Homogenizing interfacial shear stress via thickness gradient

Interfaces in bi-materials such as film-substrate systems are often subjected to shear stress due to the distinct deformation responses of two bonded materials to the external stimuli such as mechanical loading, change of temperature or humidity, or variation of internal structure induced by for example phase transformation. The distribution of such shear stress over the interface normally exhibits high concentration, which tends to initiate crack and evoke interface delamination. In such a crack propagation-mediated process of failure, the load-carrying capacity of interface has not been fully exerted as most of the interface bears little stress. To enhance the interface's resistance to delamination in bi-materials, homogenizing interfacial shear stress becomes a matter of necessity. In this paper, we propose to suppress the stress concentration on the interface by adopting films with gradient thickness. This strategy is illustrated through two typical examples of bi-material: (a) a continuous film bonded on a disk-like substrate, and (b) a discrete island film on a half-space substrate. For each case, theoretical solution to the optimal gradient film thickness is obtained, followed by computational and experimental validations. The results of this paper are believed to be of great and universal value to the enhancement of resistance to interfacial delamination in bi-materials.