Deformation of the crack front during propagation in some disordered medium: theoretical and experimental studies

摘要

In heterogeneous disordered materials, a straight crack front experi-ences toughness fluctuations during its propagation that generate geometric fluc-tuations. Their long time statistical behavior has been studied by Lazarus et al. (JMPS, 2008) using Bueckner-Rice weight function theory. In particular, the evo-lution of the auto-correlation function, power spectrum and variance of the front fluctuations have been derived. The aim here is to compare these results to some experiments performed on transparent plexiglas blocks with the same apparatus as in Schmittbuhl and Maloy (PRL, 1997) by measuring the amplitude evolution of the crack front fluctuations in addition to the self-affinity roughness parameters. In a perfectly ideal homogeneous material, an initial straight crack front remains straight during propagation. But in an heterogeneous disordered materials, it be-comes rough. The aim of the present paper is to derive an analytical description of the evolution of this roughness and to compare it to experimental results. The assumption of quasi-static brittle crack propagation will be done. Among the experimental works, one may cite on the one hand, the pioneer work of Daguier et al. [2] in which the crack front is obtained postmortem, the crack surface being marked by ink and on the other hand, the works of Delaplace, Maloy and Schmittbuhl [8, 3] in transparent plexiglas in which the crack front can be ob-served in situ during its evolution. They deal mainly with the universal self-affine character of the crack front. The roughness exponent e was measured between 0.5 and 0.6. Here, we have again used the experimental framework of [8, 3] to measure the time evolution of the fluctuations in addition to its roughness. All the theoretical studies of the statistical properties of the crack front performed in quasi-static, use Bueckner[1]-Rice[7] weight function theory, also called line elastic models, to evaluate the stress intensity factors along the perturbed crack front. Among them, one may distinguish two groups depending on the type of the advance law used. The first ones [9, 10, 6] deal with crack advance governed