热－机械荷载作用下准晶体中剪切模态平面裂纹的三维分析

Quasi-crystals are a new structural form between crystals and glass, with a long-range quasi-periodic translational order and a long-range orientation order. The present project is devoted to studying mechanical behaviors of quasi-crystals with a planar crack subjected to thermo-mechanical loadings. In the context of elasticity of quasi-crystals, shear-mode crack problems are formulated by mixed boundary-value problems, and the corresponding boundary integro-differential equations are established. When the crack is subjected to point sources, the complete and exact fundamental field variables are explicitly obtained in terms of elementary functions. The physical quantities, for instance, stress components at the crack front, stress intensity factors, crack opening displacements, which are important parameters in fracture mechanics, are explicitly derived as well. Interactions among various fields are characterized. Systematic simulations will be carried out for cracks with irregular geometries to construct some approximate models revealing the effect of geometries on distributions of field variables at the crack front. A series of non-axisymmetric analytical solutions will be proposed, which would serve as benchmarks to various numerical codes and simplified analyses. The project would promote the development of elasticity of quasi-crystals and the obtained results would guide applications of the advanced technique of infrared-thermography to materials and structures of quasicrystals for a remote nondestructive inspection.

准晶具有长程有序的原子排列，但不具备晶体的平移对称性，是介于晶体和非晶体之间一种新的结构形式。本项目致力于研究含有平面裂纹的准晶弹性体在热－机械荷载作用下的力学行为。项目拟在准晶弹性力学框架下，将受广义剪切荷载的裂纹问题转化为混合边值问题，并建立边界微分-积分方程。当裂纹受到点载荷（声子力、相位子力、温度、热流）作用时，利用势理论方法，求取用初等函数表示的三维准晶热－弹性力学基本解，并给出裂纹尖端的应力分布、应力强度因子和裂纹张开位移等断裂力学基本物理量，并揭示温度场、声子场和相位子场之间相互作用规律。在获取的解析解的基础上并配合系统的数值计算，建立近似模型，探寻裂纹几何形状对裂纹尖端场变量的影响规律。本研究拟发展出一系列非轴对称解析解，为各种简化分析和数值方法提供检验标准，推动准晶弹性力学的发展。研究成果将为红外热成像技术应用于准晶材料／结构的无损检测提供理论支撑。

准晶具有与晶体类似的长程有序的原子排列，但不具备晶体的平移对称性，是介于晶体和玻璃体之间的固体。本项目研究了热-弹性框架下准晶材料的三维力学问题。发展了一系列初等函数表示的二维准晶弹性体的通解/基本解，为求解准晶材料热-弹性力学问题奠定了基础；建立了含平面裂纹准晶材料在热-机械荷载作用下的求解框架，构建了相应的边界微分-积分方程，并基于广义势理论方法求得了币状裂纹受不同形式（集中、均布）、不同种类（声子力、相位子力、温度变化、热流）荷载作用下的全场精确解，解析地获得了应力强度因子，裂纹表面位移和能量释放率等断裂力学关键物理量，厘清了温度场、声子场和相位子场之间相互作用规律，揭示了温度场对准晶材料断裂力学行为的影响，完善了准晶材料弹性力学的求解框架。依托本项目，目前已在本领域知名刊物上发表了23篇高水平论文，并获教育部高等学校科学研究优秀成果奖自然科学二等奖1项，很好地达成了研究目标，对推动准晶弹性力学的发展有积极推动作用。