$6-12$ A $25-mm-$diameter solid round bar has a groove $2\mathrm{.}5-mm$ deep with a $2\mathrm{.}5-mm$ radius machined into it$.$ The bar is made of AISI $1020$ CD steel and is subjected to a purely reversing torque of $200N.m.$ For the $S-N$ curve of this material, let $f=0\mathrm{.}9.$

$($a$)$ Estimate the number of cycles to failure.

$($b$)$ If the bar is also placed in an environment with a temperature of $750F,$ estimate the number of cycles to failure.