This article addresses the experimental investigation and modelling of the uneven fibre distribution inside yarns of a textile composite. The test data is given for the tri-axial carbon-fibre braid; a considerable irregularity is revealed for the fibre distribution along and across the yarns. The importance of this effect for the damage resistance is illustrated with a simple finite-element (FE) model. The geometrical modelling of the internal geometry is also discussed

Ivanov, D.S.

Koissin, V.

Lomov, S.V.

Verpoest, I.

English

Koysin, V.

NARCIS 

Fibre distribution inside yarns of textile composite: gemetrical and FE modelling

University of Twente Research Information

TexComp-8 Int. Conference :: CD editionFIBRE DISTRIBUTION INSIDE YARNS OF TEXTILE COMPOSITE:GEOMETRICAL AND FE MODELLINGV. Koissin∗, D.S. Ivanov, S.V. Lomov, I. VerpoestDept. of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven,Kasteelpark Arenberg 44, B–3001 Leuven, Belgium∗Vitaly.Koysin@mtm.kuleuven.beABSTRACTThis article addresses the experimental investigation and modelling of the uneven fibre distribu-tion inside yarns of a textile composite. The test data is given for the tri-axial carbon-fibre braid;a considerable irregularity is revealed for the fibre distribution along and across the yarns. Theimportance of this effect for the damage resistance is illustrated with a simple finite-element(FE) model. The geometrical modelling of the internal geometry is also discussed.INTRODUCTIONOptimised design methods facilitate an extensive use of textile composites in load-bearing com-ponents for different applications. However, being a quite modern design concept, it is relativelyunexplored and employed with caution. Due to a natural complex structure and manufacturemethods, a textile composite contains resin-rich zones, uneven fibre content, etc. These featuresraise concerns about the damage resistance, which is closely connected with the reinforcementinternal geometry and reveals features not observed in the classical laminates (1–4). Hence,whilst the design for the stiffness of a textile composite part can be based on validated calcu-lation techniques, related to the meso-structure of textile reinforcements, the reliable strengthdesign has to be based on empirical information (5) and should account for the micro-structure.This paper focuses on the uneven fibre distribution inside the textile yarns. The object to studyis one of basic types of the textile reinforcement — multi-layer preform made of 2D braidedcarbon-fibre yarns. The braid is considered as a complex hierarchical structure. Its meso-levelincludes the variable fibre content along the yarn; this scale naturally corresponds to the unitcell size. The micro-level embraces the uneven fibre distribution over the yarn cross-section.EXPERIMENTAL STUDYMaterialsTri-axial (+45◦, 0◦, -45◦) HTS 5631 Tenax carbon fibre braid was used as the composite re-inforcement, Fig. 1(a). The fabric was composed of 2 braiding and 1 inlay yarns made of thesame 12 K tows with the linear density of 1600 tex. The average yarn width was 4.2 or 3.7 mm,respectively. The braiding yarns were organised in so-called diamond pattern 1/1 with the braid-ing angle of 91.1±1.3◦. The length of the unit cell side was 14.4 mm (sides were parallel to thebraiding yarns). The basic properties of the fibres are listed in Table 1. Four layers of the fabricwere put in a pile with the equal layup direction, i.e. a transversely orthotropic [+45,0,–45]4construction was produced. The layers were shifted as shown in Figs. 1(b)–1(d).The resin transfer moulding (RTM) equipment was employed for the impregnation. The pre-form was placed into a flat mold warmed up at 40◦C. Shell epoxy resin 828 LV and hardenerDX 6514 were used with the mix ratio of 100:17. The resin was injected into the vacuumizedmould under the differential pressure of 2–3 bars. When a complete impregnation was observedthrough the transparent mould cover (after ≈25 min), the cure stage was processed for 1 hourwith the temperature of 70◦C. After demoulding, the composite plate was post-cured in an air1TexComp-8 Int. Conference :: CD editionTable 1: Characteristics of the carbon fibres (6).diameter, density, Young’s modulus, shear modulus, Poisson’s ratio tensile strength,µm kg/m3 GPa GPa MPa7 1760 238 24 0.23 4300zone 2zone 1(a) unit cell (b) 1st and 2nd layersS23(c) 3rd layerS34(d) 4th layerFigure 1: Unit cell (a) and shifts between layers (b–d): no shift for first two layers, S23=4.7 mm— between the 2nd and the 3rd layers, S34=4.7 mm — between the 3rd and the 4th layers.oven at 160◦C for another hour. The final thickness of the plate was 3.1 mm; the average fibrevolume fraction was estimated to be about 