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

Abstract

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.

The deterministic nature of the fracture location in the dynamic tensile testing of steel sheets

“…In this section we aim at uncovering the role played by the initial conditions, the boundary conditions and the sample slenderness on the formation of multiple localization patterns. The way in which these factors either favour or preclude the emergence of multiple necking bands has been hardly investigated in the literature [73], thus we intend to give some indications about it here. Fig.…”

Effect of the third invariant on the formation of necking instabilities in ductile plates subjected to plane strain tension

“…On the other hand, while the same rationale has been employed by other authors, e.g. Zaera et al [52] and N'souglo et al [35], we are aware that it is also customary in the literature to impose the stretch rate as the loading condition [49,34], since it may bear closer resemblance to the actual boundary conditions in dynamic experiments like the expansion of hemispherical shells (see Mercier et al [30]). Hence, stability analysis results and finite element calculations obtained imposing the stretching rate, namelyε 0 xx = 4000 s −1 andε 0 xx = 80000 s −1 , are reported in Appendix A.…”

Multiple necking patterns in elasto-plastic rings subjected to rapid radial expansion: The effect of random distributions of geometric imperfections

“…Furthermore, we think that the overall trends and conclusions obtained in this paper are still valid for actual materials with flow stress dependent on strain, strain rate and temperature. On other hand, previous works reported in the literature suggested that strain hardening delays necking formation [20], the strain rate hardening increases the necking strain and the average spacing between necks [21], and the thermal softening promotes early formation of necks and leads to the decrease of the distance between consecutive necks [46]. Nevertheless, determining to which amount strain, strain rate and temperature affect the necking pattern at high strain rates, when inertia effects are important, still requires further research.…”