弹性体中纳米缺陷的表面效应

发布时间：2018-06-05 01:34

本文选题：表面效应 + 纳米材料　；参考：《西安理工大学》2017年硕士论文

【摘要】：近40年来,通过应用Gurtin-Murdoch表面弹性模型,关于考虑表面效应时研究分析纳米尺度缺陷问题的工作越来越多,但是大多数学者研究过程中大多数都忽略了对表面效应导致的表面能的研究,并且对于椭圆孔的表面效应研究也比较少。本文以无限大平面为模型,其中包含纳米孔洞缺陷,研究了无外载作用时含纳米圆孔弹性体中表面效应作用下释放的表面能,以及在无外载作用时含纳米椭圆孔的弹性体时,在表面效应作用下对弹性体进行研究,主要内容分为以下两个方面:(1)本文基于完整的Gurtin-Murdoch表面弹性理论,以无限大平面为研究对象,其中求解了只有表面效应引起释放的表面能。研究发现表面效应使得含纳米尺度孔洞的弹性材料释放表面能,无论基体材料为哪种,求解得出释放的表面能随着半径的增大最终会逐渐趋于常数。但是存在两种情况,一种表面效应作用下释放的表面能随半径的变化,会出现间断点。另一种表面作用下释放的表面能随半径变化而变化的情况是连续的。但是无论材料如何改变,随着半径的增大,表面效应作用下释放的表面能与位移都会逐渐趋于稳定。(2)我们选择开源的有限元软件工具包FEniCS,采用数值方法计算当缺陷为纳米椭圆孔时,表面效应在此模型下对材料力学性能的影响。按照材料的屈服强度极限,分析表面效应与椭圆孔尺寸比之间的相关性。研究表明,完全由表面效应作用下,椭圆孔顶点的Mises应力随着椭圆孔短长轴比呈负相关。并且求解出弹性范围内椭圆孔洞长半轴顶点处的最小曲率半径。
[Abstract]:In the last 40 years, by using the Gurtin-Murdoch surface elastic model, more and more work has been done to study and analyze nanoscale defects when considering the surface effect. However, most of the scholars have neglected the study of surface energy caused by surface effect, and the surface effect of elliptical holes is also less studied. In this paper, the infinite plane model is used to study the surface energy released by the surface effect of nano-porous elastomer without external loading and the elastic body with nano-elliptic pore without external loading. The elastomer is studied under the action of surface effect. The main contents are as follows: 1) based on the complete Gurtin-Murdoch theory of surface elasticity, the infinite plane is taken as the object of study, in which the surface energy released only by surface effect is solved. It is found that the surface energy is released by the surface effect of elastic materials containing nano-sized pores. Regardless of the matrix material, the solution shows that the released surface energy will eventually become constant with the increase of radius. However, there are two cases in which the surface energy released by the surface effect changes with the radius. In another case, the surface energy released under the action of the surface varies with the radius. But no matter how the material changes, as the radius increases, The surface energy and displacement released under the action of surface effect tend to stabilize gradually.) We choose FEni CSS, an open source finite element software tool kit, to calculate the defect when the defect is a nano-elliptical hole. The effect of surface effect on mechanical properties of materials under this model. According to the yield strength limit of the material, the correlation between the surface effect and the ratio of elliptical hole size is analyzed. The results show that the Mises stress of the elliptical hole vertex is negatively correlated with the short axis ratio of the elliptical hole under the action of surface effect. The minimum radius of curvature at the vertex of the long half axis of the elliptical hole in the elastic range is obtained.
【学位授予单位】：西安理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB383.1

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