Control of fracture at the interface of dissimilar materials using randomly oriented inclusions and networks

Fracture at or near the interface between two isotropic materials has been a subject of extensive research relevant to the problems encountered in aerospace, naval, electronic packaging, biomechanical engineering and other applications. The problems of edge cracks, semi-infinite interface cracks and substrate cracks under a thermally stressed film considered in the paper are representative of such analyses. We consider a possible improvement in the fracture resistance achieved by embedding randomly distributed stiff inclusions such as fibers, nanotubes, fiber or nanotube networks and ellipsoidal or spherical particles in the more compliant material. This results in a smaller mismatch between the stiffness of the joined materials that may prevent or alleviate fracture. Numerical examples demonstrate both the benefits and the limitations of enhancing the stiffness of the compliant material. In particular, the examples refer to the boundary between singular and non-singular interfacial edge stresses attempting to avoid the stress singularity by embedding random carbon nanotubes or networks. In the semi-infinite interfacial crack problem it is demonstrated that a small reduction in the stiffness mismatch of two materials at the interface causes a significant decrease in the strain energy release rate. The approach to the analysis of substrate cracks under a thermally stressed film is outlined accounting for the history of thermal loading and the effect of temperature on the properties of the film, substrate and embedded inclusions. The solutions presented in the paper rely on effective properties of randomly reinforced materials. The limitations of such approach in fracture problems and an estimate of its validity based on a comparison of scales at the tip of the crack and in the representative volume cell are discussed. It is suggested that fracture involving nanoparticle and nanotube reinforced materials can be characterized using effective properties.