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.
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