Determination of the volume fraction of fibre in the warp and weft orientations of composites manufactured from woven cloth
If the weight fraction of cloth in the composite is Wc and the weight fraction of matrix Wm then
The cloth itself consists of a warp and a weft such that
The composite is now divided into two halves by sectioning parallel to the plane of the cloth such that all the warp fibres lie in one half of the composite and all the weft fibres lie in the other half, each half contianing equal amounts of matrix.
Now the total weight fraction fibres in the ply containing the warp fibres is
and the weight fraction of fibres in the ply containing the weft is
The volume fraction of fibres,f, in each ply is simply the ratio of the volume of fibres,Vf, in the ply to the total volume of the ply (Vf + Vm). Given volume = mass/density
where rf and rm
are the densities of the fibre and matrix respectively.
|
Warp |
Weft |
||||||
|
Jute |
Glass |
Material |
|||||
|
44 |
56 |
Weight % of Fibre |
|||||
|
1.5 |
2.54 |
Density of Fibre (g/cc) |
|||||
|
1.25 |
Density of Matrix (g/cc) |
||||||
|
Weight Fractions |
Apparent Fractions/Ply |
Volume Fractions/Ply |
|||||
|
Wt.% |
Warp |
Weft |
Warp |
Weft |
Warp |
Weft |
|
|
19 |
0.084 |
0.107 |
0.171 |
0.208 |
0.147 |
0.115 |
|
|
33 |
0.144 |
0.184 |
0.300 |
0.353 |
0.264 |
0.212 |
|
|
48 |
0.213 |
0.271 |
0.451 |
0.511 |
0.407 |
0.340 |
|
|
59 |
0.261 |
0.333 |
0.563 |
0.621 |
0.517 |
0.446 |
|
|
65 |
0.285 |
0.363 |
0.618 |
0.673 |
0.574 |
0.504 |
|
|
64 |
0.280 |
0.357 |
0.607 |
0.663 |
0.563 |
0.492 |
|
The elastic properties of a laminate made from more than a single reinforcing fibre can easily be calculated using laminate theory. Download the MathCad document that shows how.