This work addresses ductile failure in engineering structures, particularly in aerospace, naval, automotive, and nuclear industries. During accidental overloading or metal forming, materials such as titanium and aluminum alloys experience plastic deformation and ductile damage (by void nucleation, growth, and coalescence) that may eventually lead to crack propagation and fracture. The present study concentrates explicitly on the void coalescence stage. Indeed, building upon a numerical methodology developed by the present authors and detailed in a companion paper, a novel micromechanics-based volumetric cohesive zone model (μ-VCZM) is incorporated within the Extended Finite Element Method (XFEM) to reproduce the process of void coalescence while overcoming the mesh objectivity issues of the numerical results during the softening regime. The Mode I (extension) and Mode II (shear) coalescence onset criteria and evolution laws are derived from micromechanical considerations. Subsequently, the yield surfaces and the integration algorithm necessary to determine the stress state within the coalescence band are established. Finally, the micromechanics-based μ-VCZM is applied within the XFEM-VCZM unified methodology. The numerical model, implemented as user element (UEL) into the computation code Abaqus, demonstrates efficacy in replicating the stages of ductile fracture, highlighting its potential for addressing complex finite strain three-dimensional boundary value problems. Notably, the results obtained with coarse meshes exhibit no mesh dependency below a specific mesh size, reproducing realistic Mode I and II fracture surfaces.

中文翻译：

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通过微机械 3D 体积内聚结区模型 （[公式省略]-VCZM） 描述 XFEM 内部颈缩/剪切的空隙聚结

这项工作解决了工程结构中的延性失效问题，特别是在航空航天、海军、汽车和核工业中。在意外过载或金属成型过程中，钛和铝合金等材料会发生塑性变形和延展性损伤（通过空隙成核、生长和聚结），最终可能导致裂纹扩展和断裂。本研究明确集中在空隙聚结阶段。事实上，基于本文作者开发并在姊妹论文中详细介绍的数值方法，一种新颖的基于微观力学的体积内聚力模型 （μ-VCZM） 被纳入扩展有限元法 （XFEM） 中，以重现空隙聚结过程，同时克服软化状态下数值结果的网格客观性问题。模式 I （延伸） 和模式 II （剪切） 聚结开始标准和演化定律源自微力学考虑。随后，建立确定聚结带内应力状态所需的屈服面和积分算法。最后，将基于微观力学的 μ-VCZM 应用于 XFEM-VCZM 统一方法中。该数值模型作为用户单元 （UEL） 实现到计算代码 Abaqus 中，展示了在复制韧性断裂阶段的有效性，突出了其解决复杂有限应变三维边界值问题的潜力。值得注意的是，使用粗网格获得的结果在特定网格大小下没有网格依赖性，再现了逼真的模式 I 和 II 断裂表面。