  Cosmic Rays (CR) process the matter of the Interstellar Medium. Such
energetic processing not only modifies the interstellar matter but also injects
chemical species in the gas phase. In this work, we study the effect of the CR
on the astrophysical polycyclic aromatic hydrocarbons (PAH). For events in
which many electrons are stripped out from the PAH by interaction with a heavy
cosmic ray particle, coulomb explosion takes place and carbon chains are
produced. The fragments production rates of carbon chains are of particular
interest for astrophysical models. We computed PAH multi-ionization cross
sections with an Independent Atom and Electron collisional model. We introduced
and used a model to predict the fragmentation pattern for the coulomb
explosion. Experimental measurements on small hydrocarbons, C$_{60}$ and PAHs
were used to set confidence intervals on the calculations results.
  The carbon chains production rates were calculated using different CR fluxes
and elemental compositions, to account for the variations expected in various
astrophysical environments. A range of PAH sizes and compactness were also
explored. The PAH lifetime with respect to a standard interstellar CR flux
(corresponding to an H$_2$ ionization rate of $\zeta \approx$
6.10$^{-17}$s$^{-1}$) is found to be in the order of a few billion years. The
production rates of interstellar carbon chains containing around 5-15 carbon
atoms are in the order of few to many tens of percent of the H$_2$ ionization
rate $\zeta$. The exact rate value relies on the nature of the PAH and on the
CR composition. In diffuse medium, with ten percent of the available cosmic
carbon locked in PAHs, this process leads to carbon chain fractional abundances
at steady state, in the range of $10^{-15}$-$10^{-14}$, with a confidence
interval of about one order of magnitude. It reaches $10^{-13}$ in quiescent
dense clouds.
