MODELLING OF DAMAGE IN TEXTILE REINFORCED COMPOSITES: MICRO MESO APPROACH

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1 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach MODELLING OF DAMAGE IN TEXTILE REINFORCED COMPOSITES: MICRO MESO APPROACH B. Van Den Broucke,2,, P. Middendorf, S.V. Lomov 2, I. Verpoest 2 EADS Deutschland GmbH Innovation Works, D 8663 Munich, Germany. 2 Dept. of Metallurgy and Materials Engineering, K.U.Leuven, Kasteelpark Arenberg 44, 3 Leuven, Belgium. Abstract The complex architecture of textiles used as composite reinforcement results in complex stress distributions inside the composite structure when loaded externally. The resulting local stress concentrations can cause the initiation of damage in the structure. This effect gets even more complex when uneven fibre distributions inside yarns or fibrous plies are taken into account. This paper presents a method based on finite element calculations that takes into account these effects and tries to predict the homogenised elastic behaviour of a unit cell of a textile reinforced composite, enables the prediction of a first failure envelope, and tries to predict the behaviour including damage. Three types of non crimp fabrics and UD-braids, an innovative textile structure, are used as validation examples. A concise overview of the method, the simulation results and their comparison with experimental data are presented. Keywords: damage, textile reinforced composites, finite element, homogenisation.. Introduction In the past decades more complex reinforcements like textiles have become widely used within the composite world due to their well know textile manufacturing techniques and easy handling and good mechanical properties. However, these materials have a complex internal architecture which makes their analysis not straightforward. Moreover due to handling during the production process of the composite the textile can be deformed quite significantly and hence the mechanical properties and damage behaviour will be influenced accordingly. The Micro-Meso-Macro simulation approach (figure ) has proven to be successful for predicting elastic mechanical properties taking into account the above mentioned problems []. In this approach a so called Representative Volume Element (RVE) of the material is modelled that gives a detailed description of the material on a smaller scale, and represents a material point on a larger scale. In this work it is proposed to use this method to predict the damage behaviour of textile composites. Micro: yarn Meso: textile Macro: part Figure : Multi level simulation approach Corresponding author. Tel.: +49 () ; bjoern.broucke@eads.net Finite element modelling of textiles and textile composites, St-Petersburg, September 27

2 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 2 Mandrel Braiding ring Auxiliary Carbon Figure 2: Manufacturing principle of UD braids Figure 3: UD braid textile Figure 4: Biaxial [/9] MMF. Table : Main properties of the selected MMF materials Preform ID B [a] B2 Q [a] Manufacturer code () V V () V (2) V (2) V Description Bi diagonal Bi diagonal Quadri axial carbon fabric carbon fabric carbon fabric Number of plies Orientation of plies ( ) () -45; +45 ; 9 () ; +45; 9; -45 (2) +45; -45 (2) ; -45; 9; +45 Mass of the fabric (g/m 2 ) 322 ± ± ± 3 Stitching pattern Tricot Tricot-Warp Tricot-Warp Gauge (needles/in) Ply tow 2 K Toray 24 K Toray 2 K Toray T7 5E T7 5E T7 5E Ply mass (g/m 2 ) 56 ± 8 5 ± 8 56 ± 8 Stitching yarn PES 7.6 tex PES 7.6 tex PES 7.6 tex Stitching mass (g/m 2 ) [a] The B and Q fabrics are available in two forms () and (2), respectively. One is the mirror of the other for symmetrical lay-up. 2. Materials The presented method is validated using a set of different materials. The selection of the materials was based on their applicability in aerospace applications and driven by the ITOOL ( Integrated Tool for Simulation of Textile Composites ) project funded by the European Commission. The first material, the unidirectional braid (UDB), is an innovative textile structure developed by EADS Innovation Works [2, 3]. This material is produced with a circular braiding technique using a carbon reinforcement roving as braiding yarns in one direction. An auxiliary yarn is used for the second braiding direction (figure 2). The only function of the auxiliary yarns is to support the reinforcement yarns and keep them in place on the mandrel. Once the part is infiltrated, the auxiliary yarn does not have any function any more and hence the used amount is kept as low as possible. The resulting material consists almost entirely of carbon rovings oriented in a unidirectional way (figure 3). The UDB material was extensively studied by Eisenhauer [4] to determine its geometrical and mechanical properties. Also a series of experiments to determine the Ladevèze damage parameters have been executed. The second validation example are a class of materials called multi axial multi ply fabrics (MMF). A MMF fabric is produced by combining a unidirectional placement of tows in plies and stabilising the structure using a stitching introduced by a warp knitting process. Three types of MMF s which have previously been characterised at the department of Metallurgy and Materials Engineering (MTM) of the Katholieke Universiteit Leuven [5, 6] are selected of which the biaxial [/9] MMF is shown in figure 4. A list of the main material properties is given in table. Finite element modelling of textiles and textile composites, St-Petersburg, September 27

