From microstructural features to effective toughness in disordered brittle solids

¹ Institut Jean Le Rond d'Alembert (UMR 7190), CNRS and Université Pierre et Marie Curie 75005 Paris, France
² Laboratoire Physique Théorique et Modèles Statistiques (UMR 8626), Université de Paris-Sud Orsay Cedex, France

^(a) vincent.demery@polytechnique.edu

Received: 20 September 2013
Accepted: 25 January 2014

Abstract

The relevant parameters at the microstructure scale that govern the macroscopic toughness of disordered brittle materials are investigated theoretically. We focus on a crack propagation that is planar and describe it as the motion of an elastic line within a plane with random distribution of toughness. Our study reveals two regimes: in the collective-pinning regime, the macroscopic toughness can be expressed as a function of a few parameters only, namely the average and the standard deviation of the local toughness distribution and the correlation lengths of the heterogeneous toughness field; in the individual-pinning regime, the passage from micro- to macro-scale is more subtle and the full distribution of local toughness is required to be predictive.