Abstract: In this paper, the cyclic hardening behavior of 45 # steel and LY-12CZ aluminum alloy under proportional and non-proportional combined loadings of tension and torsion at normal room temperature has been investigated.The experimental results show that the cyclic hardening levels are different for different loading paths. The least is for the pure torsion, while the highest is for the circular path. The authors have especially investigated the effect of different cyclic history on the amplitudes of stabilized...