Modeling of uncertainties in long fiber reinforced thermoplastics

The present study is concerned with a numerical scheme for the prediction of the uncertainty of the effective elastic properties of long fiber reinforced composites with thermoplastic matrix (LFT) produced by standard injection or press molding technologies based on the uncertainty of the microstructural geometry and topology. The scheme is based on a simple analysis of the single-fiber problem using the rules of mixture. The transition to the multi-fiber problem with different fiber orientations is made by the formulation of an ensemble average with defined probability distributions for the fiber angles. In the result, the standard deviations of the local fiber angles together with the local fiber content are treated as stochastic variables. The corresponding probability distributions for the effective elastic constants are determined in a numerically efficient manner by a discretization of the space of the random variables and the analysis of predefined cases within this space.