Page 72 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics ofa unidirectionul ply 57

Fig. 3.5 1.ayer-wise fiber distribution in the cross-section of a ply (or = 0.65).

where pr, pm, and pc are densities of fibers, matrix, and composite. In analysis,
volume fractions are used because they enter the stiffness coefficients for a ply, while
mass fractions are usually measured directly during processing or experimental
study of the fabricated material.
Two typical situations usually occur. First situation implies that we know the
mass of fibers used to fabricate a composite part and the mass of the part itself. The
mass of fibers can be found if we weigh the spools with fibers before and after they
are used or calculate the total length of tows and multiply it by the tow tex-number
that is the mass in grams of 1000 m long tow. So, we know the values of Mf and M,
and can use the first equations of Eqs. (3.2) and (3.4) to calculate or.
The second situation takes place if we have a sample of a composite material and
know the densities of the fibers and the matrix used for its fabrication. Then, we can
find the experimental value of material density, pz, and use the following equation
for theoretical density
Pc = Prof + Pmom . (3.5)

Putting pc = p; and taking into account Eqs. (3.3) we obtain

Consider for example carbon+poxy composite material with fibers AS4 and matrix
EPON DPL-862 for which pf = 1.79 g/cm3, pm = 1.2 g/cm3. Let p; = 1.56 g/cm'.
Then, Eq. (3.6) yields of = 0.61.
This result is approximate because it ignores possible material porosity. To
determine the actual fiber fraction we should remove resin using matrix destruction,
solvent extraction, or burning the resin out in an oven. As a result, we get Mf and
having M, can calculate mfand try with the aid of Eqs. (3.2) and (3.4). Then we find
p, using Eq. (3.5) and compare it with p:. If pc > pz, material includes voids whose
volume fraction (porosity) can be calculated using the following equation