Dynamic tension of a rod made of an ideally rigid-plastic material

A stress-strain state arising under dynamic tension of a homogeneous rod made of an incompressible ideally rigid-plastic material that satisfies the Mises–Hencky criterion is investigated. The possibility of thickening or thinning of the rod along its length is taken into account in an axisymmetric formulation, which makes it possible to simulate the formation and development of a neck. Three dimensionless time functions are introduced, one of which is a small geometric parameter, namely the ratio of an average radius to half the rod length. The ratios of the orders of smallness of the other two dimensionless functions to the small geometric parameter determine the influence of inertial terms in equations of motion on the stress and strain rate distribution. These ratios may vary at different time intervals, which determines one or another dynamic tension regimes. Two such characteristic regimes are revealed: one of them depends on a velocity at which the end sections move away from each other, and the other one depends on their acceleration. For the second regime, an asymptotic integration based analysis makes it possible to find the stress-strain state parameters, in which case this state is an “inertial correction” with respect to a quasistatic state in the rod with a cylindrical lateral surface.