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

越来越多的微型化部件和设备的使用，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陷。目前的提出者主要参与了所谓的连续体位错动力学理论的发展。该理论最初是在以位错线方向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，如何在不增加原始方法的额外维度的情况下得出理论。虽然这些理论原则上适用于一般的位错组态，但实际计算的例子基本上还局限于单滑移。到目前为止，涉及多滑移的应用仅被建模为单滑移的叠加。本项目旨在将多滑移过程中位错相互作用的影响纳入连续体位错理论。我们希望在基于密度的位错态描述的演化中发展出如何考虑位错反应、交叉滑移和位错倍增的概念。重点讨论了属于不同滑移系统的位错之间的相互作用。作为中间目标，我们确定了(I)位错(超级)JOG的模拟及其对动力学的影响，(Ii)位错反应(Lmer Lock，Hirth Lock，共线反应)的模拟及其对动力学的影响，以及(Iii)反应产物或JOG中的固定位错段对位错的倍增和位错源的形成的耦合。与第(Ii)点讨论的共线反应所需的概念密切相关，我们还旨在将交叉滑移纳入当前理论。当前项目的重点在于基本的数学描述，即本质上是运动学的描述。我们预计，这将是一个动态理论的重要几何方面。然而，实际的物理动力学，以障碍强度、位错反应的溶解和位错源的激活应力表示，将在本项目设想的延长中解决。

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.