Numerical analysis of necking conditions in a thermoviscoplastic rod in tension

Necking conditions in a thermoviscoplastic rod in tension are studied with allowance for heat transfer within a broad range of strain rates and temperatures. The problem is solved in a long-wave approximation by the methods of linear perturbation analysis. The effect of the amplitude of the perturbations on the stability of plastic deformation is studied by means of nonlinear analysis. The calculations show that: (1) a neck is formed during tension of a solid rod for the values of the parameters realized in the experiment; (2) the critical strain during active tension depends appreciably on the wave number, particularly in the region of small wave numbers; 3) the critical strain does not depend significantly on the wave number at low strain rates.