Abstract To explore the interactive influence of the deformation stress state and material microstructural grain size on the fracture behaviour in micro-scaled deformation, a series of micro-scale copper specimens of various geometrical dimensions and microstructural grain sizes are prepared and deformed to achieve various stress states represented by stress-related variables, such as the normalised third deviatoric stress invariant and the stress triaxiality. The speckle pattern method of continuous tracking is used to investigate the mechanical responses of materials in various deformation stress states and material microstructures, and a finite-element simulation of each deformation is conducted with the combined surface layer and grain boundary strengthening constitutive model, which considers the contributions of the surface grain, grain interior and grain boundary in representing the grain and geometry sizes. The interactive effects of the normalised third invariant, stress triaxiality and microstructural grain size on the fracture strain are identified and established by accounting for the correlation between the results of simulation and those of physical experimentation. Their influences on the fracture mechanism, mode and behaviour are further explored. The results reveal that greater stress decreases the fracture strain in the tensile deformation of round bar and cylindrical compression and increases the fracture strain in sheet shear and tensile deformations. The larger grain size generates fewer micro-voids, more uneven grain distribution and severer localisation deformation, which accelerates failure. Furthermore, stress triaxiality and the normalised third invariant at a low stress triaxiality are decreased with the increase of grain size, which in turn affects the occurrence of fracture. These effects coexist and compete with each other. In view of these influences, a larger grain size and a higher stress state inhibit the occurrence of fracture for sheet specimens with fracture modes from shear-dominant to dimple-dominant; in contrast, a smaller grain size and a lower stress state inhibit the occurrence of fracture in other cases.

中文翻译：

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应力状态和晶粒尺寸对铜微尺度塑性变形断裂行为的交互作用

摘要 为探究变形应力状态和材料显微晶粒尺寸对微尺度变形断裂行为的交互影响，制备了一系列不同几何尺寸和显微晶粒尺寸的微尺度铜试件，并进行变形以获得不同的应力。由应力相关变量表示的状态，例如归一化的第三偏应力不变量和应力三轴性。采用连续跟踪散斑图法研究材料在各种变形应力状态和材料微观结构下的力学响应，并结合表层和晶界强化本构模型对每种变形进行有限元模拟，该模型考虑了表面晶粒的贡献，晶粒内部和晶界代表晶粒和几何尺寸。通过考虑模拟结果与物理实验结果之间的相关性，确定并建立归一化第三不变量、应力三轴性和微观结构晶粒尺寸对断裂应变的交互作用。进一步探讨了它们对断裂机制、模式和行为的影响。结果表明，较大的应力降低了圆棒和圆柱压缩拉伸变形中的断裂应变，并增加了板材剪切和拉伸变形中的断裂应变。晶粒越大，产生的微孔越少，晶粒分布越不均匀，局部变形越严重，加速失效。此外，应力三轴度和低应力三轴度下的归一化第三不变量随着晶粒尺寸的增大而减小，进而影响断裂的发生。这些影响并存，相互竞争。考虑到这些影响，较大的晶粒尺寸和较高的应力状态抑制了断裂模式从剪切为主到凹坑为主的薄板试样的断裂发生；相反，在其他情况下，较小的晶粒尺寸和较低的应力状态会抑制断裂的发生。较大的晶粒尺寸和较高的应力状态抑制了断裂模式从剪切主导到凹坑主导的板材试样的断裂；相反，在其他情况下，较小的晶粒尺寸和较低的应力状态会抑制断裂的发生。较大的晶粒尺寸和较高的应力状态抑制了断裂模式从剪切主导到凹坑主导的板材试样的断裂；相反，在其他情况下，较小的晶粒尺寸和较低的应力状态会抑制断裂的发生。