Question

Compute the longitudinal strength of an aligned carbon fiber-epoxy matrix composite having a 0.25 volume fraction of fibers, assuming the following: (1) an average fiber diameter of 10  10-3 mm, (2) an average fiber length of 1 mm, (3) a fiber fracture strength of 2.5 GPa, (4) a fiber-matrix bond strength of 10 MPa, (5) a matrix stress at fiber failure of 10.0 MPa, and (6) a matrix tensile strength of 75 MPa.

Answer 1

Answer:

632.5 MPa

Explanation:

$\sigma_{m}$ = Matrix stress at fiber failure = 10 MPa

$V_f$ = Volume fraction of fiber = 0.25

$\sigma_f$ = Fiber fracture strength = 2.5 GPa

The longitudinal strength of a composite is given by

$\sigma_{cl}=\sigma_{m}(1-V_f)+\sigma_fV_f\\\Rightarrow \sigma_{cl}=10(1-0.25)+(2.5\times 10^3)\times 0.25\\\Rightarrow \sigma_{cl}=632.5\ MPa$

The longitudinal strength of the aligned carbon fiber-epoxy matrix composite is 632.5 MPa