金属泡沫材料平面应变裂纹缓慢扩展的奇异摄动分析  

Singular perturbation analysis of plane strain crack growing quasi-statically in metal foams

作　　者：郭瑞平[1] 刘官厅[2] 范天佑[3] 

机构地区：[1]装备指挥技术学院基础部,北京101416 [2]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [3]北京理工大学理学院,北京100081

出　　处：《功能材料》2007年第A10期3827-3829,共3页Journal of Functional Materials

摘　　要：利用奇异摄动分析法研究了金属泡沫材料中平面应变Ⅰ-型裂纹的纹缓慢扩展问题，对裂纹尖端附近的应力场和速度场进行了分析，并得到了扩展裂纹尖端速度场和角应力函数的的最低阶摄动解。Metal foams have sub-structure-cells whose effects leads to the plastic compressibility of foams, which is different to the classical plasticity. Although it is very complicated and difficult, studying the mechanical properties and fracture problems of metal foams becomes more and more important with the functional applications of metal foams in engineering. This paper treats steadily-growing plane strain mode-Ⅰ cracks in metallic foams and focus upon finding approximate analytic solution of the near-tip field for them. In study, DF model, a continuum constitutive model put forward by Deshpande and Fleck, and a singular perturbation expansion method are used, and the lowest order perturbation solutions of velocity field and angular stress functions for asymptotic field of the growing crack tip, which are the dominant singular solution, are constructed. The work presents an analytic approach for calculating slowly extending crack-tip fields in metal foams.

关 键 词：金属泡沫材料 平面应变Ⅰ-型裂纹 裂纹缓慢扩展 DF本构模型 奇异摄动分析 

分 类 号：O346[理学—固体力学]