Homogenization of metallic fiber-reinforced composites under stochastic ageing

The main aim of this paper is to present an application of the generalized stochastic perturbation technique to model stochastic ageing processes of the metallic fibre-reinforced periodic composite materials in terms of their effective properties. Those ageing processes are modelled here as two-parametric time series having Gaussian random initial values and time rate, both defined uniquely by their expectations and standard deviations. Computational homogenization procedure is discrete and based on the Finite Element Method program MCCEFF as well as the computer algebra system MAPLE, where the Response Function Method and the stochastic analysis are entirely implemented. This numerical strategy is used to analyze probabilistic moments of the effective elastic tensor of the few metal matrix composites as well as to simulate stochastic ageing of two representative composites – MoSio2–SiC and Ti–SiC. The approach proposed and results of computations may be further applied in the reliability analysis of metallic or the other composites.

► Homogenization of the fiber-reinforced metallic composites is provided.
► Gaussian uncertainty in Young modulus of the constituents is analyzed.
► The stochastic perturbation technique and the effective modules method are used.
► The Gaussian homogenized tensor is obtained for the random Young modulus.
► Stochastic ageing reduces the expectations and increases variances of the effective tensor.