反平面V形切口塑性应力奇异性分析  

ANALYSIS OF PLASTIC STRESS SINGULARITIES OF ANTI-PLANE V-NOTCHES IN HARDENING MATERIALS

作　　者：葛仁余[1] 牛忠荣[2] 程长征[2] 胡宗军[2] 杨智勇[2] 

机构地区：[1]安徽工程大学力学重点实验室,芜湖241000 [2]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《固体力学学报》2015年第1期76-84,共9页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11272111和11372049);安徽省教育厅项目(TSKJ2014B16)资助

摘　　要：论文提出了用插值矩阵法计算幂硬化塑性材料反平面V形切口和裂纹尖端区域的应力奇异性.首先在切口和裂纹尖端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性特征指数和特征角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反平面V形切口和裂纹的前若干阶应力奇异阶和相应的特征角函数,该法的重要优点是以上求解的特征角函数和它们各阶导函数具有同阶精度,并且一次性地求出前若干阶特征对.同时,插值矩阵法计算量小,易于和其他方法联合使用,这些优点在后续求解尖端区域完全应力场非常优越.论文方法的计算结果与现有结果对照,发现吻合良好,表明了论文方法的有效性.In this paper,an interpolating matrix method for determining higher-order singular stress field at anti-plane V-notch region of power-law hardening materials is presented.Firstly,the asymptotic displacement field at the notch tip where the plastic deformation takes place is adopted.By substituting the displacement expressions into the governing differential equations of the plastic theory,an eigenvalue problem of nonlinear ordinary differential equations with the stress singularity orders and the associated eigenfunctions is obtained.Then,the interpolating matrix method is adopted to solve the eigenvalue problem by an iteration process.Several leading plastic stress singularity orders of antiplane V-notches and cracks are obtained.Meanwhile,the associated eigenvectors of the displacement and stress fields in the notch tip region also are determined with the same degree of accuracy.One of the important advantages of the present method is that the computational results of the angular eigenfunctions and their derivative functions corresponding to each asymptotic expansion term have the same order of accuracy.Another advantage of the present method is that all useful eigenpairs in the asymptotic expansion can be obtained at the same time.In addition,only few computational cost is needed to solve the eigenvalue problems by the interpolating matrix method.These advantages are very beneficial to solve the stress field in V-notches and cracks tip region.By comparing with the existing results of numerical examples,the validity of the present method is confirmed.

关 键 词：应力奇异性 反平面V形切口 插值矩阵法 幂硬化材料 

分 类 号：O344.1[理学—固体力学]