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Fracture and fatigue analysis of functionally graded and homogeneous materials using singular integral equation approach.

机译：使用奇异积分方程方法对功能梯度材料和均质材料进行断裂和疲劳分析。

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摘要

There are two major objectives of this thesis work. One is to study theoretically the fracture and fatigue behavior of both homogeneous and functionally graded materials, with or without crack bridging. The other is to further develop the singular integral equation approach in solving mixed boundary value problems.; The newly developed functionally graded materials (FGMs) have attracted considerable research interests as candidate materials for structural applications ranging from aerospace to automobile to manufacturing. From the mechanics viewpoint, the unique feature of FGMs is that their resistance to deformation, fracture and damage varies spatially. In order to guide the microstructure selection and the design and performance assessment of components made of functionally graded materials, in this thesis work, a series of theoretical studies has been carried out on the mode I stress intensity factors and crack opening displacements for FGMs with different combinations of geometry and material under various loading conditions, including: (1) a functionally graded layer under uniform strain, far field pure bending and far field axial loading, (2) a functionally graded coating on an infinite substrate under uniform strain, and (3) a functionally graded coating on a finite substrate under uniform strain, far field pure bending and far field axial loading.; In solving crack problems in homogeneous and non-homogeneous materials, a very powerful singular integral equation (SEE) method has been developed since 1960s by Erdogan and associates to solve mixed boundary value problems. However, some of the kernel functions developed earlier are incomplete and possibly erroneous. In this thesis work, mode I fracture problems in a homogeneous strip are reformulated and accurate singular Cauchy type kernels are derived. Very good convergence rates and consistency with standard data are achieved. Other kernel functions are subsequently developed for mode I fracture in functionally graded materials. This work provides a solid foundation for further applications of the singular integral equation approach to fracture and fatigue problems in advanced composites.; The concept of crack bridging is a unifying theory for fracture at various length scales, from atomic cleavage to rupture of concrete structures. However, most of the previous studies are limited to small scale bridging analyses although large scale bridging conditions prevail in engineering materials. In this work, a large scale bridging analysis is included within the framework of singular integral equation approach. This allows us to study fracture, fatigue and toughening mechanisms in advanced materials with crack bridging. As an example, the fatigue crack growth of grain bridging ceramics is studied.; With the advent of composite materials technology, more complex material microstructures are being introduced, and more mechanics issues such as inhomogeneity and nonlinearity come into play. Improved mathematical and numerical tools need to be developed to allow theoretical modeling of these materials. This thesis work is an attempt to meet these challenges by making contributions to both micromechanics modeling and applied mathematics. It sets the stage for further investigations of a wide range of problems in the deformation and fracture of advanced engineering materials.
机译：本论文的工作有两个主要目标。一种是从理论上研究均质材料和功能渐变材料在有无裂纹桥接的情况下的断裂和疲劳行为。另一种是进一步发展奇异积分方程法来解决混合边值问题。新开发的功能梯度材料（FGM）作为从航空航天到汽车到制造业的结构应用的候选材料，吸引了相当多的研究兴趣。从力学角度来看，FGM的独特之处在于它们对变形，断裂和损坏的抵抗力在空间上会发生变化。为了指导功能梯度材料制成的构件的微观结构选择和设计及性能评估，在本文工作中，对不同强度的FGMs的I型应力强度因子和开裂位移进行了一系列理论研究。在各种载荷条件下的几何形状和材料的组合，包括：（1）均匀应变下的功能梯度层，远场纯弯曲和远场轴向载荷;（2）均匀应变下的无限基底上的功能梯度涂层，以及（ 3）在均匀应变，远场纯弯曲和远场轴向载荷下在有限基底上的功能梯度涂层;在解决均质和非均质材料中的裂纹问题时，埃尔多安（Erdogan）自1960年代以来就发展了一种非常强大的奇异积分方程（SEE）方法，旨在解决混合边值问题。但是，早期开发的某些内核功能是不完整的，并且可能是错误的。在本文工作中，对均质带钢中的I型断裂问题进行了重新表述，并得出了精确的奇异柯西型核。实现了非常好的收敛速度和与标准数据的一致性。随后针对功能分级材料中的模式I断裂开发了其他内核函数。这项工作为进一步应用奇异积分方程方法解决高级复合材料的断裂和疲劳问题提供了坚实的基础。裂缝桥接的概念是统一的理论，涉及从原子分裂到混凝土结构破裂的各种长度尺度的破裂。但是，尽管工程材料中普遍存在大规模的桥接条件，但大多数先前的研究仅限于小规模的桥接分析。在这项工作中，大型积分分析包括在奇异积分方程法的框架内。这使我们能够研究具有裂纹桥接的先进材料的断裂，疲劳和增韧机理。例如，研究了晶粒桥接陶瓷的疲劳裂纹扩展。随着复合材料技术的出现，越来越复杂的材料微观结构被引入，诸如不均匀性和非线性之类的更多力学问题也开始发挥作用。需要开发改进的数学和数值工具以允许对这些材料进行理论建模。本论文旨在通过为微力学建模和应用数学做出贡献来应对这些挑战。它为进一步研究高级工程材料的变形和断裂中的各种问题奠定了基础。

著录项

  • 作者

    Zhao, Huaqing.;

  • 作者单位

    The Johns Hopkins University.;

  • 授予单位 The Johns Hopkins University.;
  • 学科 Applied Mechanics.; Engineering Mechanical.; Engineering Materials Science.
  • 学位 Ph.D.
  • 年度 1999
  • 页码 161 p.
  • 总页数 161
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 应用力学;机械、仪表工业;工程材料学;
  • 关键词

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