Weight of fiber 1

[mechnano]

In a hybrid preform the total volume fraction of fiber is 15%.
How can we calculate the weight of each fiber for making the preform.

Thanks in advance

 

[RPstress]

If you are choosing fibre volume fraction (Vf) and fibre areal weight, then you essentially need fibre density information *and* a final desired thickness.

For a unit area and a total thickness t (total volume is 1*1*t), with average fibre density rho_f (see below for calculating rho_f):

With 15% Vf, volume of fibres = 1*1*t * 0.15

Areal weight of fibres Wf = vol*density = 0.15*t * rho_f

Finding the weight of type of fibre and the average density depends on how the amounts of the types of fibre are defined. I'll assume just two types of fibre for simplicity.

If you have two fibre components of *mass* percentages:
75%/25%, say, and densities rho_f1 (the 75%) and rho_f2:

Areal weight fibre1 = 0.75*Wf = 0.75*0.15*t * rho_f
Areal weight fibre2 = 0.25*Wf = 0.25*0.15*t * rho_f

Average fibre density, rho_f = 1 / (0.75/rho_f1 + 0.25/rho_f2)

Else you presumably have the fibre types defined by volume percentages:
75%/25% again (but volumes):

Volume fibre1 = 0.75*0.15*t, so areal weight fibre1 = vol*density = 0.75*0.15*t * rho_f1
Areal weight fibre2 = 0.25*0.15*t * rho_f2

And in fact you don't actually need the average fibre density in this case, but for completeness:

rho_f = 0.75*rho_f1 + 0.25*rho_f2


You can simplify the formulas a bit, but it can be dangerous, as it's particularly easy to lose track of what you're doing with percentages by weight and volume knocking around. I've done a few checks on the above, but it's quite possible I've let an error (or two).

Also, do remember to use consistent units for weight, density and volume:

Metric areal weights are usally in grammes per square metre (gsm), and thicknesses tend to be in mm. It's safest to make all weights kg per square metre, all densities kg per cubic metre and all thicknesses in m. Then convert back at the end to gsm or whatever.

In Imperial/US customary, try to use areas in square inches, thicknesses in inches and densities in lb per cubic inch. If you want final areal weights in lb per square yard then convert afterwards.

-RP.