可压缩粘弹性材料Ⅰ型动态扩展裂纹尖端场  

Crack tip field of a mode I dynamically growing crack in a visco-elastic compressible material

作　　者：杨勇[1] 唐立强[1] 边科 

机构地区：[1]哈尔滨工程大学航天与建筑工程学院,黑龙江哈尔滨150001

出　　处：《哈尔滨工程大学学报》2008年第7期687-691,共5页Journal of Harbin Engineering University

基　　金：黑龙江省自然科学基金资助项目(A2004-08);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,建立了可压缩粘弹性材料Ⅰ型动态扩展裂纹的力学模型,推导了可压缩材料Ⅰ型动态扩展裂纹的本构方程.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.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解,并采用打靶法求得了裂纹尖端应力、应变和位移的数值结果,给出了应力、应变和位移随各种参数的变化曲线.数值计算表明,弹性可压缩变形对Ⅰ型裂纹尖端应力场影响甚微,而对应变场和位移场影响较大.裂纹尖端场主要受材料的蠕变指数n和马赫数M控制.当泊松比v=0.5时,可以退化为不可压缩粘弹性材料Ⅰ型动态扩展裂纹.A mechanical model of a viseo-elastie compressible material was developed in order to investigate the asymptotic field at the proximity of mode Ⅰ crack tip which is dynamically growing under the viscous effect. The constitutive equation for mode-Ⅰ viseo-elastie compressible materials was derived. It is argued that in the stable creep growing stage, elastic-deformation and visco-deformation are equally dominant in the near-tip field. The stress and the strain have the same order of singularity. Asymptotic solutions in the form of separative variables for stress, stain and displacement in the crack-tip field were obtained by asymptotic analysis. Further, the numerical solutions of stress, strain and displacement in the crack-tip field were obtained using the shooting method. The curves of stress, strain and displacement in terms of various parameters are given. Through numerical calculations, it is shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M. The stress field is slightly affected by elastic incompressible deformation, but the strain and displacement fields are mainly affected by elastic incompressible deformation. When v = 0.5, the dynamically growing mode Ⅰ crack of visco-elastic compressible material may behave as a viseo-elastie incompressible material.

关 键 词：可压缩粘弹性材料 Ⅰ型裂纹 尖端场 动态扩展 

分 类 号：O34[理学—固体力学]