Random distributions of initial porosity trigger regular necking patterns at high strain rates

Abstract

At high strain rates, the fragmentation of expanding structures of ductile materials, in general, starts by the localization of plastic deformation in multiple necks. Two distinct mechanisms have been proposed to explain multiple necking and fragmentation process in ductile materials. One view is that the necking pattern is related to the distribution of material properties and defects. The second view is that it is due to the activation of specific instability modes of the structure. Following this, we investigate the emergence of necking patterns in porous ductile bars subjected to dynamic stretching at strain rates varying from 10 to 0.5×10 using finite-element calculations and linear stability analysis. In the calculations, the initial porosity (representative of the material defects) varies randomly along the bar. The computations revealed that, while the random distribution of initial porosity triggers the necking pattern, it barely affects the average neck spacing, especially, at higher strain rates. The average neck spacings obtained from the calculations are in close agreement with the predictions of the linear stability analysis. Our results also reveal that the necking pattern does not begin when the Considère condition is reached but is significantly delayed due to the stabilizing effect of inertia.

Dynamics of Necking and Fracture in Ductile Porous Materials

“…In the calculations, the material is modeled using a constitutive framework that includes many of the hardening and softening mechanisms that are characteristics of ductile metallic materials, such as strain hardening, strain rate hardening, thermal softening and damage-induced softening. The contribution of the inertia effect to the loading process is evaluated through a dimensionless parameter that com-locities delay the onset of plastic flow localization (and necking) and gives rise to a post-critical deformation regime [4,17], so that the necks are not incepted at the maximum load (or Considère strain) and are significantly delayed [21]. Intuitively, neck retardation due to the stabilizing effects of inertia will also delay fragmentation as necking is often the precursor to fracture in ductile metallic materials.…”

“…Several authors have carried out finite element calculations of multiple necking in dynamically expanding circular rings, or in long cylindrical bars with initial conditions consistent with the expanding ring [13,17,[20][21][22]. For the initial and boundary conditions applied in these finite element calculations, in the absence of any perturbation, the ring expands or the bar stretches uniformly during loading, according to the fundamental solution of the problem, and localization never occurs [21]. In order to break the symmetry of the problem and trigger localization a perturbation such as geometric or material heterogeneity is readily introduced [20][21][22].…”

“…For the initial and boundary conditions applied in these finite element calculations, in the absence of any perturbation, the ring expands or the bar stretches uniformly during loading, according to the fundamental solution of the problem, and localization never occurs [21]. In order to break the symmetry of the problem and trigger localization a perturbation such as geometric or material heterogeneity is readily introduced [20][21][22]. Note, that some commercial finite element codes such as ABAQUS/Explicit [23], introduce numerical perturbations (likely due to round-off errors) that are sufficient to break the symmetry and trigger localization [13,17,20].…”

“…The amplitude and distribution of the geometrical or material heterogeneities have been shown to affect the multiple necking pattern (i.e. number, location and growth of the necks) at low loading rates [21,22]. However, at high loading rates where inertia effects dominate, the effect of geometrical or material heterogeneities on multiple necking pattern becomes less significant [21,22].…”

“…number, location and growth of the necks) at low loading rates [21,22]. However, at high loading rates where inertia effects dominate, the effect of geometrical or material heterogeneities on multiple necking pattern becomes less significant [21,22]. Furthermore, it has also been shown that the variations in material properties that greatly affect the multiple necking pattern and fragmentation at relatively low loading rates [13] becomes less significant at high loading rates [17].…”