Problem $1$

A small steel rod is to be utilized as a part in a high$-$performance automobile engine. The rod is made from a new ultra$-$high strength alloy steel known as HP $9-4-20($composition $\backslash (9\backslash \%\backslash$mathrm$\{$Ni$\},4\backslash \%\backslash$mathrm$\{$Co$\}\backslash )$ and $\backslash (0\mathrm{.}2\backslash \%\backslash$mathrm$\{$C$\}\backslash )),$ heat$-$treated by austenitizing, quenching and tempering at $\backslash (550^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ to give an ultimate tensile strength of $210$ ksi $.$ The rod must support in service a mean tensile stress of $60$ ksi $,$ but will also be subjected to an alternating stress $($of roughly constant amplitude$)$ superimposed on the mean stress. Allowing for a safety fraction of $3,$ what would be your recommendation for the maximum allowable alternating stress that the rod could withstand to last $\backslash (10^\{5\}\backslash )$ cycles.

Given the particular loading conditions that the rod must endure, suggest ways in which you might improve the fatigue resistance of the component.