A SIMULATION APPROACH FOR TEXTILE COMPOSITE REINFORCEMENTS

Transcription

1 THE 19 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS A SIMULATION APPROACH FOR TEXTILE COMPOSITE REINFORCEMENTS T. Gereke *, O. Döbrich, M. Hübner, C. Cherif Technische Universität Dresden, Institute of Textile Machinery and High Performance Material Technology, Dresden, Germany * Corresponding author (thomas.gereke@tu-dresden.de) Keywords: draping, finite element method (FEM), textile reinforcement, wrinkling Summary Textile-reinforced composites provide many advantages compared to or materials. Their properties can be tailored and material and structure can be manufactured at same time. The fundamental challenge is to combine component design and manufacturing process. A macroscopic material model for finite element simulations of textile composite reinforcement forming process is presented. The model reflects material behavior of textile reinforcements and ir nonlinear character. Typically, bending and shear stiffness of textile structures are low compared to in-plane tensile stiffness in fiber directions. This was taken into account within continuum mechanics approach. 1 Introduction The possibility to tailor properties of textilereinforced composites provides engineer creative freedom. The reinforcement architecture in complex shaped components can be aligned with expected stresses and, thus, potential of this advanced materials group can be utilized more advantageously. The fundamental challenge is to combine component design and manufacturing process. Firstly, design possibilities such as roving alignment, textile architecture and textile drapability have to be known. Secondly, a production process has to ensure reproducibility and stability such that textile reinforcement in component has desired properties. To analyze and solve se issues and challenges systematically and efficiently, numerical simulations are preferable compared to experimentally focused trial-and-error approaches. During manufacturing of textile-reinforced composites dry textile reinforcement is typically formed to a preform of final geometry and subsequently injected or infiltrated with a rmoset or rmoplastic matrix. During forming of complex double-curved shapes large global and local deformations of textile reinforcement structure occur [1]. The fiber orientation, fiber volume fraction, component thickness and occurrence of wrinkles and gaps between yarns determine reproducibility of forming process and thus final product quality. Due to possible motion between yarns textile reinforcements typically exhibit very small shear and bending rigidities compared to ir large inplane tensile stiffness. Out-of-plane buckling (wrinkling) of textile reinforcements during forming is a combined effect of shearing and bending [2]. The simulation of wrinkles demands correct reproduction of textile bending behavior. Contrarily to classic materials such as metals bending stiffness of textiles is independent of inplane tensile stiffnesses, which requires specific consideration within a continuum mechanics model. However, bending and shear resistance of textiles depend on in-plane tensile strain. The material is of a multiscale nature: behavior of macroscopic scale corresponds to local deformations of fiber structure at mesoscopic scale. The deformation behavior of fabrics comprising of continuous high-performance fibers consists of fiber elongation (crimped yarns), fiber straining, fiber slippage, fiber shearing, fiber compression, and bending. Shearing is most relevant deformation mode during forming of textile reinforcements [-5]. From shear force vs. shear angle gradients, which can be determined in picture frame or bias extension tests, drapability of fabrics (corresponds to forming behavior on a curved surface) can be derived. The drapability essentially depends on fabric density, which in turn results from diameters of inserted weft and warp yarns, weft and warp density and binding

