Pr$.3\{$SEE APPENDIX$\}(20$ points$)$

Using the Larson$-$Miller data for an S$-590$ alloy as shown, predict the time to rupture for a component that is subjected to a stress of $500$ MPa at a temperature of $600$ degrees $C(873K).$ Show vour calculations.

Pr$.4(20$ points$)$

Shown is the S$-$N curves for several metal alloys

A cylindrical bar of $1045$ steel having the S$-$N behavior shown in the figure below is subjected to rotating$-$bending tests with reversed stress cycles. If the bar diameter is $15$ mm $,$ determine the maximum cyclic load that may be applied to ensure that fatigue failure will not occur. Use a factor of safety of four. The distance between the load bearing points is $60$ mm $.$

Use: $=\frac{16FL}{d^{3}o}$

Figure $8\mathrm{.}21$ Maximum stress $(S)$ versus logarithm of the number of cycles to fatigue failure $(N)$ for seven metal alloys. Curves were generated using rotatingbending and reversed$-$cycle tests. $($Reproduced with permission of ASM International, Materials Park, OH$,44073$: ASM Handbook, Vol. I, Properties and Selection: Irons, Steels, and High$-$Performance Alloys, $1990$; ASM Handbook, Vol. $2,$ Properties and Selection; Nonferrous Alloys and SpecialPurpose Materials, $1990$; G$.$ M$.$ Sinclair and W$.$ J$.$ Craig, "Influence of Grain Size on Work Hardening and Fatigue Characteristics of Alpha Brass," Transactions of ASM, Vol. $44,1952.)$