摘要
研究幂硬化塑性材料V形切口和裂纹尖端区域的应力奇异性.首先在切口和裂纹区域采用自尖端径向度量的渐近位移场假设,将其代入塑性全量理论的基本微分方程后,推导出包含应力奇异指数和特征函数的非线性常微分方程特征值问题.然后采用插值矩阵法迭代求解导出的控制方程,得到一般的塑性材料V形切口和裂纹的前若干阶应力奇异阶和相应的特征函数.通过两个算例给出了前若干个阶的应力奇异指数和特征函数,表明文中方法计算一般塑性材料V形切口和裂纹应力奇异性的精度和有效性,并对一般塑性材料V形切口和裂纹的奇异应力特征进行了讨论.
A higher-order analysis of the stress singularity of the plane V-notches and cracks in power law hardening materials is studied. First the asymptotic displacement field in terms of radial coordinates at the notch tip is adopted. When the material near the notch tips arises in plastic deformation, the Von Mises yield criterion and the plastic ＇total strain＇ theory are used. By introducing the displacement expressions into the governing differential equations of the plastic theory, it results in a set of the eigenvalue problem of nonlinear ordinary differential equations with the stress singularity orders and the associated eigenfunctions. Then the interpolating matrix method established by the first author is used to solve the eigenvalue problem by an iteration process. The several leading plastic stress singularity orders of plane V-notches and cracks have been obtained. Simultaneously the associated eigenvectors of the displacement and stress fields in the notch tip region have been determined with the same degree of accuracy. Finally two numerical examples have been given to illustrate the accuracy and the effectiveness of the present method to determine the singularity orders of the plastic V-notch and crack. Based on the computed results, some characteristics related to the stress singularity of the plastic notches and cracks are discussed.
出处
《中国科学：物理学、力学、天文学》
CSCD
北大核心
2014年第1期79-90,共12页
Scientia Sinica Physica,Mechanica & Astronomica
基金
国家自然科学基金资助项目(批准号:11272111)
关键词
应力奇异性
V形切口
塑性
硬化材料
插值矩阵法
stress singularity, V-notch, plasticity, hardening material, interpolating matrix method
