Abstract
We consider the Equal-Load-Sharing Fiber Bundle Model as a model for composite materials under stress and derive elastic energy and damage energy as a function of strain. With gradual increase of stress (or strain) the bundle approaches a catastrophic failure point where the elastic energy is always larger than the damage energy. We observe that elastic energy has a maximum that appears after the catastrophic failure point is passed, i.e., in the unstable phase of the system. However, the slope of elastic energy {\it vs.\/} strain curve has a maximum which always appears before the catastrophic failure point and therefore this can be used as a reliable signal of upcoming catastrophic failure. We study this behavior analytically for power-law type and Weibull type distributions of fiber thresholds and compare the results with numerical simulations on a single bundle with large number of fibers.
Highlights
Accurate prediction of upcoming catastrophic failure events has important and far-reaching consequences
The central question is—when does the catastrophic failure occur? Is there any prior signature that can tell us whether catastrophic failure is imminent? The inherent heterogeneities of the systems and the stress redistribution mechanisms make things complicated and a concrete theory of the prediction schemes, even in model systems, is still lacking. We address this problem in the Fiber Bundle Model (FBM) which has been used as a standard model [11,12,13,14] for fracturing in composite materials under external stress
We will show theoretically that in the Equal-Load-Sharing (ELS) model: (1) At the catastrophic failure point, the elastic energy is always larger than the damage energy
Summary
Accurate prediction of upcoming catastrophic failure events has important and far-reaching consequences It is a central problem in material science in connection with the durability of composite materials under external stress [1,2,3,4,5]. In medical science, understanding fracturing of human bones exposed to a sudden stress is an important research area [8] These phenomena belong to the class of phenomena called stress-induced fracturing, where initially micro-fractures are produced here and there in the system and at some point, due to gradual stress increase, a major fracture develops through coalescence of micro-fractures and the whole system collapses (catastrophic event). We will show theoretically that in the Equal-Load-Sharing (ELS) model: (1) At the catastrophic failure point, the elastic energy is always larger than the damage energy.
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