Dislocation patterns beyond optimality

超出最优的位错模式

基本信息

批准号：
EP/N035631/1
负责人：
Lucia Scardia
金额：
$ 12.19万
依托单位：
University of Bath
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2016
资助国家：
英国
起止时间：
2016 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FN035631%2F1
关键词：
Dislocation patterns beyond optimality

项目摘要

Metals, and steel in particular, play a fundamental role in our everyday life and are used in countless applications, from the construction industry to transport, energy, packaging, and house appliances. Different applications, however, require different material properties of the metals, which need to be designed to meet the requirements. Materials design in its turn requires a deep understanding of the dependence of the mechanical behaviour of the metal on its chemical composition and microstructure. This is not possible without a good understanding of dislocations.Dislocations are defects in the atomic structure of metals which collectively, at the macroscopic scale, determine how metals deform. For this reason, any macroscopic model that aims for a predictive power has to take into account the presence of these defects. However, since the typical number of dislocations in even a small sample of metal is very high, formulating a model that keeps track of every single dislocation is unfeasible except for very small-scale problems. Although good models for dislocations are available at the level of the atomic lattice, it is not yet well-understood how to incorporate the effect of their presence and motion in a model at the macroscopic, engineering scale. This challenge has become the focus of intensive research in the last decade - in the engineering community because of the need of good macroscopic models for the development of new metals and alloys, and in the mathematical community for the central role it plays in understanding complex multiscale systems. Over the years, and in different communities, this challenge has been approached in several ways. The great advantage of a rigorous approach is that it is exact; the price to pay, however, is a strong limitation on the configurations that can be analysed. In the majority of the mathematical literature, dislocations are modelled as straight and parallel lines, while they are in fact three-dimensional curves. This assumption reduces the complexity of the theory enormously, although the mathematical challenges in this idealised setting are still countless. A special configuration that has received great attention in recent years is that of vertically periodic dislocation walls, similar to low-angle grain boundaries. One of the reasons why they are so popular is the general belief that they represent minimum energy arrangements for dislocations. The proposed research poses a more fundamental question: what are the energetically favourable configurations of dislocations? And, also, how do low-energy dislocation structures vary when a small but non-zero temperature is introduced in the model?Low-energy dislocation structures (LEDS) like walls, clusters and cells are one of the main features of the microstructure in metals. These high-density configurations increase the resistance of the material against plastic slip, thus leading to a stronger material. Characterising and hence exploiting and optimising LEDS is a key step in materials design: it would allow designers to construct lightweight structures which nevertheless have a high resistance to deformation, resulting, e.g., in safer and more fuel-efficient cars. Therefore, every advance in our research is relevant to mechanical engineering and industry.The research in this project however goes beyond the specific example of defects in metals. Dislocations are a paradigmatic example of a complex particle system and the analysis developed here would be applicable to a variety of problems dealing with the derivation of the collective behaviour of a large number of individual agents, e.g., crowd and traffic dynamics, swarming, networks.

金属，尤其是钢铁在我们的日常生活中起着基本作用，并用于从建筑业到运输，能源，包装和房屋的无数应用中。但是，不同的应用需要不同的金属材料特性，这些材料特性需要设计以满足要求。材料设计反过来需要深入了解金属对化学成分和微观结构的机械行为的依赖性。如果没有对错位的良好理解，这是不可能的。依次是金属的原子结构中的缺陷，这些缺陷在宏观尺度上共同确定金属的变形。因此，任何旨在实现预测能力的宏观模型都必须考虑到这些缺陷的存在。但是，由于即使是一小部分金属样本中的典型位位数也很高，因此制定了一个模型，该模型可以跟踪每个位错，除了非常小的问题外，这是不可行的。尽管在原子晶格的级别上可以使用良好的位错模型，但尚不妥善理解如何将其存在和运动的效果纳入宏观工程量表的模型。在过去的十年中，这一挑战已成为强化研究的重点 - 在工程社区中，由于需要良好的宏观模型来开发新的金属和合金，以及在数学社区中，它在理解复杂的多尺度方面所扮演的核心作用系统。多年来，在不同的社区中，这一挑战已通过多种方式应对。严格方法的最大优势是它是准确的。但是，支付的价格是对可以分析的配置的强烈限制。在大多数数学文献中，位错被建模为直线和平行线，而实际上它们是三维曲线。尽管这种理想化的环境中的数学挑战仍然无数，但这种假设降低了理论的复杂性。近年来，一种特别关注的特殊配置是垂直周期性的脱位壁，类似于低角度的晶界。他们之所以如此受欢迎的原因之一是人们普遍认为它们代表了脱位的最低能量安排。拟议的研究提出了一个更基本的问题：脱位的能量有利的配置是什么？而且，当模型中引入小但非零的温度时，低能脱位结构如何变化？低能脱位结构（LED）（例如墙壁，簇和细胞）是微观结构的主要特征之一金属。这些高密度构型增加了材料对塑料滑动的阻力，从而导致了更强的材料。表征并利用和优化LED是材料设计的关键步骤：它将允许设计师构建轻质的结构，尽管如此，这些结构仍然具有很高的变形，例如，以更安全，更省油的汽车为例。因此，我们研究中的每一个进步都与机械工程和行业有关。但是，该项目的研究超出了金属缺陷的具体例子。位错是复杂粒子系统的范式示例，此处开发的分析将适用于处理大量单个代理的集体行为的各种问题，例如人群和流量动态，蜂群，网络，网络。