Abstract Recent Electron Backscatter Diffraction (EBSD) experiments have revealed the emergence of heterogeneous dislocation microstructures forming under a wedge indenter in fcc crystals, where micro-meter dislocation patterns challenge the predictions of traditional models of plasticity. In order to explain the formation of these features and develop a relationship between the force-displacement curve and the dislocation substructure, we present here a model of wedge indentation based on the continuum theory of dislocations. The model accounts for large deformation kinematics through the multiplicative split of the deformation gradient tensor, where the incompatible plastic component of deformation results from the flux of dislocations on different and interacting slips systems. Constitutive equations for dislocation fluxes are determined from a dissipative variational principle. As a result, each dislocation density satisfies an initial-boundary value problem with convective-diffusive character, which is coupled to the macroscopic stress and displacement fields governing the deformation process. Solution to the self-consistent continuum formulation is found using the finite element method. Computer simulations mimic the experimental conditions of wedge micro-indentation experiments into Ni single-crystals used by Kysar et al. (2010a). A comparison of overall dislocation density distribution and macroscopic mechanical response shows good overall agreement with the experimental results in terms of the detailed features of dislocation patterns and lattice rotations as well as the macroscopic force-displacement response.

中文翻译：

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基于连续位错的单晶楔形显微压痕模型

摘要 最近的电子背散射衍射 (EBSD) 实验揭示了在 fcc 晶体中楔形压头下形成的异质位错微结构的出现，其中微米位错模式挑战了传统塑性模型的预测。为了解释这些特征的形成并建立力-位移曲线与位错子结构之间的关系，我们在这里提出了一个基于位错连续理论的楔形压痕模型。该模型通过变形梯度张量的乘法分裂来解释大变形运动学，其中变形的不相容塑性分量是由不同且相互作用的滑移系统上的位错通量引起的。位错通量的本构方程由耗散变分原理确定。因此，每个位错密度都满足具有对流扩散特性的初始边界值问题，这与控制变形过程的宏观应力和位移场耦合。使用有限元方法找到自洽连续体公式的解。计算机模拟模拟了 Kysar 等人使用的 Ni 单晶楔形微压痕实验的实验条件。(2010a)。整体位错密度分布和宏观力学响应的比较表明，在位错模式和晶格旋转的详细特征以及宏观力-位移响应方面与实验结果具有良好的总体一致性。