【作者】 梁拥成；

【导师】 刘一华；

【作者基本信息】 合肥工业大学 ， 固体力学， 2003， 硕士

【摘要】 本文基于弹性力学平面问题的基本方程，引入两个Airy应力函数，推导了均质材料Ⅴ型切口尖端和裂纹尖端的应力奇异性特征方程及其附近的奇异应力场和位移场。提出了确定单应力强度因子和双应力强度因子的数值方法以及提高应力强度因子求解精度的结点选取方法。利用上述数值方法和有限元程序MSC／Nastran的数值分析结果，对Ⅰ型、Ⅱ型、Ⅰ与Ⅱ复合型平面裂纹以及多种Ⅴ型切口问题进行了具体计算。计算结果表明，本文所提出的数值方法具有简单、通用和精度高的特点，便于实际工程应用。本文基于断裂力学原理，推导出了Ⅴ型切口的临界应力强度因子K_C与材料的平面应变断裂韧度K_10C之间的关系，给出了平面单奇异性和双奇异性Ⅴ型切口问题的最大周向应力脆性断裂准则，并用有机玻璃板材加工了两种Ⅴ型切口试样，进行了实验验证。实验表明，本文提出的最大周向应力脆性断裂准则与实验结果基本吻合。更多还原

【Abstract】 Based on the basic equations of the elasticity plane problem and the two Airy stress functions in the thesis, stress singularity eigenequations and displacement fields as well as singular stress fields near the V-notch tip and the crack tip for homogeneous materials are obtained. Numerical methods to determine the stress intensity factors for single and double stress singularity problems are presented and a pathway is provided to select nodes for improving the accuracy of the stress intensity factor. By utilizing the above methods and the results of the finite element program named MSC/Nastran, the paper carries through specific calculations corresponding to the single stress singularity and the double stress singularity issues, which consist of the cracks for Mode I , Mode II, the mixed mode crack of mode I and II and many V-notched problems. The calculations show that the numerical methods advanced in the paper have the advantages of simplicity, applicability and high accuracy, so that they are perfectly applied for the projects.Based on the theory of Fracture Mechanics, the relation between the critical stress intensity factors for V-notch Kc and the plane strain crack toughness K10c and the brittle fracture criterion of the maximum circumferential stress for single and double stress singularity with the V-notch problems are proposed. Experiments were carried out using two kinds of V-notched specimens made out of plexiglas to verify this brittle fracture criterion. It is indicated that the maximum circumferential stress criterion coincides with the experimental results.更多还原