$(4)$ 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 XYZ$0$ lbf $.$ in$.$ For the $S-N$ curve of this material, let $f=0\mathrm{.}9.($Where $xYZ$ are the last three digits of your rocket number. For example, a rocket number $140613$ will have $x=6,Y=1,$ and $Z=3$ and the reversing torque will by $6130$ lbf $.$ in $(5$ points$)$

$($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.