A multi-scale correlating model for predicting the mechanical properties of tri-axial braided composites

This paper presents a multi-scale correlating model to simulate the elastic and failure behavior of two-dimensional tri-axial braided composites. Unlike the traditional information-passing multi-scale approaches, the present analytical model enables a two-way coupling of scales through a bottom-up homogenization procedure and a top-down decomposition procedure, based on the continuum mechanics and homogenization method. The main feature of this model is that it not only concurrently obtains the stress/strain fields in multiple scales but also allows the application of constituent-based failure criteria to reveal local failure mode, failure sequence and the resulting failure progression of the composites. Using the multi-scale correlating model, the stiffness and strength of a braided composite are predicted solely from its corresponding constituent properties and braid geometrical parameters, which can be easily obtained. The predicted failure events and the corresponding stiffness degradation are in good agreement with experimental data found in the literature. Parametric studies are also performed to examine the effect of various geometrical parameters such as braid angle, tow undulation and manufacturing-induced defects on the resulting mechanical properties. It is found that micro-structural imperfections play a role in the strength reduction, and the most detrimental factors are the defects of bias tow.