A helical compression spring made from $4$ mm diameter chrome$-$silicon wire and has an outside diameter of $50$ mm with squared ends and $12$ total coils. The length of the spring is such that, when compressed solid, the torsional stress is $815$ MPa $.$

$1\mathrm{.}1$ Determine the spring rate.

$2538\mathrm{.}012\frac{N}{m}$

$1\mathrm{.}2$ Determine the free length of the spring. $209\mathrm{.}17$mm

$1\mathrm{.}3$ This is a shot$-$peened spring. Based on the Goodman fatigue failure locus witt Zimmerli data, determine whether a fatigue failure can be expected if the spring is cycled between the loads $F_{\text{m}\text{i}\text{n}}=50N$ and $F_{\text{m}\text{a}\text{x}}=400N.1\mathrm{.}13$MPa