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
Received: 20 September 2013
Accepted: 25 January 2014
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.
PACS: 46.50.+a – Fracture mechanics, fatigue and cracks / 64.60.av – Cracks, sandpiles, avalanches, and earthquakes / 68.35.Ct – Interface structure and roughness
© EPLA, 2014