含裂縫複合平板受彎矩之破壞力學分析

Abstract

本文考慮含裂縫雙材料之異向彈性板受彎矩問題中，利用平板受拉伸和彎矩問題之間的對應關係，探討在界面裂縫尖端處有應力場的奇異性，由此關係也可用於計算在無窮遠處，多個內部裂縫受均勻彎矩作用的應力強度因子。 在計算應力強度因子時，裂縫被視為錯位的連續分佈，以建立受力矩作用與錯位密度相關的積分方程式，高斯-謝比雪夫積分(Gauss-Chebyshev quadrature)可將積分方程式轉換為代數方程式，本文的算例包括，包含單裂縫和雙裂縫在無限板受均勻彎矩，考慮等向性以及正交性兩種材料

In this thesis cracked anisotropic elastic bi-material plates under bending are considered. Correspondence relationships between plate stretching and bending problems are utilized to investigate the stress singularities at the tip of an interface crack. The relationships are also used to compute the stress intensity factors for multiple internal cracks under remote uniform bending. In computing the stress intensity factors cracks are regard as continuous distributions of dislocations to establish integral equations relating dislocation densities with the applied moment. Gauss-Chebyshev quadrature is used to convert integral equations to algebraic equations. The numerical examples include infinite plates containing one and two cracks under uniform bending; isotropic as well as orthotropic materials are considered.