Failure Probabilities and Tough-Brittle Crossover of Heterogeneous Materials with Continuous Disorder

Details Failure Probabilities and Tough-Brittle Crossover of Heterogeneous Materials with Continuous Disorder Failure Probabilities and Tough-Brittle Crossover of Heterogeneous Materials with Continuous Disorder

1998-11-04

arxiv.org/abs/cond-mat/9811044v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, revtex, 7 figures

Scientific paper

10.1103/PhysRevB.59.4002

The failure probabilities or the strength distributions of heterogeneous 1D systems with continuous local strength distribution and local load sharing have been studied using a simple, exact, recursive method. The fracture behavior depends on the local bond-strength distribution, the system size, and the applied stress, and crossovers occur as system size or stress changes. In the brittle region, systems with continuous disorders have a failure probability of the modified-Gumbel form, similar to that for systems with percolation disorder. The modified-Gumbel form is of special significance in weak-stress situations. This new recursive method has also been generalized to calculate exactly the failure probabilities under various boundary conditions, thereby illustrating the important effect of surfaces in the fracture process.

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