NSF-BSF: DYNAMICS OF MATERIALS FAILURE

美国国家科学基金会和美国-以色列两国科学基金会（BSF）共同支持美国研究人员和以色列研究人员之间的合作。NSF材料研究部（DMR）资助该奖项，该奖项支持专注于材料失效动态的研究和教育活动。为运输、储能或生物医学植入物设计安全、坚固的材料需要对裂纹扩展有基本的了解，这是材料失效的最常见模式。 该项目旨在了解裂纹如何在脆性材料中传播，如玻璃，陶瓷和一些聚合物材料和金属，这些材料通常会突然断裂。虽然传统断裂力学预测脆性裂纹应该沿着沿着直线路径快速加速，以达到声音在平坦表面上传播的速度，但实验观察到裂纹达到不到该速度的一半。由于根本上不了解的原因，裂纹扩展变得动态不稳定，从而导致裂纹强烈偏离直线路径，并阻止它们达到其音速极限速度。这项研究将集中在使用计算和模型，以产生一个更完整的图片不稳定的裂纹扩展脆性材料的各种断裂几何形状的实验研究和不同的材料结构和性能。 对动态断裂不稳定性的基本认识有望提高我们对材料失效的基本理论理解，有助于计算方法和裂纹理论的进一步发展。理解的进步可能有助于预测各种生物，工程和地球物理材料的失效。该项目将有助于在美国和以色列的本科生和研究生的培训，并包括在这两个国家的学校推广和教学活动。美国国家科学基金会和美国-以色列两国科学基金会（BSF）共同支持美国研究人员和以色列研究人员之间的合作。美国国家科学基金会材料研究部资助该奖项，支持裂纹扩展的研究和教育，这是一个既有基础又有实际意义的主题。虽然线弹性断裂力学的经典理论预测，脆性材料中的裂纹应平稳地加速到其声波极限速度，但广泛观察到裂纹在达到该速度之前发展动态不稳定性。根据不稳定性的起始速度和维数，不稳定性可以是多种多样的和复杂的。它们可以表现为刻面形成、微分支、裂纹尖端振荡或尖端分裂。尽管它们与凝聚态物理学和材料科学中的其他界面模式不稳定性具有根本的重要性和明显的相似性，但维度和材料特性，如弹性非线性和非均匀性，PI建议将新的理论和计算方法联合收割机结合起来，从根本上理解这些机制，各种动态断裂不稳定性的相互关系。计算研究将利用相场方法，该方法描述了一组自洽方程内的故障和宏观弹性的短尺度物理学，可用于模拟复杂的裂纹路径，并建立与实验的定量基准比较。模拟将指导，他们的结果解释，进一步发展的理论，占弹性非线性裂纹。研究将集中在调查的维度，异质性和非线性的动态不稳定性的作用，帮助解决很大程度上悬而未决的问题，如：为什么裂纹加速到接近其音速在准二维（2D）的几何形状，但成为不稳定的小平面形成或微分支的形式在3D几何形状在低得多的速度？3D不稳定性是由于裂纹前缘从2D中的点到3D中的线的维数增加，还是小平面或微分支的成核需要裂纹前缘与局部异质性的相互作用？最近相场模拟表明，弹性非线性及其相关的新兴长度尺度在2D高速裂纹的振荡不稳定性中发挥了关键作用，在3D不稳定性中发挥了作用？此外，刻面形成和微分支有何关系？模拟结果将定量比较脆性凝胶，这提供了独特的能力，可视化在断裂过程中的2D和3D在原位裂纹前沿动态的实验观察。对动态断裂不稳定性的基本认识有望提高我们对材料失效的基本理论理解，有助于相场方法和裂纹理论的进一步发展，这可能有助于预测各种自然、技术和地球物理脆性材料的失效。此外，该项目提供了独特的机会，通过K-12学校推广活动和研究生水平的教学材料，吸引和培训下一代科学家，这些材料由美国和以色列的PI开发和共享，使用简单的实验，教学模块，该奖项反映了NSF的法定使命，并被认为值得支持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。

NON-TECHNICAL SUMMARYThe National Science Foundation and the United States-Israel Binational Science Foundation (BSF) jointly support this collaboration between a US-based researcher and an Israel-based researcher. The NSF Division of Materials Research (DMR) funds this award, which supports research and educational activities focused on the dynamics of materials failure. Designing safe and robust materials for transportation, energy storage, or biomedical implants requires a basic understanding of crack propagation that is the most common mode of materials failure. This project is aimed at understanding how cracks propagate in brittle materials such as glass, ceramics, and some polymeric materials and metals, which typically fracture abruptly. While traditional fracture mechanics predicts that brittle cracks should rapidly accelerate along a straight path to reach the speed at which sound travels over a flat surface, cracks are experimentally observed to reach less than half of that speed. For reasons that are not fundamentally understood, crack propagation becomes dynamically unstable, thereby causing cracks to strongly deviate from a straight path and preventing them from reaching their sonic limiting speed. This research will center on using computation and models to produce a more complete picture of unstable crack propagation in brittle materials for various fracture geometries investigated experimentally and different materials structures and properties. Basic insights into dynamic fracture instabilities are expected to improve our fundamental theoretical understanding of materials failure, contributing to both further developments of computational methods and the theory of cracks. Advances in understanding may help predict the failure of a wide range of biological, engineering, and geophysical materials. This project will contribute to the training of undergraduate and graduate students in the US and Israel, and include school outreach and teaching activities in both countries. TECHNICAL SUMMARYThe National Science Foundation and the United States-Israel