Singular Stress Fields in Anisotropic Bonded Joints Considering Interface Stress and Interface Elasticity

Abstract

Surface stress and surface elasticity are related to the organization of surface morphology, surface patterns, and surface atomic structures. As the size of the structure approaches the nanometer level, the surface-to-volume ratio increases. Generally the surface energy in deformable solids depends on the surface strain. The surface stress and elasticity influence the distribution of bulk stress near the surface. Interface stress and elasticity also exist at material interfaces and determine the interface properties. In the present study, the singular stress at a wedge corner in an anisotropic two-dimensional joint under tensile loading is analyzed using the molecular dynamic (MD) method and the anisotropic elasticity theory using a boundary condition with interface stress and interface elasticity. Not only the interface stress but also surface stress on the free surface are considered as a special case of an interface. The interface stress and interface elasticity are obtained through the MD analysis. In the case of a two-dimensional joint, the interface stress and elasticity depend on the distance from the wedge corner. In the analysis of anisotropic elasticity, the eigenequation used to determine the order of the stress singularity is newly derived using a boundary condition that considers the interface stress and interface elasticity. The order of the stress singularity varies with distance from the wedge corner. The stress distribution near the wedge corner can be expressed by the relation between the order of the stress singularity and the distance from the wedge corner.

Mechanics of finite cracks in dissimilar anisotropic elastic media considering interfacial elasticity

“…It should be mentioned that in the third problem, for the sake of clarity and avoid any confusion, we chose not to consider surface stresses (in the Gibbsean sense) on the crack faces. As mentioned earlier, such developments have been considered by others (Feng et al, 2008;Antipov and Schiavone, 2011;Kim et al, 2011;Nan and Wang, 2012;Koguchi and Suzuki, 2014;Wang et al, 2015;Sigaeva and Schiavone, 2016). Surface stresses for free surfaces of the crack faces may be on the same order of magnitude as the interface stresses outside of the crack segment but their constitutive relationships differ from the ones introduced in Eqs.…”

“…The methodology described above is similar to the one used by Sudak and Wang (2006) and is based on complex analysis. However, an alternative approach (Koguchi and Suzuki, 2014) based on Fourier transform could have been used instead to obtain similar results.…”

“…More recently, due to the growing interests in the so-called field of nanomechanics, the above mentioned seminal developments for perfectly bonded interfaces have been augmented by incorporating surface elasticity effects on the crack surface (Feng et al, 2008;Antipov and Schiavone, 2011;Kim et al, 2011;Nan and Wang, 2012;Koguchi and Suzuki, 2014;Wang et al, 2015;Sigaeva and Schiavone, 2016). The inclusion of the Gurtin and Murdoch (1975) surface elasticity theory in these models has been shown to also modify the nature and functional form of the singularity at the cracktip.…”

Back Propagation Neural Network in Predicting the Thermal Fatigue Life of Microelectronic Chips

“…Three dimensional thermal conduction and thermal stress analysis have been carried out to obtain inter- shows the stress variation at the E12 and E45 with thermal cycles, where σt=(σ 2 +τ 2 ) 1/2 donates the maximum traction when the normal stress is tensile at the interface. It can be found that the E12 is under compress, while the E45 is under tension at the heating According to the instant singular field theory [27][28][29],…”

Simulation on the Interfacial Singular Stress-strain Induced Cracking of Microelectronic Chip Under pPower On-off Cycles

“…Therefore, the interfacial singular characteristics, as the key factor affecting the fatigue life, should be discussed in detail. According to the singular field theory, the instant singular stress and strain fields can be expressed as [20] ( ) ( )…”