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

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.