Ⅰ型定常扩展裂纹尖端的弹黏塑性场  

THE ELASTIC-VISCOPLASTIC FIELD AT MODE ⅠSTEADILY PROPAGATING CRACK-TIP

作　　者：贾斌[1] 王振清[2] 李永东[3] 

机构地区：[1]哈尔滨工业大学航天学院,哈尔滨150001 [2]哈尔滨工程大学建筑工程学院,哈尔滨150001 [3]装甲兵工程学院机械工程系,北京100072

出　　处：《力学学报》2005年第4期421-427,共7页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：考虑材料在扩展裂纹尖端的黏性效应,假设黏性系数与塑性应变率的幂次成反比,对幂硬化材料中平面应变扩展裂纹尖端场进行了弹黏塑性渐近分析,得到了不含间断的连续解,并讨论了Ⅰ型裂纹数值解的性质随各参数的变化规律.分析表明应力和应变均具有幂奇异性,并且只有在线性硬化时,尖端场的弹、黏、塑性才可以合理匹配.对于Ⅰ型裂纹,裂尖场不含弹性卸载区.当裂纹扩展速度趋于零时,动态解趋于准静态解,表明准静态解是动态解的特殊形式;如果进一步考虑硬化系数为零的极限情况,便可退化为Hui和Riedel的非线性黏弹性解.The viscosity of material is considered at propagating crack-tip. Under the assumption that the artificial viscosity coefficient is in inverse proportion to power law of the plastic strain rate, an elastic-viscoplastic asymptotic analysis is carried out for moving crack-tip fields in power-hardening materials under plane-strain condition. A continuous solution is obtained containing no discontinuities. The variations of numerical solution are discussed for mode Ⅰ crack according to each parameter. It is shown that stress and strain both possess power law singularity. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. And the tip field contains no elastic unloading zone for mode Ⅰ crack. The quasi-static solution is recovered when the crack moving speed approaches zero, which show that the quasi-static solution is a special case of a dynamic one. If the limit case of zero hardening coefficient is further considered, the solution can be transformed to the elastic-nonlinear-viscous one of Hui and Riedel.

关 键 词：准静态扩展 动态扩展 幂硬化 弹黏塑性材料 裂纹尖端场 

分 类 号：O346.1[理学—固体力学]