The present study is a comprehensive experimental investigation of the uncertainties in the mechanical response of short fibre-reinforced composites. The reference material investigated is a short glass fibre-reinforced phenolic resin matrix material, manufactured in a thermoset injection-moulding process. The mechanical material response was investigated in experiments on three different scales, considering ISO-size, miniature, and micro tensile samples. Further to the tensile experiments, compressive and shear tests were performed on macroscopic samples. Experiments on breadboard samples featuring more complex stress and deformation states complete the study. The injection-moulding process was found to control the basic fibre orientation. However, the nominal local fibre orientation distribution is superimposed with a pronounced local uncertainty. This microstructural uncertainty strongly affects the uncertainty in the local mechanical properties as well as variations between samples taken from identical positions in different but nominally identical plates.

This study focuses on the scatter in the mechanical properties in short fibre composites caused by uncertain fibre orientations. To interrelate the microstructural geometric and topological uncertainty with the material uncertainty on the macroscopic level, a numerical approach is utilized. Considering short fibre reinforced microstructures statistically described in terms of the probability distributions for the main stochastic variables such as fibre orientation, length, and density, statistically equivalent microstructural geometric models are generated using random number generation. The mechanical response of these microstructures is analysed in finite element analyses under different independent loading situations. The large-scale representative volume elements are subdivided for the evaluation into non independent stochastic volume elements. Like this the surrounding microstructure is included in the boundary conditions. A numerical homogenization analysis is applied on the statistic volume elements to evaluate effective macroscopic material parameters and their probability distributions. The results are correlated with the uncertainty of the input parameters.

The present study is concerned with a numerical scheme for prediction of the effective properties of solid foams considering their uncertainty. The approach is based on an analysis of a large-scale, statistically representative volume element which is subdivided into small-scale testing volume elements. Application of a standard homogenization scheme to the testing volume elements together with a stochastic evaluation yields a complete probabilistic characterization of the material which may be used for a random field definition of the material behaviour in a macroscopic effective field analysis of foam structures. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)