Three-dimensional asymptotic mode I/II stress fields at the front of interfacial crack/anticrack discontinuities in trimaterial bonded plates

Abstract

An eigenfuntion expansion method is employed for obtaining three-dimensional asymptotic displacement and stress fields in the vicinity of the front of a crack/anticrack discontinuity weakening/reinforcing an infinite pie-shaped trimaterial plate, of finite thickness, formed as a result of bimaterial (matrix/ARC plus reaction product/scatterer) deposit over a substrate (fiber/semiconductor). The wedge is subjected to mode I/II far field loading. Each material is isotropic and elastic, but with different material properties. The material 2 or the substrate is always taken to be a half-space, while the wedge aperture angle of the material 1 is varied to represent varying composition of the bimaterial deposit. Numerical results pertaining to the variation of the mode I/II eigenvalues (or stress singularities) with Young’s moduli ratio, as well as with the wedge aperture angle of the material 1 (reaction product/scatterer) are presented. Hitherto generally unavailable results, pertaining to the through-thickness variations of stress intensity factors or stress singularity coefficients for symmetric exponentially growing distributed load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial plates under investigation, bridge a longstanding gap in the stress singularity/interfacial fracture mechanics literature.