Elastic Deformation of Materials with Ellipsoidal Inclusion and Polycrystals

Abstract

The elastic deformation of inhomogeneous materials, especially materials with spherical or ellipsoidal inclusion and polycrystals is investigated, by expressing them with several models. Constraint ratio proposed previously is used to express deformation behaviour of materials, which is obtained from the strain distribution calculated numerically based on the models. At first, inclusion imbedded in matrix is studied by finite element model of inclusion as well as by Eshelby's analysis. The value of constraint ratio is nearly equal to 0.5 when the inclusion is spherical. The result is closely related to that of the self-consistent model of polycrystals. The value of constraint ratio in spheroidal inclusion increases when it is oblate in the stress direction, while it decreases when it is prolate. Next, the influence of irregularity of grain size in polycrystals on deformation behaviour is discussed. The overall deformation behaviour of the polycrystals is correlated with constraint ratio in each grain. The deformation mode of ply crystals changes into that under constant strain when the irregularity increases.