Irradiation of nanotube structures with electron and ion beams has been used to produce functionalized nanotubes and fundamentally new structures, including junctions. Here, we build on previous studies to investigate the low-energy electron and ion (Ar and CF3) beam irradiation of triple walled carbon nanotubes that consist entirely of either chiral or armchair tubes. Effective incident energies of 50 eV/ion and 50 keV/electron are considered. The approach is classical molecular dynamic simulations using reactive empirical bond-order potentials and the primary knock-on atom approach to model the effects of electron irradiation. The results indicate that these various irradiation processes produce local damage to the nanotubes that includes crosslinking, that the degree of damage depends to some degree on the chirality of the nanotubes, and that the radial distribution of crosslinks depends significantly on the irradiating particle. Importantly, the effect of these crosslinks, and their radial distribution along the circumference of the nanotube, on the tendency of multiwalled nanotubes to fail by the sword-in-sheath mechanism is examined.