Subcritical crack growth: the microscopic origin of Paris's law
| dc.creator | Vieira, André P. | |
| dc.creator | Andrade Jr., José S. | |
| dc.creator | Herrmann, Hans J. | |
| dc.date | 2008-06-23 | |
| dc.date.accessioned | 2026-07-07T09:46:10Z | |
| dc.date.available | 2026-07-07T09:46:10Z | |
| dc.description | We investigate the origin of Paris's law, which states that the velocity of a crack at subcritical load grows like a power law, $da/dt \sim (ΔK)^{m}$, where $ΔK$ 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 %damage accumulation exponent $γ$, namely, $m=6-2γ$ for $γ< γ_{c}$, and $m=γ$ for $γ\ge γ_{c}$, reflecting the existence of a critical value $γ_{c}=2$. %In this way, here we discover the existence of a critical %value $γ_{c}=2$ characterized by a scaling law with a critical %exponent separating two regimes of different linear functions $m %(γ)$. We performed numerical simulations to confirm this 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. | |
| dc.description | 4 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0806.3658 | |
| dc.identifier | http://arxiv.org/abs/0806.3658 | |
| dc.identifier | Phys. Rev. Lett. 100, 195503 (2008) | |
| dc.identifier | doi:10.1103/PhysRevLett.100.195503 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163436 | |
| dc.subject | Materials Science | |
| dc.subject | Statistical Mechanics | |
| dc.title | Subcritical crack growth: the microscopic origin of Paris's law | |
| dc.type | text |