On the mechanics of sinusoidal interfaces between dissimilar elastic-plastic solids subject to dominant mode I

We compute the effective toughness of a weak, sinusoidal cohesive interface between two dissimilar elastic-plastic solids subjected to dominant mode I loading. We use a computational model that takes into account the cohesive behavior of the interface, and the elastic-plastic behavior of two different materials. Using a dimensionless analysis, we found relationships between the normalized fracture toughness, the sinusoidal aspect ratio (amplitude to wavelength) and key dimensionless groups that are related to material behavior. Transitions between several failure mechanisms, including unstable crack propagation, intermittent periods of stable/unstable behavior, such as stick-slip, void-to-void crack growth, crack tip blunting, and stable crack propagation are found in terms of the sinusoidal geometry parameters and the assumed constitutive behavior of the two materials. We present design maps in which the sinusoidal aspect ratio arises as a natural design variable that can be manipulated to increase the resistance to crack propagation in bimaterial interfaces.