Ilan Be'ery

On the lower limiting velocity of a dynamic crack in brittle solids

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.

Shape and energies of a dynamically propagating crack under bending

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 specimens 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.

NONLINEAR ANALYSIS OF THE FRACTURE SURFACE OF A SINGLE-CRYSTAL BRITTLE SOLID

Abstract The dynamical behavior of a spatial fracture mechanism in a rapid crack in a single-crystal brittle solid was under investigation. Wide thin strips like specimens were fractured under three-point bending. The spatial mechanism was photographed and digitized, and the results were then studied using nonlinear analysis. The nonlinear tools used were correlation dimension, false nearest neighbor, null hypothesis surrogate data, and the dominant Lyapunov exponent. The governing equation of motion in the analyzed region is a differential equations with a minimum of seven independent dynamical variables, in contrast to a single independent variable used in analytical calculations.

Measuring drift velocity and electric field in mirror machine by fast photography

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.

Spectroscopy of a nitrogen capillary discharge plasma aimed at a recombination pumped X-Ray laser

Summary form only given. The recombination pumping scheme for soft X-Ray lasers has better energy scaling, than the collisional-excitation pumping scheme. Implementation of an H-like 3→2 Nitrogen recombination laser, at »∼13.4nm requires initial conditions of at least 50% fully stripped Nitrogen, kTe∼140eV and electron density of ∼1020cm−3. In order to reach population inversion, the plasma cooling to below 60eV should be faster than the typical three-body recombination time. The goal of this study is achieving the required plasma conditions using a capillary discharge z-pinch apparatus. The experimental setup includes a 90mm alumina capillary coupled to a pulsed power generator of ∼60 kA peak current, with a rise time of ∼60ns. Various diagnostic techniques are applied to measure the plasma conditions, including X-Ray diode, time-resolved pinhole imaging and time-resolved spectroscopy analysed with a multi-ion collisional-radiative atomic model. For optimization of the plasma conditions, experiments were carried out in different capillary radii and different initial N pressures. The results show a fast cooling rate to below 60eV, demonstrating the feasibility of capillary discharge lasers.

Towards recombination pumped H-like N X-Ray laser

The recombination pumping scheme for soft X-Ray lasers has better energy scaling, than the collisional-excitation pumping scheme. Implementation of an H-like 3 → 2 Nitrogen recombination laser, at λ∼13.4 nm requires initial conditions of at least 50% fully stripped Nitrogen, kTe∼140eV and ne∼1020cm−3. In order to reach population inversion, the plasma cooling to below 60eV should be faster than the typical three-body recombination time. The goal of this study is achieving the required plasma conditions using a capillary discharge Z-Pinch apparatus. The experimental setup includes an alumina capillary coupled to a pulsed power generator of ∼60 kA peak current, with a quarter-period of 60 ns.