Cohesive zone traction-separation relations, and the related phenomenological parameters, for steady-state ductile plate tearing, are strongly tied to the micro-mechanics governing the void nucleation and growth process leading to localized deformation and micro-crack formation. The effects of such local variations on the damage evolution and cohesive zone parameters, respectively, are brought out in this study. A 2D plane strain model setup, first considered in Nielsen and Hutchinson (Int J Impact Eng 48:15–23 (2012)], is adopted, but here by discretely modeling a finite number of finite-size void nucleation sites distributed randomly in the plate material. It is found that the heterogeneous material conditions, resulting from the nucleation process, strongly affect the localization of damage and fracture, which influence the cohesive energy. By considering a number of realizations of the random distribution for each material configuration, it is concluded that: (i) the peak force in the cohesive traction-separation relation is, essentially, unaffected by the heterogeneity coming into play through the damage-related microstructure, while (ii) the cohesive energy decreases when either increasing the number or the size of the nucleation sites. The cohesive energy is found to be in the range of those previously reported for homogeneous materials, but a direct comparison should be made with caution. The results imply that care should be taken if the actual material configuration diverges from a homogeneous microstructure such as when considering very thin plates and for plates with a few void nucleation sites.

中文翻译：

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具有随机分布的空隙成核点的延性板撕裂的内聚牵引-分离关系

内聚区牵引-分离关系以及稳态延性板撕裂的相关现象学参数与控制导致局部变形和微裂纹形成的空隙成核和生长过程的微观力学密切相关。本研究分别介绍了这种局部变化对损伤演化和内聚区参数的影响。采用了 2D 平面应变模型设置，首先在 Nielsen 和 Hutchinson (Int J Impact Eng 48:15–23 (2012)] 中考虑，但这里通过离散建模有限数量的有限尺寸空隙成核位点随机分布在研究发现，形核过程产生的异质材料条件强烈影响损伤和断裂的定位，从而影响内聚能。通过考虑每种材料配置的随机分布的许多实现，得出的结论是：（i）内聚牵引-分离关系中的峰值力基本上不受通过与损伤相关的微观结构发挥作用的非均质性的影响，而（ii）当增加成核位点的数量或大小时，内聚能会降低。发现内聚能在先前报道的均质材料的范围内，但应谨慎进行直接比较。结果表明，如果实际的材料配置偏离均匀的微观结构，例如在考虑非常薄的板和具有少量空隙成核位置的板时，应该小心。