FEA of textiles and textile composites: a gallery

Transcription

1 FEA of textiles and textile composites: a gallery Stepan V. Lomov, Dmitry S. Ivanov, Vitaly Koissin, Ignaas Verpoest Department MTM, Katholieke Universiteit Leuven Kasteelpark Arenberg 44 B-3001 Leuven Belgium Masaru Zako, Tetsusei Kurashiki, Hiroaki Nakai Department of Management of Industry and Technology, Osaka University, 2-1, Yamadaoka, Suita, Osaka, , Japan ABSTRACT Meso-scale finite element modelling of textiles and textile composites (scale of the unit cell of the textile structure) is a powerful tool for homogenisation of mechanical properties, study of stress-strain fields inside the unit cell, determination of damage initiation conditions and sites and simulation of damage development and associated deterioration of the homogenised mechanical properties of the composite. The paper presents a gallery of cases of such a modelling, discussing issues of building finite element models of textile structures (geometry, meshing, boundary conditions), of interpretation of the results (homogenization, damage initiation criterion, damage propagation) and of verification of the models. The following cases are considered: x Composites reinforced by 2D woven fabrics: validation of FE modeling using full-field strain measurements x 3-axial braided composites: building of an adequate geometry and mesh, boundary conditions for ¼ of the unit cell, damage initiation and propagation x Structurally stitched thick woven composite: interaction of the stitching with the body of the plate x Knitted fabrics made of shape memory alloy wires: hyperelastic material behaviour, contacts and slipping of the wires All the cases are supported by comparison with experimental data.

2 INTRODUCTION Finite element (FE) meso-modelling of textile composites and textiles themselves, apart from being a popular research topic, is more and more considered as a tool for industrially relevant calculations, especially for prediction of damage threshold and progressive damage. The term meso refers to the scale level of unit cell of the textile reinforcement. FE simulation can provide detailed information on the stress-strain fields inside the unit cell of textile composites, for elastic or nonelastic behaviour of fibres and matrix, leading to prediction of damage initiation and further development of damage. Homogenised stiffness of composite can be as well predicted using FE models, but their computational expense is much higher then simpler methods, which accurately predict homogenised stiffness (e.g. method of inclusions [1, 2]). An overview of the state-of-the-art can be found in the proceedings of a micro-symposium FE modelling of textiles and textile composites (St.-Petersburg, 2007). An initiative of creating The Textile Composite Archives [3], to be hosted on a server at Texas A&M University is a follow-up of discussions during that meeting. The gallery presented in this paper lies in the streamline of the proposal of this data bank. The tools (as enumerated in conclusion of the review paper [4]) used in the examples of FE analysis given in the present paper, are shown in Table I. TABLE I SOFTWARE TOOLS 2D woven 3-axial braided Structurally stitched Knitted Geometric modeller WiseTex Geometry corrector of intermediate mesh contact pairs in MeshTex yarn interpenetration analysis in ANSYS superposition ANSYS Meshing MeshTex ANSYS MeshTex ANSYS Material properties MeshTex ANSYS macros MeshTex ANSYS macros Boundary conditions MeshTex ANSYS macros MeshTex ANSYS macros FE solver, post-processor SACOM ANSYS SACOM ANSYS Homogenisation MeshTex ANSYS macros MeshTex ANSYS macros Damage SACOM ANSYS macros SACOM n/a References: WiseTex [2], MeshTex [4], SACOM [5], mesh superposition [6], intermediate FE analysis for correction of geometry [7], damage analysis [4, 5, 7] 2D WOVEN COMPOSITE: HOMOGENISED PROPERTIES AND ELASTIC STRAIN FIELDS The work reported in this section is a part of a wider modelling effort, done in collaboration with A.E. Bogdanovich and D. Mungalov [8], which also includes modelling of 3D woven composites, performed using MOSAIC 3D model [9]. The plain weave was made of 2275 tex PPG Hybon 2022 E-glass roving in both warp and fill directions: 1.95 ends/cm and 1.60 picks/cm. Note the difference between fibre amounts in warp and fill directions, which asked to alternate fabric layer orientation in the 4-layer preform. Composite material samples were fabricated in a vacuum bag with Dow Derakane 8084 Epoxy-Vinyl Ester resin as a stack of four woven layers of 815 g/m 2 with orientation 0 /90 /90 /0.

