Cleavage due to dislocation confinement in layered materials

The effects of dislocation confinement on fracture behavior in laminates consisting of alternating submicron ductile and brittle layers are studied. When the ductile layer thickness is below the micron level, dislocations must be treated individually. Dislocations emitted from the crack tip have two effects: they blunt the crack and thereby reduce the tensile stress at the crack tip ; and pile up against an interface and send a back stress to the crack tip to hinder further dislocation emission. Consequently, an equilibrium number of dislocations exists at a given load level. We estimate this number by considering the stability conditions for dislocations threading in the ductile layer, and dislocation pile-up is treated as an equivalent superdislocation. Furthermore, the competition between further dislocation emission and cleavage at the blunted crack tip is considered. Our result shows that because of the confinement, as the applied load increases, the tensile stress at the blunted crack tip also increases. Cleavage occurs when the tensile stress at the crack tip reaches the theoretical strength. Given a sufficiently thin constraining layer, cleavage can even occur in ductile metals such as copper and aluminum. The implications of this model for several material systems are discussed.