Edge-Bonded Dissimilar Orthogonal Elastic Wedges Under Normal and Shear Loading

Abstract

The plane-strain and generalized plane stress problems of two materially dissimilar orthogonal elastic wedges, which are bonded together on one of their faces while arbitrary normal and shearing tractions are prescribed on their remaining faces, are treated within the theory of classical elastostatics. The asymptotic behavior of the solution in the vicinity of the intersection of the bonded and loaded planes is investigated. The stress fields are found to be singular there with singularities of the type r−α, where α depends on the ratio of the two shear moduli and on the two Poisson’s ratios. This dependence is shown graphically for physically relevant values of the elastic constants. The largest value of α for the range of constants considered is 0.311 and occurs when one material is rigid and the other is incompressible.

A review of theoretical analysis techniques for cracking and corrosive degradation of film-substrate systems

“…For the case of bi-layer material, the interfacial stress near the edge show singularity response [90,91]. To address this, many researchers have established advanced theories to examine the corresponding singularity behaviour for various edge orientations under different mechanical and thermal loadings [92,93].…”

In-Situ Mechanical Testing of Nano-Component in TEM

“…At a dissimilar interface edge, stress is concentrated owing to the free-edge effect (Bogy, 1968). Although an interfacial crack may appear at the top interface edge in the cantilever specimen, the cracking criterion on the basis of continuum mechanics such as "critical stress" is questionable in a nano-component because only a few tens or a few hundreds atoms exist in the stress concentrated region.…”

“…2. Dissimilar interface is one of the most favorable potential crack initiation sites in a micro-and nano-scale component because it often has weak bonding (low resistance to fracture) and stress concentration (high driving force to fracture) due to the deformation mismatch between dissimilar materials (Bogy, 1968). In the component, the region governed by the stress concentration is confined in the nano-scale.…”

Multi-fracture of ceramic composites

“…Furthermore, the_',e shear stresses do not satisfy the boundary conditions (8b) and (10). These shortcomings are l tot surprising because an approximate solution cannot handle the extremely intricate comer singularity that, under perfect interfacial contact, occurs along the circle r = a, z =/./2, where the symmetry of the stress tensor no longer holds and Xzr * Xrz (Bogy 1968). * On the other hand, the inadequacy of our solution is mitigated by the fact that the approximation is optimized through the use of a minimum potential energy principle and guided by a numerical solution to a simpler, but closely related, problem.…”