3 The geometrical model (Figure 1a) is based on the following data obtainable without cross-sectioning of the composite plate: Thickness of the composite plate, which was measured to be 2.45±0.08 mm. This value gives the fibre volume fraction of the plate 52.4% and the average thickness of the layers mm, not accounting for the nesting of the yarns. Spacing of the warp and weft yarns directly used in WiseTex model. Thickness of the warp and weft yarns was assumed to be 0.3 mm, which, together with the crimp of the yarn calculated using WiseTex, produced the thickness of one layer equal to the measured value mm. The areal density of the fabric in WiseTex model is 809 g/m 2 and the overall fibre volume fraction is 52.0%, which correspond to the specified and measured values. Width of the warp and weft yarns was estimated using the images of the plate as 5.1 mm, which gives fibre volume fraction inside the yarns of 75%. The shape of the warp and fill yarn cross section was assumed to be elliptical TABLE II. EFFECTIVE PROPERTIES OF 2D WOVEN LAMINATE experiment OA M-T FE E 1, GPa 26.0± E 2, GPa 26.0± E 3, GPa n/a G 12, GPa n/a ± n/a E 45º, GPa 12.2± n/a G 45º, GPa n/a n/a 45º 0.610± n/a a b c Figure 1. 2D woven laminate model: (a) WiseTex model of a ply; (b) H x field calculated in FE overlapped with the optically registered field, applied strain <H x >=0.1%; (c) profile of H x along AB FE model for unit cell of the 2D plain weave composite (Figure 1a) was built and solved using MeshTex/SACOM software, which directly imports geometrical model of one layer of the fabric from WiseTex. In order to mesh the unit cell, MeshTex inserts thin (0.005 mm) layers of matrix in between the warp and fill yarns and on the surface of the unit cell. The resulting V f of the unit cell is hence slightly decreased to 47.2% (52.0% in WiseTex model). The unit cell is unbalanced, hence it is difficult to impose correct boundary conditions on the laminate model. Because of these two factors, the following calculation route was adopted: 1. Perform FE homogenisation for a woven ply using periodic boundary conditions in all the directions

4 2. Scale elastic properties to fibre volume fraction 52.0% 3. Calculate homogenised laminate properties using Classical Laminate Theory with properties of lamina calculated as above Use of periodic boundary conditions in thickness direction may be questioned as the plate has only four plies and free surfaces are not far from the middle of the plate. However, the overestimation of the stiffness, connected with that, is believed to compensate the underestimation of the stiffness resulting from the neglecting of the nesting of the layers. Table II shows effective elastic properties of the 2D weave composites calculated using iso-strain Orientation Averaging (OA), Mori-Tanaka (M-T), FEA and experimental results. The OA, M-T and FE analyses give results very close to the experimental data for all the considered engineering constants. All theoretical YDOXHV RI 3RLVVRQ V UDWLR 12 are consistently lower (about two times) than the average experimental value, but they are near the edge of the experimental scatter, ZKLFKLVYHU\ODUJHIRUWKLVFKDUDFWHULVWLF)(JLYHVVOLJKWO\EHWWHUDJUHHPHQWIRU 12. Figure 1b compares the H x field (loading in x direction) calculated in FE overlapped with the optically registered field (LIMESS system was used). Comparison of the two should be done bearing in mind, hat the FE calculation were done for periodicity of the fields in z-direction, whilst the experimental strains are measured on the free surface of the sample [10]. FE modelling provides good agreement with the experimental data both for homogenised properties of the composite and for the strain fields inside the unit cell. THREE-AXIAL BRAIDED COMPOSITE: INTERPENETRATION OF THE YARN VOLUMES, ¼ UNIT CELL, DAMAGE MODELLING The reinforcement (Figure 2a) is a triaxial braid made of carbon rovings (linear density 1600 tex), areal density of 600 g/m 2. The four-layer braided composite has interlacing yarns in three directions: braiding yarns (r45q) and inlay yarns. Five yarns (two in each biaxial direction and one inlay yarn) are interlaced at a relatively small distance, which leads to a complex shape of the yarn mid-lines and cross sections. The unit cell has a large open inner space, which is not occupied by the reinforcement and which causes nesting of the layers. There is variation of fibre volume fraction across the yarns: at the edges the fibre volume fraction is 15% lower than in the middle zone. The composite is impregnated with epoxy matrix (Epicote 828 LV/Epicure DX 6514, mixing ratio 100/17). The composite samples were tested in tension in three directions (indicated in Figure 2a) with acoustic emission (AE) registration. Typical diagrams of cumulative energy of events are shown in Figure 2d together with diagrams of degradation of stiffness. These diagrams are used to determine the strain corresponding to onset of damage H 1 and a second stage of the damage accumulation (called H 2 ) as a "knee" on AE curves, which is close to a slope change in the tensile (stiffness degradation) diagrams. More details of the experiments can be found in [7]. Periodic boundary conditions (based on the translation symmetry of the unit cell as a whole) are used. In order to decrease the computational efforts, following [11] the internal symmetry of the unit cell is accounted for (Figure 2b). The yarn shapes were adjusted to avoid interpenetration of the volumes, using separate and