43%. The areal weight of the plate was 600 g/m2.Meso-geometry of the preformTo investigate the preform’s internal structure after the RTM, series of specimens were sectionedacross the inlays and polished to allow for inspection with an optical or electron microscope.Typical through-the-thickness micrograph is shown in Fig. 2(left). A high deformation of theyarns is seen; this effect can be attributed to a severe compression during the RTM process.In order to assess the fibre volume fraction in the inlay yarns, a number of the micrographs wasinvestigated. First, the area of each inlay cross-section was calculated approximately. Then,knowing the number of filaments and their diameter, Table 1, the average fibre volume fractionwas easily obtained for each position. The results are shown in Fig. 2(right), which illustratesthe fibre volume fraction distribution along the inlay yarns. A prominent (about 10%) rise isseen nearby the area of nesting with the braiding yarns. The distribution is not symmetrized.0 5 10 15 2050556065←    diagonal of the unit cell (UC), mm    →Vf, %zone 1 zone 2averaged and reduced to the UCFigure 2: Micrograph of the cross-section cut across the inlay yarns (left, colors are impliedmanually) and measured distribution of the fibre volume fraction along the inlays (right, (7)).2TexComp-8 Int. Conference :: CD edition−50 0 500.850.90.9511.05distance from the center of the cross−section, %Vf normalized against the mean valueaveraged for 6 slices and symmetrizedFigure 3: Typical micrograph of the cross-section cut across the inlay yarns (left, only the yarnedge is shown) and measured distribution of the fibre volume fraction across the inlays (right).Micro-geometry of the preformIt is a well-known fact that the multifilament yarns have a non-uniform fibre distribution overthe cross-section. The fibre content usually decreases towards the edge of a yarn; however,the maximum can be observed somewhere in between the centre and edge (8). In the preform,then, the braiding process, nesting in the mould, etc. changes the virgin distribution of the fibrevolume fraction. Figure 3(left) shows a typical microscope image of the fibre placement at theyarn edge. It is clearly seen that the local fibre content is lower near the edge.The statistical data is obtained taking micrographs with the SEM, stitching them automaticallyinto one image, extracting small sub-images across the yarn, black & white thresholding, andcalculating the fibre area in a Matlab applet. The results are shown in Fig. 3(right), which illus-trates the fibre volume fraction distribution across the inlay yarns; the distribution is normalizedagainst its average value (59%). A prominent (about 15%) decrease is seen nearby the edges;this observation is in agreement with the data reported by other authors (1, 2, 8) for fibrousbundles in woven fabrics. In Ref. (2), it is shown also that the fibre fraction may vary not onlyalong the bundle cross-section but also across it (again, with lower fraction at the edge).MODELLINGGeometrical modellingThe geometrical modelling is performed using the textile simulating software WiseTex. Fig-ures 1(b)–1(d) show the results; comparison with the photos of the real fabric (6, 7) reveals thatthe model captures its important features. Unfortunately, although due to inherent propertiesof the geometrical approach, the simplifying assumption of idealized (elliptic in the presentcase) yarn cross-section is coded in the WiseTex. Therefore, the yarn nesting is modelled notperfectly, and some local intersections of the yarns can be observed as seen in Figs. 1(b)–1(d).Since distortion of the shape of the cross-section can not exactly be modelled without an FEanalysis, a rotation of the yarns is introduced for a more realistic description. As a result, theintersection of the yarns decreases considerably. However, it is not eliminated completely; theremaining penetration represents an error of the current geometrical modelling (9).In the braids with inlays, axial yarns are inlaid between the braided yarns in the machine di-rection. Study of the geometry of tri-axial braids (10) reveals almost no crimp for axial yarns(inlays). This is logical for balanced braids, as the one used in the present study. If a braid is3TexComp-8 Int. Conference :: CD editionFigure 4: WiseTex dialogue window for the modelling of the local fibre distribution in a yarn.Left — uniaxial case, right — biaxial case of the distribution. For the better view, the yarndimensions and the fibre distribution do not correspond to the braid configuration and internalstructure discussed in the present study.unbalanced (which is a rare case in practice), then the crimp of inlays, fixed between the twosystems of