Subcritical Crack Growth: The Microscopic Origin of Paris' Law

André P. Vieira, José S. Andrade, Hans J. Herrmann
2008 Physical Review Letters  
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
more » ... 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.
doi:10.1103/physrevlett.100.195503 pmid:18518459 fatcat:4iewk7kugban7hx4w2fyext2ba