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梁文彦 王振清 吕红庆. II型动态扩展裂纹尖端的弹黏塑性渐近场[J]. 力学学报, 2009, 41(1): 76-83. DOI: 10.6052/0459-1879-2009-1-2007-345
引用本文: 梁文彦 王振清 吕红庆. II型动态扩展裂纹尖端的弹黏塑性渐近场[J]. 力学学报, 2009, 41(1): 76-83. DOI: 10.6052/0459-1879-2009-1-2007-345
Zhenqing Wang. The asymptotic elastic-viscoplastic field at mode II dynamic propagating crack-tip[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(1): 76-83. DOI: 10.6052/0459-1879-2009-1-2007-345
Citation: Zhenqing Wang. The asymptotic elastic-viscoplastic field at mode II dynamic propagating crack-tip[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(1): 76-83. DOI: 10.6052/0459-1879-2009-1-2007-345

II型动态扩展裂纹尖端的弹黏塑性渐近场

The asymptotic elastic-viscoplastic field at mode II dynamic propagating crack-tip

  • 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\to 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.

     

    Abstract: Investigations on crack-tip stress-strain fields indifferent media are of engineering significance. The development of crack isdetermined by the mechanical state of high stress zone near crack tip due todynamic fracture failure as the major structural catastrophic form. Thestructure of crack tip field is complex and it is hard to get the solutionof asymptotic fields with the viscous effect. In the present paper, amechanical model is established in order to investigate the viscous effectin dynamic growing crack-tip field of mode II crack. Under the assumptionthat the viscosity coefficient is in inverse proportion to power law of theplastic equivalent strain rate, the elasticity, plasticity and viscosity ofmaterial at crack-tip can be matched reasonably by asymptotic analysis, andthe boundary conditions can be served as the supplementary conditions tosolve the growing crack-tip field. An elastic-viscoplastic asymptoticanalysis is carried out on the moving crack-tip fields in perfect plasticmaterials under plane-strain condition. A continuous solution withoutdiscontinuities is obtained And the variations of numerical solution formode II crack are discussed. It is shown that both stress and strain possessexponential singularity, and the tip field contains no elastic unloadingzone for mode II crack. By introducing Airy stress function, the governingequation of mode II quasi-static crack tip has been obtained and analyzednumerically. When the crack moving speed approaches zero, the quasi-staticsolution is recovered to show that the quasi-static solution is a specialcase of a dynamic one.

     

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