braiding yarns and therefore prevented from a significant bending, must be quite lowalso. Reasoning from these considerations and the experimental evidence, it is usually assumedin the WiseTex algorithms that the inlays are perfectly straight. However, some crimp of theinlays can also be modelled, if necessary. In a simulated laminate (LamTex software), whenseveral layers of the braid are nested together, the inlays are supposed to keep the crimp createdby the WiseTex. In the real laminate, certain crimp is also observed for the inlays (7).Once the geometrical model is built, the fibre distribution inside the yarns is modelled to pro-duce a complete description of the unit cell fibrous structure. In the simplest case, such a modelassumes the even fibre placement over the cross-sections, taking into account only the variabil-ity along the yarn due to its compression by the nesting forces. On the programme request, thelocal fibre volume fraction and the fibre orientation are generated for any point inside the unitcell. Particularly, the fibre content can be zero, if the point does not lie inside a yarn.Alternatively, the refined model of the local fibre distribution can be employed. For the presentcase of the flattened yarn, the unidirectional fibre distribution is modelled, when the fibre contentchanges only at the long axis of the elliptic cross-section. The distribution is given with the 2nd-order polynomial using two parameters 1) ratio between the fibre content at the core (mechanicalcentre) and edge of the yarn and 2) shape coefficient. The function is normalized automaticallywith the weight factor, which implies that the average fibre volume fraction equals to the oneobtained using the number of fibres, their diameter, and the total area of the yarn’s cross-section.In a general case, if the fibre distribution is not unidirectional, the options of angular or “biaxial”distribution can be used in the WiseTex. The examples are shown in Fig. 4.When calculating the compressed state of a yarn, in the case of need, the polynomial is changedautomatically to fit the average fibre fraction in the compressed yarn. If possible, only the weightfactor is changed in this case; otherwise, the function is flattened reducing the shape coefficientto zero and approaching the core-to-edge ratio to unity. In the limit case, the auto-correction ofthe fibre distribution leads to the uniform compaction, when the average fibre content reachesits threshold value. On default, the hexagonal grid packing of uncompressible equal cylindricalfibres is assumed that yields that the maximal fibre content can not exceed 91%.4TexComp-8 Int. Conference :: CD editionyarnmatrixFigure 5: FE model.(a) normal stress σx (longitudinal)(b) shear stress τxyFigure 6: Stress distribution in the FE model; cases of the uniform (left) or nonuniform (right)fibre distribution across the yarn.FE modellingTo assess a possible influence of the uneven fibre distribution in the yarns on the stress field, amodel FE problem is considered: 2D mesh of an elliptical impregnated yarn cross-section ina rectangular matrix domain. The uniaxial tensile load (prescribed displacement) is applied inthe longest ellipse axis direction as shown in Fig. 5. Due to the symmetry, only a quarter of thestructure is meshed. The properties of the fibres correspond to the ones listed in Table 1; thetypical epoxy resin properties (E=3.1 GPa, G=1.2 GPa) are accepted for the matrix.Two variants of the problem are studied: 1) even fibre distribution or 2) uneven distributionshown in Fig. 3(right). In the latter case, the cross-section is subdivided into 10 parts alongthe x semi-axle; each part is associated with certain fibre volume fraction. Hence, the fractionvaries in a step-wise manner, and the homogenised Young’s modulus decreases gradually from10.1 GPa at the yarn core till 7.9 GPa at its edge. The average modulus of the yarn in theproblem #2 is the same as the constant modulus of the impregnated yarn in the problem #1.The results of the linear-elastic analysis are shown in Fig. 6. The overall view of the stressfields is very similar for the problems #1 and #2. However, the uniform fibre distribution resultsin a relatively sharp stress concentration inside and nearby the yarn tip. This fact suggests theinitiation of damage at this location, which is contrary to the experimental observations. Thestress fields in the case of the uneven fibre distribution are smoother (as it could be expectedlooking at Fig. 3) and have significantly lower (by 15–25%) maximums. Accordingly, the testdata reveals no preferential crack position in the yarn cross-sections (6, 7).CONCLUSIONSThe presented experimental study deals with the irregularity of the