Subcritical crack growth: the microscopic origin of Paris's law

Abstract

We investigate the origin of Paris's law, which states that the velocity of a crack at subcritical load grows like a power law, $da/dt\sim (\Delta K{)}^m$, where $\Delta K$ is the stress intensity factor amplitude. Starting from a damage accumulation function proportional to $(\Delta \sigma {)}^{\gamma }$, $\Delta \sigma$ 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 $\gamma$, namely, $m=6-2\gamma$ for $\gamma <{\gamma }_c$, and $m=\gamma$ for $\gamma \ge {\gamma }_c$, reflecting the existence of a critical value ${\gamma }_c=2$. %In this way, here we discover the existence of a critical %value ${\gamma }_c=2$ characterized by a scaling law with a critical %exponent separating two regimes of different linear functions $m$. We performed numerical simulations to confirm this result for finite sizes. Finally, we introduce bounded disorder in the breaking thresholds and find that below ${\gamma }_c$ disorder is relevant, i.e., the exponent $m$ is changed, while above ${\gamma }_c$ disorder is irrelevant.

4 pages, 4 figures

References in corpus (1)

• Statistical Models of Fracture

Cited by in corpus (1)

• A mesoscopic approach to subcritical fatigue crack growth