An isotropic epoxy resin (E=2GPa, ν=0.3) is reinforced by unidirectional glass fibers (Eglass=70GPa), aligned in the 2 direction, such that the fiber composite is transversely isotropic, with the 1-3 plane being the plane of isotropy. The elastic constants of the fiber composite are:

E1=3.3GPa,


ν13=0.25

E2=29.2GPa,


ν12=0.3

E3=3.3GPa,


G12=1.27GPa

What is the volume fraction of fibers in the composite?

Vf:

can you share the source of this question?

Final in a EDX-mechanics course - the deadline is today, so answer it tomorrow. :-)

PS. So I'm curious too about the source, as I can see that the question is posted in 2014, and is the same as another question in here posted this year.

To find the volume fraction of fibers in the composite (Vf), we need to use the formula:

Vf = (Vfiber) / (Vmatrix + Vfiber)

where Vfiber is the volume of the fiber and Vmatrix is the volume of the matrix.

To determine the volume fraction, we first need to calculate the volume of the fiber and the matrix.

1) Volume of the fiber (Vfiber):
Vfiber = Afiber * Lfiber

where Afiber is the cross-sectional area of the fiber and Lfiber is the length of the fiber.

2) Volume of the matrix (Vmatrix):
Vmatrix = Amatrix * Lmatrix

where Amatrix is the cross-sectional area of the matrix and Lmatrix is the length of the matrix.

Now, let's calculate the volume of the fiber and the matrix:

3) Area of the fiber (Afiber):
Afiber = π * (diameter/2)^2

where the diameter can be assumed or given in the problem.

4) Area of the matrix (Amatrix):
Amatrix = π * (diameter/2)^2

assuming that the fibers are circular in cross-section and have the same diameter as the matrix.

5) Length of the fiber (Lfiber):
This information is not given in the problem, so we need additional information.

6) Length of the matrix (Lmatrix):
This information is not given in the problem, so we need additional information.

Once we have the values for Afiber, Amatrix, Lfiber, and Lmatrix, we can calculate the volume fraction (Vf) using the formula mentioned earlier.

Please provide the additional information about the lengths of the fiber and matrix so that we can proceed with the calculation.