准晶动态断裂的广义不连续位移-边界元法研究

Due to its unique quasi-periodic structure, quasicrystal has low electrical conductivity and thermal conductivity. As a new functional material, quasicrystal has wide applications in various engineering fields. In engineering application, defects in the quasicrystal will damage the structure performance or cause fracture. In actual working conditions, structures are often under dynamic loadings. Therefore, the study on the fracture, especially dynamic fracture behavior of quasicrystals is of great importance. This project aims in developing extended displacement discontinuity-boundary element method conduct a research on the dynamic fracture of quasicrystal theoretically and numerically: give the dynamic general solution for some typical quasicrystal materials with the aid of potential theory method; derive the fundamental solutions for extended displacement discontinuities in Laplace space using Laplace transform technique; develop the mathematical mechanical models for the dynamic fracture of cracks in quasicrystal, and construct the extended displacement discontinuity boundary integral equations; conduct the study on the dynamic fracture of interface cracks in quasicrystals, and construct the boundary integral differential equations; analyze the singularity of the fields near the crack tip, and give the expressions for dynamic extended stress intensity factors and energy release rate as fracture criterion. Propose the boundary element method to numerically analyze the dynamic fracture in three-dimensional in infinite and finite body of quasicrystal, conduct quantitative analysis of the influence of different factors on the fracture criterion. The implementation of the project will optimize the preliminary theoretical analysis and numerical simulation system on the dynamic fracture of quasicrystals. Furthermore, the project will provide theoretical foundation for the related experiments and engineering applications, and promote the development of fracture mechanics in multi-field coupling materials.

准晶材料具有独特的准周期结构，表现出低导电导热率等特性，作为一种新兴功能材料，应用前景广阔。在工程应用中，准晶内部的缺陷将影响结构性能或引起失效破坏。实际工况中，结构多在动载荷作用下工作。因此对准晶断裂尤其是动态断裂的研究具有重要意义。本项目旨在发展广义不连续位移-边界元法，对三维准晶体裂纹及界面裂纹的动态断裂开展理论和数值研究：运用势理论方法，给出动态通解；利用Laplace变换，得到Laplace域内广义不连续位移基本解；建立准晶动态断裂的数学力学模型，给出广义不连续位移边界积分方程；研究界面裂纹动态断裂，给出边界积分微分方程；分析裂尖场的奇异性，给出动态广义应力强度因子和能量释放率；提出研究有限大、无限大准晶体动态断裂的边界元数值方法，分析各因素对断裂行为的影响。本项目的开展，将初步构建准晶动态断裂的理论分析和数值计算方法，为相关实验及工程应用提供理论依据，促进多场耦合断裂力学的发展

准晶是一种介于晶体和非晶体之间新的固体结构，其相位子场的存在使其与普通晶体有着本质区别。本项目以准晶智能复合材料/结构为研究对象，推广发展不连续位移-边界元法，分析三维动态断裂行为，构建若干典型准晶材料的动态断裂力学模型，引入Dugdale模型分析弹塑性断裂行为。采用理论分析和数值模拟相结合的方法，建立准晶涂层界面断裂力学模型，深化对准晶涂层结构断裂失效行为的理解。分析各种工况和力学模型下准晶涂层结构的断裂行为，讨论了力热耦合载荷、涂层厚度、材料错配、裂纹形貌尺寸、边界条件等因素对其断裂行为的影响，得到若干重要结论。本项目建立了完整、系统的准晶涂层界面断裂分析的研究方法，发展了高精度、适用范围广的边界元数值计算方法。该方法不仅适用于准晶材料，也可应用于其他多场耦合材料的断裂失效分析，具有很好的可推广性。项目执行期间，发表相关高水平SCI论文7篇，培养2名硕士研究生获国家奖学金，圆满完成任务目标。本项目的研究给出了准晶动态断裂判据、初步揭示了相位子场的影响规律，为工程上准晶材料用做结构表面涂层、增强复合材料和太阳能选择吸收装置提供重要的理论依据，对准晶材料的功能化设计和安全评估具有重要意义。