3 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 3 3. Methodology This analysis of the materials described above is based on the evaluation of a representative volume element (RVE) of the textile reinforced composite. The method presented can be split in three parts: model preparation, material and damage properties and homogenisation. Each of these steps is described in more detail below. 3.. Model preparation A geometrical description of the textile structure is the starting position of the simulation chain. This model is generated using the WiseTex software package developed at the MTM department [7] and is based on a series of simple measurements like yarn width and thickness, yarn spacing, interlacing pattern, etc. The second step is the conversion from the geometrical model to a FE mesh. This is achieved by using the software tool FETex, also developed at MTM. Imperfections like small yarn interpenetration are removed by manual modifications and contact simulation using the non linear FE software MSC.Marc. The final mesh is transferred back to FETex to be able to define correct material properties as described in the next section Material properties and damage model implementation The elements inside the FE-model are given material properties depending on their location in the structure. The fibre orientation and local fibre volume faction can vary inside yarns [8] or fibrous plies [9] and hence their local mechanical properties will change accordingly. This information, which is available in the WiseTex geometrical model, is translated using the Chamis micro mechanical mixing formulas [] into local mechanical properties for each element in the FE mesh. On micro-level (scale of the yarn or fibrous ply) the Ladevèze continuum damage mechanics based model for unidirectional composites [] is used to predict the damage behaviour. This model distinguishes between fibre tension, fibre compression, transverse tension and shear loads and translates them into a deterioration scheme for the mechanical properties of the defined composite materials. The Ladevèze model requires a set of material parameters that require quite some experimental work to fully characterise. Within the framework of this work, it was only possible to characterise the UDB material. Therefore based on the very similar carbon fibre which is used for both UDB and MMF material and the similar resin types, the assumption was made that the damage parameters for the MMF can be taken equal to the ones of UDB material. A second problem which is encountered is the dependency of the damage parameters on the fibre volume fraction. Also for this problem no experimental work is available and could not be investigated. However, for all fibre volume fractions present in the selected models there are one lage differences in fibre volume fraction, and hence the same damage properties are used Homogenisation Using homogenisation techniques [2, 3] the average elastic material properties of an RVE can be determined. This technique uses the so called average operator to calculate the average quantity T(x) of a tensor field T(x) in a certain volume Ω and is written for the average stress and strain tensor fields as σ = V Ω Ω σ(x)dv Ω ǫ = V Ω Ω ǫ(x)dv Ω () The integrals in equation are approximated within the FE environment by numerical Gaussian integration. Finite element modelling of textiles and textile composites, St-Petersburg, September 27

