On the singular stress field near the edge of bonded joints

A stress singularity of the form Hr λ-1 develops at the corner where the interface between two bonded elastic solids intersects a traction-free edge. Here H is the intensity of the singularity, λ-1 is the order of the stress singularity and r is the radial distance from the interface corner. The intensity H of the singularity is evaluated for a butt joint consisting of a thin elastic layer sandwiched between two substrates and subjected to a uniform remote tension. The magnitude of H is determined using a combination of the finite element method (FEM) and a path-independent integral. The obtained values of H depend on the material elastic properties and on the magnitude of the applied loading. The results for H are compared with those obtained via the commonly used extrapolation method. The extent of the elastic singularity is determined as a function of the material elastic properties, and the implications of the results in developing an H-based free-edge failure initiation criterion are discussed.