Morphological instability of two stressed spherical shells

The morphological stability of the external free surface of a composite structure made of two shells stressed through the interface has been investigated when mass rearrangement along the surface is controlled by surface diffusion. Due to epitaxy or thermal change, an eigenstrain located in the inner shell is considered. The resulting stress and strain tensors have been first calculated assuming that the interface between the two initially spherical shells is coherent. The roughness appearing by surface diffusion on the external surface of the structure has been then developed on a basis of complete spherical harmonics and the linear stability of the surface has been investigated with respect to each harmonic Yml ðh;uÞ. The growth rate of the lth order harmonic has been determined and the influence of the geometric and physical parameters such as the radius of the interface, the radii of the free surfaces, the intrinsic deformation or the surface energy has been characterized. The case of a spherical solid embedded in a finite-size matrix has been also discussed