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 void formation and the energy release rate due to interfacial debonding induced by manufacturing imperfections. This research is aimed at the investigation of the critical condition of growth of the interfacial debonding and the corresponding volume increase due to void formation. 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 singularities in front of the interfacial debonding between two dissimilar materials, a condition of free slipping at the interface is considered first. A Fredholm singular integral equation of the first kind is formulated based on continuity conditions in the normal components of stress and displacement at the interface. For the cases of remote tension in the axial direction of the spherical inclusion and the remote compression in the transverse direction with respect to the axis of the spherical inclusion, the energy release rate and the volume of the voids are computed for a given size of initial debonding. In order to study the fracture of matrix, the stress normal to the meridian plane is also calculated. For sufficiently large initial debonding size, the maximum tensile stress for fracturing the matrix occurs at the equator of the inclusion.; For the case of the remote tension in the axial direction of the spherical inclusion the condition of free slipping at the interface can be relaxed by introducing small contact zone near the tip of bonded zone. The size of contact zone that eliminates oscillatory stress singularities is determined by trial and error process as a function of initial debonding size. Normal stresses in the contact region and both normal and shear stress in the bonded region appeared to be singular at the crack tip. The void volume and the energy release rate were computed following the same procedure as in the case of free slippage at the interface. The crack branching was found to be unlikely in the case of shear stress present at the interface.