Effect of velocity on flow localization in tension

Abstract

One-dimensional dynamic numerical simulations of sheet tensile tests and expanding ring tests have been carried out to study the variation of ductility over a wide range of deformation velocities where inertial effects are significant. For materials following the Hollomon-type constitutive law with power-law strain rate sensitivity, the results showed that ductility in both tests is invariant to velocity at low test velocity. Beyond certain velocities, as the test velocity increases, ductility of a tensile specimen first increases, fluctuates with velocity at higher rates and finally drops rapidly. However, in ring expansion ductility increases monotonically. This predicted behavior is quite consistent with experimental observations, suggesting that inertial effects are likely to be a first-order factor responsible for enhanced ductility observed in high velocity deformation. To characterize the velocity-dependent behavior of ductility, two critical velocities in the tensile test and one critical velocity in the expanding ring tests were defined and numerically determined as a function of material parameters. For rate-insensitive materials, these values can be simply estimated in closed-form.