Data-driven modelling of irradiation induced defects in fusion materials

摘要：用于建造聚变反应堆的材料受到高能辐射的轰击。就金属而言，辐照会导致位错环的积累，这些位错环自组织成复杂的微结构，从而改变材料的机械性能。为了准确预测这一现象，需要新的模型。因此，这个项目将致力于开发一种新的数学框架，将位错环的离散原子模型与连续介质微分方程联系起来。所得到的模型层次将被用于计算预测位错环微结构的演变，提供对钨适合于聚变应用的评估。背景：位错是晶体中发现的拓扑线缺陷，是金属塑性的载体，即不可逆变形。位错的发现是20世纪的一项关键科学成就，为数千年来人类能够加工金属的机制提供了解释。因此，了解位错在金属样品中的行为对于了解它可能如何变形、破裂和失效至关重要。研究位错的一个关键复杂性是位错的数量：一立方厘米的钨可能含有大约1万公里的位错线。此外，位错通过材料中的应力场以复杂的非局部方式相互作用。描述这一点的数学理论在过去的60年里已经得到了发展，这个项目试图在一个新的环境中利用其中的一些进展(见下面的参考文献)。特别是在聚变材料中，材料暴露在高能辐射的轰击下，使它们脱离通常的平衡环境。这是材料工程的一个全新的前沿，因此新的数学和计算模型正在开发中。使用HetSys培训中开发的计算和数学方法，参与该项目的学生将研究钨的物理性质，并将其与实验数据一起用于开发位错环微结构的新模型体系。我们将在该项目中探索的一个可能方向是，采用位错环相互作用的离散模型，并传递到环密度的连续极限，从而允许高效的统计计算，以便与实验数据进行比较。

Summary: The materials used to build a fusion reactor undergo bombardment from high-energy radiation. In the case of metals, irradiation causes the accumulation of dislocation loops which self-organise into complex microstructures, changing the mechanical properties of the material. To predict this phenomenon accurately, new models are needed. This project will therefore focus on developing a new mathematical framework to connect discrete atomistic models of dislocation loops to continuum differential equations. The resulting modelling hierarchy will be applied computationally to predict the evolution of dislocation loop microstructures, providing an assessment of tungsten's suitability for fusion applications.Background: Dislocations are topological line defects found in crystals, and are the carriers of plasticity in metals i.e. irreversible deformation. The discovery of dislocations was a key scientific achievement of the 20th century, providing an explanation of the mechanism by which humanity has been able to work metals for thousands of years. As such, understanding how dislocations behave in a metal sample is crucial to understanding how it may deform, crack and fail. A key complexity in studying dislocations is their number: a single cubic centimetre of tungsten may contain on the order of 10,000km of dislocation line. Moreover, dislocations interact in a complex non-local fashion through stress fields in the material. Mathematical theories to describe this have been developed over the last 60 years, and this project seeks to exploit some of these advances in a new setting (see references below).In fusion material in particular, materials are exposed to bombardment by high-energy radiation, taking them out of the usual equilibrium setting. This is a completely new frontier in materials engineering, and so new mathematical and computational models are in development in this setting. Using the computational and mathematical methodologies which are developed in HetSys training, the student working on this project will study the physical properties of Tungsten, and use this along with experimental data to develop a new modelling hierarchy for dislocation loop microstructures. A possible direction we will explore in the project is to take a discrete model of dislocation loop interaction and pass to a continuum limit for a density of loops, allowing efficient computation of statistics for comparison with experimental data.