Three-dimensional singular stress fields near the circumferential junction corner line of an island/substrate system either free-standing or fully/partially bonded to a rigid block

The primary motivation of the present investigation stems from the need for understanding the three-dimensional singular stress fields in the vicinity of the re-entrant circumferential bimaterial junction corner line between a thin film island and the underlying substrate, either free-standing or fully/partially bonded to a super-rigid block. A three-dimensional eigenfunction expansion approach is employed for determination of the singular stress field in the vicinity of the re-entrant circumferential bimaterial junction corner line. The island-substrate bimaterial system is subjected to extension/bending (mode I), shear/twisting (mode II) and torsional (mode III) far field loadings. Both the island and substrate materials are assumed to be isotropic and elastic. The boundary conditions, prescribed on either side of the interfacial bond line between the island and substrate materials (free–free, fixed–fixed, free–fixed and fixed–free), are exactly satisfied. Numerical results include the dependence of the lowest eigenvalue(s) (or most severe order(s) of stress singularity) on the wedge aperture angle of the island material (looking at a axisymmetric cross-section). Variation of the same with respect to the shear moduli ratio of the constituent island and substrate materials is also an important part of the present investigation. Hitherto unobserved interesting and physically meaningful conclusions in regards to the mixed free–fixed type singularity and delamination type flaw sensitivity of an island-substrate bimaterial system are also presented.