Collective behaviour and spacing of necks in ductile plates subjected to dynamic biaxial loading

• Plastic instabilities in metallic sheets subjected to dynamic biaxial stretching are analysed.
• Two methodologies have been used: a linearized stability analysis and finite element simulations.
• The role of loading rate and thermal coupling is uncovered.
• The effect of the loading path on necking strain and necking pattern is highlighted.

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.