#Subsonic vs supersonic full
#Subsonic vs supersonic crack

Our main technical tool to provide this discussion is the atomic theory of dynamic cracks.

#Subsonic vs supersonic crack

The deformations around the crack tip take a completely different form from the one they have in the subsonic regime. In particular, we will show that, as a crack approaches the Rayleigh wave speed, the stress intensity factor K I, upon which the continuum theory depends, stops being defined. What we will explain in detail is the specific way that the continuum argument breaks down. Thus, we are not sure that hyperelasticity is actually needed to promote supersonic cracks.įurthermore, the original objection from continuum theory about the impossibility of supersonic cracks has not directly been addressed. As shown, for example, in the current article supersonic cracks exist equally well in materials without hyperelastic constitutive laws. Supersonic cracks were also observed for cracks with hyperelastic constitutive laws that cause stiffening near the tip. This last reference contains an extended discussion of how crack speed depends upon loading for the models studied in this manuscript. Both explicit numerical solutions for atomic equations of motion and the corresponding analytical solutions show the supersonic cracks do in fact exist. The experiments led to theoretical descriptions for supersonic cracks in tension.

Additional experimental work confirmed that the cracks do travel faster than the transverse wave speed. Ĭracks in rubber under tension were found to have a wedge-like tip suggestive of supersonic motion. Dynamic fracture theory was extended to include these ‘intersonic’ cracks. These suggested computer simulations, and laboratory experiments for cracks that move by sliding faces past each other, showing that cracks in shear (mode II) can move faster than the transverse wave speed c t (and hence the Rayleigh wave speed as well) and reach speeds close to the longitudinal speed c l.

The first indications came from measurements of earthquakes. However, there is evidence that such cracks exist after all. One resolution of these problems is to conclude that cracks travelling faster than the Rayleigh wave speed in tension are not physically allowed. An expression saying that cracks moving above the Rayleigh wave speed need negative energy seems physically impossible, and an expression requiring imaginary energy seems even worse. Once the crack speed exceeds the transverse wave speed, the expression becomes imaginary. The denominator of this expression vanishes when the crack speed v reaches the Rayleigh wave speed, and for slightly higher velocities it becomes negative. Where v is the crack speed, c l and c t are longitudinal and transverse wave speeds, respectively,, , μ is a Lamé constant, and K I, the mode I dynamic stress intensity factor, is the coefficient of a universal singularity that develops outside of cracks that run as they are pulled symmetrically in tension from above and below. This is one reason supersonic cracks in tension had been thought not to exist. Thus, while supersonic cracks are no less physical than subsonic cracks, the connection between microscopic and macroscopic behaviour must be made in a different way. Subsonic cracks are characterized by small-amplitude, high-frequency oscillations in the vertical displacement of an atom along the crack line, while supersonic cracks have large-amplitude, low-frequency oscillations.

For supersonic cracks, the stress intensity factor disappears. Subsonic cracks feature displacement fields consistent with a stress intensity factor. Using our analytical methods, we examine in detail the motion of atoms around a crack tip as crack speed changes from subsonic to supersonic. Cracks that propagate faster than the Rayleigh wave speed have been thought to be forbidden in the continuum theory, but clearly exist in lattice systems. This allows quick numerical evaluation of solutions for very large systems, facilitating comparisons with continuum fracture theory.

#Subsonic vs supersonic full

We present the full analytical solution for steady-state in-plane crack motion in a brittle triangular lattice.