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We consider the impact fragmentation of two spherical solid bodies sensitiveto strain rate in a three-dimensional (3D) setting. We use both dimensionalanalysis and numerical simulations by smoothed-particle hydrodynamics (SPH)method to shed light on this problem. The key point of the work is theassumption of complete self-similarity of the problem under consideration withrespect to the effective strain rate parameter Eeff, which is verified bynumerical simulations. As a result we consider the two cases corresponding tothe high-velocity Eeff >> 1, and low-velocity Eeff <<1 loading. The size of thesystem may be characterized by the total number of the SPH particles Ntotapproximating each sphere. It is shown that for finite system the criticalvelocity of fragmentation at high-velocity loading exceeds that at low-velocityloading . With an unlimited increase in the system size these velocities becomethe same. It is shown that the critical velocity of fragmentation depend on thesystem size in a quadratic manner, i.e. Vc^2 -Vc(inf)^2 ~ Ntot ^(1/3nu) wherenu is a correlation length exponent.

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