$6-12$ A $1-$in$-$diameter solid round bar has a groove $0\mathrm{.}1-$in deep with a $0\mathrm{.}1-$in radius machined into it$.$ The bar is made of AISI $1020$ CD steel and is subjected to a purely reversing torque of $1800$ lbf $-$ in$.$

$($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.