Discrete-Continuum Dislocation Dynamics at Surfaces and Interfaces with Application to Plasticity of Nanolaminated Composites

我们开发了改进的位错动力学模拟方法来研究纳米层化金属复合材料的塑性变形。这种复合材料将不同的金属结合成层状结构，层厚在纳米范围内。它们的塑性变形性能是由晶格位错与层压板双材料界面的相互作用决定的。在原子尺度上，这些相互作用类似于发生在内部界面（晶粒和孪晶界）的过程，因为原子重排控制着位错的成核、吸收或传递。然而，在由弹性不同材料组成的层压板中，界面处的弹性边界条件导致了额外的、长期的弹性相互作用：弹性较弱的材料的位错被具有较强材料的界面排斥，而较强材料的位错被吸引（克勒效应）。同时，位错应力场和应力诱发的位错相互作用也被边界所改变。因此，在纳米层合材料塑性的离散位错动力学模拟中，准确评估双材料界面对内应场的影响至关重要，而内应场是位错运动的驱动力。近年来，所谓的离散连续体方法（DCM）在弹性表面和界面效应的位错动力学模拟方面取得了重要进展。DCM采用一种混合方法来评估位错相关的内应力场，该方法将位错段的奇异应力场与缓慢变化的内应力场叠加，该内应力场来源于粗粒本征应变问题的解，并考虑了表面和界面的边界条件。然而，奇异段应力场一直使用体积表达式来评估，这在表面/界面附近是不准确的，导致与粗粒度解决方案不匹配，并且不准确地表示作用于位错的力。我们通过计算Yuan教授近年来以墨卡托研究员身份参与该项目的奇异应力场的分析修正来解决这个问题。我们改进的DCM方法将准确描述纳米层合材料塑性变形中的界面效应和复杂变形边界条件（纳米压痕）。我们将利用这种能力来理解复杂的观察结果，如Cu-Au层压板的强度反转（弹性较强的Cu可能比弹性较弱的Au表现出更多的塑性变形），并分析和优化不同负载条件下渐变纳米层压板的行为。

We develop improved dislocation dynamics simuation approaches to investigate plastic deformation of nanolaminated metal composites. Such composites combine different metals into layered structures with layer thicknessse in the nanometre range. Their plastic deformation properteies are governed by the interactions of crystal lattice dislocations with the bimaterial interfaces of the laminate. On the atomic scale, these interactions are similar to processes occuring at internal interfaces (grain and twin boundaries), as atomic re-arrangements control the nucleation, absorption or transmission of dislocations. However, in laminates consisting of elastically dissimilar materials the elastic boundary conditions at the interfaces lead to additional, long-ranged elastic interactions: Dislocations of an elastically weaker material are repulsed by an interface with a stronger material, whereas dislocations of the stronger material are attracted (Koehler Effect). At the same time, the dislocation stress fields and stress-induced dislocation interactions are modified by the boundaries. In discrete dislocation dynamics simulations of nanolaminate plasticity it is therefore essential to accurately evaluate the influences of the bimaterial interfaces on the internal stress fields which enter the driving forces for dislocation motion. In recent years, the so-called discrete-continuum method (DCM) has led to important progress in dislocation dynamics simulation of elastic surface and interface effects. DCM uses a hybrid method to evaluate dislocation-related internal stress fields by superimposing the singular stress fields of dislocation segments with a slowly varying internal stress field that derives from solution of a coarse grained eigenstrain problem and accounts for boundary conditions at surfaces and interfaces. However, the singular segment stress fields have always been evaluated using bulk expressions which are inaccurate near surfaces/interfaces, leading to a mismatch with the coarse grained solution and to an inaccurate representation of the forces acting on dislocations. We resolve this problem by accounting for analytical corrections to the singular stress fields near surfaces and interfaces as derived in recent years by Prof. Yuan, who participates in the Project as a Mercator Fellow. Our improved DCM approach will provide an accurate description of interface effects and complex deformation boundary conditions (nanoindentation) in plastic deformation of nanolaminates. We will exploit this capability to understand complex observations such as strength inversion in Cu-Au Laminates (the elastically stronger Cu may show more plastic deformation than the elastically weaker Au), and to analyze and optimize the behavior of graded nanolaminates under different loading conditions.