Question

t is desired to produce aligned carbon fiber-epoxy matric composite having a longitudinal tensile strength of 800 MPa. Given (a) the average fiber diameter and length are 0.01 7 mm and 2.3 mm, respectively, (b) the fiber fracture strength is 5500 MpPa. (c) the fiber- matric bond strength is 18 Mpa, and (d) the matric stress at fiber failure is 13.5 Mpa. Calculate (a) the critical fiber tength and (b) the volume fraction of fibers

Answer 1

Answer:

The value of critical length = 3.46 mm

The value of volume of fraction of fibers = 0.43

Explanation:

Given data

$\sigma_{T}$ =  800 M pa

D = 0.017 mm

L = 2.3 mm

$\sigma_{f}$ = 5500 M pa

$\sigma_{m}$ = 18 M pa

$\sigma_c$ = 13.5 M pa

(a) Critical fiber length is given by

$L_{c} = \sigma_{f} (\frac{D}{2 \sigma_{c} } )$

Put all the values in above equation we get

$L_{c} =5500 (\frac{0.017}{(2) (13.5)} )$

$L_{c} = 3.46$ mm

This is the value of critical length.

(b).Since this  critical length is greater than fiber length Than the volume fraction of fibers is given by

$V_{f} = \frac{\sigma_T - \sigma_m}{\frac{L\sigma_c}{D} - \sigma_m }$

Put all the values in above formula we get

$V_{f} = \frac{800-18}{\frac{(2.3)(13.5)}{0.017} - 18 }$

$V_{f}$ = 0.43

This is the value of volume of fraction of fibers.