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Effective toughness of heterogeneous brittle materials

Stephane Roux·Damien Vandembroucq·Francois Hild
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Abstract

A heterogeneous brittle material characterized by a random field of local toughness Kc(x) can be represented by an equivalent homogeneous medium of toughness, Keff. Homogenization refers to a process of estimating Keff from the local field Kc(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.

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Stephane Roux, Damien Vandembroucq, Francois Hild. 2004-09-02. Effective toughness of heterogeneous brittle materials. https://doi.org/10.1016/s0997-7538(03)00078-0

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