Fracture initiation at the interface corner of bimaterial solids

It is well known that the elastic stress field in the vicinity of the interface corner of a bi-material joint is of the form Hr^1-λ, where H is the stress intensity factor, r is the radial distance from the corner, and λ-1 is the order of the stress singularity. Both λ and H depend on the details of the geometry near the corner and on the material combination. In addition, the magnitude of H depends on the applied load. Although the use of a critical value of the intensity factor H = H_c as a fracture initiation criterion at the interface corner has been suggested in the literature, the application of this criterion to the design of bi-material joints has been very limited. This is partly due to the unusual units of H, which is the form (stress)(length)^1-λ, and also to the fact that the validity of the H-based criterion for predicting the onset of fracture in bi-material non-linear solids is not yet well understood. In this paper, the validity and limitations of the H-based criterion for predicting the onset of fracture in bi-material joints with at least one elastic-plastic solid is examined. The evolution of the plastic deformation at the interface corner is determined, and the solution is compared with the zone of dominance of the elastic H-field. For the critical value of the interface corner stress intensity factor, Hc, to be a valid fracture parameter, the plastic zone at fracture must be encapsulated in the elastic H-field. This condition is used to obtain a relationship between the characteristic length scale of a joint geometry and the ratio of Hc to the yield stress of the elastic/plastic solid, for which the experimentally determined value of Hc can be used as a valid initiation fracture toughness.