On the interplay between material flaws and dynamic necking

Abstract

In this paper we investigate the interplay between material defects and flow localization in elastoplastic bars subjected to dynamic tension. For that task, we have developed a 1D finite difference scheme within a large deformation framework in which the material is modelled using rate-dependent J 2 plasticity. A perturbation of the initial yield stress is introduced in each node of the finite difference mesh to model localized material flaws. Numerical computations are carried out within a wide spectrum of strain rates ranging from 500 s −1 to 2500 s −1 . On the one hand, our calculations reveal the effect of the material defects in the necking process. On the other hand, our results show that the necking inception, instead of being a random type process, is the deterministic result of the interplay between the mechanical behaviour of the material and the boundary conditions. This conclusion agrees with the experimental evidence reported by Rittel et al. [1] and Rotbaum et al.[2].

Non-uniform distributions of initial porosity in metallic materials affect the growth rate of necking instabilities in flat tensile samples subjected to dynamic loading

“…The specific nodes with positive initial porosity are selected randomly using the function randperm of MATLAB. Each of these nodes has allotted a random value of initial porosity that was generated using the normal distribution function normrnd (see [24]) which is also pre-implemented in MATLAB. The mean of this distribution is µ = f 0 /P and the standard deviation is σ = µC v , where the relative standard deviation, C v , determines the maximum dispersion of the generated random values of porosity.…”