The 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.
The 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.
