【摘要】：壓電半導(dǎo)體是同時(shí)具有壓電特性和半導(dǎo)體特性的材料,由于這類材料的性能對(duì)于裂紋等缺陷非常敏感,所以對(duì)裂紋的分析、斷裂方面的研究至關(guān)重要。不同于彈性、壓電、電磁等材料,由于壓電半導(dǎo)體材料控制方程的特殊性,其斷裂問(wèn)題的解析解比較困難,本文發(fā)展廣義不連續(xù)位移邊界積分方程、邊界元法來(lái)分析壓電半導(dǎo)體介質(zhì)中的裂紋問(wèn)題。本文主要工作如下:(1)基于二維n型壓電半導(dǎo)體材料的控制方程,根據(jù)其通解和Fourier變換,求解出以裂紋面上法線、切線方向的不連續(xù)位移、不連續(xù)電勢(shì)和不連續(xù)載流子密度為基本綜量的廣義不連續(xù)位移基本解。在此基礎(chǔ)上,提出了二維壓電半導(dǎo)體中的直線裂紋受多場(chǎng)作用時(shí)的廣義不連續(xù)位移邊界元法,計(jì)算給出裂紋面上的廣義不連續(xù)位移和裂紋尖端的廣義應(yīng)力強(qiáng)度因子。(2)將廣義不連續(xù)位移法推廣到二維n型熱壓電半導(dǎo)體材料中的裂紋問(wèn)題,求出在裂紋面上分別作用均布的廣義不連續(xù)位移時(shí)所對(duì)應(yīng)的基本解,并且利用廣義不連續(xù)位移邊界元法計(jì)算了裂紋面的不連續(xù)位移、不連續(xù)溫度和裂紋尖端的應(yīng)力強(qiáng)度因子、熱流強(qiáng)度因子。(3)考慮到裂紋腔內(nèi)的介質(zhì)及真實(shí)裂紋的邊界條件,在電半可穿透與熱半可穿透的邊界條件下,給出迭代算法,計(jì)算得到相關(guān)數(shù)值結(jié)果,研究壓電半導(dǎo)體材料中的裂紋問(wèn)題。
[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.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TN304

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本文編號(hào)：2371252