Problem $5.(12$ pt$)$ Mechanical Properties

$($a$)$ Copper and nickel form a binary isomorphous system. Pure copper has a tensile strength $\backslash (\backslash$sim $220\backslash$mathrm$\{$MPa$\}\backslash )$ and pure nickel has a tensile strength $\backslash (\backslash$sim $340\backslash$mathrm$\{$MPa$\}\backslash ).$ For a $\backslash (50\backslash$mathrm$\{$wt$\}\backslash \%\backslash$mathrm$\{$Cu$\}\backslash )$ and $\backslash (50\backslash$mathrm$\{$wt$\}\backslash \%\backslash$mathrm$\{$Ni$\}\backslash )$ alloy, which of the following do you expect for the tensile strength and for ductility and explain why. $(4$ pts $)$

Tensile strength

i$.$ Tensile strength less than pure Cu

ii$.$Tensile strength between pure Cu and pure Ni

iii. Tensile strength higher than pure Ni

Ductility

i$.$ Ductility less than pure Cu

ii$.$ Ductility between pure Cu and pure Ni

iii. Ductility higher than pure Ni

$($b$)$ A structure component is to be fabricated from a metal alloy with a plane$-$strain fracture toughness of $\backslash (25\backslash$mathrm$\{$MPa$\}-\backslash$mathrm$\{$m$\}^\{1/2\}\backslash )$ and a yield strength of $860$ MPa $.$ The flaw size detection limit of the equipment is $3\mathrm{.}0$ mm $.$ If the design stress is one half of the yield strength and $\backslash (\backslash$mathrm$\{$Y$\}=1\mathrm{.}0\backslash ),$ determine whether a critical flaw for this component is subject to detection. $(8$ pt $)$