Deterministic and Stochastic Continuum Models of Dislocation Patterning

该项目的主要目标是了解自发出现的位错通量的时空波动如何引起不均匀的位错排列，如细胞结构（位错模式），以及这些位错模式的存在如何反过来改变位错通量并将新的出现长度尺度引入位错动力学。为了分析位错模式和位错通量/塑性流动的相互关联动力学，我们使用了DFG-FOR1650在过去三年中开发的CDD框架。我们研究了以下具体问题：(i)假设位错通量以确定性的方式依赖于位错微观结构，CDD演化方程能否解释从小的初始波动（无边界约束）中自发形成的非均质位错模式？（二）作为塑性流动固有特征的位错通量的大幅波动如何纳入CDD框架？这些波动是有助于位错模式的出现，还是制造了一种阻碍模式形成的“噪音”？（iii）在小样本和受限几何结构中，哪些因素控制着位错模式的存在或不存在，即，位错模式的出现长度尺度如何与相微观结构、晶粒和样品尺寸相关的外部尺度相互作用？

The main goal of this project is to understand how spontaneously emerging spatio-temporal fluctuations of dislocation fluxes give rise to inhomogeneous dislocation arrangements such as cell structures (dislocation patterning), and how in turn the presence of these dislocation patterns alters the dislocation fluxes and introduces new emergent length scales into the dislocation dynamics. To analyze the inter-related dynamics of dislocation patterns and dislocation fluxes/plastic flow, we use the CDD framework developed in DFG-FOR1650 over the past three years. We investigate the following specific questions: (i) can the CDD evolution equations explain the spontaneous formation of heterogeneous dislocation patterns in bulk samples (no boundary constraints) from small initial fluctuations, assuming that the dislocation fluxes to depend on dislocation microstructure in a deterministic manner? (ii) how can large fluctuations of the dislocation fluxes, which are an intrinsic feature of plastic flow, be incorporated into the CDD framework? Do these fluctuations assist the emergence of dislocation patterns, or do they rather create a "noise" which impedes pattern formation? (iii) Which factors control the presence or absence of dislocation patterns in small samples and confined geometries, i.e., how does the emergent length scale of dislocation patterns interact with external scales related to phase microstructure, grain and sample size?