摘要
本文利用弹-粘-塑性材料力学模型,对动态扩展裂纹尖端的指数奇异性和对数奇异性进行了渐近分析。文中假定,弹性阶段的粘性效应可以略去,仅在塑性应变中粘性才起作用,对于这种模型,推导出了其率敏感型的本构关系。以Ⅱ型裂纹为例,进一步推导了两种奇异性下裂纹尖端场的渐近微分控制方程,并进行了数值仿真分析。同时讨论了粘性系数α、马赫数M2对裂纹尖端应力应变场的影响,即,弹粘塑性材料扩展裂纹的奇异性取决于其粘性系数和马赫数,粘性系数较大时,裂纹尖端场具有对数奇异性;粘性系数较小时,裂纹尖端场具有指数奇异性。修正了文献[1]中对数奇异性区域的大小;解释了文献[1]中过渡区的成因;给出了过渡区尖端应力场解的形式,从而建立了裂纹尖端场的统一解。
An elastic visco-plastic material model was adopted to the asymptotic analysis on power law and logarithmic singularity of dynamic growing crack tip. It is assumed that the viscosity coefficients can be omitted in elastic stage and only contribute in plastic strain. Based on this model the constitutive law of ratio sensitive material has been achieved. In terms of mode Ⅱ crack, the asymptotic differential governing equation in cracking tip fields under two different singular modes was obtained and the numerical simulation has been used. Furthermore, the impact of viscosity coefficient α and the Mach number M2 on the stress-strain cracking tip fields were discussed, because the growing crack singularity of the elastic visco-plastic material was determined by its viscosity coefficient and Mach number. When the viscosity coefficient is big, the cracking tip field expresses logarithmic singularity. While the viscosity coefficient is relatively small, it shows power law singularity. The logarithmic singular zone in [1] was modified and the forming of transitional zone in [1] was explained. Moreover, the solution to tip stress field in transitional zone has been given. Therefore, the united resolution of cracking tip field was established.
出处
《力学季刊》
CSCD
北大核心
2005年第2期190-197,共8页
Chinese Quarterly of Mechanics
基金
哈尔滨工程大学基础基金
关键词
粘性系数
马赫数
指数奇异性
对数奇异性
统一解
viscosity coefficients
Mach number
power law singularity
logarithmic singularity
unite resolution
