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

632.5 MPa

Step-by-step 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* 10^3)* 0.25\\\Rightarrow \sigma_(cl)=632.5\ MPa`

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