Abstract In this paper we have investigated, using finite element calculations performed in ABAQUS/Explicit [1], the effect of ab initio geometric imperfections in the development of multiple necking patterns in ductile rings subjected to dynamic expansion. Specifically, we have extended the work of Rodriguez-Martinez et al. [2], who studied the formation of necks in rings with sinusoidal spatial perturbations of predefined amplitude and constant wavelength, by considering specimens with random distributions of perturbations of varying amplitude and wavelength. The idea, which is based on the work of El Mai et al. [3], is to provide an idealized modeling of the surface defects and initial roughness of the rings and explore their effect on the collective behavior and spacing of the necks. The material behavior has been modeled with von Mises plasticity and constant yield stress, and the finite element simulations have been performed for expanding velocities ranging from 10 m/s to 1000 m/s, as in ref. [2] . For each speed, we have performed calculations varying the number of imperfections in the ring from 5 to 150. In order to obtain statistically significant results, for each number of imperfections, the computations have been run with five random distributions of imperfection wavelengths. For a small number of imperfections, the variability in the wavelengths distribution is large, which makes the imperfections play a major role in the necking pattern, largely controlling the spacing and growth rate of the necks. As the number of imperfections increases, the variability in the wavelengths distribution decreases, giving rise to an array of more regularly spaced necks which grow at more similar speed. A key outcome is to show that, for a large number of imperfections, the number of necks formed in the ring comes closer to the number of necks obtained in the absence of ab initio geometric imperfections.

中文翻译：

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受到快速径向膨胀的弹塑性环中的多个颈缩模式：几何缺陷随机分布的影响

摘要 在本文中，我们使用在 ABAQUS/Explicit [1] 中执行的有限元计算研究了从头算几何缺陷对动态膨胀的延性环中多个颈缩模式发展的影响。具体来说，我们扩展了 Rodriguez-Martinez 等人的工作。[2]，他通过考虑具有变化幅度和波长的扰动的随机分布的样本，研究了具有预定义幅度和恒定波长的正弦空间扰动的环中颈部的形成。这个想法基于 El Mai 等人的工作。[3]，是提供环的表面缺陷和初始粗糙度的理想化建模，并探索它们对颈部的集体行为和间距的影响。材料行为已使用 von Mises 塑性和恒定屈服应力进行建模，并且已针对从 10 m/s 到 1000 m/s 的扩展速度进行了有限元模拟，如参考文献中所示。[2] . 对于每种速度，我们执行了将环中的缺陷数量从 5 变化到 150 的计算。为了获得统计上显着的结果，对于每个缺陷数量，已经使用缺陷波长的五个随机分布运行计算。对于少数缺陷，波长分布的可变性较大，这使得缺陷在颈缩模式中起主要作用，在很大程度上控制颈的间距和生长速率。随着缺陷数量的增加，波长分布的可变性减小，产生了一系列更规则间隔的颈部，它们以更相似的速度生长。一个关键结果是表明，对于大量缺陷，环中形成的颈部数量更接近于没有从头几何缺陷时获得的颈部数量。