Question $2$

A $60mm$ wide sample plate of $7074-$T$8$ aluminium alloys is shown in Fig. Q$2$ and it contains a

central crack length, $2$a$,$ and fracture toughness, $K_c=22,200,000N{m}^{-\frac{3}{2}}$ and the yield strength, ${}_y$

$=520,000,000\frac{N}{m^2}.$

Fig. Q$2$: A $7074-$T$8$ aluminum alloys plate.

$($A$)$ If the applied stress, $=150,000,000\frac{N}{m^2},$ determine if the plate will fracture for a crack

half$-$length of $6mm.$

$($B$)$ Determine the critical half crack$-$length, $ac,$ below which the plate will fail by yielding $($Take

$Y=1).$