Fracture of an elliptical inclusion and its implications for the properties of short fiber composites

A model is developed to analyze the effect of fiber fracture on the elastic properties of short fiber composites.; Tensile test specimens were prepared from 26.6%, 12.9% fiber V{dollar}sb{lcub}f{rcub}{dollar} samples. The specimens were tested in tension to failure. Fractography and optical metallography performed in the plane of the reinforcement showed fragmentation of fibers which eventually led to overall material failure.; To model the fiber failure in an infinite matrix, the problem of crack and elliptical inclusion interaction is solved. The crack in the inclusion is formulated in terms of a distribution of dislocations. The dislocation solution is used as a Green's function and resulting singular integral equations are solved numerically. Stress intensity factors are tabulated for both a crack inside and outside the elastic elliptical inclusion. The specific case of a completely cracked inclusion is solved.; The solution of a completely cracked inclusion is then used in a micromechanics model of the damaged composite. The energy dissipated through the opening of the crack in the inclusion is calculated and used in a self consistent method to find the overall effective moduli of the composite. The results are given for the prediction of the effective moduli, E and {dollar}mu{dollar}, of the 2-D composite containing cracked fibers which are randomly distributed and oriented.