Stability and roughness of tensile cracks in disordered materials

Abstract

We study the stability and roughness of propagating cracks in heterogeneous brittle two-dimensional elastic materials. We begin by deriving an equation of motion describing the dynamics of such a crack in the framework of linear elastic fracture mechanics, based on the Griffith criterion and the principle of local symmetry. This result allows us to extend the stability analysis of Cotterell and Rice [B. Cotterell and J. R. Rice, Int. J. Fract. 16, 155 (1980)] to disordered materials. In the stable regime we find stochastic crack paths. Using tools of statistical physics, we obtain the power spectrum of these paths and their probability distribution function and conclude that they do not exhibit self-affinity. We show that a real-space fractal analysis of these paths can lead to the wrong conclusion that the paths are self-affine. To complete the picture, we unravel a systematic bias in such real-space methods and thus contribute to the general discussion of reliability of self-affine measurements.

Morphology and dynamics of a crack front propagating in a model disordered material

“…Indeed, the proposed cutoff is found to scale as the geometrical mean between the crack length and the typical size of defects. This is agreement with a recent set of studies showing the importance of finite size effects in related systems but in different geometry and dimensionality (Katzav et al, 2007;Katzav and Adda-Bedia, 2013). Our results show explicitly that the morphology of the crack front only provides a limited access to the whole crack dynamics.…”

Nominally brittle cracks in inhomogeneous solids: from microstructural disorder to continuum-level scale

“…We now derive an equation of path by making use of the principle of local symmetry [41]. To do so, we take inspiration from the work of Katzav et al [44,47] to model crack path in a model 2D situation and extend it for three-dimensional solids. The idea is to decompose the front propagation along x-axis into infinitesimal straight kinks of length , identified with the microstructural length-scale characterizing the spatial distribution of (x, y, z) (see Figure 1:right).…”

Unified scenario for the morphology of crack paths in two-dimensional disordered solids

“…In the last part, we take inspiration from Refs. [26,27] and propose a model of crack propagation through disordered brittle solids that sheds light on our findings. Our study suggests a unified scenario for the morphology of fracture paths in 2D disordered solids that is discussed in the concluding section.…”

“…In general, brittle cracks in homogeneous media recover a straight trajectory after any small perturbation. Consequently, LEFM based models of crack propagation in disordered 2D solids predict antipersistent fracture profiles, with ζ 2D 0.5 [8], or even no self-affine regime at all [26,27]. These predictions are in contradiction with experiments that systematically report exponents in the range ζ 2D ≈ 0.6-0.7 as in paper sheets [28][29][30], wood [31], or nickel-based alloy [32].…”

“…But does this mean that crack paths in 2D solids are systematically driven by void coalescence, or can another behavior compatible with LEFM be observed? If it exists, what are the geometrical features of the resulting fracture profiles that have recently been a matter of debate [26,27]? Last but not least, how would one roughening mechanism be selected over the other?…”