Pressure shock fronts in dynamic shear ruptures
Dynamic fracture of both engineering and geological materials and structures produces effects that are part of our everyday experience due to their catastrophic consequences. How fast can shear cracks propagate is a fundamental problem in fracture mechanics that has attracted the attention of the scientific community for several decades.
When a shear crack propagates faster than the shear wave speed of the material, a shock front results from the coalescence of the shear wavelets emitted by the near-crack-tip region. Cracks in solids emit both pressure and shear waves, but such a shock front should not be possible for pressure waves, because cracks should not be able to exceed the pressure wave speed in isotropic linear-elastic solids.
We have experimentally observed for the first time dynamic shear cracks in viscoelastic polymers that result in the formation of a pressure shock front (Gori, Rubino, Rosakis, Lapusta, Nature Communications, 2018), in addition to the shear one, using our ultrahigh-speed imaging technique. This apparent violation of classic theories is explained by the highly strain-rate-dependent material behavior of polymers, resulting in a heterogeneous field of effective elastic properties. While the crack speed exceeds the lower, far-field, wave speed, it remains below the highest pressure wave speed prevailing locally around the crack tip.
Full-field particle velocities and strain rates for supersonic ruptures. Ruptures in both PMMA (left) and Homalite-100 (right) exhibit two pairs of shock fronts, the pressure and the shear one (colored dashed lines). (a,b) Interface-parallel particle velocity. (c, d) Volumetric strain rate. (e, f) Shear strain rate. The volumetric strain-rate field (c and d) clearly shows the presence of the pressure shock front, whereas the shear strain-rate field (e and f) highlights the shear shock front. Credit: Gori, Rubino, Rosakis, Lapusta, Nature Communications (2018).
The time evolution of the volumetric strain rate clearly shows the formation of pressure and shear shock fronts. Note that the pressure shock front is extensional for the top half of the specimen and compressional for the bottom half, according to the left-lateral motion of the right-traveling shear rupture.
Rupture displaying pressure and shear shock fronts
These findings are of great interest for a number of engineering and geological applications, such as failure of bonded solids and earthquake dynamics, since they explain how viscoelastic media can fracture catastrophically in the presence of highly non-uniform strain-rate conditions. This is important because most man-made and natural materials, including rocks, exhibit some viscoelastic behavior in the presence of high strain rates, which are typically associated with propagating dynamic cracks.