THE OVERALL ELASTOPLASTIC STRESS-STRAIN RELATIONS OF DUAL-PHASE METALS

Two simple, albeit approximate, theories are developed to estimate the stress-strain relations of dual-phase metals of the inclusion-matrix type, where both phases are capable of undergoing plastic flow. The first one is based upon Hill's recognition of a weakening constraint power in a plastically deforming matrix, whereas the second one is based on Kröner's elastic constraint in the treatment of the single inclusion-matrix interaction. The inclusion-inclusion interaction at finite concentration is accounted for by the Mori-Tanaka method in both cases. Consistent with the known elastic behavior, the first theory discloses that the geometrical arrangement of the constituents has a significant influence on the overall elastoplastic response. When the harder phase takes the position of the matrix the composite is far Stiffer than that when it takes the position of inclusions. The strong elastic constraint associated with the second theory tends to provide an upper-bound type of estimate regardless of whether the matrix is the harder phase or the softer, and, therefore, it is suggested that this theory be used only for the class of composites whose matrix is the harder phase. Both theories are finally applied to predict the stress-strain relations of dual-phase stainless steels, and the results are found to be in satisfactory agreement with the test data. © 1990.