Ⅲ型裂纹的二个动态扩展问题

程靳¹, 巴颖¹, 吕念春^1,2, 林敏¹, 郭宝科¹

1.哈尔滨工业大学航天科学与力学系;2.沈阳理工大学材料科学与工程学院



摘要:

通过复变函数论的方法,对Ⅲ型裂纹的2个动态扩展问题进行研究.本文提出了裂纹动态扩展的1个新的力学模型,即裂纹坐标原点分别受增加载荷Px/t、Pt3/x2的作用,采用自相似函数的方法将所讨论问题迅速转化为Riemann-Hilbert问题,并求得了该模型的应力、位移和应力强度因子的解析解.利用这些解并采用叠加原理,即可求得任意复杂问题的解.

关键词:  复变函数  Ⅲ型裂纹  动态扩展  解析解

DOI：10.11918/j.issn.0367-6234.2011.09.006

分类号:O346.1

基金项目:



Two dynamic propagation problems of mode Ⅲ crack

CHENG Jin¹, BA Ying¹, Lü Nian-chun^1,2, LIN Min¹, GUO Bao-ke¹

1.Dept.of Astronautics and Mechanics,Harbin Institute of Technology,150001 Harbin,China;2.School of Material Science and Engineering,Shenyang Ligong University,110168 Shenyang,China)

Abstract:

In order to solve two dynamic propagation problems on mode Ⅲ crack by theory of complex functions,a new mechanical model for dynamic crack propagation,in which the crack is under the conditions of increasing loads Px/t、Pt3/x2 located at the origin of the coordinate of the crack is presented in this paper.The problems are transformed into Riemann-Hilbert problems by the approaches of self-similar functions,and the analytical solutions of stress,displacement and stress intensity factor are attained.With the solutions and superposition theorem,the solutions of discretionary complex problems can be acquired.

Key words:  complex functions  mode Ⅲ crack  dynamic propagation  analytical solutions