A new model of gradient crystal plasticity is developed in which the incompatibility of plastic deformation field is simultaneously included in two different ways. The first one is well known and incorporates the gradient effect of accumulated rotation of the crystallographic lattice on the kinematic hardening in the Cosserat crystal plasticity model. The second way incorporates the effect of the current incompatibility of lattice spin on the total dislocation density rate, resulting in an additional isotropic hardening term in the gradient-enhanced hardening law. The latter effect involves a natural length scale that is fully determined in terms of standard quantities of a non-gradient hardening law and evolves during plastic deformation. The relative significance of the two effects depends on the values of material parameters, which is demonstrated by the results of calculations of 1D and 3D examples for a Cu single crystal. If the second effect is predominant, then the Cosserat formulation provides only a regularization, and then the model can be used to predict size effects. This is shown by 3D simulations of the size effect in spherical indentation of a copper single crystal. Since the gradient-enhanced hardening law does not involve any adjustable parameter, the obtained agreement of the model prediction with the experimental indentation size effect on hardness can be regarded as surprisingly good.

建立了一种新的梯度晶体塑性模型，其中塑性变形场的不相容性以两种不同的方式同时包含。第一个是众所周知的，它在 Cosserat 晶体塑性模型中结合了晶格累积旋转对运动硬化的梯度效应。第二种方法结合了当前晶格自旋不相容性对总位错密度率的影响，从而在梯度增强硬化定律中产生了额外的各向同性硬化项。后一种效应涉及自然长度尺度，该尺度完全根据非梯度硬化定律的标准量确定，并在塑性变形过程中演变。两种效应的相对重要性取决于材料参数的值，铜单晶的 1D 和 3D 示例的计算结果证明了这一点。如果第二个效应占主导地位，那么 Cosserat 公式只提供正则化，然后该模型可用于预测尺寸效应。铜单晶球形压痕中尺寸效应的 3D 模拟显示了这一点。由于梯度增强硬化定律不涉及任何可调参数，因此模型预测与实验压痕尺寸对硬度的影响的一致性可以说是出乎意料的好。铜单晶球形压痕中尺寸效应的 3D 模拟显示了这一点。由于梯度增强硬化定律不涉及任何可调参数，因此模型预测与实验压痕尺寸对硬度的影响的一致性可以说是出乎意料的好。铜单晶球形压痕中尺寸效应的 3D 模拟显示了这一点。由于梯度增强硬化定律不涉及任何可调参数，因此模型预测与实验压痕尺寸对硬度的影响的一致性可以说是出乎意料的好。