A Multi-scale Correlating Model For Predicting The Mechanical Properties Of Textile Composites

Compared with tape laminates, textile composites show enhancedtransverse and out-of-plane mechanical properties, better design flexibilityand lower manufacturing cost, while keeping the quality of high strengthand stiffness versus weight ratio. Based on these advantages, textilecomposites are preferred increasingly in the fields of aviation, automobile,naval construction and biomedical engineering. To derive the maximumbenefits of textile composites, the variation of their mechanical propertieswith constituent materials, fiber volume fraction, braid angle and towundulate level must be studied. However, most existing models can beclassified as information-passing multi-scale approaches, in which thefiber/matrix scale, tow architecture scale and RUC scale are consideredindividually and material properties are passed from lower to higher scales.While these models are able to characterize the averaged behavior, such asstiffness or strength, they have difficulty in predicting the damage andfailure mechanisms at the constituent fiber/matrix scale.This paper presents a new analytical model, the multi-scale correlatingmodel, to simulate the elastic and failure behavior of textile composites.Unlike the traditional information-passing multi-scale approaches, thepresent model enables a two-way coupling of scales through a bottom-uphomogenization procedure and a top-down decomposition procedure, basedon the continuum mechanics and homogenization method. The mainfeature of this model is that it not only concurrently obtains the stress/strainfields in multiple scales but also allows the application of constituent-basedfailure criteria to reveal local failure mode, failure sequence and the resulting failure progression of the composites. In this model, effect of theconstituent fiber and matrix properties, fiber volume fraction, braid angle,tow undulation and manufacturing induced defects are all taken intoconsideration. The homogenization procedure is employed to determine theelastic stiffness of textile composite, solely from its correspondingconstituent properties and braid geometrical parameters, which can be easilyobtained. Based on the continuum mechanics and homogenization method,a multi-scale stress-correlating matrix is developed to bridge the stressesbetween different scales. Local stress in a constituent material is necessaryfor accurately predicting the initial and final failure of the composite.Therefore, in this model, stress analysis is carried out using a top-downdecomposition procedure that sequentially considers the RUC scale, towarchitecture scale and fiber/matrix scale. At every load level, theinstantaneous stress and strain states in the constituent fiber/matrix areexplicitly determined from the RUC stress and strain fields. Local stressesin the fiber and matrix phases of each tow are calculated and checkedagainst the micromechanical failure criteria. When local failure occurs, astiffness discount is carried out. In this way, the stiffness, strength, failureinitiation and progression of the composites are obtained.In this paper, the multi-scale correlating model is applied to predict themechanical properties of tri-axial braided composites, woven fabriccomposites (including plain weave, twill woven fabric and satin weavecomposites), and textile composite laminates. The accuracy of the presentmodel is demonstrated by comparing the predicted stiffness and strengthwith available experimental data. Despite the use of the simple failurecriteria, both the failure events and the corresponding stiffness degradationagree well with experimental observation. Parametric studies are alsoperformed to examine the effect of various geometrical parameters such asbraid angle, tow undulation and manufacturing induced defects on theresulting mechanical properties. As for tri-axial composites, it is found thatmicro-structural imperfections play a role in the strength reduction and the most detrimental factors are the defects of bias tow.Because of the high computational efficiency and sufficient accuracyof the multi-scale correlating model, the software for strength analysis oftextile composites, called MCM v1.0, is developed based on themulti-scale correlating model. The developed software can provideessential constituent level information that would otherwise be lost duringtraditional homogenization techniques. This software has been applied fornational software copyright. In future work, it can be used for structuralanalysis and design applications.