A simplified probabilistic macroscopic model for estimating microscopic fracture development in idealized planar fiber network materials

Abstract

The overall aim of this study is to derive a simplified probabilistic theory to reveal the ‘hidden’ mechanisms controlling random fracture evaluation in idealized network structures observed as diffuse material failure on the macro scale. The model is based on the classical theory of combinatorics and the practical implications for understanding material failure in network materials, such as non-woven felts made of nanofibers or glass fibers, is addressed. The simplified theory reveals a number of important results regarding the evolution of microscopic fractures in planar random fiber networks where the only active microscopic fracture mechanism is bond fracture and the network is loaded so that a homogeneous macroscopic mechanical field is present. A simple probabilistic expression is derived that estimates the fraction of fractured bonds achieved during the loading history. The equation includes a term for potential energy and assumes that there exists an inherent characteristic bond-strength parameter that is the same for all bonds. Subsequent finite element analyses confirm the simplified probabilistic theory and lend confidence in the rather rough assumptions made. The model is justified by observations in acoustic emission monitored tensile experiments performed elsewhere.