Progressive debonding of aligned oblate inclusions and loss of stiffness in a brittle matrix composite

Abstract

A micromechanical theory is developed to examine the progressive debonding process of a brittle matrix composite containing aligned oblate inclusions under a high state of triaxial tension. Complete debonding is taken to be the debonding mode under such a high triaxial loading and its debonding strength is assumed to be governed by a Weibull probability function in terms of the hydrostatic tension of the inclusions. The micromechanical theory provides the required hydrostatic tensile stress at a given stage of debonding for a given inclusion shape and concentration. This allows one to calculate the debonding process progressively as the applied stress increases. The resulting stress-strain relation of the progressively debonded system is found to start out with that of the perfectly bonded composite, then deviates from it and eventually approaches the stress-strain curve of the corresponding porous material. It is further revealed that debonding with spherical inclusions is completed faster than with thin discs and it also occurs faster at a lower volume concentration of inclusions. The loss of stiffness of the transversely isotropic composite is also established as a function of inclusion shape and concentration for all five independent moduli; these moduli are seen to decrease gradually in the initial stage, then drop sharply while progressively debonding and finally level off again as all inclusions become debonded.