Where, for surface flaws:

$K=1\mathrm{.}1(\frac{a}{Q}{)}^{\frac{1}{2}}$

and for embedded flaws:

$K=(\frac{a}{Q}{)}^{\frac{1}{2}}$

A thick plate of steel contains a central through$-$thickness flaw of length $16$ mm $,$ which is

subjected to a stress of $350$ MPa applied perpendicularly to the flaw plane. The $0\mathrm{.}2\%$ flow stress

of the material is $1350$ MPa.

a$)$ Calculate the plastic zone size and the effective stress intensity $(K_{\text{e}\text{f}\text{f}\text{.}})$ at the crack tip,

making reasonable assumptions about the state of stress.

b$)$ If$,$ after heat treatment, the flow stress of the steel dropped to $800$ MPa $,$ what would the

plastic zone size be under the applied stress of $350$ MPa $,$ and what conclusions would you

draw about the use of LEFM $($with the small scale yielding $($SSY$)$ assumption$)?$

$($Note: if the plastic zone is less than $2-3\%$ of crack size, iteration is not required for computation$)$