The timing performance of silicon sensors bump-bonded to Timepix3 ASICs is investigated, prior to and after different types of irradiation up to $8 times 10^{15} 1 mathrm{,Mekern -0.1em V} mathrm{ ,n_{eq}} {mathrm{ ,cm}}^{-2}$. The sensors have been tested with a beam of charged particles in two different configurations, perpendicular to and almost parallel to the incident beam. The second approach, known as the grazing angles method, is shown to be a powerful method to investigate not only the charge collection, but also the time-to-threshold properties as a function of the depth at which the charges are liberated.