A. (2013). Identification of the critical wavelength responsible for the fragmentation of ductile rings expanding at very high strain rates. Solids, 61, 6, 1357- Journal of the Mechanics and Physics of ández-Sáez tériaux UniversitéThis 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 axisymm etric 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 L 0 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.

a b s t r a c tIn this work the inception and development of multiple necks in dynamically expanded ductile rings with ab initio geometric imperfections has been addressed. Finite element simulations and linear perturbation analysis have been applied for that task. In the numerical calculations a selected wavelength is included into the model defining along the circumference of the ring an array of periodic geometric imperfections of predefined amplitude. In the stability analysis a perturbation of a given mode is added to the background solution and the growth rate of the perturbation is evaluated. The attention has been focused on the extinction of both long and short wavelength imperfections and the appearance of a dominant necking pattern which emerges when the geometric imperfections are vanished. The role played by the loading rate on the extinction of imperfections is also addressed. Moreover, the necking strain is found to be dependent on the imperfection pattern and the loading rate. Its maximum value is registered for the loading cases in which the initial imperfections distribution is completely extinguished.

Diffuse or localized dynamic necking of a sheet metal is a major issue in high speed forming processes, leading to unacceptable thinning and even failure if fully developed, and in the dynamic behaviour of metallic structural elements of small thickness used for energy absorption purposes. This process is frequently related to the collective development of localization bands resulting in a necking pattern which depends on the sheet properties and on the loading conditions. This work investigates the spacing between necking bands in sheets made of a thermoviscoplastic metal and submitted to dynamic biaxial loading. For that task a linear perturbation technique, derived within a 2D framework which specifically accounts for stress triaxiality effects upon strain localization, has been developed. Using this methodology, a dominant instability mode can be identified, whose wavelength is related to the necking-band spacing. Likewise, fully 3D finite element simulations have been performed in order to verify and complement the outcomes of the aforementioned theoretical approach. The effects of loading conditions (loading path and loading rate), and thermal coupling on the stability of the deformation process and on the distance between necking bands are examined. We have shown that the neck spacing increases with the ratio of strains and decreases with the loading rate and the temperature rise.

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