Interfacial debonding of a spherical inclusion embedded in an infinite medium under remote stress

In the study of strength of particle reinforced composites, it is important to understand the energy release rate due to interfacial debonding between the particle and the matrix which is induced by manufacturing imperfection. This paper is aimed at the investigation of the critical condition for growth of the interfacial debonding and the corresponding volume increase due to void formation. The model used in the study is an isotropic elastic spherical inclusion embedded in an infinite isotropic elastic matrix under remote stress. Initial axisymmetrical interfacial debondings are assumed to exist in the vicinity of poles of the spherical inclusion. Axisymmetrical deformations of the matrix and the inclusion are analyzed based on the theory of three-dimensional elasticity in spherical coordinates. In order to avoid oscillatory stress singularity at the interfacial debonding front between two dissimilar materials, a condition of free slipping without friction at the interface is imposed. A Fredholm integral equation of the first kind is formulated based on the continuity conditions in the normal components of stress and displacement at the contact interface. The kernel function of the integral equation is expressed in terms of an infinite series of Legendre functions. Two types of remote stresses are considered in this study. The first type is the remote tension in the axial direction of the spherical inclusion and the second type is the remote compression in the transverse direction with respect to the axis of the spherical inclusion. Energy release rate is determined according to the rate of change of work done by remote stresses. In this paper, energy release rate and volume of the deformed void due to debonding are computed for any given size of initial interfacial debonding.