多场加载环境下压电半导体断裂分析的边界元方法研究

The coupling of the semiconductor properties and the piezoelectric effect in piezoelectric semiconductors makes the piezotronics effect occur, the relationships among the mechanical field, the electric field and the electric current field are complex, it is very hard to find the analytical solutions for the fracture problems in piezoelectric semiconductors. This project focuses on the mechanical and electric properties of the piezoelectric semiconductors, and works on the study of the boundary element method for the two-dimensional and three-dimensional fracture problems in piezoelectric semiconductors under multi-field loading circumstance. This project is carried out in the following aspects: establishing the fracture models for the two dimensional and three dimensional piezoelectric semiconductors; under considering as well as not considering the influence of the electric field and the electric current field in the crack cavity conditions, giving the boundary conditions on the crack surface; solving the fracture models by boundary element and a cyclic iteration process; regarding the crack cavity as a single domain, solving the electric displacement and the electric current density in the crack cavity by multi-domain boundary element and a cyclic double-iteration process. This project aims at revealing the influences of the mechanical field, the electric field and the electric current field to the extended displacement fields inner piezoelectric semiconductors, the extended stress fields inner piezoelectric semiconductors and the extended stress intensity factors near the crack tip under coupling loading circumstance, giving the distributions of the electric field and the electric current field in the crack cavity, and providing a commonly and effectively numerical method for the fracture problems in piezoelectric semiconductors.

半导体特性和压电效应的两相耦合产生了压电电子学效应，使得压电半导体本构关系中机械场-电场-电流场之间存在复杂的耦合关系，解析求解压电半导体的断裂问题十分困难。本项目以压电半导体的力学、电学特性为研究基础，对二维、三维压电半导体在多场耦合加载环境下的断裂问题进行边界元方法研究。具体内容包括：建立二维、三维压电半导体的断裂力学模型；分别给出考虑与不考虑裂纹腔内电参数影响的裂纹面边界条件；通过边界元方法和一个循环迭代过程数值求解二维、三维压电半导体的断裂力学模型；将裂纹腔视为一个单独的子区域，通过多区域边界元方法和一个双重迭代循环过程求解裂纹腔内的电位移和电流密度。本项目旨在揭示在多场加载环境下，机械场、电场、电流场对压电半导体内部广义位移场、广义应力场及裂纹尖端广义应力强度因子等断裂参数影响及裂纹腔内真实的电场、电流场分布情况，为压电半导体断裂问题的研究提供一个通用有效的数值分析方法。

本项目主要采用边界元方法研究了多场环境下压电半导体等智能材料的断裂问题，并取得如下研究成果。基于二维压电半导体的非线性本构，采用“压电-导体”迭代边界元方法，研究了压电半导体的平面问题和孔洞问题，数值给出了不同形状椭圆孔的应力集中系数。基于载流子小扰动理论，将压电半导体的本构方程线性化处理，考虑裂纹面的精确电边界条件，结合有限元方法和双重迭代法研究了二维压电半导体的中心裂纹问题，得到了裂纹腔内的电场分布和裂纹尖端的应力、电位移和电流密度强度因子，比较了不同裂纹面边界条件下裂纹尺寸对广义应力强度因子的影响。采用迭代边界元方法，研究了精确裂纹边界条件下电磁固体中心裂纹问题，得到了裂纹腔内的电场、磁场分布以及裂纹尖端的广义应力强度因子的数值解。基于一维简化杆模型，采用同伦分析法，研究了非线性本构下纳米纤维的力电耦合特性，揭示了机械场对载流子传输特性的调控机理。同样基于一维简化杆模型，采用打靶法，给出了温差环境下具有热电效应的压电半导体纤维的机电场分布，揭示了温度对载流子传输的调控机理。采用单边裂纹试样的三点弯实验和有限元分析确定了GaN陶瓷的断裂韧性，揭示了外部电流对GaN陶瓷断裂特性的影响。基于Stroh公式，得到了一维六方压电准晶的广义位错基本解，进而得到裂纹面张开位移、强度因子和能量释放率等断裂参数。同样利用Stroh公式，引入delta函数消除了积分震荡奇异性，得到一维六方压电准晶界面裂纹的广义位错无奇异性的积分微分方程，采用边界元法得到裂纹面张开位移、强度因子和能量释放率等断裂参数的数值解。本项目取得的成果对压电半导体器件的可靠性评估和设计提供了重要的理论依据。