Three-dimensional singular antiplane shear stress fields at the fronts of interfacial crack/anticrack/contact type discontinuities in tricrystal anisotropic plates

Abstract

A recently developed eigenfunction expansion technique, based in part on separation of the thickness-variable and partly utilizing a modified Frobenius type series expansion in conjunction with the Eshelby–Stroh formalism, is employed to derive three-dimensional singular stress fields in the vicinity of crack/anticrack/junction front of an infinite tricrystal plate, made of monoclinic/hexagonal/orthorhombic/cubic phases, of finite thickness and subjected to far-field antiplane shear loading. Such tricrystals are used in solar cells and superconductivity application among others. Crack/anticrack-face boundary and/or interface contact conditions and those that are prescribed on the top and bottom (free or fixed) surfaces of the tri-crystal plate are exactly satisfied. Five different through-thickness boundary conditions are considered: (i) slit crack, (ii) anticrack or perfectly bonded rigid inclusion, (iii) tri-crystal junction, and (iv and v) rigid inclusion located alongside a crack. Numerical results pertaining to the variation of the mode III order of stress singularity with various wedge aperture angles of the material 1 (e.g., scatterer in a solar cell), are also presented. Finally, results, pertaining to the through-thickness variations of mode III stress intensity factors or stress singularity coefficients for symmetric exponentially growing distributed load and their skew-symmetric counterparts that also satisfy the boundary conditions on the top and bottom surfaces of the tricrystal plate under investigation, also form an important part of the present investigation.