Keywords: textile composite reinforcements, fibrous material mechanical behaviour, virtual tests, meso macro analyses.

Knowledge of the mechanical behaviour of woven composite reinforcements is necessary for simulation of composite performance manufacture. This study aims to recall the specificity of the mechanical behaviour of dry fabrics and to determine these mechanical properties from virtual tests. For this, 3D finite element analyses of unit cells are performed. These computations are not classic computations due to the constitution of the yarns, which are made of thousands of small fibres. The possible motion of the yarn allows undulations, leading to nonlinear biaxial tensile behaviour, and renders most of the rigidities, other than tensile stiffness, very weak. The specificities of the calculation in order to reach this mechanical behaviour are described. Several specific aspects of the analysis will be detailed; especially the use of a hypoelastic law based on an objective derivative using the rotation of the fibre which allows a strict evolution of the directions of orthotropy according to the fibre direction. The virtual tests are compared to experimental biaxial tests and shear tests on several reinforcements. Such an approach allows us to understand the phenomena implicated in the behaviour and the main aspects that lead to the specific behaviour of woven media. It can also help in the design of new fabrics by changing some mechanical and geometrical parameters in order to obtain prescribed properties.

Simulation of preforming [1,2] requires the knowledge and modelling of the mechanical behaviour of woven reinforcements. These are highly specific because of the internal structure of the fabrics. Motion is possible between fibres and yarns. Weaving also plays a part in the mechanical properties. Mechanical behaviour can be investigated by experimental tests such as biaxial tensile tests and in-plane shear tests [3,4,5,6]. However, these experimental tests are rather difficult to perform and above all it is sometimes necessary to obtain information on the mechanical behaviour of a fabric which has not yet been manufactured. For instance, it may be interesting to know the influence of certain fabric parameters (yarn geometry, yarn density, fibre material, type of weaving) on a forming process. To this end, virtual tests permit the mechanical properties of a woven reinforcement to be obtained relatively easily, without performing the experiments and hence without necessarily manufacturing the fabric under consideration. The virtual tests that are presented in this paper are 3D finite element simulations performed on a unit woven cell. Because of the specific mechanical behaviour of woven material, tensile biaxial tests and in-plane shear tests are performed. The finite element of the unit woven cell must account for the constitution of the yarn that is made of thousands of fibres. The specificities of the numerical models will be presented in the paper. This paper focuses particularly on a hypoelastic model based on an objective derivative using the fibre rotation [7]. The results obtained in the case of biaxial tension of an unbalanced fabric are presented. Virtual tests in in-plane shear are presented in the last section. For all these virtual tests the results are compared to experimental results and both sets of tests agree well.

1

Hsiao S.W. and Kikuchi N. "Numerical analysis and optimal design of composite thermoforming process", Comp. Meth. Appl. Mech. Engrg., 177, 1-34. 1999. doi:10.1016/S0045-7825(98)00273-4

2

Zouari B., Daniel J.L., Boisse P., "A woven reinforcement forming simulation method Influence of the shear stiffness", Computers and structures, 84, 351-363, 2006. doi:10.1016/j.compstruc.2005.09.031

3

Kawabata, S., "Nonlinear mechanics of woven and knitted materials, Textile structural composites", Elsevier, Ed. by T.W. Chou and F.K. Ko, 3, 67-116, 1989.

4

McBride, T.M. and Chen, J., "Unit-cell geometry in plain-weave fabrics during shear deformations", Composites Science and Technology, 57, 3, 345-351, 1997. doi:10.1016/S0266-3538(96)00136-4

5

McGuinness G.B., Bradaigh C.M.O, "Development of rheological models for forming flows and picture-frame shear testing of fabric reinforced thermoplastic sheets", Journal of Non-Newtonian Fluid Mechanics, 73,1-2, 1-28, 1997. doi:10.1016/S0377-0257(97)00040-2

6

Buet K., Boisse Ph., "Experimental analysis and models for biaxial mechanical behaviour of composite woven reinforcements", Experimental Mech., 41, (3),260-269, 2001. doi:10.1007/BF02323143

7

Hagège B., Boisse P. and Billoët J.-L., "Finite element analyses of knitted composite reinforcement at large strain", European Journal of Computational Mechanics, 14 (6-7), 767-776, 2005. doi:10.3166/reef.14.767-776

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