4 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 4 ǫ ǫ 2 ǫ 3 ǫ 4 ǫ 5 ǫ 6 Figure 5: The six different load cases to be solved in order to calculate the homogenised elastic properties of an RVE. Under the assumption that the stress and strain tensors are symmetric and hence the matrix notation can be used, the homogenised stiffness matrix Cij H of the considered RVE can be calculated by subjecting it to the six load cases shown in figure 5. For each of these load cases all strain components are kept zero except one. For the load case where the strain component ǫ j is non zero, the stiffness matrix components Cij H are obtained from: C H ij = σ i ǫ j, i, j =, 2,, 6. (2) The inverse of the stiffness matrix, i.e. the compliance matrix, then leads to the homogenised engineering constants of the RVE. To be able to apply the intended load case periodic boundary conditions (PBC) are used. These PBC are implemented within the MSC.Marc simulation environment via user subroutines programmed in FORTRAN. 4. Damage modelling The Ladevèze damage model is based on the internal strain energy density which is written as [ σ 2 W = 2( d l ) E t + Ψ( σ 2 ( ) ν2 E c E + ν ) ( 2 ν3 E2 σ σ 2 E + ν ) 3 E3 σ σ 3 ( ν23 E2 + ν ) ] [ 32 E3 σ 2 σ 3 + σ 2 2 2E2 t + σ 3 2 σ 2 2 2E3 t + 2( d t ) E2 + σ 3 2 E3 + 2( d s ) [ σ 2 4 G 2 + σ2 5 G 23 + σ2 6 G 3 ]. (3) The material function Ψ takes into account the non-linear behaviour in compression. The variables d l, d t and d s are three scalar values describing the longitudinal, transverse and shear damage state inside the material, respectively. The micro-defects closure effect is taking into account by introducing the Macauly brackets x, where x = x if x and x = if x <. Based on the strain energy density function the thermodynamic equivalent forces associated to the damage parameters are defined as: Z f = W d f = Z t = W d t = Z s = W d s = 2( d l ) 2 ( ν3 E 2( d t ) 2 2( d s ) 2 [ σ 2 + ν 3 E 3 E t + Ψ( σ 2 ) ) σ σ 3 [ σ 2 2 E 2 E c ( ν23 E 2 + σ 3 2 E 3 [ σ 2 4 G 2 + σ2 5 G 23 + σ2 6 G 3 ( ν2 E + ν 2 + ν ) ] 32 E3 σ 2 σ 3 ] E 2 ) σ σ 2 ] (4) (5) ]. (6) Finite element modelling of textiles and textile composites, St-Petersburg, September 27

5 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 5 d d max Y c Y Y L Y Figure 6: Relation between the damage parameter and the governing force Ladevèze then defines the governing forces of damage evolution as Y f = max Z f (τ) (7) τ t Y t = max Zt (τ) + b t Z s (τ) (8) τ t Y s = max Zs (τ) + b s Z t (τ) (9) τ t where b t and b s are material parameters that provide a coupling between the transverse and shear contributions. As explained in [] the coupling parameter b t can be taken zero for many materials and is implemented using this simplification. For quasi static loading the progressive damage of the material can be written in function of the governing forces. This typically linear relation is obtained by fitting experimentally obtained data points. The resulting curve defines an initial threshold value Y after which the damage parameter is gradually increased with slope Y C. At a certain load level the material undergoes a brittle fracture which is defined by a limit value Y L (figure 6). At the limit value, the damage variable is set a maximum allowed damage value d max. Summarised this gives if Y < Y d = Y Y if Y Y Y L Y C d max if Y L < Y. To predict matrix damage, a similar approach based on the internal strain energy is used, but an isotropic damage state is assumed. Both the Ladevèze damage model and the matrix damage model are implemented in the non linear FE solver MSC.Marc using FORTRAN subroutines. () 5. Results and discussion 5.. Elastic response The calculated engineering constants of the UD-braid material are plotted in figure 7. The polar graphs represent the Youngs s modulus, shear modulus and in plain Poisson s ratio (from left to right, respectively) plotted against an in plane rotation of the material. The results from the experimental investigations are also indicated on the graph. The calculated properties show very good agreement with the experimental data points. This is more or less straightforward as the material properties used for input are calculated based on the properties that are used as validation. They only differ by a change in fibre volume fraction. Finite element modelling of textiles and textile composites, St-Petersburg, September 27

6 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 6 5 Young s modulus Shear modulus Poisson s ratio Figure 7: UDB: Simulation results for different orientations. 5 4 Young s modulus 25 2 Shear modulus.75 Poisson s ratio Figure 8: NCF B: Simulation results for different orientations. Nevertheless this shows that the micro mechanical formulas of Chamis can be used to perform (small) changes in fibre volume fraction. The calculated engineering constants of the three different multi axial multiply fabrics are plotted in figure 8, figure 9 and figure. As for the UDB material, the polar graphs represent the Youngs s modulus, shear modulus and in plain Poisson s ratio (from left to right, respectively) plotted against an in plane rotation of the material. Again the results from the experimental investigations are indicated on the graph. The two biaxial MMF s clearly show there non isotropic material behaviour. The predicted stiffness shows good compliance with the experimental observed values, expect for the directions which are parallel to the fibre direction in one layer. The source of these differences is most likely a 5 Young s modulus 25 Shear modulus Poisson s ratio Figure 9: NCF B2: Simulation results for different orientations. Finite element modelling of textiles and textile composites, St-Petersburg, September 27

