半无穷大裂纹端部粘聚力分析  

Analysis on the Cohesive Stress at Half Infinite Crack Tip

作　　者：王利民[1] 徐世烺[2] 

机构地区：[1]山东理工大学建工系力学组,山东淄博255012 [2]大连理工大学土木工程系,大连116024

出　　处：《应用数学和力学》2003年第8期812-820,共9页Applied Mathematics and Mechanics

基　　金：国家973资助项目(2002CB412709);国家自然科学基金资助项目(10272068;50178015);山东省自然科学基金资助项目(Y202A02)

摘　　要：　准脆性材料裂纹端部断裂过程区粘聚力是导致非线性断裂特性的重要原因,根据准脆性材料的断裂特性,对存在粘聚力分布的半无穷大裂纹力学分析模型,由变形叠加原理得到以该粘聚应力分布为未知函数的积分方程,通过对积分方程的分析推证,得到了该分布函数解的数学结构和级数型表达式;提出了由实际裂纹张开位移,确定裂纹端部粘聚力分布函数的两种方法:其一由连续的裂纹张开位移通过积分变换求解未知函数级数展开项的系数,其二是由离散的裂纹张开位移数据通过最小二乘法确定该函数;推导出了相应方法求解未知量的代数方程。The nonlinear fracture behavior of quasi_brittle materials is closely related with the cohesive force distribution of fracture process zone at crack tip. Based on fracture character of quasi_brittle materials, a mechanical analysis model of half infinite crack with cohesive stress is presented. A pair of integral equations is established according to the superposition principle of crack opening displacement in solids, and the fictitious adhesive stress is unknown function. The properties of integral equations are analyzed, and the series function expression of cohesive stress is certified. By means of the data of actual crack opening displacement, two approaches to gain the cohesive stress distribution are proposed through resolving algebra equation. They are the integral transformation method for continuous displacement of actual crack opening, and the least square method for the discrete data of crack opening displacement. The calculation examples of two approaches and associated discussions are given.

关 键 词：准脆性材料 裂纹粘聚力 积分方程 最小二乘法 积分变换 代数方程 

分 类 号：O346.1[理学—固体力学]