Macroscopic failure (fracture) processes are an ubiquitous phenomenon of immense practical importance. In this work, we use liquid aqueous foam as a soft matter model system to study crack propagation and fracture dynamics on length and time scales that are easily accessible in experiment. The experiment injects air at a given pressure into a single layer of bubbles between the parallel plates of a Hele-Shaw setup (a quasi-two-dimensional foam) and is thus able to track the positions and shapes of individual bubbles, which allows for a complete observation of microstructural processes during fracture. We observe that two very different modes of crack propagation are sustained by the system: a relatively slow propagation of an air finger characterized by plasticity around the crack tip (analogous to ductile failure), and a much faster propagation that breaks successive films without large deformations around the crack (analogous to brittle failure). Being composed of only air, water, and surfactant, the foam system allows for a detailed fluid-mechanical description of these processes, for which we derive quantitative relations of both ductile and brittle crack speed as a function of driving pressure. We show that there is a velocity gap between ductile and brittle speeds, and how the upper limit of ductile propagation speed and the lower limit of brittle propagation speed are determined by viscous dissipation and wave propagation in the foam, respectively. Our system also shows a novel phenomenon of transition between the brittle and ductile modes: a brittle crack can undergo a brittle-to-ductile transition (BDT) spontaneously, i.e., while it is propagating. We describe this process by taking into account the dissipative air flow in the crack opening behind the brittle crack tip, and succeed in predicting the location of the BDT as a function of the applied driving. In a given experiment, the speed, direction, and morphology of the crack is influenced significantly by the microstructure of the foam, i.e., the presence and orientation of defects and other irregularities. Throughout this work, we find that the geometry of foam bubbles and the liquid-carrying structures between them is the main determinant for the rich variety of processes observed. The novel experimental model system we have built therefore extends our knowledge of foam physics to previously unexplored phenomena and serves as a minimal model for failure of a cellular material, in which all physical processes and their relation to the material geometry are observable and quantifiable.
|Commitee:||Keer, Leon M., Lichter, Seth|
|School Location:||United States -- Illinois|
|Source:||DAI-B 71/12, Dissertation Abstracts International|
|Subjects:||Mechanical engineering, Condensed matter physics, Materials science|
|Keywords:||Aqueous foam, Brittle, Brittle-to-ductile transition, Crack propagation, Ductile, Fracture, Viscous fingering|
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