that the complete set of input data necessary for such a detailed geometric description is very large and difficult to quantify.There- fore,the geometric analysis is carried out on the yarn level.We assume that all individual fibres in the yarn run in the same direction as the yarn.The A intra-yarn fibre volume fraction or fibre packing density K,defined as the fibre to yarn area ratio,is assumed to be a constant for the woven fabric composite.Interlacing of the yarns and processing of the composite leads 豆 to thread or yarn flattening.On the basis of microscopic observations,a lenticular shape was selected to describe the cross-sectional shape of the yarn (Fig.3.4). The geometric characteristics of a hybrid weave can be subdivided in three groups (Table 3.4).The first group,the know group,contains those parameters that are supplied by the weaving company.All the parameters that one has to measure on a real woven fabric composite are put together in the second group,the measure group.This fabric information can be obtained by microscopic observation of warp and weft sections of the fabric composite.The aspect ratio f of the yarn,defined as the width w over the thickness t of the lenticular yarn cross-section,is the most important one.The crimp parameter h describes the undulation of the filling yarns. Of course,the undulation of the yarns in the warp direction is related to this parameter because the increase of undulation in one direction of the fabric reduces the undulation in the other direction [36].Finally,the third group,the calculate group,contains all values that are calculated from the previous parameters,using formulas based on simple geometric considerations.The most detailed geometric analysis would consider the path of each single fibre in the unit cell. The greatest practical problem, however, is caused by the fact that the complete set of input data necessary for such a detailed geometric description is very large and difficult to quantify. There￾fore, the geometric analysis is carried out on the yarn level. We assume that all individual fibres in the yarn run in the same direction as the yarn. The intra-yarn fibre volume fraction or fibre packing density K, defined as the fibre to yarn area ratio, is assumed to be a constant for the woven fabric composite. Interlacing of the yarns and processing of the composite leads to thread or yarn flattening. On the basis of microscopic observations, a lenticular shape was selected to describe the cross-sectional shape of the yarn (Fig. 3.4). The geometric characteristics of a hybrid weave can be subdivided in three groups (Table 3.4). The first group, the know group, contains those parameters that are supplied by the weaving company. All the parameters that one has to measure on a real woven fabric composite are put together in the second group, the measure group. This fabric information can be obtained by microscopic observation of warp and weft sections of the fabric composite. The aspect ratio f of the yarn, defined as the width w over the thickness t of the lenticular yarn cross-section, is the most important one. The crimp parameter hf describes the undulation of the filling yarns. Of course, the undulation of the yarns in the warp direction is related to this parameter because the increase of undulation in one direction of the fabric reduces the undulation in the other direction [36]. Finally, the third group, the calculate group, contains all values that are calculated from the previous parameters, using formulas based on simple geometric considerations. 80 3-D textile reinforcements in composite materials 3.4 Lenticular yarn cross-section. W is width of yarn, t is yarn thickness, R is radius of curvature. RIC3 7/10/99 7:37 PM Page 80 Copyrighted Material downloaded from Woodhead Publishing Online Delivered by http://woodhead.metapress.com Hong Kong Polytechnic University (714-57-975) Saturday, January 22, 2011 12:30:11 AM IP Address: 158.132.122.9