Pinning and Relaxation of Dislocations in Continuum and Atomistic Models

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动是在外部载荷下延性晶体金属塑性变形的最重要机制。因此，研究脱位运动对于理解金属和合金的机械强度至关重要。在这里，我们建议使用离散的原子和连续方法研究一些开放的位错运动问题，这是对两个建模领域的相互益处。在连续方面，我们将研究基于线张力的异质环境中位错的变化演变。与异质环境的位错的相互作用导致位错线的粘性行为。数学兴趣现在在于有效进化模型的推导，这需要对有效的脱位线张力进行描述。为此，我们还将考虑放松问题。我们将使用完整的原子或介观（即Peierls-Nabarro-type）模型在各个长度尺度上构建能量最佳的微观结构。在实验中可以观察到从PEIERLS-NABARRO型模型中得出的微观结构是一个开放的问题。这种放松现象尚未使用现实的原子模型研究。因此，我们建议将具有现实相互作用势的分子动力学模拟使用，以研究是否可以稳定从PEIERLS-NABARRO模型预测的位错结构。为了能够对观察这种介绍性弛豫现象所需的长度尺度进行原子模拟，我们将开发出新颖的基于Green的基于函数的方法，以为原子模拟提供精确的弹性边界条件。 除经典材料外，我们还将考虑高熵合金（HEAS），这是一种通常由高浓度的五个或更多元素组成的材料。 HEAS由于其潜在的特殊强度和硬度，耐磨性以及腐蚀和抗氧化的耐药性以及其他理想的特性而引人入胜。从建模的角度来看，Heas构成了新的挑战，因为这些材料中的位错浸入了随机的空间波动环境中。我们将获得新的数学工具以及原子模拟方法，用于对这种随机环境的随机均质化。