Crack propagation in disordered materials How to decipher fracture surfaces

For a half-century, engineers know how to describe and predict thepropagation of a crack in a model elastic homogeneous medium. The case of real ma-terials is much more complex. Indeed, we do not know how to relate their lifetime ortheir resistance to their microstructure. To achieve such a prediction, understandingthe role of the microstructural disorder on the behavior of a crack is determinant.Fracture surfaces represent a promising field of investigation to address this question.From the study of various disordered materials, we propose a statistical descrip-tion of their roughness and determine to which extent their properties are dependentof the material. We show that fracture surfaces display an anisotropic scale invariantgeometry characterized by two universal exponents. Glass ceramics is then stud-ied because its microstructure can be tuned in a controlled manner. Their fracturesurfaces display the same general anisotropic properties but with surprisingly low ex-ponents independent of the detail of the ceramics microstructure. This suggests theexistence of a second universality class in failure problems. Using finally theoreticaltools from out-of-equilibrium statistical physics and fracture mechanics, we relate thestatistical properties of fracture surfaces with the mechanisms occurring at the mi-croscopic scale during the failure of a material. In particular, we show that the firstclass of fracture surfaces results from a failure involving damage processes while thesecond one results from a perfectly brittle failure.