Three-phase elliptical inclusions with internal uniform hydrostatic stresses

摘要

For an elastic inclusion embedded within an elastic matrix, it is the interfacial stresses that control mechanical integrity of the inclusion/matrix system. To eliminate the stress peaks at the interface, the uniform hydrostatic stress state within the inclusion is of particular interest because it achieves both uniform normal stress and vanishing tangential stress along the entire interface, Motivated by practical significance of interfuse layer, the present paper studies the internal stress state of a three-phase elliptic inclusion which is bonded to an infinite matrix through an intermediate elastic layer. What is essential is that the interfaces of the three-phase elliptic inclusion considered are two confocal ellipses. A simple condition is found that ensures that the internal stress state within the elliptic inclusion is uniform and hydrostatic, For given remote stresses and material parameters, this condition gives a simple relationship between the thickness of the interfuse layer and the aspect ratio of the elliptic inclusion. The exact stress field is obtained in elementary form when this condition is met. In particular, the hoop stress in the interfuse layer is found to be uniform along the entire interfuse/inclusion interface. It is believed that the availability of this condition relies on the conical character of the elliptic interfaces.