A solid round bar, $25$ mm in diameter, has a grove $2\mathrm{.}5$ mm deep, with a $2\mathrm{.}5$ mm radius

machined into it$.$ The bar is made of AISI $1018$ CD steel and is subjected to purely reversing

torque $200N-m.$ For the S$-$N curve of this material, let $f=0\mathrm{.}9.$

$($A$)$ Find the number of cycles to failure.

$($B$)$ If the bar is also placed in an environment with a temperature of $450C,$ estimate the number

of cycles to failure.