Scale Bridging in Ductile Fracture via Kernel-based Machine Learning

铝和钢等延展性金属在能源、国防和交通等各种行业中无处不在，因此影响着每个人的日常生活。不幸的是，人们对韧性金属失效或断裂的机制知之甚少，这使得准确预测断裂何时发生变得困难。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、更耐断裂材料的能力，例如高温材料。该项目的目标是制定一种基于物理的、机器学习的韧性断裂模型，从而降低产品成本，提高能源效率。例如，生产更轻的车辆结构的能力将减少车辆的碳排放，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新的建模和机器学习模块向高中生推广科学和工程。在与一名高中教育工作者的合作下，这些学习模块将在一所高中物理教室中进行试点。通过孔洞成核、生长和合并的韧性断裂模型在很大程度上是现象学的，具有许多难以确定的不确定参数。在该项目下，将通过将分子动力学模拟与基于核的机器学习相结合，开发一种预测的、微机械的空洞成核模型。分子动力学模拟将揭示硬粒子空穴成核的基本机理，同时量化空穴成核速率。这一速率受到一系列特性的影响，包括应力、温度和空位、溶质和位错等缺陷。为了使模型开发易于处理，将制定一组基于核的机器学习模型和算法，其目标有两个：(i)提取和设计用于量化微结构成核速率的最小尺寸的物理特征集，以及（ii）概率地在该微结构特征集和成核速率之间建立精确的封闭式统计映射。最后，所得到的机器学习模型将作为常用的韧性断裂Gurson-Tvergaard-Needleman模型的一部分实现到有限元方法中。这项工作将作为机器学习的原型，用于将纳米和微尺度信息升级为工程尺度模型。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.