  The analysis of cosmic rays fluxes as a function of energy reveals a {\it
knee} slightly below $10^{16}$ eV and an {\it ankle} close to $10^{19}$ eV.
Their physical origins remain up to now quite enigmatic; in particular, no
elementary process is known which occurs at energies close to $10^{16}$ eV. We
propose a phenomenological approach along the lines of nonextensive statistical
mechanics, a formalism which contains Boltzmann-Gibbs statistical mechanics as
a particular case. The knee then appears as a crossover between two
fractal-like thermal regimes, the crossover being caused by process occurring
at energies ten million times lower than that of the knee, in the region of the
quark hadron transition ($\simeq 10^{9}$ eV). This opens the door to an
unexpected standpoint for further clarifying the phenomenon.
