The effect of disorder on the fracture nucleation process

Abstract

The statistical properties of failure are studied in a fiber bundle model with thermal noise. We show that the macroscopic failure is produced by a thermal activation of microcracks. Most importantly the effective temperature of the system is amplified by the spatial disorder (heterogeneity) of the fiber bundle. The case of a time dependent force and the validity of the Kaiser effects are also discussed. These results can give more insight to the recent experimental observations on thermally activated crack and can be useful to study the failure of electrical networks.

Andrade, Omori, and time-to-failure laws from thermal noise in material rupture

“…Based on the analysis of a simple fiber bundle rupture model, Refs. [3,4] showed that the average lifetime of the fiber-bundle takes an Arrhenius form with an effective temperature renormalized from the bare temperature T to a value strongly amplified by the presence of the frozen disorder in the rupture thresholds f c (i), in agreement with experiments and numerical simulations. This result suggests that the usual assumption of neglecting the role of thermal fluctuations in material rupture processes at room temperature may actually be incorrect (see [5] for early discussions): due to frozen heterogeneities, tiny thermal fluctuations can be amplified many times, thus actually controlling the time-dependent aspects of failure.…”

“…(B11) in [3]), which shows that, for Φ > Φ * , the failure rate accelerates towards a finite-time singularity approximately as ∼ 1/(t c − t). Such a behavior has been documented extensively in experiments on rupture of heterogeneous material [6].…”

“…Up to now, there are no theory encompassing all these regimes. Here, we propose a simple mechanism that provides an explanation of all these observations, which is based on the recent proposal [3,4] that thermal noise is strongly renormalized by quenched heterogeneities. Based on the analysis of a simple fiber bundle rupture model, Refs.…”

“…Our purpose is to extend the analysis of this model by showing that it is able to reproduce all the empirical observations mentioned above in creep (constant applied stress) experiments. This shows that the simplest possible ingredients of a rupture model together with thermal fluctuations can render essentially all of the richness of creep experiments.The democratic fiber-bundle model (DFBM) with thermal noise [3,4] can be seen as a mean field treatment of rupture. A macroscopic constant load F = N f 0 is applied at time t = 0 to an initially undamaged system made of a very large number N of parallel elastic fibers (the results derived below are obtained in the thermodynamic limit N → ∞).…”

“…Taking the time derivative of Φ(t) and replacingQ(f, t) by −Q(f, t) G(f − f a ) expressing that the rate of breaking is controlled the thermally activated rupture process acting on each fiber independently, we getΦ = +∞ −∞ df Q(f, t) G(f − f a ). Putting (2) in this equation and taking for P d (f ) a normal distribution centered on 1 with variance T d as in [3,4] …”