Effective toughness of heterogeneous brittle materials

A heterogeneous brittle material characterized by a random field of local toughness K-c(x) can be represented by an equivalent homogeneous medium of toughness, K-eff. Homogenization refers to a process of estimating K-eff from the local field K-c(x). An approach based on a perturbative expansion of the stress intensity factor along a rough crack front shows the occurrence of different regimes depending on the correlation length of the local toughness field in the direction of crack propagation. A weak pinning,'' regime takes place for long correlation lengths, where the effective toughness is the average of the local toughness. For shorter correlation lengths, a transition to strong pinning occurs leading to a much higher effective toughness, and characterized by a propagation regime consisting in jumps between pinning configurations. (C) 2003 Editions scientifiques et medicales Elsevier SAS. All rights reserved.