A space rocket motor casing is fabricated from a Cr$-$Mo low alloy stuel of vield stress of $1230$ MPa $,$ in the form a long cylinder of diameter $0,6m$ and wall thicknese $3\mathrm{.}0$ mri $,$ The design pressure at the highest thrust is $10$ APa $.$ The Critical Crack Tip Opering Digplacement $($CTOD$)$ measured in a small test plece is $50m$ and Youne's modulus is $200$ GPij $,($assume the plane atreas is valid as the section thickness is small$)$

a$)$ What are the fracture parametors typically used in Elasto$-$Plastic Fracture Mechanics?

b$)$ Cilculate the largest crack size that could be colerated in the rocket motor cage, without the risk of fallure at blast$-$off?

c$)$ What is the plastic zone size at the crack tip? Does it satiofy plane stress assumptions?

$($:$r_1=\frac{k_i}{k_2}$