【作者】 王志勇；

【导师】 马力；

【作者基本信息】 哈尔滨工业大学 ， 工程力学， 2008， 硕士

【摘要】 功能梯度材料作为一种典型的非均质复合材料,旨在满足航天、国防等高新技术领域对材料提出的苛刻要求。研究功能梯度材料的断裂行为具有十分重要的意义。研究此类问题,通常采用实验观测、理论分析以及数值模拟等方法。实验研究由于设备的限制以及高昂的费用,给实际工作带来了很大的困难。理论研究则需要做大量的假设,而且很难求解材料属性和边界条件复杂的问题。数值方法在理论上可以处理任意材料、载荷、结构形式的问题,因此成为人们分析断裂行为的一个重要工具。本文采用一种新的数值计算方法——扩展有限元法来模拟功能梯度材料中的准静态裂纹扩展问题。本文由四个部分组成。第一章对功能梯度材料断裂行为的研究现状进行了综述。介绍了扩展有限元法的发展现状并讨论了将其应用与求解功能梯度材料断裂问题的可能性。第二章详细阐述了扩展有限元法的基本原理以及在线弹性断裂力学中的应用。该方法只是在有限元位移模式中,基于单位分解的思想加进一个跳跃函数和渐进裂尖位移场,对不连续体附近的结点自由度局部加强,反映出位移的不连续性,从而不需要在裂纹体和裂尖附近进行高密度的网格划分,而且,在模拟裂纹准静态扩展的时候也不需要重新划分网格。第三章具体给出了扩展有限元法的数值实现过程。在此基础上,研究了平面应力或平面应变状态下,含有内部裂纹或边裂纹的二维均质板条的断裂问题,分析了结构的几何参数、载荷类型、网格疏密和裂纹的位置对裂纹尖端应力强度因子的影响。第四章研究了功能梯度材料中裂纹的准静态扩展问题。模拟时采用裂尖局部均匀化的假设,同时取高斯积分点处真实的材料属性进行计算,将数值计算的结果与理论和实验结果做比较,验证了算法的有效性和可靠性。更多还原

【Abstract】 As a kind of typical non-homogeneous composite materials, functionally graded materials(FGMs) are designed to meet the harsh requirements of many important industrial fields. Significant experimental, theoretical and mumerical research efforts on FGMs in nowadays are devoted to this subject. Due to the limitation of condition and high cost, experimental observations could bring us many difficulties. Theoretical analysis needs rigid assumptions and cannot easily sovle problems with complicated properties and boundary conditions. Owing to the ability to solve problems of any materials, loads and structures, numerical methods become an important tool to investigate the fracture behaviors. The present article addresses the numerical simulation of mixed-mode crack propagation in FGMs by using the extended finite element method(XFEM).There are four parts in this article. The First Chapter makes a summary of the relative research on fracture problems of FGMs, including the advances of XFEM and the possibility of its applications in FGMs. The Second Chapter reviews the principle of XFEM in detail and its applications in lineaer elastic fracture mechanics. In XFEM, a standard displacement-based approximation is enriched near a crack by incorporating both discontinuous fields and the near tip asymptotic fields through a partition of unity method. This enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence quasi-static crack propagation simulations can be carried out without remeshing. The process of XFEM is provided in Chapter Three. Based on this, XFEM is used to analysis the fracture problem of two dimensional homogeneous strips with inner crack or edge crack in the plane stress or plane strain condition. The influences of geometric parameters, loads, mesh and location of the crack on the stress intensity factors (SIFs) at crack tip are investigated. In Chapter Four, numerical simulation of quasi-static crack propagation in FGMs is investigated by adopting the actual properties at Guass points and taking the assumption of local homogenization. To validate the effectiveness and robustness of this method, we compare the results of numerical caculus with experimental and theoretical conclusions.更多还原