Macroscopic strength estimates for metal matrix composites embedding a ductile interphase

The influence of an interphase region on the macroscopic strength of unidirectional fiber-reinforced metal-matrix composites (MMCs) is investigated. The three phases of the composite are supposed to be elastic-perfectly plastic and to conform with J₂-plasticity. First, theoretical bounds to the macroscopic strength are derived, according to homogenization theory for heterogeneous periodic media: the gap between these bounds is quite narrow for certain stress conditions, volumetric proportions of the constituents, and ratios of the interphase-to-matrix strength. Then, a numerical model previously developed by Taliercio (2005) is employed to predict the macroscopic response of three-phase MMCs under any 3D stress through the analysis of a single representative unit cell. The model is applied to the numerical identification of the macroscopic strength properties of MMCs under uni-, bi- and triaxial stresses, in cases where the theoretical bounds are not sufficiently close to identify the actual macroscopic yield surface. The influence of the weakening interphase on the predicted macroscopic strength is critically discussed. A decrease in interphase strength is found to affect the transverse tensile and shear strength of the composite to a moderate extent, whereas the macroscopic longitudinal shear strength is extremely sensitive to the interphase strength.