On the complete extinction of selected imperfection wavelengths in dynamically expanded ductile rings

Abstract

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.

Dynamic necking in materials with strain induced martensitic transformation

“…These results confirm that, when inertia controls the loading process, the inception of necks is a deterministic process, rather than a random one. This conclusion is consistent with the observations reported by the authors (Rodríguez-Martínez et al, 2013c).…”

“…The correction factor θ (Bridgman, 1952;Walsh, 1984;Fressengeas and Molinari, 1985) is used to take into account that, in case of necking, the local axial stress is enhanced by the hydrostatic stress. The use of this specialized form of the yield stress is a key point of the model since it allows for damping short wavelength modes, which is consistent with the results published by Rodríguez-Martínez et al (2013c). The factor θ is defined as…”

Dynamic Necking of Notched Tensile Bars: An Experimental Study

“…One should also note that those results all indicate the high level of reproducibility of the observations as to neck location. These results also reinforce previous conclusions found in Osovski et al [19], Sørensen and Freund [21] and Rodríguez-Martínez et al [22] as to the deterministic character of the neck location in dynamic tensile and ring expansion tests, respectively.…”

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

“…The localization is triggered by the numerical round-off which is sufficient to perturb the stress and strain fields. One should note that, although numerical round-offs are essential to trigger flow localization, the nature of the necking pattern is deterministic as recently discussed by Rodríguez-Martínez et al (2013).…”