An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of $39$MPa$\sqrt[\phantom{2}]{m}.$ It has been determined that fracture results at a stress of $211$MPa when the maximum $($or critical$)$ internal crack length is $2\mathrm{.}83mm.$

a$)$ Determine the value of $Y_{}\sqrt[\phantom{2}]{a}$ for this same component and alloy at a stress level of $274$MPa when the maximum internal crack length is $1\mathrm{.}42mm.$

MPa$\sqrt[\phantom{2}]{m}$

b$)$ Under these circumstances will the component fail?