Effect of an electric current on necking in a tensile rod

Necking conditions in a tensile thermoviscoplastic rod with passage through it of an alternating electric current are studied. Modeling is performed with allowance for the complex constitutive relations for the rod material, heat transfer in the rod, and the current distribution across the section of the rod as a function of the current frequency (skin effect). The stability of uniform tension is examined by linear analysis of perturbations using the Routh–Hurwitz theory. The results were refined by nonlinear analysis taking into account the effect of the amplitude curve of perturbations on the stability of plastic deformation.