Three-dimensional singular stress field at the front of a crack and lattice crack deviation (LCD) in a cubic single crystal plate

Abstract

A novel eigenfunction expansion technique, based in part on separation of the thickness variable, is developed to derive three-dimensional asymptotic stress fields in the vicinity of the front of a semi-infinite through-crack weakening an infinite plate made of a homogeneous cubic single crystal. Crack-side boundary conditions and those that are prescribed on the top and bottom (free) surfaces of the cubic crystal plate are exactly satisfied. Explicit expressions for singular stress fields in the vicinity of the front of through-thickness cracks, weakening cubic single crystal plates subjected to far-field extension/bending (mode I), sliding shear/twisting (mode II) and antiplane shear (mode III) loadings are presented. The present investigation considers three through-crack systems (crack plane)[crack front] × [propagation direction], (010)[001] × [100], and , weakening cubic crystals, and their relatively easier cleavage planes for propagation. It also introduces a new concept of lattice crack deviation (LCD) barrier, which can explain the reported discrepancy between simulations and experiments with regards to crack deviation from a “difficult” cleavage system to an easier one. Additionally, the relationships of the easier cleavage systems based on the present solutions with the structural chemistry aspects of various single crystals, such as bcc alkali metals, bcc transition alkali metals, fcc transition metals, group IVA (diamond cubic) elements, usually ionic compounds (rock salt and fluorite structures), covalent compounds (zinc blende structure), etc., are also discussed. Finally, the LCD parameter is strongly correlated with the anisotropic ratio for the cracked cubic crystal concerned.