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Computation of Strength and Failure of Textile Composites
in a Multiscale Simulation
C. Hühne, M. Vogler, G. Ernst and R. Rolfes
Institute for Structural Analysis,
Leibniz University of Hannover, Germany
E-mail: c.huehne@isd.uni-hannover.de
Keywords multiscale analysis, textile composites, voxel meshing, damage, failure,
anisotropy, material model
Abstract
Textile composites describe a broad range of polymer composite materials with textile
reinforcements, from woven and non-crimp commodity fabrics to three dimensional textiles.
In a general manner textile composites are based on textile preforms manufactured by some
textile processing technique and on some resin infiltration and consolidation technique. Due
to the complex three-dimensional structure of textile composites, experimental determination
of strength parameters is not an easy procedure. Especially the through-thickness parameters
are hardly to obtain. Therefore, in addition to real material testings, virtual material testings
are performed by use of an information-passing multiscale approach. The multiscale approach
consists of three scales and is based on computation of representative volume elements
(RVE’s) on micro-, meso- and macroscale. The micromechanical RVE enables to determine
stiffness and strength parameters of unidirectional fiber bundle material. Further, statistical
distribution of fibers is investigated. The homogenized material parameters at microscale are
used as input data for the next scale, the mesoscale. In the mesomechanical RVE, fiber
architecture, in particular fiber undulations and the influence of through-thickness
reinforcements, are studied. The obtained stiffnesses and strengths are used as input for the
macroscale. On macroscale, structural components are calculated. On each scale, numerical
results are compared with experimental test data for validating the numerical models.
1. Textile Composites
Textile composites are characterized by the manufacturing process which involves machines
usually used for production of textiles. With these machines, the dry rovings are laid and
connected, e.g. knitted, woven or braided, in a preform. Figure 1 shows different preforms
used in textile composites. The lay-up of these dry preforms is easier than with less flexible
pre-impregnated layers and allows for more draping and easier connection of the layers via
pinning or stitching etc. The resin infiltration of the fibers after the lay-up is followed
immediately by the consolidation. During the infiltration process the fibers are held in place
by the textile structure of the preform. Because the consolidation process, beginning with the
infiltration, does not have to be stopped, textile composites are cheaper than prepreg material,
which generate storage cost.
Compared to prepreg-composites, the structure of textile composites is much more
heterogeneous. In textile composites, the fibers are only equally dispersed throughout the
fiber bundles, but not over the whole layer. Between the fiber bundles there are epoxy resin
pockets and fiber undulations due to reinforcements in thickness direction, which have an
influence on the mechanical properties. Compared to prepregs, textile composites have
advantages in through-thickness strength, delamination sensitivity and crashworthiness.
Figure 1: Different preforms used in textile composites
2. Multiscale Analysis
Figure 3 shows the scheme of the multiscale algorithm. At microscale, fiber and matrix are
modeled. As input serve experimentally obtained stress-strain curves for epoxy resin under
different loading states and the elasticity parameters of the fiber material. The exakt
determination of matrix and fiber properties is essential for the applicability of the
information passing multiscale simulation. With the micromechanical unit cell stiffnesses and
strengths of unidirectional fiber bundle material can be determined. For the elastic properties
representative volume elements with a stochastic fiber distribution are investigated, see Figure
3a. Figure 3b shows the unit cell of a weft-knitted fabric. By comparison of test data and
results of numerical analysis the numerical models are validated. The strengths computed on
the mesoscale serve as input parameters for the failure criterion of Juhasz [1] that is used on
macroscale for the evaluation of failure.
(a) Micromechanical RVE with stochastic fiber
distribution (b) Mesomechanical unit cell of weft-knitted fabric
Figure 2: Representative Volume Elements (RVE)
Figure 3: Multiscale algorithm
3. Material Models
In order to consider the special characteristics of epoxy resin and fiber bundles, two material
models are developed. Both materials exhibit load state dependent yield and failure behavior,
that is especially under shear considerable plastic deformations occur. This non-linear
hardening is considered via tabulated input, i.e. experimental test data is used directly without
time consuming parameter identification. A quadratic criterion is used to detect damage
initiation based on stresses. Thereafter softening is computed with a strain energy release rate
formulation. To alleviate mesh-dependency this formulation is combined with the
voxelmeshing approach.
3.1. Isotropic elastic-plastic material model
Firstly, an isotropic elastoplastic material model regarding a pressure dependency in the yield
locus, see Figure 4, is presented for epoxy resin. A different yield behavior under uniaxial
tension, uniaxial compression, simple shear and biaxial stress states can be regarded, see also
[2]. As the assumption of constant volume under plastic flow does not hold for epoxy resin, a
special plastic potential is chosen to account for volumetric plastic straining. If at any point in
stress space the failure surface is achieved, stiffness degradation starts, governed by the
fracture energy formulation according to Hillerborg [4].
Figure 4: Yield surface for epoxy resin
3.2. Transversely isotropic elastic-plastic material model
Secondly, a transversely isotropic, elastoplastic material model is developed for fiber bundles.
The constitutive equations for transverse isotropy are formulated as isotropic tensor functions,
see [3]. This enables to account for pressure dependency in the yield surface and different
hardening under different stress states. Under transverse and in-plane shear pronounced
plasticity can be observed, whereas under uniaxial stress states in fiber direction and
transverse quasi brittle behavior occurs and nonlinearity is very low. This different behavior
in dependence of the loading state can be regarded in the developed formulation of the
transversely isotropic material model.
Once again hardening curves are provided as tabulated data which can be obtained by
experiment, if available, or by simulation performed with the micromechanical model.
Together with the failure criterion of Juhasz, these material models enable the computation of
failure of textile composites on all scales of the presented multiscale approach.
References
[1] J. Juhasz, R. Rolfes, and K. Rohwer. “A new strength model for application of a
physically based failure criterion to orthogonal 3D fiber reinforced plastics”. Composite
Science and Technology, Vol. 61, 1821–1832, 2001.
[2] B. Fiedler, M. Hojo, S. Ochiai, K. Schulte, and M. Ando. “Failure behavior of an epoxy
matrix under different kinds of static loading”. Composites Science and Technology,
Vol.61, 1615–1624, 2001.
[3] T.G. Rogers. “Yield criteria, flow rules and hardening in anisotropic plasticity”. In J.P.
Boehler, editor, Yielding, damage and failure of anisotropic solids, Vol. 5, 53–79, EGF
Publication, 1987.
[4] Hillerborg, A., Modeer, M., & Petersson, P. E. (1976). Analysis of crack formation and
crack growth in concrete by means of fracture mechanics and finite elements. Cement
and Concrete Research, 6, 773–782.
