  In the manufacturing process of a filler-reinforced composite, the fillers in
the matrix are aligned due to the shear flow occurring during the drawing
stage, and the interface between the matrix and the fillers form various
imperfections that lead to debonding and slip under mechanical loading. Hence,
there have been numerous micromechanics studies to predict effective moduli of
the composites in the presence of partial alignment of fillers and interface
imperfections. In this study, we present an improved theory that overcomes two
limitations in the existing micromechanics based approaches. First, we find
that the interface damage tensor, which has been developed to model the
weakened interface between matrix and fillers, has singularities that cause
non-physical predictions (such as infinite or negative effective moduli). We
correct the mathematical mistakes to remove singularities and derive analytic
expressions of the damage tensor for ellipsoidal inclusions. Second, we reveal
that the previous theory on the effective moduli with axisymmetric filler
orientation distribution fails because the longitudinal and transverse moduli
do not converge in the limit of random orientation distribution. With
appropriate corrections, we derive an analytic expression for the orientation
average of arbitrary transversely isotropic 4th order tensor under general
axisymmetric orientation distribution. We apply the improved method to compute
the effective moduli of a representative composite with non-uniform filler
orientation and interface damage.
