THE EFFECTIVE ELASTIC-MODULI OF MICROCRACKED COMPOSITE-MATERIALS

The self-consistent mechanics method has been widely used to estimate the macroscopic elastic moduli of solids containing microvoids and inc lusions. Another method based on the crack energy release and potentia l energy balance has also been used to estimate the overall elastic mo duli of a microcracked solid. It is shown here that these two approach es are equivalent for microcracked solids, thus one can take advantage of both methods to estimate the elastic moduli of inclusion-crack-mat rix composites, i.c. microcracked composite material. A solid containi ng spherical inclusions and randomly distributed penny-shaped cracks i s then studied. The effective elastic moduli of a solid with spherical inclusions and parallel-distributed penny-shaped cracks are also stud ied. It is established that the effects of inclusions and microcracks on overall moduli are approximately decoupled for stiff inclusions, wh ich are in most metal matrix composites. This conclusion is particular ly useful since one may then obtain the moduli of composites by a simp le two-step estimation. For compliant inclusions, including the limiti ng case of voids, the decoupling does not hold.