Structure, Self-Similarity, and Fracture of Fiber-Reinforced Composites

Abstract

We propose a theory for the relationship between structure and the self-similarity principle with initial damage and final fracture of composites. This relationship does not depend on the type of stress state, the dimensions of the composite, or the time scale. Based on the self-similarity principle, we have constructed the theoretical time-to-fracture distribution functions vs. the applied stress level, allowing us to estimate the lower limit corresponding to zero fracture probability. The distribution functions can be constructed without long-term testing. An estimate of the distribution of initial damage is obtained from the short-term strength distribution. As the critical parameter for the transition of the composite to final fracture, we take a critical measure of the stress tensor. At each instant of time, fracture is determined by a differential operator depending on the state of the system at that instant and the applied stress level. The theory is supported by experiments. The experiments were performed on model fiberglass-reinforced composites based on a phenol formaldehyde matrix under tension, compression, pure shear, and hydrostatic tension. The maximum testing time was ~ 20 000 hours. The theory is applicable to any systems with a partially ordered structure and satisfying the self-similarity principle (geophysical, social, economic, etc.).