【作者】 李冬；

【导师】 宋天舒；

【作者基本信息】 哈尔滨工程大学 ， 固体力学， 2011， 博士

【摘要】 压电材料作为一种新型的智能材料,已经被广泛应用到国防建设、工业生产以及和人民生活密切相关的许多领域中,其力电耦合特性得到了广大学者的普遍重视,而含各类缺陷压电材料的断裂力学分析更是人们关注的焦点。本文在线性压电理论的框架下,对压电介质、双相压电介质以及直角域压电介质中含圆孔、裂纹、夹杂或复合缺陷的反平面动力学问题进行了研究,得到了一些有价值的结论。论文的主要工作可总结为以下三部分：第一部分求解了压电介质和双相压电介质中圆孔边径向裂纹的反平面动态问题。首先给出满足本问题边界条件的Green函数,得到不含裂纹情况下介质中的总位移场和总电位势场,然后利用契合思想和裂纹切割技术将问题转化为求解一组第一类Fredholm定解积分方程,采用直接数值积分方法求解,最后作为算例,给出了裂纹长度、圆孔半径、入射波频率以及材料参数等因素对裂纹尖端动应力强度因子的影响规律。结果表明,孔边裂纹尖端的动应力强度因子在动态情况下并不总是小于将圆孔看作裂纹的一部分而得到的直线型裂纹尖端的动应力强度因子,而是围绕其动应力强度因子曲线呈现一定的波动性。第二部分研究了双相压电介质中界面附近单圆孔和双圆孔以及圆孔与界面裂纹相互作用的动态反平面问题。利用满足问题边界条件的Green函数,根据契合思想得到求解界面上附加外力系和外电场的两组第一类Fredholm积分方程,采用直接数值积分法进行求解,得到附加外力系和外电场在各离散点上的值,从而写出圆孔周边动应力集中和电场强度集中的表达式。对于界面裂纹问题,同样采用契合思想和裂纹切割技术将问题简化为求解一组第一类Fredholm积分方程,并通过代换使其直接包含裂纹尖端的动态应力强度因子。作为算例,给出了圆孔半径、圆孔与界面之间的距离、入射波频率、材料参数以及裂纹长度对圆孔处的力电场集中和裂纹尖端动应力强度因子的影响规律。第三部分分析了直角域各向同性压电介质中含有单一圆柱形缺陷的动力反平面问题。利用镜像法构造出满足控制方程以及两自由表面处边界条件的力电波场,然后采用复变函数法、多极坐标移动技术以及叠加原理构造出满足各边界条件的散射力电波场,最后写出缺陷内部的力电波场并根据缺陷处的边界条件对表达式中的各未知系数进行求解,从而得到缺陷附近应力集中和电场强度集中的解析表达式。给出了缺陷半径、缺陷与两自由表面之间的距离、材料参数以及入射波频率对缺陷附近力电场分布的影响规律。本文关于含缺陷压电材料的反平面动力学问题的研究,希望能够对工程设计、生产和安全使用提供一定的参考。更多还原

【Abstract】 As a kind of new intelligent materials, the piezoelectric material, which has been widely used in national defense construction, industrial production and many areas which closely relates to the people’s lives, attracts extensive attention of many researchers due to its properties of electromechanical coupling. And more attention is paid to the investigation of the fracture behaviors on piezoelectric materials with various kinds of defects. Dynamic antiplane problems of the piezoelectric medium, piezoelectric bimaterials and quarter-infinite piezoelectric medium which contain circular cavity, crack, inclusion and composite defects are investigated in this article using the linear piezoelectric theory. Some useful conclusions are obtained.The main work in present paper can be summarized into three parts as follows:In part one, dynamic antiplane behaviors of the radial cracks at the edge of the circular cavity are solved in piezoelectric medium and piezoelectric bimaterials. Firstly, the Green’s functions which satisfy the boundary conditions of this problem are given. The total displacement field and the total electric potential field are also obtained in piezoelectric medium without any cracks. Secondly, the problems are reduced to a set of the first kind of Fredholm integral equations by the conjunction method and the crack-division technique. And the integral equations are solved by the direct numerical integration method. Finally, the numerical results reveal the effects of the length of the crack, the circular cavity radius, the incident wave frequency and the material parameters on dynamic stress intensity factors of the crack-tip. It can be concluded that the values of radial crack-tip DSIFs on a circular cavity aren’t invariably less then those on a reduced straight crack with an effective length at the dynamic situation. The oscillating phenomenon can be seen around the straight crack DSIFs.Then, dynamic antiplane behaviors of one cavity and two cavities near the interface are investigated in piezoelectric bimaterials. And the dynamic interaction between a circular cavity and a interface crack is also analyzed in the present paper. Based on the Green’s functions which are agreed with the boundary conditions, a pair of the first kind of Fredholm integral equations for solutions of the unknown stresses and the unknown electric fields at the interface can be established according to the conjunction method. The values of the additional stress and electric fields on the discrete points are obtained to solve the integral equations by the direct numerical integration method. And the expressions of dynamic stress concentration and electric intensity concentration at the edge of the circular cavity are also given. The interface crack problem is also reduced to solve a set of the first kind of Fredholm integral equations by the conjunction method and the crack-division technique. Dynamic stress intensity factors of the crack-tip can be contained in the integral equations by a substitution. As a numerical example, the effects of the circular cavity radius, the distance between the hole and the interface, the incident wave frequency, the material parameters and the length of the crack on dynamic stress concentration, electric field intensity concentration at the edge of the circular cavity and dynamic stress intensity factors at the crack-tip are given.Dynamic antiplane problems in the quarter-infinite piezoelectric medium with a single cylindrical defect are studied in part three. Firstly, the displacement field and the electric potential field, which satisfy the governing equations and the boundary conditions at the two free surfaces, are structured by the image method. Secondly, the scattering fields of displacement and electric potential are constructed by the complex variable function method, multi-polar coordinate transformation and the superposition theorem. And the scattering fields satisfy all the boundary conditions. Finally, the expressions of displacement field and electric potential field in the defect are given. And the unknown coefficients in the expressions can be solved according to the boundary conditions at the edge of the defect. The analytical expressions of the stress concentration and the electric field intensity concentration at the edge of the defect are achieved. The effects of the defect radius, the distances between the defect and the two free surfaces, material parameters and the incident wave frequency on the distributions of stress and electric field at the edge of the defect are drawn.It is expected that the investigations on dynamic antiplane behaviors of piezoelectric material with various kinds of defects can provide some references for the project designing, manufacture and application of piezoelectric material.更多还原