Meso cell model of fiber reinforced composite: Interface stress statistics and debonding paths

The primary goal of this work is to develop an efficient analytical tool for the computer simulation of progressive damage in the fiber reinforced composite (FRC) materials and thus to provide the micro mechanics-based theoretical framework for a deeper insight into fatigue phenomena in them. An accurate solution has been obtained for the micro stress field in a meso cell model of fibrous composite. The developed method combines the superposition principle, Kolosov–Muskhelishvili’s technique of complex potentials and Fourier series expansion. By using the properly chosen periodic potentials, the primary boundary-value problem stated on the multiple-connected domain has been reduced to an ordinary, well-posed set of linear algebraic equations. The meso cell can include up to several hundred inclusions which is sufficient to account for the micro structure statistics of composite. The presented numerical examples demonstrate an accuracy and high numerical efficiency of the method which makes it to be a promising tool for studying progressive damage in FRCs. By averaging over a number of random structure realizations, the statistically meaningful results have been obtained for both the local stress and effective elastic moduli of disordered fibrous composite. A special attention has been paid to the interface stress statistics and the fiber debonding paths development, which appear to correlate well with the experimental observations.