压电准晶材料的宏细观力学研究

项目名称： 压电准晶材料的宏细观力学研究

项目编号： No.11502123

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 郭俊宏

作者单位： 内蒙古工业大学

项目金额： 20万元

中文摘要： 准晶作为一种新的固体材料，既不同于晶体，又不同于非晶体，这导致准晶的力、电、磁、热及其相关物理性能与普通晶体有本质性的区别。因此，研究准晶材料的这些耦合效应具有重要的科学意义。本课题拟通过热力学定律导出的基本方程，利用晶体点群的对称性给出特殊准晶晶系的电弹性耦合基本方程，利用叠加原理，将基本方程化解为两个简单问题来处理，为准晶的力电耦合行为提供重要的理论基础。进一步，将准晶体作为增强颗粒，利用Stroh法研究在压电基体中的复合材料力学性能，包括基体中含有圆形夹杂、椭圆等夹杂的有效性能。提出准晶材料的力电耦合问题断裂力学的解析方法，即半逆解法和复变函数法。作为应用，利用该方法研究裂纹或孔洞与位错的相互作用，给出其电弹性场的基本解。本项目的研究为工程中制备新型复合材料提供重要的理论参考。

中文关键词： 准晶；压电；夹杂；位错；Stroh型公式

英文摘要： Quasicrystals as a new structure materials, are different from crystals as well as non-crystals. There is an essential difference between quasicrystals and common crystals from the mechanical, electrical, thermal and other physical property point of view. Therefore, it is of great importance to study the coupling effects of quasicrystal materials. On the basis of the fundamental equations of piezoelasticity of quasicrystal materials deduced by thermodynamic law, the linear piezoelasticity behavior of one-dimensional (1D) hexagonal quasicrystals is investigated by using the symmetry operations of point groups. Moreover, the piezoelaticity problem of 1D hexagonal quasicrystals is decomposed into two uncoupled problems by the principle of superposition, i.e., the classical plane elasticity problem of conventional hexagonal crystals and the phonon-phason-electric coupling elasticity problem of 1D hexagonal quasicrystals, which can provide a theoretical foundation for mechanical-electrical coupling behavior of quasicrystals. Further, regarding quasicrystals as reinforced particles, the mechanical property of composite materials with the matrix of piezoelectricity are considered by Stroh formalism, such as the effective property of matrix with circular inclusion, elliptical inclusion and so on. After that, the analytical methods for solving fracture mechanics of mechanical-electrical coupling problem of quasicrystal materials including semi-inverse method and complex variable method are proposed. Finally, the analytical methods are applied to solve the interaction on between dislocation and cracks/hole and the basic solutions of electro-elastic fields are derived. The research of this project will provide an important theoretical reference for preparing new-type composite materials.

英文关键词： quasicrystal;piezoelasticity;inclusion;dislocation;Stroh-formalism