= Solution
\b[<Irradiation softening> occurs when irradiation removes pre-existing strengthening obstacles faster than it creates new ones.] It is particularly plausible in an initially hardened <alloy>, rather than an initially soft annealed reference.
In a material strengthened by <cold working>, the starting <dislocation density> is high. Irradiation-generated <point defects> can assist <dislocation climb>, rearrangement and annihilation, reducing the contribution of <work hardening>. A schematic estimate is
$$
\sigma_y=\sigma_0+\alpha\mu b\sqrt{\rho_d}+\Delta\sigma_p+\Delta\sigma_{\rm irr},
$$
where $\mu$ is the <shear modulus>, $b$ the magnitude of the <Burgers vector>, $\rho_d$ the <dislocation density>, and the last two terms represent precipitate and irradiation-obstacle strengthening. It is an illustrative decomposition, not an exact additive law for every alloy. A sufficiently large decrease in the pre-existing contributions can exceed the increase in $\Delta\sigma_{\rm irr}$.
In a material strengthened by <precipitation hardening>, ballistic mixing can dissolve or disorder the original obstacles. <Radiation-enhanced diffusion> can change their composition or accelerate coarsening; increasing obstacle spacing can reduce strength. In an ordered alloy, irradiation-induced loss of order can also remove a strengthening contribution. None of these outcomes is inevitable: <irradiation> can instead create new strengthening precipitates.
The required conditions therefore include an appropriate initial <microstructure>, enough <displacement dose> to modify it, and a <temperature> and <displacement dose rate> at which obstacle removal or recovery can compete with new defect accumulation. Compare with an unirradiated specimen held for the same time at the same <temperature> to separate ordinary thermal aging from an irradiation effect.
A drop in <yield strength> or <hardness> need not restore <ductility>: cavities, <helium embrittlement> or localization of <dislocation glide> can coexist with softening. Conversely, an initially annealed <steel> may show strong <irradiation hardening> under the same exposure conditions.
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