2 point density. Due to complex deformation mechanisms, which take place on smaller length scales, mechanical properties of textile reinforcements are highly nonlinear. Typically, bending and shear stiffness of textile structures are low compared to ir in-plane tensile stiffness. This is due to relative movement among yarns during forming processes. However, a small bending stiffness results from yarn bending rigidity and friction at yarn crossing points. The bending stiffness, B, of textiles is not directly dependent on Young s modulus, E, and moment of inertia, I, as in classic construction materials (e. g. metals), where (1) This approach would be insufficient for a general textile material model due to very high tension stiffness and nearly negligible bending stiffness of most technical textiles. In a numerical model a reinforcing textile t structure can be regarded simplified as a continuum material. It exhibits anisotropic mechanical properties with high shear and bending deformations. In suchh a continuum mechanics approach bending rigidities have to be independent of membrane rigidities. In continuum mechanics approaches low bending stiffness was often neglected and membrane elements were used [6]. However, correct prediction of wrinkles is required r forr a successful simulation of fabric draping. Typically macroscopic modeling approaches were used. Various material formulations were developed: rate dependent material models [7, 8] and non- orthogonal rate-independent models [9, 10]. Recently, hyperelastic material models have been proposed [11, 12]. A detailed overview andd a discussion are given in [1]. A membrane element, which considered bending energy, has been introduced in [1]. Hamila et al. [ 14] includedd tension, shear and bending moments into ir formulation of internal virtual work for a triangular shell element. A shell element based on Coserat ory, where rigidities r were independent of each or, was presented in [15]. In current paper a macroscopic material model for finite element simulations is presented that reflects material behaviorr of textile reinforcements and its nonlinear character. 2 Numerical Material Model 2.1 Laminate Formulationn In developed material model a homogenous continuum replaces textile structure. The tensile, shear and bending b properties of textile reinforcement are required as an input into constitutive law l and can be determined by experimental testing. t Shell elements were used for simulationn in finite element software LS- DYNA. A user u subroutine was developed that reflects material m behavior of textile structures during forming processes. The formulation was based on laminate ory. A laminate assembly is schematically shown in Fig. 1. The dominant deformation mechanisms of textile structures are in-plane stretching, in-plane shearing and out-of-plane bending. The correspondin ng engineering constants are Young ss modulus, E, shear modulus, G andd bending stiffness, B. The Young s modulus m of laminate is i given by E laminate e=e 1 E 2 E n n (2) and in-plane shear modulus is calculated as G laminate In Eqs. (2) and () volume fraction of n layer is given by n =t n /h ( n =1), where t n is layer thicknesss of n th layer and h iss thickness of laminate. The bending stiffnesss is calculated as integral over thickness z of laminate as B laminate = h =G 1 G 2 G n n / 2 h / Ez dz Fig. 1. Laminatee assembly. Due to specific s material behavior of textile reinforcementss material rigidities must be independent of each or and laminate formulation has to be such that it results r in macroscopic textile material law. Thus, three layers (n = ) are assumed. A definition of different stress- n i 1 E i i z i () z 1 (4) n th

3 A SIMULATION APPROACH FOR TEXTILEE COMPOSITE REINFORCEMENTS strain-behaviors for several layers allows for different bending rigidities on top- and bottom sides in heterogeneous textile structures, e. g. E 1,compression E,tension. Some assumptions are requi- red to achieve a closed form solution [16, 17]. The material formulation allows to adjust bending stiffness while tensile stiffnesses are constant. Furrmore, it becomes possible to handle different bending rigidities in 0 and 90 directions. 2.2 Implementation The constitutive model was implemented in commercial explicit finite element code, LS-DYNA, as a user material routine (UMAT) for shell elements. Large deformations were handled with Green-Lagran nge strain. The 2. Piola-Kirchhoff stress, S ij, is related to Green-Lagrangee strain, E kl, by material stiffness tensor, C ijkl, as S ij =C ijkl E kl (5) The nonlinear Young s and shear moduli that represent material stiffness tensor were formulated in dependence of current strain state in each time step as given by experimental tests. The most important deformation mode in textile forming processes is shearing, i. e. change in angle between 0 and 90 yarns. It was measured with a picture frame, where textile was pinned onto frame with needles and was, thus, ablee to rotate freely at fixation. Typical shear diagrams are presented in Fig. 2. The non-linear characterr is due to laterall contact and compression between yarns at higher shear angles. The mesoscopic textile structure and yarn properties significantly influence shear properties and thus drapability of textile reinforcement. Or important input properties into model are tensile stiffnesses in warp and weft directions (equates to 0 and 90 directions) and bending stiffness. Those were determined with tensile tests according to [18] and cantilever bending tests according to [19], respectively. The resulting bending rigidity of fabrics is mainly resultt of mechanical yarn properties ass well as technology and parameters of textile manufacturin ng process. The resistance against bending results from friction of yarns. An application of classical ory of bending stiffness is accordingly not possible. Fig. 2. Typical shear s force vs.. shear angle curves c as measured with a picture framee test. 2. Validationn The material model m was firstly validated with patch tests. Furrmore, a forming simulation of a double curved geometry was performed. With spherical draping, material m model can be tested for its boundaries. It allows verification of applica- bility of model for prediction off deformation, shear angles, fiber orientation and wrinkles. For validation of material model a hemisphere punch test was s performed and results were comparedd to simulation. The hemisphere is a double-curved shape, which causes large shear angles. A hemisphere geometry was punched into fabric through a circular counterpart as shown in Fig.. Flexiblee blank holders fixed fabric. The distance of o reinforcing fiberss was used as mesh size for e discretization of macroscopic textile model. Based on deformation of o shell elements it becomes possible to trace fiber orientation during and after deformation. Thus, shearr angle in textile can be determined. d Fig.. Hemisphere punch testt

