二维压电半导体的断裂问题分析
发布时间：2018-12-10 21:48
【摘要】：压电半导体是同时具有压电特性和半导体特性的材料,由于这类材料的性能对于裂纹等缺陷非常敏感,所以对裂纹的分析、断裂方面的研究至关重要。不同于弹性、压电、电磁等材料,由于压电半导体材料控制方程的特殊性,其断裂问题的解析解比较困难,本文发展广义不连续位移边界积分方程、边界元法来分析压电半导体介质中的裂纹问题。本文主要工作如下:(1)基于二维n型压电半导体材料的控制方程,根据其通解和Fourier变换,求解出以裂纹面上法线、切线方向的不连续位移、不连续电势和不连续载流子密度为基本综量的广义不连续位移基本解。在此基础上,提出了二维压电半导体中的直线裂纹受多场作用时的广义不连续位移边界元法,计算给出裂纹面上的广义不连续位移和裂纹尖端的广义应力强度因子。(2)将广义不连续位移法推广到二维n型热压电半导体材料中的裂纹问题,求出在裂纹面上分别作用均布的广义不连续位移时所对应的基本解,并且利用广义不连续位移边界元法计算了裂纹面的不连续位移、不连续温度和裂纹尖端的应力强度因子、热流强度因子。(3)考虑到裂纹腔内的介质及真实裂纹的边界条件,在电半可穿透与热半可穿透的边界条件下,给出迭代算法,计算得到相关数值结果,研究压电半导体材料中的裂纹问题。
[Abstract]:Piezoelectric semiconductors are materials with both piezoelectric and semiconductor properties. Because the properties of these materials are very sensitive to defects such as cracks, the study on crack analysis and fracture is very important. Because of the particularity of the governing equation of piezoelectric semiconductor material, the analytical solution of the fracture problem is difficult, so the generalized discontinuous displacement boundary integral equation is developed in this paper. The boundary element method is used to analyze the crack problem in piezoelectric semiconductor medium. The main work of this paper is as follows: (1) based on the governing equation of two-dimensional n-type piezoelectric semiconductor material, the discontinuous displacement along the normal line and tangent direction on the crack surface is obtained according to its general solution and Fourier transformation. The discontinuous potential and the density of discontinuous carriers are the fundamental solutions of the generalized discontinuous displacement. On this basis, the generalized discontinuous displacement boundary element method for linear cracks in two-dimensional piezoelectric semiconductors under the action of multiple fields is proposed. The generalized discontinuous displacement on the crack surface and the generalized stress intensity factor at the crack tip are calculated. (2) the generalized discontinuous displacement method is extended to the crack problem in two-dimensional n-mode thermoelectric semiconductor materials. The corresponding basic solutions are obtained when the generalized discontinuous displacements are uniformly distributed on the crack surface, and the discontinuous displacement, discontinuous temperature and stress intensity factor at the crack tip are calculated by using the generalized discontinuous displacement boundary element method. Heat flux intensity factor. (3) considering the medium in the crack cavity and the boundary conditions of the real crack, the iterative algorithm is given under the boundary conditions of electric semi-penetrating and thermal semi-penetrating, and the relevant numerical results are obtained. The crack problem in piezoelectric semiconductor materials is studied.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN304
本文编号：2371252
[Abstract]:Piezoelectric semiconductors are materials with both piezoelectric and semiconductor properties. Because the properties of these materials are very sensitive to defects such as cracks, the study on crack analysis and fracture is very important. Because of the particularity of the governing equation of piezoelectric semiconductor material, the analytical solution of the fracture problem is difficult, so the generalized discontinuous displacement boundary integral equation is developed in this paper. The boundary element method is used to analyze the crack problem in piezoelectric semiconductor medium. The main work of this paper is as follows: (1) based on the governing equation of two-dimensional n-type piezoelectric semiconductor material, the discontinuous displacement along the normal line and tangent direction on the crack surface is obtained according to its general solution and Fourier transformation. The discontinuous potential and the density of discontinuous carriers are the fundamental solutions of the generalized discontinuous displacement. On this basis, the generalized discontinuous displacement boundary element method for linear cracks in two-dimensional piezoelectric semiconductors under the action of multiple fields is proposed. The generalized discontinuous displacement on the crack surface and the generalized stress intensity factor at the crack tip are calculated. (2) the generalized discontinuous displacement method is extended to the crack problem in two-dimensional n-mode thermoelectric semiconductor materials. The corresponding basic solutions are obtained when the generalized discontinuous displacements are uniformly distributed on the crack surface, and the discontinuous displacement, discontinuous temperature and stress intensity factor at the crack tip are calculated by using the generalized discontinuous displacement boundary element method. Heat flux intensity factor. (3) considering the medium in the crack cavity and the boundary conditions of the real crack, the iterative algorithm is given under the boundary conditions of electric semi-penetrating and thermal semi-penetrating, and the relevant numerical results are obtained. The crack problem in piezoelectric semiconductor materials is studied.
【学位授予单位】：郑州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN304
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