Stochastic multi-scale modelling of macro-scale textile composites
using experimental data of random geometry
A. Vanaerschot1, B.N. Cox2, S.V. Lomov3, D. Vandepitte1
1
KU Leuven, Dept. of Mechanical Engineering, Leuven, Belgium
2
Teledyne Scientific LLC, Thousand Oaks, CA, USA
3
KU Leuven, Dept. of Metallurgy and Materials Engineering, Leuven, Belgium
The internal geometry of textile composites is subjected to a significant amount of variability. The
need for reliable numerical analysis of composite structures demands for a realistic description of the
tow reinforcement with the corresponding mechanical properties. Such a representation can only be
achieved by [1] (i) collecting enough experimental data on the short- and long-range of the spatially
correlated random fluctuations of uncertain tow path parameters and (ii) using the lower scale
mechanical characteristics to derive the probabilistic information at the macro-scale. This work
presents the general approach and successive steps to build random virtual specimen, which can
subsequently be used to evaluate the spatial variation in the mechanical properties such as stiffness.
The methodology is applied on a typical twill 2/2 woven carbon-epoxy textile composite.
First, experimental data are collected of the random geometrical structure of the woven textile
composite. Tow path properties, such as centroid coordinates and tow cross-sectional parameters,
are quantified on the short- and long-range, i.e. spanning several unit cells. Two different
experimental techniques are used to analyse the tow components at different scales, permitting to
derive detailed information of the path at the scale of 7 μm. The spatial variation of each tow
parameter is decomposed in non-stochastic, periodic systematic trends and non-periodic stochastic
fluctuations. The systematic trend represents the average behaviour of the tow parameter, while the
stochastic characteristics are given in terms of the standard deviation and correlation length.
The next step consists in generating virtual random structures possessing the same statistical
properties as the experimental sample. While the systematic trends are applied to model the average
behaviour of all tow components, two different techniques are proposed to generate the deviations.
A distinction is made in (i) tow properties which are only correlated along the tow path, and (ii) tow
properties which are correlated along and between the tow paths. The first type of tow components
are produced using a Monte Carlo Markov Chain algorithm [2], where the transition matrix of each
tow component is calibrated with its experimental standard deviation and correlation length. For
components correlated along and between tows, a series expansion technique is used [3]. In the
latter case, tow properties are represented as one-dimensional random fields along the tow, which
are cross-correlated between neighbouring tows. A virtual specimen is obtained by combining the
generated deviations, from both generation methods, with the experimental systematic trends.
These representations can be used to quantify the spatial variation in the mechanical properties due
to geometrical variation at the meso- and macro-level.
References:
[1] Charmpis D.C., Schuëller G.I., Pellisetti M.F. Comput Mater Sci 2007; 41(1):27-37
[2] Blacklock M., Bale H., Begley M., Cox B. J Mech Phys Solids 2012;60:451-470
[3] Vorechovsky M., Struct Saf 2008; 30:337-363