Nc. Huang et My. Korobeinik, Interfacial debonding of a spherical inclusion embedded in an infinite medium under remote stress, INT J FRACT, 107(1), 2001, pp. 11-30
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 gr
owth of the interfacial debonding and the corresponding volume increase due
to void formation. The model used in the study is an isotropic elastic sph
erical inclusion embedded in an infinite isotropic elastic matrix under rem
ote stress. Initial axisymmetrical interfacial debondings are assumed to ex
ist in the vicinity of poles of the spherical inclusion. Axisymmetrical def
ormations 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 th
e 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 in
clusion and the second type is the remote compression in the transverse dir
ection 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 s
tresses. In this paper, energy release rate and volume of the deformed void
due to debonding are computed for any given size of initial interfacial de
bonding.