Surface tension-induced interfacial stresses around a nanoscale inclusion of arbitrary shape
Surface tension-induced interfacial stresses around a nanoscale inclusion of arbitrary shape
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任意形状的纳米级夹杂物周围的表面张力引起的界面应力
DOI：
10.1007/s00033-017-0876-7
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发表时间：
2017-10
期刊：
影响因子：
--
通讯作者：
Cun-Fa
中科院分区：
文献类型：
--
作者：
Wang;Shuang Dai;Ming Ru;C. Q. Gao;Cun-Fa
研究了无限大弹性平面内任意形状纳米夹杂周围的表面张力诱导应力场，重点研究了表面张力和任意形状夹杂的综合效应。Muskhelishvili的复变方法制定的基本方程，解决了与保角映射和级数展开法的援助。本解决方案的准确性进行了验证，通过比较其预测与已知的结果的任意形状的孔。对四种形状的夹杂物（椭圆形、近似正三角形、正方形和带圆角的正五边形）进行了表面张力诱导应力场的演示。数值结果表明，随着夹杂物由“软”向“硬”（相对于基体）的转变，夹杂物侧夹杂物-基体界面上的环向应力和正向应力沿着增大，基体侧的环向应力和正向应力沿界面上的环向应力和正向应力沿基体侧减小。然而，沿夹杂物-基体界面的剪切应力沿着并不显著改变夹杂物从“软”到“硬”的变化。还发现，最大环向应力的矩阵侧的一个“软”夹杂物和最大剪应力总是发生附近，但不完全是在圆角，所有其他应力的所有讨论的夹杂物形状达到最大值。此外，对于所讨论的四种夹杂形状，由于对称性，沿夹杂-基体界面的剪切应力沿着在所有角部为零。
Investigated in this paper is the surface tension-induced stress field around a nanoscale inclusion of arbitrary shape embedded in an infinite elastic plane, with an emphasis on the combined effects of surface tension and arbitrary inclusion shape. Muskhelishvili’s complex variable method is employed to formulate the basic equations that are solved with the aid of conformal mapping and series expansion methods. Accuracy of the present solution is verified by comparing its predictions with known results of an arbitrarily shaped hole. The surface tension-induced stress field is demonstrated for four shapes of inclusions (ellipse, approximately regular triangle, square and regular pentagon with round corners). The numerical results show that as the inclusion changes from a “soft” to a “hard” one (compared to the matrix), hoop and normal stresses along the inclusion–matrix interface on the inclusion side will increase, while those on the matrix side will decrease. However, shear stress along the inclusion–matrix interface does not considerably change as the inclusion changes from a “soft” to a “hard” one. It is also found that the maximum hoop stress on the matrix side of a “soft” inclusion and the maximum shear stress always occur nearby, but not exactly at the round corners where all other stresses for all four discussed inclusion shapes attain their maximums. Besides, for the four inclusion shapes discussed, shear stress along the inclusion–matrix interface vanishes at all corners as a consequence of the symmetry.
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