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Register a new userHow moving cracks in brittle solids choose their path
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Lital Rozen-Levy
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While we fundamentally understand the dynamics of simple cracks propagating in brittle solids within perfect (homogeneous) materials, we do not understand how paths of moving cracks are determined. We experimentally study strongly perturbed cracks that propagate between 10-95% of their limiting velocity within a brittle material. These cracks are deflected by either interaction with sparsely implanted defects or via an intrinsic oscillatory instability in defect-free media. Dense, high-speed measurements of the strain fields surrounding the crack tips reveal that crack paths are governed by the direction of maximal strain energy density. This fundamentally important result may be utilized to either direct or guide running cracks.
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Statistical models are essential to get a better understanding of the role of disorder in brittle disordered solids. Fiber bundle models play a special role as a paradigm, with a very good balance of simplicity and non-trivial effects. We introduce here a variant of the fiber bundle model where the load is transferred among the fibers through a very compliant membrane. This Soft Membrane fiber bundle mode reduces to the classical Local Load Sharing fiber bundle model in 1D. Highlighting the continuum limit of the model allows to compute an equivalent toughness for the fiber bundle and hence discuss nucleation of a critical defect. The computation of the toughness allows for drawing a simple connection with crack front propagation (depinning) models.
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Predicting when rupture occurs or cracks progress is a major challenge in numerous elds of industrial, societal and geophysical importance. It remains largely unsolved: Stress enhancement at cracks and defects, indeed, makes the macroscale dynamics extremely sensitive to the microscale material disorder. This results in giant statistical uctuations and non-trivial behaviors upon upscaling dicult to assess via the continuum approaches of engineering. These issues are examined here. We will see: How linear elastic fracture mechanics sidetracks the diculty by reducing the problem to that of the propagation of a single crack in an eective material free of defects, How slow cracks sometimes display jerky dynamics, with sudden violent events incompatible with the previous approach, and how some paradigms of statistical physics can explain it, How abnormally fast cracks sometimes emerge due to the formation of microcracks at very small scales.
Amorphous solids display a ductile to brittle transition as the kinetic stability of the quiescent glass is increased, which leads to a material failure controlled by the sudden emergence of a macroscopic shear band in quasi-static protocols. We numerically study how finite deformation rates influence ductile and brittle yielding behaviors using model glasses in two and three spatial dimensions. We find that a finite shear rate systematically enhances the stress overshoot of poorly-annealed systems, without necessarily producing shear bands. For well-annealed systems, the non-equilibrium discontinuous yielding transition is smeared out by finite shear rates and it is accompanied by the emergence of multiple shear bands that have been also reported in metallic glass experiments. We show that the typical size of the bands and the distance between them increases algebraically with the inverse shear rate. We provide a dynamic scaling argument for the corresponding lengthscale, based on the competition between the deformation rate and the propagation time of the shear bands.
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