Solution (source code)

= Solution

\b[<Irradiation creep> adds stress-directed, time-dependent strain driven by the irradiation-generated defect population.] It can be appreciable where ordinary thermal <material creep> would be slow, because <irradiation> maintains mobile <point defects> far above their equilibrium populations.

Absorption or emission of <vacancies> and <self-interstitials> permits <dislocation climb>. Applied <stress> can make differently oriented <dislocations> or <dislocation loops> absorb defects at different rates: <stress-induced preferential absorption> then produces a directional strain. Climb can also allow a pinned <dislocation> to bypass an obstacle and continue <dislocation glide>, providing a second route to strain.

A useful small-strain empirical form, over a limited range of conditions, is
$$
\dot\varepsilon_{\rm irr}=B\sigma\dot d,
\qquad
\varepsilon_{\rm irr}\simeq B\sigma d
$$
for constant <stress> $\sigma$ and approximately constant irradiation-creep compliance $B$. Here $d$ is the accumulated <displacements per atom> and $\dot d$ the <displacement dose rate>; $B$ is measured per unit <stress> and per unit dpa. This relation explains why creep can scale approximately with both <stress> and <neutron flux> when the damage spectrum is fixed. It is not a constitutive law valid at every dose or <temperature>.

The total strain can also include thermal <material creep>, <void swelling>, <irradiation growth> and changes due to precipitation or recovery. Stress-free swelling is not itself <irradiation creep>. Experiments on pressurized type316 tubes separated these contributions and found that correcting stress-enhanced swelling materially affected comparisons between annealed and specimens strengthened by <cold working>.<The influence of cold-work level on the irradiation creep and swelling of AISI 316 stainless steel by E. R. Gilbert and F. A. Garner>[PNNL publication abstract; Journal of Nuclear Materials 367–370, pp.954–959, experimental separation of creep, swelling and precipitation strains]{ref}

At sufficiently high <temperature>, thermal <material creep> can dominate. Changes in <microstructure> caused by <irradiation hardening>, softening, bubbles and cavities can either alter the creep rate or shorten rupture life. Thus enhanced defect-driven creep is the central effect, while the net rate and lifetime remain material- and history-dependent.