A strain gradient void-driven ductile fracture model of single crystals is proposed and applied to simulate crack propagation in single and oligo-crystal specimens. The model is based on a thermodynamical framework for homogenized porous solids unifying and generalizing existing thermodynamical formulations. This porous single crystal ductile fracture model relies on a multi-surface representation of porous crystal plasticity in which the standard Schmid law is enhanced to account for porosity, including void growth and void coalescence mechanisms. A new criterion to detect the onset of void coalescence in porous single crystals is proposed and validated by comparison to porous single crystal unit-cell simulations. This criterion can either be used as an additional yield surface or it can be used to follow the well established Gurson–Tvergaard–Needleman approach based on an effective porosity to model void coalescence. The strain gradient formulation relies on a Lagrange multiplier based relaxation of strain gradient plasticity. Material points simulations are performed in order to depict the elementary features of the porous single crystal ductile fracture model without strain gradient effects. The model is then applied to the simulation of plane strain single crystal specimen loaded in tension up to failure. The regularization ability and convergence with mesh refinement are demonstrated. Finally two- and three-dimensional simulations of ductile fracture of single and oligo-crystal specimens are presented. The significant influence of plastic anisotropy on the crack path, ductility and fracture toughness is highlighted.

提出了一种应变梯度空隙驱动的单晶韧性断裂模型，并将其应用于模拟单晶和寡晶试样中的裂纹扩展。该模型基于均质多孔固体的热力学框架，统一和推广了现有的热力学公式。这种多孔单晶韧性断裂模型依赖于多孔晶体塑性的多表面表示，其中标准施密德定律得到增强以解释孔隙率，包括空隙生长和空隙聚结机制。通过与多孔单晶晶胞模拟的比较，提出并验证了检测多孔单晶中空隙聚结开始的新标准。该标准既可以用作附加屈服面，也可以用于遵循基于有效孔隙度的成熟 Gurson-Tvergaard-Needleman 方法来模拟空隙聚结。应变梯度公式依赖于基于拉格朗日乘子的应变梯度塑性松弛。执行材料点模拟是为了描述没有应变梯度效应的多孔单晶韧性断裂模型的基本特征。然后将该模型应用于模拟平面应变单晶试样，在拉伸状态下加载直至失效。证明了网格细化的正则化能力和收敛性。最后给出了单晶和寡晶试样韧性断裂的二维和三维模拟。