Problem $3$

A component in the shape of a large sheet is to be fabricated from $4340$ steel, which has a fracture toughness $\backslash (\backslash$mathrm$\{$Kc$\}=98\mathrm{.}9\backslash$mathrm$\{$MPa$\}-\backslash$mathrm$\{$m$\}^\{0\mathrm{.}5\}\backslash )$ and a tensile yield strength of $860$ MPa $.$ The sheets are inspected for crack flaws after fabrication, but the inspection device cannot detect flaws smaller than $3$ mm central crack. The part is too heavy as designed. An engineer has suggested that the thickness be reduced and the material be heat$-$treated to increase its tensile strength to $1515$ MPa $,$ which would result in decreasing the fracture toughness to $60\mathrm{.}4\backslash (\backslash$mathrm$\{$MPa$\}-\backslash$mathrm$\{$m$\}^\{0\mathrm{.}5\}\backslash ).$ Assuming that the stress level does not exceed one half the yield strength, is the suggestion feasible? If not, why not?