Why does necking ignore notches in dynamic tension?

Abstract

Abstract. Recent experimental work has revealed that necking of tensile specimens, subjected to dynamic loading, is a deterministic phenomenon, governed by the applied boundary conditions. Furthermore it was shown that the potential sited, dictated by the boundary conditions, may prevail even in the presence of a notch, thus necking may occur away of the notched region. The present paper combines experimental and numerical work to address this issue. Specifically, it is shown that the dynamic tensile failure locus is dictated by both the applied velocity boundary condition and the material mechanical properties, specifically strain-rate sensitivity and strain-rate hardening. It is shown that at sufficiently high impact velocities, the flows stress in the notch vicinity becomes quite higher than in the rest of the specimen, so that while the former resists deformation, it transfers the load to the latter, resulting in the formation of a local neck and failure away from the notch. Small local perturbations in the material properties are shown to be sufficient to stabilize the structure under local failure until a neck forms elsewhere. While the physical observations are quite counterintuitive with respect to the engineering views of stress concentrator's effect, the present work rationalizes those observations and also provides information for the designers of dynamically tensioned structures that may contain notches or similar flaws.

On the interplay between material flaws and dynamic necking

“…While material defects may play a role in the necking process, this fact does not entail that the inception of dynamic necks has random character. On the contrary, our results show that, in agreement with the experimental findings of Rittel et al [1] and Rotbaum et al [2], the location and development of dynamic necks is the result of the interplay between material behaviour and boundary conditions. Nevertheless, further investigations are required to check the validity of our conclusions with materials and specimens different from those used in this paper.…”

“…We carry our finite difference calculations within the spectrum of impact velocities 3 m/s ≤ V imp ≤ 15 m/s which is attained in typical Split Hopkinson Tensile Bar experiments [1,2]. The applied velocities lead to initial strain rates which range between 500 s −1 and 2500 s −1 .…”

“…2), as a typical tensile specimen. The dimensions of the bar correspond to samples used in Split Hopkinson Tensile Bar experiments [2,14]. The problem is posed in one-dimensional form.…”

“…It has been frequently assumed in the literature that, despite the stress waves intervention within the specimen, the necking inception in the impact tensile test is a random process. However, recent experimental works [1,2] suggested that flow localization in the dynamic tensile test is the deterministic result of the interplay between material behaviour, specimen geometry and boundary conditions. In this paper we develop a numerical methodology which supports such experimental finding.…”

Why does necking ignore notches in dynamic tension?

“…The viscoplastic response is described by a power law up to a transition strain rateε m from which it becomes exponentials. For a detailed description of the numerical mode, the reader is referred to [12]. The material properties used in the simulations are of a generic character and do not represent accurately the experimental materials of This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.…”