Scale Bridging in Ductile Fracture via Kernel-based Machine Learning

铝和钢等延性金属广泛应用于能源、国防、交通等各个行业，影响着每个人的日常生活。不幸的是，人们对延性金属失效或破裂的机制知之甚少，因此很难准确预测何时会发生断裂。这些知识差距推高了产品的成本，降低了它们的能源效率，并限制了我们开发未来能源和国防应用所需的更强大、更耐断裂的材料的能力，例如高温材料。该项目的目标是制定一种基于物理知识、机器学习的延性断裂模型，从而降低产品成本和提高能源效率。例如，生产更轻的汽车结构的能力将减少汽车的碳排放，同时降低消费者的燃料成本。该项目将通过研究项目和丰富的课堂教学向本科生推广科学和工程，并通过为高中课堂开发以建模和机器学习为重点的新模块向高中生推广科学和工程。在与高中教育工作者的合作下，这些学习模块将在高中物理课堂上进行试点。通过空洞形核、长大和合并而形成的韧性断裂模型在很大程度上是现象学的，有许多不确定的参数很难确定。在该项目下，通过将分子动力学模拟与基于核的机器学习相结合，将开发一个可预测的、微观力学信息的空穴成核模型。分子动力学模拟将揭示硬粒子上空穴成核的基本机制，同时量化空穴成核率。这一速率受到一大组特征的影响，包括应力、温度和缺陷，如空位、溶质和位错。为了使模型开发变得容易，一组基于核的机器学习模型和算法将被制定为两个目标：(I)提取和设计用于量化微结构中的成核率的最小尺寸的物理特征集，以及(Ii)在该微结构特征集和成核率之间以概率的方式建立精确的闭合形式的统计映射。最后，将得到的机器学习模型应用到有限元方法中，作为常用的Gurson-Tvergaard-Needleman延性断裂模型的一部分。这项工作将作为使用机器学习将纳米和微尺度信息提升到工程规模模型的原型。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Ductile metals such as aluminum and steel are used ubiquitously across a variety of industries such as energy, defense, and transportation, and thus impact everyone’s daily life. Unfortunately, the mechanisms by which ductile metals fail or crack are poorly understood, making it difficult to accurately predict when fracture will occur. These knowledge gaps drive up the costs of products, decrease their energy efficiency, and limit our ability to develop stronger, more fracture-resistant materials needed for future energy and defense applications, e.g., high-temperature materials. The goal of this project is to formulate a physics-informed, machine-learning-enabled model for ductile fracture that will lead to reduced product costs and higher energy efficiency. For example, the ability to produce lighter vehicle structures would reduce vehicle carbon emissions while simultaneously reducing fuel costs for consumers. The project will promote science and engineering to undergraduates through research projects and enriched classroom instruction, and to high school students through the development of new modeling- and machine learning-focused modules for high school classrooms. In collaboration with a high school educator, these learning modules will be piloted in a high school physics classroom. Models of ductile fracture via nucleation, growth and coalescence of voids are largely phenomenological with many uncertain parameters that are difficult to determine. Under this project, a predictive, micromechanically informed model for void nucleation will be developed by coupling molecular dynamics simulations with kernel-based machine learning. Molecular dynamics simulations will reveal the fundamental mechanics underlying void nucleation at hard particles while quantifying the void nucleation rate. This rate is affected by a large set of features, including stress, temperature, and defects such as vacancies, solutes, and dislocations. To render model development tractable, a set of kernel-based machine learning models and algorithms will be formulated with two objectives: (i) to extract and engineer a minimally sized set of physical features for quantifying nucleation rates in microstructures, and (ii) to probabilistically establish an accurate closed-form statistical mapping between this microstructural feature set and the nucleation rates. Finally, the resulting machine learning model will be implemented into the finite element method as part of the commonly used Gurson-Tvergaard-Needleman model for ductile fracture. This effort will serve as a prototype for the use of machine learning towards upscaling of nano- and microscale information to engineering scale models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.