On the interplay between strain rate and strain rate sensitivity on flow localization in the dynamic expansion of ductile rings

In this work a stability analysis on flow localization in the dynamic expansion of ductile rings is conducted. Within a 1-D theoretical framework, the boundary value problem of a radially expanding thin ring is posed. Based on a previous work, the equations governing the stretching process of the expanding ring are derived and solved using a linear perturbation method. Then, three different perfectly plastic material constitutive behaviours are analysed: the rate independent material, the rate dependent material showing constant logarithmic rate sensitivity and the rate dependent material showing non-constant and non-monotonic logarithmic rate sensitivity. The latter allows to investigate the interaction between inertia and strain rate sensitivity on necking formation. The main feature of this work is rationally demonstrate that under certain loading conditions and material behaviours: (1) decreasing rate sensitivity may not lead to more unstable material, (2) increasing loading rate may not lead to more stable material. This finding reveals that the relation between rate sensitivity and loading rate controls the unstable flow growth. Additionally a finite element model of the ring expansion problem is built in ABAQUS/Explicit. The stability analysis properly reflects the results obtained from the numerical simulations. Both procedures, perturbation analysis and numerical simulations, allow for emphasizing the interplay between rate sensitivity and inertia on strain localization.