Theoretical framework and experimental procedure for modelling mesoscopic volume fraction stochastic fluctuations in fiber reinforced composites

Abstract : Many engineering materials exhibit fluctuations and uncertainties on their macroscopic mechanical properties. This randomness results from random fluctuations observed at a lower scale, especially at the meso-scale where microstructural uncertainties generally occur. In the present paper, we first propose a complete theoretical stochastic framework (that is, a relevant probabilistic model as well as a non-intrusive stochastic solver) in which the volume fraction at the microscale is modelled as a random field whose statistical reduction is performed using a Karhunen-Loeve expansion. Then, an experimental procedure dedicated to the identification of the parameters involved in the probabilistic model is presented and relies on a non-destructive ultrasonic method. The combination of the experimental results with a micromechanical analysis provides realizations of the volume fraction random field. in particular, it is shown that the volume fraction can be modelled by a homogeneous random field whose spatial correlation lengths are determined and may provide conditions on the size of the meso-volumes to be considered.