7 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 7 4 Young s modulus 5 Shear modulus.4 Poisson s ratio Figure : NCF Q: Simulation results for different orientations. too high assumed stiffness of the carbon fibre which was used for the micro mechanical material formulas. This property was taken from the material data sheet. It is also possible that during the production process of the MMF materials, the stiffness is slightly influenced and hence does not correspond to the fibre manufacturer data. Another possible cause is that the experimental investigations where not exactly aligned with the fibre direction. However to compensate for the magnitude of difference the test should have been performed in a direction approximately 5 % off axis, which is most unlike. The prediction of the shear modulus as well as Poisson s show relative good compliance with the experimental results. The quadri axial MMF shows a quasi isotropic material behaviour and very good compliance to the experimental values. The highest difference is found for the shear modulus, which is in general rather difficult to measure Damage predictions To evaluate the damage behaviour in the material the FE model of the RVE is incrementally loaded and for each increment the average stress and strain is calculated according to the method explained in section 3.3. The stress strain curve for a certain load case is plotted and evaluated. From the evaluation the ultimate strength are extracted. The characteristic strain levels as observed during experimental investigations are obtained from the evaluation of the FE results. Table 2 gives an overview of the results. One result which is clearly observed from the stress strain plots (figure, figure 2 and figure 3) is the fact that the simulated curve shows a stiffer material than the experimental curve. The reason for this difference lies in the fact that the simulation and experiment are performed using different boundary conditions. During experiment, the material is subjected to an increasing tensile load and is allowed to contract in the directions perpendicular to the load direction. During the simulation the RVE is subjected to an increasing strain in one particular direction but is prevented from contraction perpendicular to it. Hence the curves can not be compared directly. Future work is planned to change boundary conditions in such a way that they represent the experimental set up. The B material (biaxial [±45]) shows a strong overestimate for the in plain properties and the stress strain curves show a much more linear behaviour than the experiment. The different boundary conditions as explained before are a possible cause of the large difference. Moreover, the physical phenomena occurring during the experiment, i.e. the inter laminar failure of the matrix followed by the shearing of the fibres in the different layers requires simulations with large deformations, which have not been taken into account. Another possible cause of difference are wrong values for the composite shear or matrix damage properties. Unfortunately it was not possible to investigate this before writing this publication, but will be executed in future work. The first characteristic strain level ǫ, which indicates the initial damage in the material, was located at Finite element modelling of textiles and textile composites, St-Petersburg, September 27

8 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 8 3 MD Simulation MD CD Simulation CD Figure : NCF B: Stress strain curve comparison. MD Simulation MD CD Simulation CD Figure 2: NCF B2: Stress strain curve comparison. MD Simulation MD CD Simulation CD Figure 3: NCF Q: Stress strain curve comparison. Finite element modelling of textiles and textile composites, St-Petersburg, September 27

9 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach 9 Table 2: Results for the MMF materials: simulation versus experiment Mat. property Simulation Unit σu MD 22.6± MPa B σu CD 94.8± MPa τ (a) u 6.5± MPa ǫ % σu MD 75.8± MPa σu CD 72.3± MPa B2 τ u 53.8±2. 4. MPa ǫ % σu MD 566.5±27.8 MPa Q σu CD 55.6±23.3 MPa τ u 222.± MPa ǫ % (a) The experiment was performed in bias direction. is predicted significantlly lower than the strength in machine direction σu MD due to the presence of the non structural stitching sites which introduce weak spots in the material. The first characteristic strain level ǫ is predicted at the same lavel as observed in experimental investigations. The simulation for the quadri axial [/+45/9/ 45] material had conversion problems when reaching a strain level of approximatly.85%. Hence no in plane strengths could be calculated for this material. The shear strength τ u is predicted exactly the same as the experimental value (only 3 % difference). a level of %. The results from simulation for the B2 (biaxial [/9]) material show very good comparison with experimental observations. A maximum deviation of 25% for the shear strength τ u is observed. The strength in cross direction σ CD u 6. Conclusion A multi level simulation approach based on finite element calculations is proposed to calculate the elastic properties of a textile reinforced composite and to predict its damage behaviour. The prediction of elastic properties has shown to be successful for all selected materials. The biaxial [/9] multi axial multi ply fabric was used as a validation for the damage prediction and shows good predicted properties compared with experimental observations. The quadri axial [/ + 45/9/ 45] shows good compliance for the shear strength whereas the in-plane properties could not be calculated due to convergence problems. The biaxial [+45/ 45] material show less good compliance, mainly due to geometrical non linearities not taken into account within the simulation. Acknowledgments This study was done within the ITOOL ( Integrated Tool for Simulation of Textile Composites ) project funded by the European Commission and is gratefully acknowledged. Finite element modelling of textiles and textile composites, St-Petersburg, September 27

