From microstructural features to effective toughness in disordered brittle solids

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.