= Solution
<Orowan bypass> bows a <dislocation> around an unshearable obstacle and leaves a loop. A <dislocation line-tension estimate> for a segment with tension $T_\ell$ gives the limiting shear-stress scale
$$
\Delta\tau\simeq\frac{2T_\ell}{b\ell},
$$
where $\ell$ is a free obstacle gap on the slip plane. For an FCC perfect <dislocation>,
$$
b=\frac a{\sqrt2}
=\frac{0.36}{\sqrt2}\ {\rm nm}
\simeq0.2546\ {\rm nm}.
$$
Using $T_\ell\simeq Gb^2/2$ and the simple gap estimate $\ell\simeq L-d\simeq0.34\ {\rm \mu m}$ gives
$$
\boxed{\Delta\tau\simeq\frac{Gb}{\ell}
\simeq5.5\times10^7\ {\rm Pa}.}
$$
Converting to tensile <stress> requires an orientation factor. With an explicitly assumed polycrystalline FCC <Taylor factor> $M\simeq3$,
$$
\boxed{\Delta\sigma_y\simeq M\Delta\tau
\sim(1.6\text{--}1.7)\times10^8\ {\rm Pa}\approx160\text{--}170\ {\rm MPa}.}
$$
The graph and spacing approximations do not justify a precise last digit. A favorably oriented single crystal with Schmid factor1/2 would instead give $\Delta\sigma_y\simeq2\Delta\tau$, around110MPa.
This is a line-tension estimate. A true slip-plane obstacle distribution, line character, logarithmic elastic corrections and <precipitate> size distribution are not specified. If the quoted pitch is used directly as an effective free spacing, neglecting diameter, the same simplified calculation gives $\Delta\tau\simeq19\ {\rm MPa}$ and $M\Delta\tau\simeq57\ {\rm MPa}$. The larger gap-corrected estimate explicitly uses the size inferred above; the tensile factor and spacing convention must not be silently treated as provided measurements.
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