We investigate the origin of Paris's law, which states that the velocity of a crack at subcritical load grows like a power law, da/dt ∼ (Δ K)^m, where Δ K is the stress intensity factor amplitude. Starting from a damage accumulation function proportional to (Δσ)^γ, Δσ being the stress amplitude, we show analytically that the asymptotic exponent m can be expressed as a piecewise-linear function of the γ_c, and m=γ for γ>γ_c, reflecting the existence of a critical value γ_c=2. the existence of a

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... ritical law with a critical functions m result for finite sizes. Finally, we introduce bounded disorder in the breaking thresholds and find that below γ_c disorder is relevant, i.e., the exponent m is changed, while above γ_c disorder is irrelevant.