Internal stresses due to an oblate spheroidal inclusion: Misfit, inhomogeneity and plastic deformation effects

Abstract

Internal stress in and around an oblate spheroidal inclusion is evaluated by using Eshelby theory. We consider three different sources of internal stress as a function of the aspect ratio and elastic moduli ratio; these are 1. (1) misfit effect, 2. (2) inhomogeneity effect 3. (3) plastic deformation effect. The misfit effect arises from the difference of thermal expansion coefficients of the matrix and inclusion. Normal stresses within the inclusion (or the principal stresses), maximum shear stress inside the inclusion, total strain energy and the normal stress at the matrix-inclusion boundary are determined. The inhomogeneity effect arises from the difference of the elastic moduli of the matrix and inclusion, which perturbs otherwise uniform applied stress. The direction of applied stress is parallel to the axis of revolution of the inclusion. Normal stresses within the inclusion and at the matrix-inclusion boundary are obtained. Plastic deformation of the matrix in the presence of a plastically non-deformable inclusion produces internal stresses, as shown by Ashby and by Tanaka and Mori. The approach developed by Tanaka and Mori is extended here to evaluate the internal stresses for the inclusion geometries appropriate to the analysis of technically important cases. The results of the present calculations in limiting cases agree with previously published calculations. Implications of the results are discussed in connection with several experimental studies.