Proton irradiation will produce a high density of point defects inside your sample of Zr, particularly vacancies and self-interstitials. Then, the curve of the potential interaction of atoms will be locally modified. As the elastic modulus is given by the second derivative of the curve of atomic potential energy, it is expected a variation of the modulus.
It could be also expected an anelastic relaxation linked to the evolution of the atomic defects created by the irradiation, when their recovery would be thermally activated.
I beilieve that these changes before and after irradiation and also after annealing, could be observed through precise measurents of modulus by nanoindentation. Good luck.