On the anti-plane shear of an elliptic nano inhomogeneity
On the anti-plane shear of an elliptic nano inhomogeneity
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关于椭圆纳米不均匀性的反平面剪切
DOI：
10.1016/j.euromechsol.2009.04.001
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发表时间：
2009-09
影响因子：
4.1
通讯作者：
Wang, X.
中科院分区：
文献类型：
--
作者：
Luo, J.;Wang, X.
用复变方法研究了反平面剪切作用下嵌入无限矩阵中的椭圆纳米非均匀体的弹性场。用Gurtin-Murdoch模型解释了纳米非均匀性的界面应力效应。然后应用保角映射法求解公式边值问题。将所得数值结果与现有的圆形纳米非均匀性和传统的椭圆非均匀性在反平面下的闭合解进行了比较。结果表明，所提出的半解析方法是有效和准确的。然后系统地研究了不同界面参数和几何参数下非均匀性和基体内部的应力场。研究发现，由于界面效应的影响，椭圆纳米非均匀性内部的应力场不再均匀。当非均匀性尺寸在纳米量级时，非均匀性和基体内部的剪应力分布与尺寸有关。数值结果还表明，界面局部曲率对界面效应的影响很大。本文还研究了椭圆纳米孔周围的弹性场。发现在椭圆纳米孔表面无牵引边界条件被打破。随着椭圆孔长径比的增大，可以看作是iii型钝裂纹。即使对于长钝裂纹，钝裂纹尖端周围的表面效应仍然很明显。最后，讨论了非均匀性内均匀本征应变与远程加载的等价性。
The elastic field of an elliptic nano inhomogeneity embedded in an infinite matrix under anti-plane shear is studied with the complex variable method. The interface stress effects of the nano inhomogeneity are accounted for with the Gurtin–Murdoch model. The conformal mapping method is then applied to solve the formulated boundary value problem. The obtained numerical results are compared with the existing closed form solutions for a circular nano inhomogeneity and a traditional elliptic inhomogeneity under anti-plane. It shows that the proposed semi-analytic method is effective and accurate. The stress fields inside the inhomogeneity and matrix are then systematically studied for different interfacial and geometrical parameters. It is found that the stress field inside the elliptic nano inhomogeneity is no longer uniform due to the interface effects. The shear stress distributions inside the inhomogeneity and matrix are size dependent when the size of the inhomogeneity is on the order of nanometers. The numerical results also show that the interface effects are highly influenced by the local curvature of the interface. The elastic field around an elliptic nano hole is also investigated in this paper. It is found that the traction free boundary condition breaks down at the elliptic nano hole surface. As the aspect ratio of the elliptic hole increases, it can be seen as a Mode-III blunt crack. Even for long blunt cracks, the surface effects can still be significant around the blunt crack tip. Finally, the equivalence between the uniform eigenstrain inside the inhomogeneity and the remote loading is discussed.
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