Shown below is the relationship between the stress$-$intensity factor, $K_{\text{I}},$ crack length and internal pressure for a radially cracked cylindrical pressure vessel used for the Space Shuttle air filtration system. If the vessel is fabricated from $2024-$T$351$ aluminum alloy with a measured fracture toughness of $44$MPa$-m^{\frac{1}{2}},r_i=8cm,$ and $r_0=10cm,$ what internal pressure is indicated for:

a$.$ Crack initiation $($assume $a={10}^{-2}mm)$ as source of fracture.

b$.$ Leak before break $($crack is through wall but no catastrophic failure$).$