The influence of stochastic interfacial parameter distribution on the stiffness of composites with complex fibre orientation

This paper deals with the overall stiffness determination of a short-fibre-reinforced composite with complex fibre orientation and soft interfaces. The fibres are oriented differently in the matrix through a distribution function of the Euler angles. No fibre length distribution function is used, i.e. the fibres are of the same length. The approach is based upon the Mori–Tanaka mean-field theory. Furthermore, the effects of an interface with stiffness differing from those of the matrix and fibre are considered through a modified Eshelby tensor. The parameter describing the interfacial stiffness is considered as a stochastic variable described by a statistical distribution function. It is shown that when the fibres are oriented mainly towards the directions of the principal stresses the effects of the soft interface is diminishing. Furthermore, it is shown that when the interfacial stiffness parameter is described by a β distribution the resulting composite stiffness distribution resembles a uniform distribution.