  We consider the impact fragmentation of two spherical solid bodies sensitive
to strain rate in a three-dimensional (3D) setting. We use both dimensional
analysis and numerical simulations by 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 Eeff, which is verified by
numerical simulations. As a result we consider the two cases corresponding to
the high-velocity Eeff >> 1, and low-velocity Eeff <<1 loading. The size of the
system may be characterized by the total number of the SPH particles Ntot
approximating each sphere. It is shown that for finite system the critical
velocity of fragmentation at high-velocity loading exceeds that at low-velocity
loading . With an unlimited increase in the system size these velocities become
the same. It is shown that the critical velocity of fragmentation depend on the
system size in a quadratic manner, i.e. Vc^2 -Vc(inf)^2 ~ Ntot ^(1/3nu) where
nu is a correlation length exponent.
