Abstract 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.

中文翻译：

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具有表面弹性的双材料中的纳米级 III 型界面裂纹

摘要 本文研究了在反平面剪切载荷下两种不同材料之间的界面处的 III 型纳米裂纹。结合表面弹性的经典弹性用于解决与反平面剪切界面裂纹相关的混合边界值问题。分析了表面弹性对纳米级 III 型裂纹裂纹尖端场的影响。通过使用傅里叶变换，问题被简化为一组超奇异积分微分方程。位移和体应力跳跃随着切比雪夫正交多项式被扩展，并且使用伽辽金方法来近似确定界面裂纹尖端附近的奇异弹性场。考虑表面弹性不会导致裂纹尖端奇异性的消失。通常的平方根逆奇点是在裂纹尖端附近导出的。检查表面弹性对应力强度因子的影响并以图形方式显示。表面残余应力不会改变 III 型界面裂纹的应力场。