Question

Assume circular and continuous fibers, and hexagonal packing, with the given volume

fractions of fibers Vf and voids Vv.
1) Determine the corrected volume fractions of fibers and of matrix.

GIVENS:

Vv=3%=0.03

Vf=50%=0.5

Pf=0.09 lb/in³

Pc=0.05 lb/in³

Show all steps clearly and how you found values.

Answer 1

The corrected volume fraction of the fibers remains at 50% (0.5) and the corrected volume fraction of the matrix is calculated to be 47% (0.47), while the volume fraction of voids is 3% (0.03).

Step-by-step explanation:

To determine the corrected volume fractions of fibers and matrix, given the volume fractions of fibers (Vf) and voids (Vv), we first need to identify the volume fraction of the matrix (Vm). Since the sum of the volume fractions of fibers, matrix, and voids must equal 1 (100%), we can write the equation:

Vf + Vm + Vv = 1

We have been given Vf = 0.5 and Vv = 0.03. Substituting these values into the equation, we can solve for Vm:

Vm = 1 - Vf - Vv
Vm = 1 - 0.5 - 0.03
Vm = 0.47

Therefore, the corrected volume fraction of the fibers is 50% (or 0.5), as given, and the corrected volume fraction of the matrix is 47% (or 0.47). The volume fraction of voids remains at 3% (or 0.03), as given.