Clusters and avalanches of fibre breaks in a model of an impregnated unidirectional fibre bundle under tension

Abstract

Development of clusters and avalanches of damage events is a key characteristic in statistical physics of structures susceptible to a catastrophic failure. This paper applies the concepts of such descriptions to the process of fibre breakage under tension in an impregnated fibre bundle model (IFBM). The following parameters are analysed: (1) susceptibility (damage caused by change in loading); (2) spatial clustering of breaks and its interdependency with avalanches; (3) the size distribution of fibre break clusters and avalanches; (4) fractal dimensions; and (5) correlation lengths of breaks. A systematic workflow and algorithms for this analysis are presented and applied for two realisations of a random fibre placement of carbon fibre/epoxy bundles with fibre volume fractions of 50% and 60%. For these two realisations: (1) the susceptibility divergence near the failure point is affected by the finite-size effect, being nearly constant for the last ~1/20th of strain life; this behaviour can be considered as a failure predictor; (2) the morphology of the break system is a spatially distributed multi-defect occurrence with the dimensionality of 3 for all breaks together and weak planarity demonstrated only by the largest clusters near failure; (3) the exponents of the cluster-size and avalanche-size power law distributions reached 2.5–3 for both statistics near the bundle failure, which may constitute an imminent failure indicator. Damage evolution of the carbon/epoxy IFBM up to the final failure is found to be short-correlated (with correlation length of the order of one fibre break stress redistribution zone) in the absence of collective long-range defect interactions. During the catastrophic avalanche, the spatially distributed morphology of breaks is gradually reorganized into a translaminar fracture mode.