SGER: Stress State Dependence of Peierls Barriers and Dislocation Kinetics at the Nanoscale

晶体材料的塑性行为是由位错滑动控制的，而屈服应力和流动应力是由位错绕过障碍物的能力决定的。局部障碍，可以克服的援助，热激活控制温度和应变速率依赖关系。其中，佩尔斯势垒尤为重要。它是一种特定材料的固有特性，与位错核心的原子结构有关。除非材料的性质被改变，否则它不能通过净化、退火等处理来改变。虽然位错核心结构在所有尺度上都影响变形特性，但在纳米尺度上，当样品和/或组分的尺寸与克服佩尔斯势垒的临界热激活事件的程度相当时，它是最重要的。此外，在这个尺度下，其他障碍可以被分离，从而降低其重要性，而佩尔斯势垒与固有的晶格阻力有关。当位错核心效应很重要时，意外的变形模式以及屈服应力和流动应力对温度和晶体取向的强烈且通常不寻常的依赖是常见的。塑性流动的一个显著特征是受整个应力张量的影响，而不仅仅受施密德应力的影响，即滑移面内滑移方向上的剪应力。一个突出的挑战是确定和量化原子水平的核心性质如何通过位错的热激活运动投射到纳米尺度上，然后通过位错的中尺度动力学渗透到宏观流动性质。这两个最低层次之间的联系和相互作用是探索性研究小额赠款的重点。由研究人员进行的最先进的原子计算，揭示了佩尔斯应力与张拉应力状态的确切依赖关系，这是在0K时克服佩尔斯势垒所需的应力。然而，他们并没有单独揭示佩尔斯势垒及其应力状态依赖性。因此，提出的研究的主要挑战是在热激活位错运动的理论分析中利用对佩尔斯应力的应力状态依赖的原子水平的理解。为此，研究人员将采用多维克雷默方法，在该方法中，能量势垒上的热活化使用随机朗之万方程和相关的反应和非反应模式的“摩擦系数”来处理。在目前的情况下，“摩擦”代表了由施加应力张量引起的核心转换的累积效应，它减缓和/或加速了越过屏障的逃逸动力学。这个项目的探索性方面主要与摩擦系数如何与佩尔斯应力的应力状态依赖关系联系起来有关，这是由位错岩心的原子模拟和0K时的相关滑动决定的。本研究的结果将是位错迁移率的本构关系，它包含了温度和应力诱导原子水平核心转变的影响。这些关系可用于从纳米级位错动力学到单晶和多晶塑性屈服连续分析的建模。这样的分析结果将准确地反映原子水平的位错核性质在纳米尺度和进一步的粗晶化，以及微观和宏观尺度上对塑性流动的影响。这项将位错动力学与位错的原子水平性质联系起来的研究具有广泛的影响。它可能为在有限温度下位错的原子结构如何影响位错动力学提供全新的见解。这是至关重要的，因为功能和结构材料在化学和晶体学上都变得越来越复杂。当新制定的本构关系成为建模工具的一部分，可以被材料研究人员和设备设计师使用时，预计所提出的研究将不仅作为科学进步，而且在工业发展中产生重大影响。

The plastic behavior of crystalline materials is governed by dislocation glide and the yield and flow stress is determined by the ability of dislocations to circumvent obstacles. Localized obstacles that can be overcome with the aid of thermal activations control temperature and strain rate dependencies. Among those, the Peierls barrier is particularly significant. It is an intrinsic property of a specific material, related to the atomic structure of the dislocation cores. It cannot be altered by treatments, such as purification, annealing etc., unless the nature of the material is altered. While the dislocation core structure affects deformation properties at all scales, it is most important at nanocale when the size of the samples and/or components becomes comparable with the extent of the critical thermally activated event of overcoming the Peierls barrier. Furthermore, at this scale other obstacles may be separated so as to diminish in importance, while the Peierls barrier relates to the inherent lattice resistance. When the dislocation core effects are important, unexpected deformation modes together with strong and often unusual dependence of the yield and flow stress on temperature and crystal orientation are common. A prominent feature is that the plastic flow is influenced by the entire stress tensor rather than only by the Schmid stress, i. e. the shear stress in the slip direction in the slip plane. An outstanding challenge is to identify and quantify how the atomic level core properties project onto the nanoscale via thermally activated motion of dislocations and then percolate through the mesoscale dynamics of dislocations up to the macroscopic flow properties. The link and interplay between the two lowest levels of this hierarchy is the focus of this Small Grant for Exploratory Research.The state-of-the-art atomistic calculations, carried out by the investigators, expose the exact tensorial stress-state dependence of the Peierls stress, which is the stress needed to overcome the Peierls barrier at 0K. However, they do not reveal the Peierls barrier alone and its stress-state dependence. Hence, the principal challenge of the proposed research is to utilize the atomic level understanding of the stress-state dependence of the Peierls stress in the theoretical analysis of the thermally activated dislocation motion. The researchers will employ for this purpose the multidimensional Kramers approach in which the thermal activation over the energy barrier is treated using the stochastic Langevin equation with associated 'friction coefficients' for the reaction and nonreaction modes. In the present context, the 'friction' represents the cumulative effect of core transformations induced by the applied stress tensor, which slows down and/or accelerates the kinetics of escape over the barrier. The exploratory aspect of this project is primarily related to how the friction coefficients can be connected to the stress-state dependence of the Peierls stress determined by atomistic simulations of the dislocation cores and related glide at 0K.The outcome of this research will be constitutive relations for the dislocation mobility that encapsulate the effects of temperature and stress induced atomic level core transformations. These relations may then be employed in modeling that ranges from nanoscale dislocation dynamics to continuum analyses of plastic yielding in single and polycrystals. The results of such analysis will accurately reflect the effect of atomic level core properties of dislocations on plastic flow at the nanoscale and via further coarse graining, also on micro and macro scale.This research that links dislocation kinetics at the nanoscale with the atomic level properties of dislocations has wide ramifications. It may provide entirely new insights into how the atomic structure of dislocations affects the dislocation kinetics at finite temperatures. This is of paramount importance, as both functional and structural materials are becoming more complex chemically and crystallographically. It is expect that the proposed research will have major impact not only as a scientific advancement but also in industrial developments when newly formulated constitutive relations become parts of modeling tools, which can be used by materials researchers, as well as device designers.