Multiple slip in continuum dislocation dynamics: dislocation reactison, cross slip and the formation of dislocation sources

越来越多的微型零件和设备的使用以及对高精度工程的日益增长的需求，最近使晶体塑性的基本原理再次成为应用科学的焦点。特别是在小尺度上，这揭示了晶体塑性的经典连续统概念的一些缺点。目前的提议者主要参与了所谓的连续位错动力学理论的发展。这一理论最初是在一个包含位错线方向作为自变量的高维位形空间中发展起来的。然而，最近有一些系统的方法可以从原始方法中导出没有额外维度的理论。虽然这些理论原则上适用于一般的位错组态，但实际计算出的例子还基本上限于单滑移。涉及多重滑移的应用，至今只被模拟为单一滑移的叠加。本计画旨在将多重滑移时的位错交互作用的影响，纳入连续位错理论中。我们要发展的概念，如何考虑位错反应，交叉滑移和位错增殖的位错状态的密度为基础的描述的演变。重点讨论了属于不同滑移系的位错的相互作用。作为中间目标，我们确定（一）的位错（超）慢跑及其对动力学的影响建模，（二）的位错反应（洛默锁，Hirth锁，共线反应）及其对动力学的影响建模和（iii）固定的位错段的耦合反应产物或慢跑的位错源的倍增和形成。密切相关的共线反应所需的概念下讨论点（ii），我们也旨在将交叉滑移到目前的theory.The当前项目的重点在于基本的数学，即基本上是运动学，描述。我们期望这已经是动力学理论的重要几何方面的特征。然而，实际的物理动力学，表现在障碍强度，溶解的位错反应和激活应力的位错源将在目前的项目的预期延长处理。

The use of ever more miniaturized parts and devices and the increasing demand for high precision engineering recently brought the fundamentals of crystal plasticity again in the focus of applied science. Especially on small scales this revealed some shortcomings of classical continuum concepts of crystal plasticity. The current proposer was centrally involved in the development of the so-called continuum dislocation dynamics theory. This theory was originally developed in a higher dimensional configuration space, which contains the dislocation line-direction as independent variable. Yet there are recent systematic approaches how to derive theories without extra dimensions from the original approach. Although these theories are in principle applicable to general dislocation configurations, the actually worked out examples are as yet essentially restricted to single glide. Applications involving multiple slip were so far only modeled as a superposition of single glide.This project aims at incorporating effects of dislocation interactions during multiple slip into the continuum dislocation theory. We want to develop concepts how to consider dislocation reactions, cross slip and dislocation multiplication in the evolution of the density based description of the dislocation state. Emphasis is put on the interaction of dislocation belonging to different glide systems. As intermediate goals we identify (i) the modeling of dislocation (super) jogs and their effect on the dynamics, (ii) the modeling of dislocation reactions (Lomer lock, Hirth lock, collinear reaction) and their effect on the dynamics and (iii) the coupling of immobilized dislocation segments in reaction products or jogs on the multiplication of dislocations and the formation of dislocation sources. Closely related to the concepts needed for the collinear reaction discussed under point (ii) we also aim at incorporating cross slip into the current theory.The focus of the current project lies on the basics mathematical, that is essentially kinematical, description. We expect that this will already feature important geometric aspects of a dynamic theory. However, the actual physical dynamics, expressed in obstacle strengths, dissolving of dislocation reactions and the activation stress of dislocation sources will be tackled in the envisaged prolongation of the current project.