Nanoscale mode-III interface crack in a bimaterial with surface elasticity

• Published in: Mechanics of materials Vol. 140; p. 103246
• Main Authors: Yang, Ying, Hu, Zhen-Liang, Li, Xian-Fang
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2020
• Subjects: Crack-tip field; Hypersingular integro-differential equation; Interface crack; Mode-III crack; Surface elasticity; Mode-III crack; Hypersingular integro-differential equation; Interface crack; Crack-tip field; Surface elasticity
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2019.103246

•A mode-III interface nanocrack with surface elasticity is analyzed.•Hypersingular integro-differential equations for displacement/stress jumps are derived.•The influences of surface elasticity on the stress intensity factor are discussed.•Usual inverse square-root singularity is exhibited near the crack-tip field. This paper studies a mode-III nanocrack at the interface between two bonded dissimilar materials under antiplane shear loading. The classical elasticity incorporating surface elasticity is applied to solve a mixed boundary value problem associated with an anti-plane shear interface crack. The influence of surface elasticity on the crack-tip field for a nanoscale mode-III crack is analyzed. By use of the Fourier transform, the problem is reduced to a set of hypersingular integro-differential equations. The displacement and bulk stress jumps are expanded as the Chebyshev orthogonal polynomials and the Galerkin method is used to approximately determine the singular elastic field near the interface crack tips. Consideration of surface elasticity does not cause the disappearance of crack-tip singularity. A usual inverse square-root singularity is derived near the crack tips. The influences of surface elasticity on the stress intensity factor are examined and displayed graphically. The surface residual stress does not alter the stress field for a mode-III interface crack.