Universality class of fiber bundles with strong heterogeneities

We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0<\alpha<1 of fibers is unbreakable, while the remaining 1-\alpha fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components \alpha_c which separates two qualitatively different regimes of the system: below \alpha_c the burst size distribution is a power law with the usual exponent \tau=5/2, while above \alpha_c the exponent switches to a lower value \tau=9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena

A simple beam model for the shear failure of interfaces

We propose a novel model for the shear failure of a glued interface between two solid blocks. We model the interface as an array of elastic beams which experience stretching and bending under shear load and break if the two deformation modes exceed randomly distributed breaking thresholds. The two breaking modes can be independent or combined in the form of a von Mises type breaking criterion. Assuming global load sharing following the beam breaking, we obtain analytically the macroscopic constitutive behavior of the system and describe the microscopic process of the progressive failure of the interface. We work out an efficient simulation technique which allows for the study of large systems. The limiting case of very localized interaction of surface elements is explored by computer simulations.Comment: 11 pages, 13 figure

Break-up of shells under explosion and impact

A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on brown and white hen egg-shells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-dimensional discrete element model of shells is constructed. Molecular dynamics simulations of the two loading cases resulted in power law fragment mass distributions in satisfactory agreement with experiments. Based on large scale simulations we give evidence that power law distributions arise due to an underlying phase transition which proved to be abrupt and continuous for explosion and impact, respectively. Our results demonstrate that the fragmentation of closed shells defines a universality class different from that of two- and three-dimensional bulk systems.Comment: 11 pages, 14 figures in eps forma

Slip avalanches in a fiber bundle model

We study slip avalanches in disordered materials under an increasing external load in the framework of a fiber bundle model. Over-stressed fibers of the model do not break, instead they relax in a stick-slip event which may trigger an entire slip avalanche. Slip avalanches are characterized by the number slipping fibers, by the slip length, and by the load increment, which triggers the avalanche. Our calculations revealed that all three quantities are characterized by power law distributions with universal exponents. We show by analytical calculations and computer simulations that varying the amount of disorder of slip thresholds and the number of allowed slips of fibers, the system exhibits a disorder induced phase transition from a phase where only small avalanches are formed to another one where a macroscopic slip appears.Comment: 6 pages, 6 figure

Disorder induced brittle to quasi-brittle transition in fiber bundles

We investigate the fracture process of a bundle of fibers with random Young modulus and a constant breaking strength. For two component systems we show that the strength of the mixture is always lower than the strength of the individual components. For continuously distributed Young modulus the tail of the distribution proved to play a decisive role since fibers break in the decreasing order of their stiffness. Using power law distributed stiffness values we demonstrate that the system exhibits a disorder induced brittle to quasi-brittle transition which occurs analogously to continuous phase transitions. Based on computer simulations we determine the critical exponents of the transition and construct the phase diagram of the system.Comment: 6 pages, 6 figure