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

Abstract

This paper presents a multi-scale correlating model to simulate the elastic and failure behavior of two-dimensional triaxial 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.

Predicting the Failure Behavior of Textile Composite Laminates by Using a Multi-Scale Correlating Approach

“…This work extends our previous work [21] to the case of failure analysis for textile composite structures. A unified approach is developed by combining the multi-scale correlating model and the classical lamination theory.…”

“…According to the continuum mechanics, the four sub-cells must satisfy the traction continuity conditions and displacement continuity conditions at the same time. The overall stiffness of the UD composite is given by [21] …”

“…The stiffness of the whole RUC is evaluated by averaging the contribution of each layer. Therefore, for the k th lamina, the overall stiffness [C] k can be obtained from its corresponding constituent properties and geometrical parameters, by using the multi-scale correlating model [21]. The laminate analysis is carried out based on the classical laminate theory.…”

“…In the authors' previous work, a multi-scale stress-correlating matrix, [M], which represents the load share capacity of each constituent fiber/matrix sub-cell, was developed to bridge the effective global stress and the constituent based local stress [21]. This matrix is employed here, and thus the stress/strain fields in the fiber and matrix phases are obtained at the present load level.…”

“…While these models are able to characterize the averaged behavior, such as stiffness or strength, they have difficulty in predicting the damage and failure mechanisms at the constituent fiber/matrix scale. Recently, a new analytical model, called the multi-scale correlating model, was proposed by Deng et al [21] to predict the overall stress-strain response, failure mechanisms, failure sequence, and the resulting failure initiation and progression of braided composites. By using this model, the effects of the constituent fiber and matrix properties, fiber volume fraction, braid angle, tow undulation and manufacturing induced defects can be taken into consideration.…”