No abstract

The existence of forbidden velocity gap in dynamic crack propagation in brittle crystals has been proposed previously, based on analytical calculations and numerical simulations. These suggested that the minimal velocity of a dynamically propagating crack is a significant portion of the Rayleigh wave speed. On the other hand, theoretical analysis based on continuum mechanics does not identify any lower limit to the crack velocity. In this work, we studied experimentally the crack velocity in glass and single-crystal silicon, in a geometry that constrains the crack profile to a nearly quarter elliptical shape, such that at a certain part of the crack it is forced to move appreciably slowly. Direct measurements show that the crack velocity along this profile decreases to less than 1% of the Rayleigh wave speed, both at room temperature and at 77 K, which is notably below the expected velocity gap.

We report on the exact shape of a propagating crack in a plate with a high width/thickness ratio and subjected to bending deformation. Fracture tests were carried out with brittle solids—single crystal, polycrystalline, and amorphous. The shape of the propagating crack was determined from direct temporal crack length measurements and from the surface perturbations generated during rapid crack propagation. The shape of the crack profile was shown to be quarter-elliptical with a straight, long tail; the governing parameter of the ellipse axes is the specimen's thickness at most length of crack propagation. Universality of the crack front shape is demonstrated. The continuum mechanics approach applicable to two-dimensional problems was used in this three-dimensional problem to calculate the quasistatic strain energy release rate of the propagating crack using the formulations of the dynamic energy release rate along the crack loci. Knowledge of the crack front shape in the current geometry and loading configuration is important for practical and scientific aspects.

The flute instability in mirror machines is driven by spatial charge accumulation and the resulting E×B plasma drift. On the other hand, E×B drift due to external electrodes or coils can be used as a stabilizing feedback mechanism. Fast photography is used to visualize Hydrogen plasma in a small mirror machine and infer the plasma drift and the internal electric field distribution. Using incompressible flow and monotonic decay assumptions we obtain components of the velocity field from the temporal evolution of the plasma cross section. The electric field perpendicular to the density gradient is then deduced from E=-V×B. With this technique we analyzed the electric field of flute perturbations and the field induced by electrodes immersed in the plasma.

We show that intrinsic dislocations in brittle single crystals can be a source of strong local perturbations along the crack path. A theoretical model was developed which predicts substantial crack front deflections. Investigating the crack surfaces in Si crystals with induced dislocation density of 10(9)-10(10) cm(-2) revealed a significant amount of crack front perturbations in the form of V-shaped grooves, which were completely missing in dislocation-free Si specimens. The measured depths of the perturbations were in the range of 2-20 nm and in excellent agreement with the theoretical model.