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

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.

Energy considerations in crack deflection phenomenon in single crystal silicon

“…its velocity on the bottom surface and parallel to the x axis of the specimen, see Fig. 1a) versus time on the top surface is similar to that on the bottom surface (Be'ery et al 2003), indicating that the velocity on the bottom surface is free of constraint. Indeed, that velocity is on the same scale as the Rayleigh surface wave speed.…”

“…It is again emphasized that these calculations were based on the Wallner lines in the thin (1 × 25 × 45 mm 3 ) glass specimen. It was found to match the crack front completely in silicon in the case of a crack propagating along the (1 1 0) cleavage plane (Be'ery et al 2003;Sherman and Be'ery 2003a). In both materials the fracture surfaces are atomistically smooth.…”

“…A computerized procedure was used to correlate between the voltage-time plot obtained during dynamic crack propagation and the required crack tip velocity-crack length plot via the resistivity-crack length relationship of the calibration. Crack velocity had previously been analyzed in glass, polycrystalline alumina, and silicon (Sherman and Be'ery 1998a, b, 2000, 2002, 2004aBe'ery et al 2003). An example of the measurements of the temporal crack length along the bottom and the top surfaces of glass and of silicon on the (1 1 0) plane are shown in Fig.…”

“…The crack's normal velocity on the bottom side is parallel to the x direction, but as the crack climbs to the upper side, its normal velocity gradually rotates towards the y direction, which coincides with the [0 0 1] direction in our specimens. The amplitude of the normal velocity decreases by two orders of magnitude and was estimated (Be'ery et al 2003) to be of the order of several tens of m/s. A summary of the behavior of the crack front is shown in Fig.…”

Low Speed Crack Propagation via Kink Formation and Advance on the Silicon (110) Cleavage Plane

“…Lattice trapping on this scale would imply that perfect brittle crystals are much stronger than the Griffith strength 2γ and that cracks, once they move, always move very fast [9]. These two conjectures have not been universally confirmed by experiments, some of which have detected cracks moving at less than 1% of the Rayleigh speed at both room temperature and 77 K [16]. We note, however, that these experiments were carried out in air, and the measured speed is low enough to enable propagation by stress corrosion [17].…”