Current Attempt in Progress

$$ Incorrect.

It is desired to produce and aligned carbon fiber$-$epoxy matrix composite having a longitudinal tensile strength of $610$ MPa $.$ Calculate $($a$)$ the critical fiber length, and $($b$)$ the volume fraction of fibers necessary if

$(1)$ the average fiber diameter is $0\mathrm{.}029$ mm $,$

$(2)$ the average fiber length is $2\mathrm{.}2$ mm $,$

$(3)$ the fiber fracture strength is $5000$ MPa $,$

$(4)$ the fiber$-$matrix bond strength is $18$ MPa $,$

$(5)$ the matrix stress at fiber failure is $17\mathrm{.}6$ MPa $.$

$($a$)$

$0\mathrm{.}211$

mm