A stiffener in an aircraft structure is a $T$ section is made out of $7075-T651$ aluminium $(K_{IC}=30$ MPa$\sqrt[\phantom{2}]{m},{}_{Ys}=550$MPa $)$ as shown in the figure below. A crack of length $"a"$ may be present in the stiffener. A bending moment of $200N.m$ is applied about the $x-$axis such that the crack is subjected to tensile stresses. $($Assume $K=F****\sqrt[\phantom{2}]{a},$ where $F=1\mathrm{.}75)$

a$)$ What are the fracture parameters used in Linear Elastic Fracture Mechanics?

b$)$ What is the largest crack length $"$a$"$ that can be permitted if the factor of safety against brittle fracture of $3\mathrm{.}0$ considered adequate?

c$)$ Consider the possibility of making a change to a more expensive material $7475-77351$ aluminium alloy $(K_{IC}=50$MPa$\sqrt[\phantom{2}]{m},{}_{YS}=450$MPa $).$ What are the possible advantages and disadvantages of making this change? Support your comments with calculations?