10 B. Van Den Broucke et.al., Modelling of damage in textile reinforced composites: micro meso approach References [] Björn Van Den Broucke, Ferruh Tümer, Stepan V. Lomov, Ignaas Verpoest, Patrick De Luca, and Laurent Dufort. Micro-macro structural analysis of textile composite parts: case study. In Proceedings of SAMPE Europe conference & exhibition, pages 94 99, Paris Expo, in Porte de Versailles, Paris, France., March 24. [2] Andreas Geßler, Jürgen Brandt, Franz Maidl, Christoph Breu, J. Horn, and H. Schneider. Neue entwicklungen bei der fertigung von kohlenstofffaserpreforms mit der rundflechttechnik. In DGLR Tagung. Deutsche Gesellschaft für Luft und Raumfahrt, 24. [3] Andreas Geßler and Franz Maidl. Verfahren zum herstellen von faserverbund-halbzeugen mittels rundflechttechnik. patent DE A, 25. Applicant: EADS Deutschland GmbH, 8552 Ottobrunn, DE. [4] Charlotte Eisenhauer. Characterisation of ud-braids. Master s thesis, RWTH Aachen University, 26. [5] Stepan V. Lomov, E.B. Belov, T. Bischoff, S.B. Ghosh, Thanh Truong Chi, and Ignaas Verpoest. Carbon composites based on multiaxial multiply stitched preforms. part. geometry of the preform. Composites Part A: applied science and manufacturing, 33:7 83, 22. [6] Thanh Truong Chi, Matteo Vettori, Stepan V. Lomov, and Ignaas Verpoest. Carbon composites based on multiaxial multiply stitched preforms. part 4. mechanical properties of composites and damage observation. Composites Part A: applied science and manufacturing, 36:27 22, 25. [7] Stepan V. Lomov, Dmitry S. Ivanov, Ignaas Verpoest, Masaru Zako, Tetsusei Kurashiki, Hiroaki Nakai, and Satoru Hirosawa. Meso-FE modelling of textile composites: Road map, data flow and algorithms. Composites Science and Technology, 67:87 89, 26. [8] V Koissin, D.S. Ivanov, S.V. Lomov, and I. Verpoest. Fibre distribution inside yarns of textile composite: geometrical and FE modelling. In Proceedings of 8th International Conference on Textile Composites (TEXCOMP-8), Nottingham, UK, October CD-edition. [9] V. Koissin, A. Ruopp, S.V. Lomov, I. Verpoest, V. Witzel, and K. Drechsler. Internal structure of structurally stitched ncf preform. In Proceedings of 2th European Conference on Composite Materials (ECCM-2), Biarritz, France, August 29 September 26. CD-edition. [] C.C. Chamis. Mechanics of composite materials: Past, present and future. Journal of Composites Technology and Research, ():3 4, 989. [] Piere Ladevèze. A Damage Mesomodel of Laminate Composites, chapter.6, pages 4 4. San Diego (Calif.): Academic press, 2. [2] Varvara G. Kouznetsova. Computational homogenization for the multi-scale analysis of multi-phase materials. PhD thesis, Technische Universiteit Eindhoven, 22. [3] Li Shaofan. Introduction to micromechanics and nanomechanics. Lecture notes (CE236/C24), Department of Civil and Environmental Engineering, University of California, Berkeley, CA9472, USA, 25. Finite element modelling of textiles and textile composites, St-Petersburg, September 27

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