4 Results.1 Hemisphere Punch The predictedd material behavior during a hemisphere punch test is compared to actual behavior in Fig. 4. As can be seen from figure, force- displacement curves are in excellent agreement. The punch force increased significantly during test. The biaxial weft-knitted glass textile is a highly drapable fabric due to non-crimp nature of reinforcing yarns. The comparison of actual to predicted fiber orientation shown in Fig. 5 confirmss validityy of material model. The shear angles were reproduced correctly. Depending on fabric characteristics, wrinkling may occur during forming processes. During hemisphere punch test of biaxial weft-knitted glass fabric four wrinkles were observed in experiment and simulation (Fig.( 6). The simulation model correctly predictedd shape e of those wrinkles. For a more accurate measurement of yarn orientation, an optical system with a respective analysis tool would be desirable. Optical analysiss is able to determine fiber orientation on textile surface. It is challenging to get a feasible image of a reflecting textile surface made of glass or carbon fibers. For forming of a multilayer fabric, eddy current investigations would assist with determination n of invisible layers [20]. Such a system that uses electric conductivity of carbon fibers is currently under development. Fig. 5. Comparison of actual and predicted (red lines) fiber orientation after a hemisphere punch test t Fig 4. Actual vs. predicted hemisphere punch behaviorr Fig 6. Actual and predicted wrinkling during hemispheree punch test.2 Gravity load Fig. 7 illustrates influence of bending rigidity formulation within w material model. A fabric under gravity load was simulated with classic and novel laminatee models. The classic formulation as given in Eq. 1 gives a stiff s fabric due to high in-plane stiffness of high- performance yarn y materiall (Fig. 7a). Contrarily, current laminate formulation provides t possibility of high in-plane stiffnesses with concurrent low bending stiffness (Fig. 7b) ). The simulated wrinkles exhibit a realistic shape.

5 A SIMULATION APPROACH FOR TEXTILEE COMPOSITE REINFORCEMENTS Fig. 7. Wrinkling of a textilee simulated with a) classic and b) novel shell element formulation. Forming simulation of a structural part The forming of a complex shaped automotive part with a textile composite reinforcement was simulated with current approach. The results are presented in Fig. 8. Comparison of simulatedd to an actual formed component showed excellent agreement in terms of fiber orientation. The double curved shape yields little and highly sheared zones. The results of such a drape simulation provide information for furr investigations. Thus, fiber orientation is important for infiltration or injection analyses with a respective material model and simulation tool. Zones of highh yarn shearing exhibit a high fiber volume fraction. f Their permeability is low and those areas may thus be hard to infiltrate by matrix. The knowledge of fiber orientation, which is providedd by drape simulation, is also important for virtual testingg of structural part. The reinforcing textile may also be adjusted to conditions given by geometry and distribution of forces within structural component. Knowledge of fiberr orientationn is thus important for a structural simulation of composite part. Fig. 8. a) Actuall and b) simulated preform (fiber angle distribution) 4 Conclusions A material model m for simulation of textile composite reinforcemenr nt deformation was introduced that reproducedd material resistances in tension, shear and bending accurately. The novel material formulation givess excellent results r for fiber orientation after textile forming and for shape of wrinkles. Acknowledgements The authors are a grateful for support of German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) and Allianz Industrie Forschung (AiF) in scope of DFG- AiF-Cluster Leichtbau und Textilien under grants CH 174/16-1 and BR. The IGF research project BR of Forschungsvereinigung Forschungskuratorium Textil e. V., Reinhardtstr , Berlin was funded through t AiF within program for supporting Industrielle Gemeinschaftsforschung (IGF) from funds of Federal Ministry of Economics and Technology 5

