The possibility of shock hardening the weld heat affected zones of 5010 and 6063 aluminium alloys was studied using high energy electron beams (HEEB). The welded samples were irradiated for 5 s, at 6 mA current beam and 10 MeV beam energy with different doses statically by a Rudotron non-linear accelerator. A mathematical model to find the ratio between measured variables, the hardness before irradiation hb, the hardness after irradiation ha, and the distance from the centre of the weld D, is discussed in the framework of the least squares method. The ratio between the three variables is ha=Ahb + CD, therefore (dha/dhb)d=Cte and (dha/dD)d=Cte. SE/506
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