How to convert weight fraction into volume fraction?

Answer 1

Assume you have a composite material with just two constituents, fiber and matrix. Then let the weight fraction of fiber be Wf, and let the volume fraction of fiber be Vf. To convert from Wf to Vf, you'll need the density of the composite, roc, and the density of the fiber, rof.

To get the theoretical density of the composite, roc, you will need the weight fractions for fiber and matrix, Wf and Wm, and the densities of fiber and matrix, rof and rom.

Then, roc = (rof rom) / (rom Wf + rof Wm)

To convert Wf to Vf,

Vf = (Wf roc) / rof

Similarly, Vm = (Wm roc) / rom

If you want to convert from Vf to Wf, then you'll need an expression of roc in terms of the volume fractions.

roc = rof Vf + rom Vm

These expressions can be generalized to any number of constituents.