Pinning and Relaxation of Dislocations in Continuum and Atomistic Models

连续体和原子模型中位错的钉扎和弛豫

• 批准号: 441523275
• 负责人: Professor Dr. Patrick Dondl
• 金额: --
• 依托单位: Abteilung für Angewandte Mathematik
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/441523275?language=en
• 关键词: Pinning; Relaxation; Dislocations; Continuum; Atomistic

Nucleation and glide of lattice dislocations is the most important mechanism of plastic deformation of ductile crystalline metals under external load. Studying dislocation motion is therefore of fundamental importance for understanding the mechanical strength of metals and alloys. Here, we propose to study some open problems of dislocation motion using both discrete atomistic and continuum approaches, of mutual benefit to both fields of modeling. On the continuum side, we will study line-tension based variational evolution of dislocations in heterogeneous environments. Interaction of dislocations with a heterogeneous environment leads to a stick-slip-behavior of the dislocation line. The mathematical interest now lies in the derivation of effective evolution models, which requires a description of the effective dislocation line tension. To this end, we will also consider relaxation problems. We will use full atomistic or mesoscopic (i.e., Peierls-Nabarro-type) models to construct energetically optimal microstructures on various length scales. It is an open question whether the microstructures derived from Peierls-Nabarro-type models can be observed in experiments. Such relaxation phenomena have not been studied using realistic atomistic models. We thus propose to use molecular dynamics simulation with realistic interaction potentials to study whether dislocation structures predicted from Peierls-Nabarro models can be stabilized. In order to be able to perform atomistic simulations on the length scales necessary to observe such mesoscopic relaxation phenomena, we will develop novel variational Green's function-based methods to provide exact elastic boundary conditions for atomistic simulation. Aside from classical materials we will also consider High Entropy Alloys (HEAs), a class of materials composed of usually five or more elements in high concentration. HEAs are interesting due to their potentially exceptional strength and hardness, wear resistance, and corrosion and oxidation resistance, among other desirable properties. From a modeling point of view, HEAs pose new challenges, as dislocations in these materials are immersed in a random spatially fluctuating environment. We will derive both novel mathematical tools as well as atomistic simulation approaches for stochastic homogenization of this random environment.

晶格位错的成核和滑移是延性结晶金属在外部载荷作用下塑性变形的最重要机制。因此，研究位错运动对于了解金属和合金的机械强度至关重要。在这里，我们建议使用离散原子和连续方法研究位错运动的一些开放问题，这对两个建模领域都是互利的。在连续体方面，我们将研究异质环境中基于线张力的位错变分演化。位错与异质环境的相互作用导致位错线的粘滑行为。现在的数学兴趣在于有效演化模型的推导，这需要描述有效位错线张力。为此，我们还会考虑松弛问题。我们将使用完整的原子或介观（即 Peierls-Nabarro 型）模型来构建各种长度尺度上的能量最佳微观结构。由 Peierls-Nabarro 型模型衍生的微观结构是否可以在实验中观察到是一个悬而未决的问题。这种弛豫现象尚未使用现实的原子模型进行研究。因此，我们建议使用具有真实相互作用势的分子动力学模拟来研究 Peierls-Nabarro 模型预测的位错结构是否可以稳定。为了能够在观察这种介观弛豫现象所需的长度尺度上进行原子模拟，我们将开发新颖的基于变分格林函数的方法，为原子模拟提供精确的弹性边界条件。 除了经典材料之外，我们还将考虑高熵合金 (HEA)，这是一类通常由五种或更多高浓度元素组成的材料。 HEA 因其潜在的卓越强度和硬度、耐磨性、耐腐蚀和抗氧化性以及其他理想特性而备受关注。从建模的角度来看，HEA 提出了新的挑战，因为这些材料中的位错沉浸在随机空间波动的环境中。我们将推导出新颖的数学工具以及原子模拟方法来实现这种随机环境的随机均质化。