$(2$ points$)$ A large steel alloy plate designed for a new building has a plain$-$strain fracture toughness of $98\mathrm{.}8$ MPa $\sqrt[\phantom{2}]{m}$ and a yield strength of $860$ MPa $.$

The tool for finding flaws can only find cracks that are larger than $3$ mm $.$

If the design stress is one$-$half the yield strength and the value of $Y=1\mathrm{.}0,$ determine if a critical flaw for this plate would be detected.

Hint: Assume the worst case scenario between internal vs$.$ surface crack.

$(2$ points$)$ The following data was gathered from a series of Charpy impact tests on $4340$ steel alloys.

$\backslash$table$[[$Temperature $(C),$Impact Energy $($J$)],[0,105],[-25,104],[-50,103],[-75,97],[-100,63],[-113,40],[-125,34],[-150,28],[-175,25],[-200,24]]$

$($a$)$ Plot the data as impact energy versus temperature.

$($b$)$ Determine a ductile$-$to$-$brittle transition temperature by averaging the the maximum and minimum impact energies, then find the temperature that corresponds to this average number.

$($c$)$ Determine a ductile$-$to$-$brittle transition temperature as the temperature where the impact energy is $50$ J $.$