Critical behavior for impact fragmentation of spherical solid bodies sensitive to strain rate

We consider the impact fragmentation of two spherical solid bodies sensitive to the strain rate in a three-dimensional setting. We use both dimensional analysis and numerical simulations by the smoothed-particle hydrodynamics (SPH) method to shed light on this problem. The key point of the work is the assumption of complete self-similarity of the problem under consideration with respect to the effective strain rate parameter (epsilon) over dot(eff), which is verified by numerical simulations. As a result, we consider the two cases corresponding to high-velocity (epsilon) over dot(eff) >> 1 and low-velocity (epsilon) over dot(eff) << 1 loading. The size of the system may be characterized by the total number of SPH particles N-tot approximating each sphere. It is shown that for the finite system the critical velocity of fragmentation at high-velocity loading exceeds that at low-velocity loading, i.e. V-c infinity > V-c0. With an unlimited increase in the system size, these velocities become the same. It is shown that V-c8 and V-c0 depend on the system size in a quadratic manner, i.e. V-c(2) - V-c(2) (infinity) proportional to N-tot(-1/3 nu) where nu is a correlation length exponent.

Automated summary

This study examines the sensitivity of fragmentation of two spherical solid bodies in a three-dimensional environment to strain rate, using dimensional analysis and numerical simulations. The complete self-similarity of the problem with respect to the effective strain rate parameter is verified through simulations. The critical velocities of fragmentation at high-velocity loading exceed those at low-velocity loading in finite systems but become the same in infinitely large systems, with the critical velocities depending quadratically on system size.