6 (BMWi) by a resolution of German Bundestag. We thank se institutions for provision of financial resources. References [1] T. Gereke, O. Döbrich, M. Hübner and C. Cherif Experimental and computational composite textile reinforcement forming: A review. Composites A: Applied Science and Manufacturing, Vol. 46, pp 1-10, 201. [2] P. Boisse, N. Hamila, E. Vidal-Sallé and F. Dumont Simulation of wrinkling during textile composite reinforcement forming. Influence of tensile, in-plane shear and bending stiffnesses. Composites Science and Technology, Vol. 71, No. 5, pp , [] S. V. Lomov, A. Willems, I. Verpoest, Y. Zhu, M. Barburski and T. Sotilova Picture frame test of woven composite reinforcements with a full-field strain registration. Textile Research Journal, Vol. 76, No., pp , [4] J. Cao, J. et al. Characterization of mechanical behavior of woven fabrics: Experimental methods and benchmark results. Composites A: Applied Science and Manufacturing, Vol. 9, No. 6, pp , [5] G. Hivet and A. V. Duong A contribution to analysis of intrinsic shear behavior of fabrics. Journal of Composite Materials, Vol. 45, No. 6, pp , [6] J. R. Collier, B. J. Collier, G. O Toole, S. M. Sargand Drape prediction by means of finite-element analysis, Journal of Textile Institute, Vol. 82, No. 1, pp , [7] P. Badel, E. Vidal-Sallé, E. Maire and P. Boisse Simulation and tomography analysis of textile composite reinforcement deformation at mesoscopic scale. Composites Science and Technology, Vol. 68, No. 12, pp , [8] M. A. Khan, T. Mabrouki, E. Vidal-Sallé and P. Boisse Numerical and experimental analyses of woven composite reinforcement forming using a hypoelastic behavior. Application to double dome benchmark. Journal of Materials Processing Technology, Vol. 210, No. 2, pp 78-88, [9] W. R. Yu, F. Pourboghrat, K. Chung, M. Zampaloni and T. J. Kang Non-orthogonal constitutive equation for woven fabric reinforced rmoplastic composites. Composites A: Applied Science and Manufacturing, Vol., No. 8, pp , [10] X. Q. Peng and J. Cao A continuum mechanicsbased non-orthogonal constitutive model for woven composite fabrics. Composites A: Applied Science and Manufacturing, Vol. 6, No. 6, pp , [11] Y. Aimène, E. Vidal-Sallé, B. Hagège, F. Sidoroff and P. Boisse A hyperelastic approach for composite reinforcement large deformation analysis. Journal of Composite Materials, Vol. 44, No. 1, pp 5-26, [12] A. Charmetant, J. G. Orliac, E. Vidal-Sallé and P. Boisse Hyperelastic model for large deformation analyses of D interlock composite preforms. Composites Science and Technology, Vol. 72, No. 12, pp , [1] S. Sriram, R. H. Wagoner Adding bending stiffness to -D membrane FEM programs, International Journal of Mechanical Sciences, Vol. 42, No. 9, pp , [14] N. Hamila, P. Boisse, F. Sabourin, M. Brunet A semi-discrete shell finite element for textile composite reinforcement forming simulation, International Journal for Numerical Methods in Engineering, Vol. 79, No. 12, pp , [15] L. Jannski V. Ulbricht Numerical simulation of mechanical behaviour of textile surfaces, ZAMM Zeitschrift für Angewandte Mamatik und Mechanik, Vol. 80, No. S2, pp , [16] O. Döbrich, T. Gereke, O. Diestel, S. Krzywinski and C. Cherif Decoupling bending behavior and membrane properties of finite shell elements for a correct description of mechanical behavior of textiles with a laminate formulation, Journal of Industrial Textiles, online first [17] T. Gereke, O. Döbrich, M. Hübner, O. Diestel, S. Krzywinski and C. Cherif Numerical draping simulations of textile composite reinforcements. Proceedings of 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna, Austria, paper 191, [18] DIN EN ISO 194-1: Textiles - Tensile properties of fabrics - Part 1: Determination of maximum force and elongation at maximum force using strip method, [19] DIN 562: Determining flexural rigidity of plastic film and woven textile fabrics with or without plastic coating by cantilever method, 200. [20] M. H. Schulze, H. Heuer, M. Kuettner and N. Meyendorf High-resolution eddy current sensor system for quality assessment of carbon fiber materials. Microsystem Technologies, Vol. 16, No. 5, pp , 2010.