NSF-BSF: DYNAMICS OF MATERIALS FAILURE

美国国家科学基金会和美以两国科学基金会（BSF）共同支持一名美国研究人员和一名以色列研究人员之间的合作。该奖项由美国国家科学基金会材料研究部（DMR）资助，旨在支持材料失效动力学方面的研究和教育活动。为运输、能源储存或生物医学植入物设计安全和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。该项目旨在了解脆性材料（如玻璃、陶瓷、一些聚合物材料和金属）的裂纹如何扩展，这些材料通常会突然断裂。传统的断裂力学预测，脆性裂纹应该沿着一条直线迅速加速，达到声音在平面上传播的速度，但实验观察到，裂纹的速度不到该速度的一半。由于一些尚未从根本上了解的原因，裂纹扩展变得动态不稳定，从而导致裂纹严重偏离直线路径，使其无法达到音速极限速度。本研究将集中于利用计算和模型对实验研究的不同断裂几何形状和不同材料结构和性能的脆性材料中不稳定裂纹扩展产生更完整的图像。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认识，有助于进一步发展计算方法和裂纹理论。了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。该项目将有助于培养美国和以色列的本科生和研究生，并包括在两国的学校外展和教学活动。技术摘要：美国国家科学基金会和美以两国科学基金会（BSF）共同支持一名美国研究人员和一名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，以支持裂纹扩展的研究和教育，这是一个既具有基础意义又具有实际意义的主题。虽然经典的线弹性断裂力学理论预测脆性材料中的裂纹应该平滑地加速到其声速极限，但在达到该速度之前，裂纹被广泛观察到发展动态不稳定。根据不稳定的开始速度和维度，不稳定可以是变化的和复杂的。它们可能表现为小面形成、微分支、裂纹尖端振荡或尖端分裂。尽管它们与凝聚态物理和材料科学中的其他界面模式不稳定性具有基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质性）如何单独或共同促成这些动态断裂不稳定性仍然知之甚少。PIs建议将新的理论和计算方法结合起来，在基本层面上理解各种动态断裂不稳定性的机制和相互关系。计算研究将利用相场方法，该方法在一组自洽方程中描述了失效的短尺度物理和宏观弹性，可用于模拟复杂的裂纹路径，并与实验建立定量基准比较。模拟将被指导，他们的结果解释，通过裂缝理论的进一步发展，说明弹性非线性。研究将集中在调查维度、异质性和非线性在动态不稳定性中的作用，帮助解决一些悬而未决的问题，例如：为什么裂纹在准二维（2D）几何中加速到接近声速，但在三维几何中以小面形成或微分支的形式变得不稳定？三维不稳定性是由于裂缝前缘的维度从二维的一点增加到三维的一条线，还是一个面或微分支的成核需要裂缝前缘与局部非均质性的相互作用？最近相场模拟显示，弹性非线性及其相关的涌现长度尺度在二维高速裂纹的振荡不稳定性中起着关键作用，在三维不稳定性中是否也起作用？此外，关节突的形成和微分支是如何相关的？模拟结果将与脆性凝胶中的实验观察结果进行定量比较，从而提供了在破裂过程中以2D和3D方式可视化原位裂缝前缘动态的独特能力。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认识，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，该项目还为参与和培训下一代科学家提供了独特的机会，通过K-12学校外展活动和由美国和以色列的pi开发和共享的研究生水平的教材，这些教材使用简单的实验、教学模块和项目来传达理解事物如何破裂的兴奋。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。

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.