粘弹性材料中动态扩展裂纹尖端场的分析  

Analysis of the asymptotic field of a dynamically growing crack in a visco-elastic material

作　　者：吴国辉 唐立强[1] 杨勇[1] 

机构地区：[1]哈尔滨工程大学建筑工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2007年第10期1089-1094,共6页Journal of Harbin Engineering University

基　　金：黑龙江省自然科学基金资助项目(A20004-08);哈尔滨工程大学基础研究基金资助项目(HEUF04005)

摘　　要：为了研究粘性效应作用下的动态扩展裂纹尖端渐近场,建立了粘弹性材料动态扩展裂纹的力学模型.在稳态蠕变阶段,弹性变形和粘性变形同时在裂纹尖端场中占主导地位,应力和应变具有相同的奇异量级,即(σ,ε)∝r-1/(n-1).通过渐近分析求得了裂纹尖端应力、应变和位移分离变量形式的渐近控制方程;采用靶法求得了Ⅰ型Ⅱ型动态扩展裂纹尖端的应力、应变的数值解.数值计算表明:裂尖场变化主要受材料的蠕变指数和马赫数的控制.通过对裂纹尖端场的渐近分析,为动态扩展裂纹的断裂判据提供参考依据.A mechanical model of a visco-elastic material was established in order to investigate the asymptotic field of a dynamically growing crack-tip in a viscous environment. It was shown that, in the stable creep growing phase, elastic deformation and viscous deformation are equally dominant in the near-tip field, and stress and strain have the same singularity level, namely, （σ,ε）∝ r^-1（n-1）. The asymptotic governing equation with separate variables for stress, strain and displacement in a crack-tip field was obtained by asymptotic analysis. The numerical solutions for stress and strain in a crack-tip field of mode Ⅰ and mode Ⅱ were obtained by the shooting method. Numerical calculation indicates that the near-tip fields are mainly governed by the creep exponent and Mach number. This asymptotic analysis provides helpful references for fracture analysis of dynamically growing cracks.

关 键 词：粘弹性材料 Ⅰ型裂纹尖端场 Ⅱ型裂纹尖端场 动态扩展 

分 类 号：O34[理学—固体力学]