Binational Science Foundation (BSF) jointly support this collaboration between a US-based researcher and an Israel-based researcher. The NSF Division of Materials Research funds this award that supports research and education on crack propagation, a topic of both fundamental and practical interest. While the classical theory of linear elastic fracture mechanics predicts that cracks in brittle materials should smoothly accelerate to their sonic limiting velocity, cracks are widely observed to develop dynamic instabilities before reaching this velocity. Depending on the onset velocity of instability and dimensionality, instabilities can be varied and complex. They may manifest as facet formation, micro-branching, crack tip oscillations or tip splitting. Despite their fundamental importance and apparent similarities to other interfacial pattern instabilities in condensed-matter physics and materials science, how dimensionality and material properties, such as elastic nonlinearity and heterogeneities, individually or jointly contribute to produce those dynamic fracture instabilities remains poorly understood.The PIs propose to combine novel theoretical and computational approaches to understand at a fundamental level the mechanisms and interrelations of varied dynamic fracture instabilities. Computational studies will exploit the phase-field approach, which describes the short-scale physics of failure and macroscopic elasticity within a self-consistent set of equations that can be used to simulate complex crack paths and to establish quantitative benchmark comparisons with experiments. Simulations will be guided, and their results interpreted, by further development of a theory of cracks that accounts for elastic nonlinearity. Studies will center on investigating the role of dimensionality, heterogeneities, and nonlinearity in dynamic instabilities, helping to address largely unanswered questions such as: Why do cracks accelerate to nearly their sonic speeds in quasi two-dimensional (2D) geometries, but become unstable in the form of facet formation or micro-branching at much lower speed in 3D geometries? Are 3D instabilities due to the increased dimensionality of the crack front from a point in 2D to a line in 3D, or does nucleation of a facet or micro-branch require the interaction of the crack front with a localized heterogeneity? Does elastic nonlinearity and its associated emergent length scale, recently shown by phase-field simulations to play a key role in the oscillatory instability of high speed cracks in 2D, play a role in 3D instabilities? Moreover, how are facet formation and micro-branching related? Simulation results will be quantitatively compared to experimental observations in brittle gels, which provide unique capability to visualize in situ crack front dynamics in 2D and 3D during the fracture process. Basic insights into dynamic fracture instabilities are expected to improve our fundamental theoretical understanding of materials failure, contributing to both further developments of the phase-field method and the theory of cracks that may help predict the failure of a wide range of natural, technological, and geophysical brittle materials. In addition, this project offers unique opportunities for engaging and training the next generation of scientists through K-12 school outreach activities and graduate-level teaching material developed and shared by the PIs in the US and Israel, which use simple experiments, teaching modules, and projects to convey the excitement of understanding how things break.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.