Size scaling of failure strength with fat-tailed disorder in a fiber bundle model

摘要

We investigate the size scaling of the macroscopic fracture strength ofheterogeneous materials when microscopic disorder is controlled by fat-taileddistributions. We consider a fiber bundle model where the strength of singlefibers is described by a power law distribution over a finite range. Tuning theamount of disorder by varying the power law exponent and the upper cutoff offibers' strength, in the limit of equal load sharing an astonishing size effectis revealed: For small system sizes the bundle strength increases with thenumber of fibers and the usual decreasing size effect of heterogeneousmaterials is only restored beyond a characteristic size. We show analyticallythat the extreme order statistics of fibers' strength is responsible for thispeculiar behavior. Analyzing the results of computer simulations we deduce ascaling form which describes the dependence of the macroscopic strength offiber bundles on the parameters of microscopic disorder over the entire rangeof system sizes.