Stability in fiber bundle model : Existence of strong links and the effect of disorder

In this paper I have studied the fiber bundle model with a fraction {\alpha} of infinitely strong fibers. Inclusion of such unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical value {\alpha}_c . The present work has a twofold purpose: (i) study of failure abruptness, mainly the brittle to quasi-brittle transition point ({\delta}_c ) with varying {\alpha} and (ii) variation of {\alpha}_c as we change the disorder introduced in the model. The brittle to quasi-brittle transition is confirmed from the failure abruptness. On the other hand, the {\alpha}_c is obtained from the knowledge of failure abruptness and statistics of avalanches. It is observed that {\delta}_c scales to lower values, suggesting more quasi-brittle like continuous failure even at low strength of disorder, when {\alpha} is increased. Also, the critical fraction {\alpha}_c, required to make the model deviate from the conventional results, increases with decreasing {\delta} values. The analytical expression for {\alpha}_c shows good agreement with the numerical result. Finally, the findings in the paper are compared with previous results as well as with the real life application of composite materials.Comment: 8 pages, 10 figure

Creep failure in a threshold activated dynamics: Role of temperature during a sub-critical loading

Creep is a time-dependent deformation of solids at relatively low stresses, leading to the breakdown with time. Here we propose a simple model for creep failure of disordered solids, in which temperature and stress are controllable. Despite its simplicity, this model can reproduce most experimental observations. Time dependence of the strain rate is well fitted with power laws resembling the Omori-Utsu and the inverse Omori laws in the primary and the tertiary creep regimes, respectively. Distribution of the creep lifetime obeys the log-normal distribution, and the average creep lifetime decays in a scale-free manner with the increasing stress. The above results are in good agreement with experiments. Additionally, the mean avalanche size as a function of temperature exhibits a series of jumps, and finite-size scaling implies the existence of phase transitions.Comment: 9 pages, 9 figure

Modes of failures in disordered solids

The two principal ingredients determining the failure modes of disordered solids are the level of heterogeneity and the length scale of the region affected in the solid following a local failure. While the latter facilitates damage nucleation, the former leads to diffused damage, the two extreme failure modes. In this study, using the random fiber bundle model as a prototype for disorder solids, we classify every failure modes that are the results of interplay between these two effects. We obtain scaling criteria for the different modes and propose a general phase diagram that provides a framework for understanding previous theoretical and experimental attempts of interpolation between these modes.Comment: 10 pages, 13 figure