The Elastic-viscous-ideally Plastic Field At The Tip Of Mode Ⅲ Steadily Moving Crack

The research of crack-tip fields is one of the most important task of fracture mechanics. It has been attracting the attentions of mechanics researchers. Taken the viscosity into account in this paper, a rather simple but practicable elastic-viscoplastic model to describe the stress-strain relation of the material at the crack-tip of antiplane mode III Crack. With a rational assumption of the viscosity coefficient of the material, the rate-sensitive constitutive equations for the ideally elastic-viscoplastic field are derived under the model. The exponent of singularity is determined through asymptotic analyses, and the plastic shock is eliminated that exists in non-viscosity solutions.With the adoption of the rate-sensitive constitutive relationship, it is asymptotically investigated the propagating tip fields of antiplane mode III crack under the condition of incompressibility, and the dynamics equations are obtained separately governing the stress and strain fields at the crack-tip. Numerical calculations of governing equations are carried out with selections of appropriate values of each characteristic parameter by combinations of corresponding boundary conditions, and the fully continuous stress-strain fields are obtained at the crack-tip. The nature of asymptotic solution is analyzed and the variations of solutions are discussed according to different parameter.In order to compare with the extreme of dynamic solutions when the Mach number approaches zero, i.e. the quasi-static propagation, the corresponding quasi-static problem is also studied asymptotically in the paper. The governing equations of crack-tip field are derived, and numerical solutions are obtained by selections of typical parameter values with combination of boundary conditions of each problem. The two solutions agree well with each other through comparisons of numerical results. Therefore, the quasi-static solutions can be recovered from the extreme of dynamic solutions when the Mach number goes to zero for the elastic-viscoplastic constitutive model employed in this paper.In conclusion, the rationality and effectiveness of the constitutive model applied in the paper are verified through theoretical analyses and corresponding numerical calculations to provide a feasible method for final solutions of the problems of the asymptotic crack-tip field, as well as. theoretical references for solutions of the difficult problems encountered in engineering practices.