On three-dimensional singular stress field at the front of a planar rigid inclusion (anticrack) in an orthorhombic mono-crystalline plate

Abstract

A novel eigenfunction expansion technique, based in part on separation of the thickness-variable and partly on the Eshelby–Stroh type affine transformation, is developed to derive three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness anticrack reinforcing an infinite orthorhombic single crystal plate, of finite thickness and subjected to far-field mode I/II loadings. Anticrack-face boundary conditions and those that are prescribed on the top and bottom (free or fixed) surfaces of the plate are exactly satisfied. The present investigation considers six through-anticrack systems reinforcing orthorhombic single crystal plates. Explicit expressions for the singular stresses in the vicinity of the front of a through-thickness anticrack reinforcing an orthorhombic plate, subjected to far-field mode I/II loadings, are presented. Finally, hitherto largely unavailable results, pertaining to the through-thickness variations of stress singularity coefficients corresponding to symmetric and skew-symmetric sinusoidal loads that also satisfy the boundary conditions on the top and bottom surfaces of an orthorhombic mono-crystalline plate under investigation, bridge a longstanding gap in the stress singularity/fracture mechanics literature.