Geometric model for 3D through-thickness orthogonal interlock composites
Introduction
During the last years different researchers have investigated the benefits of using through the thickness reinforced textiles in composite materials for aircraft structures [1]. The use of these materials has increased because of their superior properties with respect to 2D textile composites: they are more resistant to interlaminar fracture or delamination and they show better performance in front of low-velocity and ballistic impact events [2]. For this reason, three-dimensional (3D) woven composites are used more and more in structural components for aerospace applications where mechanical and thermal stresses in multiple directions are present.
As in the case of 2D textile composites, the determination of the mechanical properties of 3D woven composites can be done through more expensive experimentation, or through more affordable analytical or numerical predictive approaches. However, the availability of types of 3D reinforcement architectures (such as through-thickness angle interlock, through-thickness orthogonal interlock, layer-layer angle interlock and layer-layer orthogonal interlock) and the complexity of taking into account the real geometry of the reinforcement result in not so accurate predictions when using current analytical or numerical approaches.
Many models have been proposed in the literature to analyse and predict the mechanical properties of this type of materials. Most of the models focus on a single 3D architecture of the reinforcement and they are not suitable for predicting these properties for other types of 3D woven reinforcements. Moreover, all the models available in the literature are based on a series of geometric simplifications that can lead to inaccurate results.
Cox et al. [3], [4], [5] and Buchanan et al. [6], [7] focused on through-thickness angle interlock 3D woven composites and formulated two different analytical models assuming that the yarns have, respectively, a circular or an ellipsoidal cross-section. Nehme et al. [8] and Hallal et al. [9] proposed analytical models for layer-layer angle interlock reinforcements considering that the transversal section of the yarns has an ellipsoidal or racetrack cross-section (being a racetrack cross-section a rectangle with semi-circles on its edges). The model presented by Naik et al. [10], [11] is valid for two types of 3D wovens: layer-layer orthogonal interlock and through-thickness orthogonal interlock. In the model, Naik and co-workers adopted the simplification of circular yarns. Different analytical models have been formulated for the most commonly used type of 3D woven reinforcement: the through-thickness orthogonal interlock. In these models, different geometries have been assumed for the cross-section of the yarns, such as rectangular (Tan et al. [12]), lenticular (Quinn et al. [13]) and ellipsoidal (Brown and Wu[14], Wu [15] and Buchanan et al. [16]). Lomov et al. [17] reviewed the developments made in modelling and characterisation of 3D woven interlock composites, both angle and orthogonal, and implemented a procedure to model them in a software suite, WiseTex [18], [19].
Desplentere et al. [20] used X-ray micro-Computed Tomography (micro-CT) to characterise the microstructural variation of different orthogonal interlock 3D composite materials. By comparison with optical micrographs, they found that micro-CT is an appropriate technique to obtain the structure and structural variation of the reinforcement. They reported variations in the structure up to 16% and analysed the effects of these variations on the mechanical properties of the material by virtual testing using WiseTex. The authors concluded that these effects on the mechanical properties are about only 5%.
Different detailed reviews about modelling of 3D woven composite materials, including some of the previous models, can be found in the works of Byun et al. [21] and Ansar et al. [22].
Unlike most of the previous models, Green et al. [23] used the finite element method to numerically model 3D woven fabrics taking into account the geometry of dry orthogonal 3D woven preforms. The method is based on meshing the real geometry of the preform and predict the effects of compaction on the geometry of the yarns. Although the authors mention the general applicability of the method to any 3D woven fabric type, it does not take into account the presence of the resin in the material. In addition, a recent study of the same authors [24] presents a finite element analysis to compute stress–strain curves for an orthogonal 3D woven composite under tensile loading using realistic geometry.
The present study reports the development of an analytical method to obtain the geometry and the volume fraction of 3D through-thickness orthogonal interlock woven composites. In contrast to most of the models present in the literature, the proposed model takes into account a more realistic definition of the geometry of the reinforcement, such as the curvature of the yarns along the longitudinal (also known as warp or stuffer) and transversal (also known as fill or weft) directions induced by the binder (also known as stitch) yarn. The model is based on the definition of a Representative Volume Element (RVE) for the composite defined through different geometrical parameters corresponding to the geometry of the reinforcement. The parameters are obtained from the architecture characteristics of the preform and optical micrographs of specific sections. According to the results of Desplentere et al. [20] this can be considered as a good approach for modelling 3D woven composites.
As a first step, the model has been validated by comparing its predictions of the fibre area fraction for each yarn with the results obtained from direct measuring with optical micrographs and the results of the analytical model proposed by Buchanan et al. [6]. Further development will allow for the prediction of the mechanical properties of the material with better accuracy.
Section snippets
Methodology
The current geometry of the different sets of fibre yarns conforming a 3D woven composite is determinant for the correct modelling and estimation of mechanical properties. Therefore, the analytical model proposed in this work takes into account the cross-section and curvatures of the yarns of the reinforcement.
As the architecture of the through-thickness orthogonal interlock preforms is periodical in the plane of the warp and fill yarns, the Representative Volume Element technique can be used
Validation of model
To validate the geometrical model proposed, a 3D woven composite has been manufactured by RTM injection of a through-thickness orthogonal interlock preform and different optical micrographs have been taken of each representative section. Then, the geometry described by the proposed model is validated with the real geometry of the composite. Additionally, the area fractions of the warp and fill yarns are determined experimentally and compared with the predictions of the proposed model and with
Conclusions
A geometric model has been proposed to account for the compaction and curvature effects on the cross-section and distribution of fill and warp yarns in 3D through-thickness orthogonal interlock composite materials. This is a clear difference between the present model and most of the geometric models already available in the literature.
In the formulated model, and based on a limited set of parameters of the material, the longitudinal and transverse contours of the yarns are defined considering
Acknowledgments
The authors would like to thank Professor Ever J. Barbero, West Virginia University, USA, for his useful insight. This work has been partially funded by the Spanish Government under contract IPT-370000-2010-003 and DPI2012-34465. The authors would like to acknowledge the help of the “Serveis Tècnics de Recerca” of Universitat de Girona to obtain the optical micrographs.
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