Three-dimensional singular stress fields in the vicinity of crack, anticrack and interfacial-contact junction (triple junction) fronts in tricrystal and trimaterial composite plates.

摘要

Three classes of elastic trimaterial/tricrystal plates, of finite thickness, and weakened/reinforced by crack/anticrack/interfacial-contact junction (triple junction) type discontinuities, are investigated. Such systems are formed as a result of bimaterial deposit, comprising matrix/semiconductor (material 3) plus reaction product/scatterer (material 1), over a flat fiber/reinforcement/substrate (material 2). The first and second groups, made of isotropic (polycrystalline) and monoclinic phases, are analyzed asymptotically using three-dimensional eigenfunction and modified eigenfunction expansion approaches, respectively, based on the separation of (i) variables and (ii) the thickness-variable (in conjunction with the Eshelby-Stroh type formalism). The third class of tricrystalline systems is composed of one diamond cubic (C) phase deposit (material 3), the remaining two phases being FCC (Au, material 1) and appropriately rotated Si3N4 serving as the substrate (material 2). This class of problems is asymptotically solved using a mixed eigenfunction expansion type method, based on the partial separation of z-variables technique, in conjunction with a mixed Frobenius type series in terms of affine-transformed x-y variables. The crack/anticrack type discontinuity always lies between materials 2 (substrate) and 3 (matrix/semiconductor).;Numerical results pertaining to the variation of the mode I/II/III eigenvalues (or stress singularities) with modular ratios, as well as with the wedge aperture angle of the material 1 are presented. For a crack lying between materials 2 and 3, material 1 acts as an amplifier or reducer of the severity of the stress intensity of the bimaterial interfacial crack, depending on the effective stiffness of the third phase (material 1) in comparison with that of material 3. More important, a crack always propagates under mixed I/II/III mode in monocrystalline diamond. The present results confirm this fact for a trimaterial system, with one diamond cubic (C) phase. Finally, hitherto unavailable results, pertaining to the through-thickness variation of stress intensity factor or stress singularity coefficient for symmetric (i) exponentially decaying, (ii) exponentially growing, (iii) parabolic and (iv) parabolic plus triangular distributed loads and their skew-symmetric counterparts that also satisfy the boundary conditions on the top and bottom surfaces of the trimaterial/tricrystalline plates under investigation, bridge a longstanding gap in the stress singularity/interfacial fracture mechanics literature.