Estudo sobre modelos micromecânicos de campos médios para homogeneização de materiais compósitos e porosos elastoplásticos

Abstract

In the present work, the effective elastic properties and elastoplastic behavior of biphasic materials are investigated through the micromechanics of mean fields. The materials have elastic inclusions perfectly adhered to the matrix or randomly distributed pores in space, which can be aligned or misaligned. The elastoplastic behavior of the effective material is evaluated in the form of stress (or strain) rate using the incremental and homogenized method according to the Mori-Tanaka scheme. The flow of the biphasic metal matrix is governed by the von Mises criterion, in which isotropic conditions and infinitesimal deformations are considered. After the flow, the isotropic constitutive tensor of the matrix takes the form of an anisotropic tangent constitutive tensor, in which, by mathematical approximation methods, the isotropic part can be used to determine the effective tangent constitutive tensor. During the elastoplastic behavior, it is assumed that the matrix has nonlinear isotropic hardening or linear kinematic hardening. To achieve the objectives of this work, algorithms were developed that enable the investigation of the limitations of using the tangent constitutive operator of the matrix, whether anisotropic or obtained by isotropic approximation, as well as the application of the tangent Eshelby tensor or Eshelby tensor for the Elastoplastic medium (EPM). The results obtained indicate that the accuracy of the elastoplastic behavior of a heterogeneous material can be affected by the choice of the method and the isotropic approximation procedure of the elastoplastic matrix constitutive operator. It was also observed that in composites that have rigid inclusions with ellipsoidal geometry, the Eshelby tensor for the EPM had limitations, providing satisfactory results only for rigid inclusions with spherical geometry. On the other hand, no limitations were observed regarding the pore geometry, showing satisfactory results for any aspect ratio. Finally, an approach was presented that deduces the strain concentration tensor for ductile matrices that have misaligned spherical or spheroidal pores, with good agreement observed with experimental results and published in the literature.