5 compress algorithm, as described in [4]. This resulted in a mesh (Figure 2c) with complex non-symmetrical shapes of the yarns. a b d c Figure 2. 3-axial braid: (a) photo and WiseTex model; (b) transformation of the unit cell; (c) FE mesh; (d) Normalised tangent moduli (descending curves) and cumulative acoustic emission energy diagrams (ascending curves) for tensile tests in three material directions (MD, CD, BD) a b Figure 3. FE analysis of 3-axial braided composite: (a) damage initiation modelling using Puck criterion; (b) stiffness degradation modelling Stiffness constants for loading in MD and CD directions were well predicted by FE calculations (inside the experimental scatter). Damage initiation (H 1 threshold) was predicted in FE calculations using Puck criterion with values of the transversal and shear strength of the UD carbon/epoxy composite 28 GPa and 74 GPa respectively. This results in a good prediction of the experimentally observed damage initiation thresholds (calculated/experimental): MD: 0.35% / 0.29r0.09%; CD: 0.24% / 0.33r0.07%, as well as the damage mode (transverse cracking) and location of the damage initiation. The stiffness degradation model was based on the damage mechanics of Ladeveze for UD composites, representing the impregnated yarns (the details can be found in [7]). Figure 3b depicts the results of the calculations. The analysis corresponds well with the experiments. STRUCTURALLY STITCHED COMPOSITE: EARLY DAMAGE ONSET Quasi-UD hybrid woven fabric (warp: 24K carbon tows alternated with thin polysulfone yarns; weft: the same polysulfone yarns) with the total areal weight of 226 g/m 2 is used as the raw material. The reinforcement was composed of 28 plies

6 having symmetric stacking sequence [90/45/0/0/-45/90/-45/0/0/45/0/-45/0/45]s, where 90q corresponds to the warp (carbon fibre) direction in the surface plies. For the structural stitching, 1K carbon yarn and the tufting method are employed. The machine direction coincides with 0q direction of the preform. The piercing pattern is square 5x5 mm; the backside loop height is also about 5 mm. Composite plates (stitched and non-stitched) are manufactured using the liquid resin (toughened epoxy) infusion. The final thickness is 5.32 mm that gives the average fibre volume fraction of 58%. The material (Figure 4) was supplied by Dassault Aviation. a b Figure 4. Structurally stitched woven composite: (a) face and back side of the preform; (b) opening inside a ply created by the structural stitching; (c) FE model: plies and the stitching yarn The composite samples were tested in tension in 0q and 90q direction, with registration of damage initiation and development using acoustic emission. An important observed phenomenon was earlier initiation of damage in the stitched samples loaded in 90q direction (Figure 5). X-ray observation has shown that this preliminary damage starts inside the stitching yarns. The early damage onset has been reproduced in FE simulation. Figure 4c shows the FE model, consisting of 28 layers of UD laminate (polysulfone properties are close to the epoxy, and carbon crimp is negligible). The stitching site is representing by a resin-filled opening. The direction of the fibres around the opening are deviated, following streamlines around the opening. The stitching yarn itself is modelled as superimposed mesh; the shape of the stitching yarn and its compressed dimensions were measured on the composite samples. Damage initiation is determined using Hoffmann criterion. Figure 5 demonstrates that the FE model predicts the early onset of damage and the location of the initial damage. c Damage initiation stress, MPa no stitching test FE stitching Figure 5. Damage in the structurally stitched laminate, loading in 90q direction: (a) AE diagrams; (b) damage initiation locations, FE model (only plies are shown); (c) damage initiation stress, MPa

