A section of an engineering assembly includes three plates $A,B$ and $C,$ with

dimensions as shown in Figure $7.$ All three plates are manufactured from

aluminium with a yield strength of $300$ MPa and a fracture toughness, Kuc $,$ of

$20\mathrm{.}0$MPa$\sqrt[\phantom{2}]{m}$

Plates A and B are connected using a single$-$shear adhesive bonded lap joint

with an overlap of $75\mathrm{.}0$ mm $.$ The shear strength of the adhesive is $1\mathrm{.}00$ MPa $.$

Plates B and C are welded together at their ends. Visual inspection reveals that

there is a $40\mathrm{.}0$ mm long crack$-$like flaw in the middle of the weld, as shown in

Figure $7.$

The assembly experiences a tensile load of $20\mathrm{.}0$ kN applied to the ends of the

plates, which is greater than the highest expected design load for the assembly.

Figure $7$ Figure for Question $11-$ a section of an engineering assembly including

three plates A$,$ B and C$,$ that are connected using a single$-$shear adhesive

bonded lap joint and a welded joint

Figure $8$ shows the $Y-$calibration for a finite$-$width centre$-$cracked plate loaded in

tension.

Figure $8$ Figure for Question $11-$ Y$-$calibration for a finite$-$width centre$-$cracked

plate loaded in tension

$($a$)($i$)$ What is the average shear stress in the single$-$shear adhesive bonded lap joint due to the applied load? State your answer to $3$ significant figures.

$($ii$)$ Assuming that the flaw in the weld behaves as a sharp centre crack, Calculate the stress intensity factor, KI$,$ for the crack? State your answer to $3$ significant figures.

$($b$)($i$)$ Based on your answers to part $($a$)$ determine whether the assembly will fail under the load experienced and, if it fails, where the failure would first occur. Consider both the adhesive joint and the weld in your answer. $($ii$)$ What is the maximum flaw size that the weld could sustain without fracture at the load experienced?

$($c$)$ Suggest three possible changes that could be made to the assembly to increase its strength.