Abstract With the aid of some explicit formulas of the elastic stress fields at the neighborhood of U- and blunt V-shaped notches and also using the Tresca and Von-Mises yield criteria, the plastic zone size at the neighborhood of such notches under mode I loading and plane-stress/strain conditions is determined by extending Irwin’s model. Then, for verifying the analytical results, elastic-plastic finite element analyses are done on some notched specimens and the corresponding numerical results are compared with the analytical estimations. It is shown that for the most cases, the effective plastic zone size, which is necessary for determining the type of ductile failure, can be successfully estimated by using the proposed analytical formulas. In addition, due to lack of accuracy of the analytical stress fields used in this study, the shapes of the plastic zones obtained by the analytical and numerical methods are not identical for most cases. It is also revealed that by using the analytical method based on the linear elastic solution instead of the elastic-plastic solutions, which are complicated and time-consuming, the effective plastic zone size at the neighborhood of blunt notches can be determined rapidly and conveniently.

中文翻译：

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通过扩展 Irwin 模型确定缺口尖端塑性区

摘要 借助 U 形和钝 V 形缺口附近弹性应力场的一些显式公式，并利用 Tresca 和 Von-Mises 屈服准则，得到 I 型缺口附近的塑性区尺寸加载和平面应力/应变条件是通过扩展 Irwin 模型来确定的。然后，为了验证解析结果，对一些缺口试件进行弹塑性有限元分析，并将相应的数值结果与解析估计进行比较。结果表明，在大多数情况下，可以通过使用所提出的分析公式成功地估计出确定延性破坏类型所必需的有效塑性区尺寸。此外，由于本研究中使用的分析应力场缺乏准确性，在大多数情况下，通过解析和数值方法获得的塑性区的形状并不相同。还表明，通过使用基于线弹性解的解析方法代替复杂耗时的弹塑性解，可以快速方便地确定钝缺口附近的有效塑性区尺寸。