Finite element simulation of steel ring fragmentation under radial expansion

This paper presents a numerical analysis of the expansion of a mild steel ring with of 50 mm diameter, 1 mm thickness and a cross section of 1 mm2. A hardening relation which takes into account strain, strain rate and temperature is proposed to define precisely the thermoviscoplastic behaviour of the material considered in the study. As a second step, an algorithm to integrate the thermoviscoplastic constitutive equations, including the hardening law, is implemented in the commercial finite element code ABAQUS/Explicit via a user subroutine. Finally, this tool is used to simulate the problem of a ring expanding radially in a broad range of strain rates, covering both low and high initial velocities (from 1 to 370 m/s). The aim is to analyse the effect of loading velocity on the number of fragments resulting from the multiple failure of the ring and also the influence of the hardening behaviour of the material on the number of fragments and on the failure mode of the ring, considering different values of the plastic strain hardening exponent n0. A simple failure criterion was used, based on a critical value of the equivalent strain which depends on the hardening exponent. The numerical predictions, in perfect agreement with the experimental observations, are compared with several analytical or numerical models used to solve the same problem in other materials such as aluminium, steel or copper.