裂纹尖端附近应力场和位移场精确解分析  

Analysis of exact solution on stress and displacement near the crack tip

作　　者：薛建阳[1] 董金爽 尚鹏[1] 

机构地区：[1]西安建筑科技大学土木工程学院,陕西西安710055

出　　处：《西安建筑科技大学学报（自然科学版）》2016年第2期160-164,共5页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金项目(51178384)

摘　　要：断裂力学中,对裂纹尖端附近应力场及位移场的确定多采用近似解,但在求解基于裂纹尖端附近精确解的物理量时,则会引起较大误差.基于断裂力学基本理论及Westergaard函数法基本原理,推导得出裂纹尖端附近三种类型裂纹任意角度方向应力场和位移场的精确解表达式.并以θ=π/6为算例,计算得出三种不同类型裂纹尖端应力场和位移场近似解的修正公式,给出了相应的曲线、数表及逼近公式.结果表明:所推导的精确解计算公式可准确描述裂纹尖端附近应力场及位移场,采用该公式求解相关物理量时,可有效提高求解的可靠度和精确度.In the fracture mechanics,the approximate solution is often adopted instead of exact solution on stress and displacement near the crack tip to solve the variables.But in the process of solving the variables which rely on the exact solution can cause errors.Based on the basic theory of fracture mechanics and the principle of the Westergaard's function methods,exact solution on stress and displacement near the crack tip was deduced beyond any angle.Take θ=π/6 as an example,the concretion formulas of the stress and displacement near the crack tip beyond the three types of cracks have been calculated,meanwhile some characteristic curves,data tables and approximate formulas have been given.The result show that the exact formulas can be used to precisely describe the stress and displacement near the crack tip,reliability,and the precision can be effectively increased in the process of solving the variables when the formulas are adopted.

关 键 词：裂纹尖端 应力场 位移场 精确解 拟合公式 

分 类 号：O346.1[理学—固体力学]