Identification of the critical wavelength responsible for the fragmentation of ductile rings expanding at very high strain rates

This work examines the mechanisms governing the fragmentation of ductile rings expanding at very high strain rates. Based on previous works three different methodologies have been addressed, namely: fully 3D finite element computations of the radial expansion of ductile rings, numerical simulations of unitary axisymmetric cells with sinusoidal spatial imperfections subjected to tensile loading and a linear perturbation technique derived within a quasi-1D theoretical framework. The results derived from these three different approaches allow for identification of a critical wavelength which dictates the fragmentation of ductile rings expanding at very high strain rates. This critical wavelength is revealed quite independent of the material properties but closely related to the ratio ( L 0 / ϕ 0 ) critical ≈ 1.5 where L0 is the fragment size and ϕ 0 is the diameter of the circular section of the ring. This work highlights the fundamental role played by material inertia in the fragmentation at very high strain rates, setting aside the mechanisms associated to the classical statistical theories.