Abstract
An important question in the theory of fracture is what kind of lifetime distributions may exist for materials under load. Here, this is studied in the context of a one-dimensional fracture model with local load sharing under a constant external load, “creep.” Simulations of the system with Weibull distributed initial lifetimes for the elements show that the limiting distribution follows from extreme statistics and takes the Gumbel form eventually, with longer and longer crossovers in the system size from a Weibull-like distribution, depending on the initial Weibull exponent.
Highlights
The statistics of strength is a classical problem in statistical fracture mechanics and is realized to be very closely related to concepts in statistical physics such as percolation and scaling [1,2,3]
Simple models have brought together a comprehensive understanding of the predictions of statistical physics [7]. This concerns the role of disorder, the phase diagrams for the statistics, and the interaction of cracks with disorder
An important point is the role of loading as in tensile failure and in the propagation of cracks, the physics is different from compressive loading with the formation of shear bands, self-averaging, and changing effective elastic interactions
Summary
The statistics of strength is a classical problem in statistical fracture mechanics and is realized to be very closely related to concepts in statistical physics such as percolation and scaling [1,2,3]. Given the lifetime distribution with a certain local stress (history), the exercise becomes to understand how or when a bigger sample fails taking into account the interactions (load sharing) in the sample. We start from an initially Weibull-like microscopic failure time distribution and evolve it using local load sharing (“growth of microcracks”).
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