$8\mathrm{.}13$ An engineering member is to be made of an aluminum alloy. It is in the shape of a plate loaded in tension that may have a crack in one edge, as shown in Fig. $8\mathrm{.}12($c$).$ The dimensions are width $b=30mm$ and thickness $t=4\mathrm{.}0mm,$ and the crack may be as long as $a=6\mathrm{.}0mm.$ The member must resist a tension force of $P=7\mathrm{.}5kN.$

$($a$)$ For a safety factor of $2\mathrm{.}8$ against brittle fracture, what minimum fracture toughness $K_{Ic}$ is required?

$($b$)$ For a safety factor of $2\mathrm{.}0$ against fully plastic yielding, what minimum yield strength ${}_o$ is required?

$($c$)$ Given your results from $($a$)$ and $($b$),$ select an aluminum alloy from Table $8\mathrm{.}1$ that meets both requirements.