7 KNITTED SHAPE MEMORY ALLOY WIRES The studied plain knitted fabric is knit with 0.15 mm diameter NiTi wires. Figure 6 shows the fabric, WiseTex model and tensile diagram of the wire. Biaxial tests were performed for two conditions: deformation in the course direction, width fixed in the wale direction, and vice versa stress, MPa Measured Idealised strain, % Figure 6. Knitted NiTi wires and tensile diagram of the wire The geometrical model of the unit cell of the fabric was first built in WeftKnit software (part of WiseTex suite), then exported in ANSYS and meshed. Interpenetrations of the wires were handled using contact algorithms in ANSYS. Figure 7 shows the results of the calculations, together with configurations of the unit cell on the different stages of deformation (note the locking of the loops) and distribution of the three phases of NiTi in the wires. 4.00E E E-01 D F x,kn FE 2.50E E-01 I II III C I II III experiment 1.50E E E-02 O A 0.00E B I II III ,% x Figure 7. Computed tensile diagrams (course direction) of knitted NiTi and comparison with experiment When compared with experiment (Figure 7), the FE simulation shows higher stiffness of the fabric starting from about 20% of the applied strain, which is not observed in the experiments. The transition from the low stiffness to the high stiffness regime is defined by the locking of the loop, which depends on the initial gap between the wires in the loop contact zone. These gaps in the real fabric have a certain statistical distribution. The model represents the average of it. When the real fabric is deformed, all the gaps should be transformed into the locking state before

8 the fabric will start resisting by the wire tension rather than by the slippage and decrimping. CONCLUSION The presented gallery of FE simulations of textiles and textile composites demonstrate that the state-of-the-art models are capable to adequately simulate deformation and damage behaviour for a wide range of materials. ACKNOWLEGEMENTS The work reported here was supported by EU funded ITOOL project, and KULeuven PhD grant for D.Ivanov. REFERENCES 1. Lomov, S.V., G. Huysmans, Y. Luo, R. Parnas, A. Prodromou, I. Verpoest, and F.R. Phelan, Textile Composites: Modelling Strategies, Composites part A, 2001, 32(10): Verpoest, I. and S.V. Lomov, Virtual textile composites software Wisetex: integration with micro-mechanical, permeability and structural analysis, Composites Science and Technology, 2005, 65(15-16): Boisse, P., J. Crookston, D.S. Ivanov, S.V. Lomov, A.C. Long, I. Verpoest, J. Whitcomb, and M. Zako. Data bank for validation of finite element analysis of textiles and textile composites: a proposal. in 13th European Conference on Composite Materials (ECCM-13). 2008, Stockholm. 4. Lomov, S.V., D.S. Ivanov, I. Verpoest, M. Zako, T. Kurashiki, H. Nakai, and S. Hirosawa Meso-FE modelling of textile composites: Road map, data flow and algorithms, Composites Science and Technology, 2007, 67: Zako, M., Y. Uetsuji, and T. Kurashiki, Finite element analysis of damaged woven fabric composite materials, Composites Science and Technology, 2003, 63: Nakai, H., T. Kurashiki, and M. Zako, Individual modeling of composite materials with mesh superposition method under periodic boundary condition, in Proceedings of the 16th International Conference on Composite Materials (ICCM-16). 2007: Kyoto, CD edition. 7. Ivanov, D.S., S.V. Lomov, F. Baudry, H. Xie, B. Van Den Broucke, and I. Verpoest, Failure analysis of triaxial braided composite, Composites Science and Technology, in print. 8. Lomov, S.V., D.S. Ivanov, I. Verpoest, A.E. Bogdanovich, D. Mungalov, M. Zako, T. Kurashiki, and H. Nakai. Predictive analyses and experimental validations of effective elastic properties of 2D and 3D woven composites. in 13th European Conference on Composite Materials (ECCM-13). 2008, Stockholm. 9. Bogdanovich, A.E., Multi-scale modeling, stress and failure analyses of 3-D woven composites, Journal of Materials Science, 2006, 41(20): Lomov, S.V., D.S. Ivanov, I. Verpoest, M. Zako, T. Kurashiki, H. Nakai, J. Molimard, and A. Vautrin, Full field strain measurements for validation of meso-fe analysis of textile composites, Composites part A, in print. 11. Whitcomb, J., C.D. Chapman, and X. Tang, Derivation of boundary conditions for micromechanics analyses of plain and satin woven composites, Journal of Composite Materials, 2000, 34(9):