Crackling Dynamics in Material Failure as the Signature of a Self-Organized Dynamic Phase Transition

Abstract

We derive here a linear elastic stochastic description for slow crack growth in heterogeneous materials. This approach succeeds in reproducing quantitatively the intermittent crackling dynamics observed recently during the slow propagation of a crack along a weak heterogeneous plane of a transparent Plexiglas block [K. J. Måløy et al., Phys. Rev. Lett. 96, 045501 (2006)10.1103/PhysRevLett.96.045501]. In this description, the quasistatic failure of heterogeneous media appears as a self-organized critical phase transition. As such, it exhibits universal and to some extent predictable scaling laws, analogous to that of other systems such as, for example, magnetization noise in ferromagnets.

Steady-State Two-Phase Flow in Porous Media: Statistics and Transport Properties

“…For a rough crack front there is in addition the competition between long range elastic forces and the disorder term (last two terms). Equation (2.27) has been modeled extensively and shown to describe a variety of systems; including in-plane fracture in PMMA [48], wetting contact line motion on a disordered substrate [49], and interfaces in disordered magnets [50]. It should be emphasised that Eq.…”

Fermi-Pasta-Ulam chains with harmonic and anharmonic long-range interactions

“…s 1 ) is above 3, then the effective continuum equation displays a long-range behaviour in the anharmonic (harmonic) terms. The power s 1 = 2 (with s 2 → ∞) has been considered for crack front propagation along disordered planes between solid blocks [32,33] and for contact lines of liquid spreading on solid surfaces [34].…”

Role of the sample thickness in planar crack propagation

“…This is reflected also in the avalanche behavior that in the stable propagation regime follows the predictions of the interface depinning model [15,16]. Besides the theoretical implications, understanding the role of thickness in planar cracks could be interesting in view of applications for the delamination of coatings [20].…”

“…This case appears to be the ideal candidate to test the theory that envisages the crack as a line moving through a disordered medium [10,11]. For planar cracks, the problem can be mapped into a model for interface depinning with long-range forces [12][13][14][15][16][17], implying a self-affine front with a roughness exponent close to ζ = 1/3 [18,19] and avalanche propagation of the front between pinned configurations with scaling exponents predicted by the theory [14][15][16]. Such results are also of importance for applications such as the failure of the interface between a substrate and a coating, or an adhesive layer, and the propagation of indentation cracks [20].…”