  The freeze-out process in heavy ion collisions is driven by the competition
between the scattering rate and the expansion rate of the matter. We analyse
the expansion rate $\Theta$ (often called Hubble flow) in relativistic heavy
ion collisions in the FAIR and RHIC-BES energy regimes and compare it to the
scattering rate $\Gamma$ using the UrQMD transport model. We observe that the
time evolution of the system is clearly separated into a compression phase and
an expansion phase with time dependent $\Theta_\parallel$ and $\Theta_\perp$.
The calculated values of the Hubble expansion at kinetic decoupling are in line
with previous simple estimates by statistical hadronization models with a
Siemens-Rasmussen type emission source. However, the actual shape of the
expanding matter is, as expected, found to be between a spherically symmetric
and a purely longitudinal expansion. We confirm for the first time in a
microscopic simulation that the decoupling hypersurface is indeed determined by
the competition of the expansion rate $\Theta$ and the scattering rate $\Gamma$
as suggested previously. This suggests that, in the range of collision energies
explored in this study, simple iso-thermal/iso-energy density criteria that are
often used in hybrid models to couple hydrodynamic and transport simulations
may not capture the true decoupling hyper-surface.
