The ATLAS experiment at the LHC will replace its current inner tracker system for the HL-LHC era. 3D silicon pixel sensors are being considered as radiation-hard candidates for the innermost layers of the new fully silicon-based tracking detector. 3D sensors with a small pixel size of $mathrm{50 times 50~mu m^{2}}$ and $mathrm{25 times 100~mu m^{2}}$ compatible with the first prototype ASIC for the HL-LHC, the RD53A chip, have been studied in beam tests after uniform irradiation to $mathrm{5 times 10^{15}~n_{eq}/cm^{2}}$. An operation voltage of only 50 V is needed to achieve a 97% hit efficiency after this fluence.