Ⅱ型动态扩展裂纹尖端的弹黏塑性渐近场  

THE ASYMPTOTIC ELASTIC-VISCOPLASTIC FIELD AT MODEⅡDYNAMIC PROPAGATING CRACK-TIP

作　　者：梁文彦[1] 王振清[1] 吕红庆 

机构地区：[1]哈尔滨工程大学航天与建筑工程学院,哈尔滨150001

出　　处：《力学学报》2009年第1期76-83,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家教育部博士点基金(20060217010);哈尔滨工程大学基础研究基金(HEUFT07005)资助项目~~

摘　　要：考虑材料的黏性效应建立了Ⅱ型动态扩展裂纹尖端的力学模型,假设黏性系数与塑性等效应变率的幂次成反比,通过分析使尖端场的弹、黏、塑性得到合理匹配,并给出边界条件作为扩展裂纹定解的补充条件,对理想塑性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Ⅱ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,对于Ⅱ型裂纹,裂尖场不含弹性卸载区.引入Airy应力函数,求得了Ⅱ型准静态裂纹尖端场的控制方程,并进行了数值分析,给出了裂纹尖端的应力应变场.当裂纹扩展速度(M→0)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.Investigations on crack-tip stress-strain fields in different media are of engineering significance. The development of crack is determined by the mechanical state of high stress zone near crack tip due to dynamic fracture failure as the major structural catastrophic form. The structure of crack tip field is complex and it is hard to get the solution of asymptotic fields with the viscous effect. In the present paper, a mechanical model is established in order to investigate the viscous effect in dynamic growing crack-tip field of mode II crack. Under the assumption that the viscosity coefficient is in inverse proportion to power law of the plastic equivalent strain rate, the elasticity, plasticity and viscosity of material at crack-tip can be matched reasonably by asymptotic analysis, and the boundary conditions can be served as the supplementary conditions to solve the growing crack-tip field. An elastic-viscoplastic asymptotic analysis is carried out on the moving crack-tip fields in perfect plastic materials under plane-strain condition. A continuous solution without discontinuities is obtained And the variations of numerical solution for mode II crack are discussed. It is shown that both stress and strain possess exponential singularity, and the tip field contains no elastic unloading zone for mode II crack. By introducing Airy stress function, the governing equation of mode II quasi-static crack tip has been obtained and analyzed numerically. When the crack moving speed approaches zero, the quasi-static solution is recovered to show that the quasi-static solution is a special case of a dynamic one.

关 键 词：动态扩展 弹黏塑性材料 裂纹尖端场 准静态扩展 

分 类 号：O34[理学—固体力学]