Answer :
Answer:
The value of critical length = 3.46 mm
The value of volume of fraction of fibers = 0.43
Explanation:
Given data
[tex]\sigma_{T}[/tex] = 800 M pa
D = 0.017 mm
L = 2.3 mm
[tex]\sigma_{f}[/tex] = 5500 M pa
[tex]\sigma_{m}[/tex] = 18 M pa
[tex]\sigma_c[/tex] = 13.5 M pa
(a) Critical fiber length is given by
[tex]L_{c} = \sigma_{f} (\frac{D}{2 \sigma_{c} } )[/tex]
Put all the values in above equation we get
[tex]L_{c} =5500 (\frac{0.017}{(2) (13.5)} )[/tex]
[tex]L_{c} = 3.46[/tex] 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
[tex]V_{f} = \frac{\sigma_T - \sigma_m}{\frac{L\sigma_c}{D} - \sigma_m }[/tex]
Put all the values in above formula we get
[tex]V_{f} = \frac{800-18}{\frac{(2.3)(13.5)}{0.017} - 18 }[/tex]
[tex]V_{f}[/tex] = 0.43
This is the value of volume of fraction of fibers.