可压缩粘弹性材料Ⅱ型动态扩展裂纹尖端场

Crack Tip Field on Mode Ⅱ Dynamic Growing Crack in Visco-Elastic Compressible Material

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II型动态扩展裂纹的力学模型,推导了可压缩材料Ⅱ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,弹性变形部分的可压缩性对Ⅱ型裂尖应力场影响甚微,而对应变场和位移场影响较大。裂尖场主要受材料的蠕变指数n和马赫数M的控制。当泊松比ν=0.5时,可以退化为不可压缩粘弹性材料Ⅱ型动态扩展裂纹。

A mechanical model of visco-elastic compressible material was established in order to investigate viscous effect in dynamic growing crack-tip field of mode Ⅱ. The constitutive equation of mode Ⅱ in the visco-elastic compressible materials was deducted. It shows that in stable creep growing stage, the elastic deformation and visco-deformation are equally dominant in the near tip field as r^-1/（n-1）. The asymptotic solutions of separative variable of stress, stain and displacement in crack-tip field were obtained by asymptotic analysis, and the results of numerical value of stress and strain in crack-tip field were got by shooting method, and the curves of stress, stain and displacement by different parameters were given. Through numerical calculate, it shows that the near tip fields are mainly governed by the creep exponent n and Mach number M. The stress field slightly affects by elastic incompressible deformation, but the strain and displacement field deeply affect by elastic incompressible deformation. The asymptotic solution of dynamic growing crack-tip field of mode II in incompressible materials can be obtained when v = 0. 5.