准晶反平面中心裂纹问题的研究

发布时间：2018-08-04 20:06

【摘要】：准晶是近二十年来发现的新固体结构和新材料。与经典晶体弹性问题相比,准晶弹性问题要复杂许多。它不仅有声子场,还多了刻画原子准周期排列的相位子场,及声子场-相位子场的耦合。关于准晶及缺陷问题的研究,前人已给出了一些求解方法,如复变函数方法、Green函数法、Fourier变换法、摄动法和有限差分法等等。相比准晶动力学问题,对其静力学问题的研究要简单的多。Westergaard应力函数法和Muskhelishvili方法作为求解线弹性断裂力学问题的两种复变函数方法,是非常实用和有效的。本文第二章分为两部分。第一部分是Dugdale模型平面问题,基于Dugdale的观点,采用复变函数方法对平面弹性中有限高狭长体中半无限裂纹进行研究。假定材料处于理想的弹塑性状态下,做一个保角变换将带有缺陷的材料从物理平面变换到映射平面的单位圆内。通过求解映射平面上的函数方程,获得了固体在受到外载荷下的应力强度因子;同时采用叠加原理,求得了内聚力区域尺寸。当狭长体的高度趋于无穷大时,所得结果和经典弹性中各向同性体结果相一致。第二部分是针对一维六方准晶中的Dugdale模型问题,利用Muskhelishvili复变函数方法,结合保角变换得到了III型裂纹尖端塑性区大小及裂纹尖端的撕开位移的解析解。所得的结果与Fan采用位错模型给出的结果一致。这为准晶材料工程度量裂纹尖端塑性变形提供了依据。本文第三章借助准晶流体-动力学模型,采用有限差分法研究了带有中心裂纹的三维二十面准晶的动态响应问题。给出了裂纹在声子场,相位子场及声子-相位子耦合效应下的理论和数值分析。最后得到应力,位移及规范化动态应力强度因子的数值解。通过与晶体结果对比,突出了声子和相位子弹性基本场的影响,从而揭示了它们在准晶动态变形中的重要地位。
[Abstract]:Quasicrystal is a new solid structure and new material discovered in the last twenty years. Compared with the classical crystal elastic problem, the quasicrystal elasticity problem is much more complicated. It not only has the phonon field, but also characterizes the phase subfield of the quasi periodic arrangement of atoms, and the coupling of the phonon field phase subfield. The research on the quasi crystal and the defect problem has been given by the predecessors. Solving methods, such as complex function method, Green function method, Fourier transformation method, perturbation method and finite difference method and so on. Compared with quasicrystal dynamics problems, the study of statics is a simple multi.Westergaard stress function method and Muskhelishvili method as two kinds of complex function methods for solving linear elastic fracture mechanics problems. The second chapter is divided into two parts. The first part is divided into two parts. The first part is the plane problem of the Dugdale model. Based on the viewpoint of the Dugdale, the semi infinite crack in the finite and long body in the plane elasticity is studied by the complex function method. From the physical plane to the unit circle of the mapping plane. By solving the function equation on the mapping plane, the stress intensity factor of the solid under the external load is obtained. At the same time, the cohesive zone size is obtained by the superposition principle. When the height of the long body tends to infinity, the results and the isotropic body knot in the classical elasticity are obtained. The second part is the Dugdale model in one dimension six square quasicrystals. By using the Muskhelishvili complex function method, the analytical solution of the size of the plastic zone of the crack tip and the tear displacement at the crack tip is obtained by combining the conformal transformation method. The results are in agreement with the results given by Fan by the dislocation model. This is a quasicrystal material. In the third chapter, the dynamic response of a three-dimensional quasicrystal with a central crack is studied by the finite difference method with the help of the quasicrystal fluid dynamics model. The theoretical and numerical analysis of the crack in the phonon field, the phase subfield and the phonon phase position coupling effect is given. Then the numerical solution of stress, displacement and normalized dynamic stress intensity factor is obtained. By comparing with the crystal results, the influence of the basic field of the phonon and phase bullets is highlighted, thus revealing their important position in the dynamic deformation of the quasicrystal.
【学位授予单位】：太原理工大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O346.1

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