Ductile Fracture of Rapidly Expanding Rings

Abstract

Heterogeneous plastic deformation (necking) of thin ductile rings given an initial outward impulse is described in terms of the ordinary differential equations of thermoplasticity and the partial differential equations of mass and momentum conservation in one spatial dimension (circumference) and time. Flaws in cross-sectional area and porosity are introduced and the resulting plastic deformation is calculated numerically for a prescribed initial radial velocity. Plastic deformation is initially homogeneous but soon concentrates in the weakest region, which then thins rapidly and fractures. Effects of flaw wavelength, work-hardening rate, thermal softening, and rate-dependent plastic flow on the flaw growth rate are studied.