Micromechanical determination of the viscoplastic behavior of a metal-matrix composite

Abstract

Abstract A micromechanical theory is developed to determine the influence of particle concentration and the applied strain-rate on the stress-strain relations of a viscoplastic composite containing elastic spherical inclusions. To estimate the nonlinear viscoplastic response of the two-phase system a linear viscoelastic comparison composite with an identical microgeometry is introduced. The elastic properties of the comparison inclusions are taken to be identical to those of the original ones and the viscoelastic matrix is taken to be of the Maxwell type, with a shear viscosity equal to the “secant” shear viscosity of the nonlinear viscoplastic matrix at a given stage of deformation. Then, the effective stress of the heterogeneously deformed viscoplastic matrix is calculated from the principle of work rate of the system. This, in turn, provides the needed secant shear viscosity of the ductile matrix. The theory is then applied to a TiC/Al system at 150°C, to examine the influence of TiC concentrations on the dilatational and shear behavior of this particle-reinforced composite over three different orders of strain rates: 10-3/hr, 10-4/hr and 10-5/hr. It is found that, for this system, the dilatational behavior is almost linear, without much strain-rate sensitivity, but its shear strength is greatly enhanced with increasing particle concentration and strain rate. A further examination on the influence of the elastic modular ratio of the inclusions to matrix further discloses that the stiffness of the inclusions can also have a significant effect on the overall behavior of the viscoplastic composite.