fibre distribution in the yarnsof the braided composite preform. The main results of this preliminary study can be outlined as• the geometrical characterization of the fabric is performed on the meso- and micro-level.A statistically significant (10–15%) variation of the local fibre volume fraction is observedalong and across the yarns. They also show randomized cross-sectional shapes;5TexComp-8 Int. Conference :: CD edition• the WiseTex software is used to build the geometrical model of the braid, including thevariable fibre content inside the yarns. The model does not account for all issues of thereal deformation of a dry textile in a composite processing. This would involve a descrip-tion of “strange” behaviour of fibrous assemblies, frictional phenomena, etc. However,the model can serve as the base for the further FE computations (9);• the general conclusion is that a non-negligible variability can exist in the micro- and meso-level geometry of a textile composite. More work should be done to achieve a correct FEdescription of the stress-strain state and homogenization of the mechanical properties.ACKNOWLEDGEMENTSThis study was done within the I-TOOL (“Integrated Tool for Simulation of Textile Compos-ites”) project founded by the European Commission. The triaxial braided fabric used in thisstudy has been sent by the Institut für Verbund Werkstoffe in Kaiserslautern (Germany) aspart of the TECABS projects (Technologies For Carbon Fibre Reinforced Modular Automo-tive Body Structures). Mr. Manuël Adams, Mr. Dirk Van den Auweele, and Mr. Rudy De Vos(Dept. of Metallurgy and Materials Engineering, K.U.Leuven) are gratefully acknowledged forhelp with the RTM, polishing, and SEM equipment.REFERENCES1. Kurashiki, T. et al. Estimation of a mechanical characterization for woven fabric compos-ites by FEM based on damage mechanics. Proceedings of 11th European Conference onComposite Materials (ECCM-11), Rhodes, Greece, May 31–June 3, 2004, CD edition.2. Summerscales, J. and Russell, P.M. Observations on the fibre distribution and fibre strain ina woven fabric reinforcement. Advanced Composite Letters, 13(3): 135–139 (2004).3. Karkkainen, R.L. and Sankar, B.V. A direct micromechanics method for analysis of failureinitiation of plain weave textile composites. Composites Science and Technology, 66(3):137–150 (2006).4. John, S., Herszberg, I., and Coman, F. Longitudinal and transverse damage taxonomy inwoven composite components. Composites: Part B, 32: 659–668 (2001).5. Lomov, S.V. et al. Experimental methodology of study of damage initiation and develop-ment in textile composites. Proceedings of 27th International SAMPE Europe Conference,Paris, France, March 27–29, 2006, CD edition.6. Baudry, F. Damage characterization of triaxial braided textile composites. MSc thesis, Dept.of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Belgium (2004).7. Xie, H. Micro-structural and damage analysis of braided composites. MSc thesis, Dept. ofMetallurgy and Materials Engineering, Katholieke Universiteit Leuven, Belgium (2005).8. Grishanov, S.A. et al. The simulation of the geometry of two-component yarns. Part II:Fibre distribution in the yarn cross-section”, Journal of the Textile Institute, 88(4): 352–372 (1997).9. Lomov, S.V., Ivanov, D.S., and Verpoest, I. Meso-FE modelling of 3-axial braided compos-ites. Proceedings of 8th International Conference on Textile Composites, Nottingham, UK,October 16–18, 2006, CD edition.10. Naik, R.A., Ifju, P.G., and Masters, J.E. Effect of fibre architechure parameters on deforma-tion fields and elastic moduli of 2D braided composites. Journal of Composite Materials,28: 656–680 (1994).6

A direct micromechanics method for analysis of failure initiation of plain weave textile composites.

Damage characterization of triaxial braided textilecomposites.MSc thesis,

Effect of ﬁbre architechure parameters on deformation ﬁelds and elastic moduli of 2D braided composites.

Estimation of a mechanical characterization for woven fabric composites by FEM based on damage mechanics.

Experimental methodology of study of damage initiation and development in textile composites.

Longitudinal and transverse damage taxonomy in woven composite components.

Meso-FE modelling of 3-axial braided composites.

Micro-structural and damage analysis of braided composites. MSc thesis,

Observations on the ﬁbre distribution and ﬁbre strain in a woven fabric reinforcement.

The simulation of the geometry of two-component yarns. Part II: Fibre distribution in the yarn cross-section”,

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Fibre distribution inside yarns of textile composite: gemetrical and FE modelling

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