Evaluation Of Mechanical Property Of Particulate Composites With Elastoplastic Matrix Using Mori-tanaka Scheme

The evaluation of the mechanical properties of composites composed ofelastoplastic matrix and reinforcement elastic particles is studied. Aimed at the problemthat the mean field approached based on the Eshelby equivalent inclusion theory mayover-evaluate the stress in the composites, a modified approach is suggested, in whichthe tangent elastoplastic modulus used in the determination of the Eshelby tensor isreplaced with the secant elastoplastic modulus. Incorporating Mori-Tanaka approach, anevaluation of the mechanical property of particulate composites with elastoplasticmatrix is developed.In order to verify the validity of the developed approach, the finite elementsimulation is performed, which is used as the benchmark. It includes the responses ofthe representative volume element (RVE) of such kind of composite subjected to puretension, pure shear, proportional tensile-shear stress, and cyclic tensile/compressiveloading. The RVE used in the simulation is a cube with a spherical inclusion embeddedat its center, the volume fraction of the spherical inclusion is equal to that of thereinforcement particles in the composite, and the periodical boundary condition areadopted in simulation. For comparison, the RVE of a cylindrical column with aspherical inclusion embedded at its center, and the thin-walled cylinder with a numberof spherical inclusions distributed in it, are also used for comparison. The constitutivemodels of the matrix and the inclusion are identical with that used in the mean fieldapproach. The results simulated with different RVE models show reasonable agreement,and are consistent with the benchmark FE simulation results obtained by the otherresearcher.The mechanical properties of the particulate composite subjected to the abovementioned loading conditions are also evaluated with the developed approach (NEW),the conventional M-T scheme (ANI) and the M-T scheme with the Eshelby tensordetermined with the isotropic approximation of the tangent elastoplastic modulus (ISO),and compared with the obtained benchmark results. It shows that ANI seriouslyover-evaluate the overall stress in the composite, but the results by NEW are almostidentical with that by ISO. Although the results by both ISO and New satisfactorilyreplicate the benchmark results, the former makes less physical sense compared with thelatter, because the latter can describe, to some extent, the actual constraint of the elastoplastic matrix to the deformation of the inclusion region. In the analysis for cyclicloading, we take the unloading point as the “new origin”, so that the developedapproach can be extended to case of unloading, reloading, and cyclic loading, withoutadditional difficulties.The proposed approach can provide an approximate evaluation of the mechanicalproperty of composites consisting of elastoplastic matrix and reinforcement elasticparticles, which may be of theoretical and practical significance.