Elastic-viscoplastic Analysis Of The Asymptotic Stress Field Near The Tip Of A Quasi-static Propagating Crack Under Plane Stress Condition

The research of crack-tip field is one of the most important tasks of fracture mechanics. High strain rate will occur at the tip of a growing crack due to the existence of strain singularity. Furthermore, the high energy concentrations at a moving crack-tip will cause irreversible deformation and a great amount of energy of deformation is released in the form of heat which can raise the temperature at the crack-tip as high as a thousand degree. As a consequence, the viscosity of material is an important factor in the study of singular field of the crack-tip. So the viscosity effect should be considered in order to solve these problems better.The viscosity is considered in the dissertation, with the adoption of elastic viscoplastic model presented by Y. C. Gao to describe the stress-strain relation of the material at the crack-tip. With a rational assumption of the viscosity coefficient of the material, the exponent of singularity is determined through asymptotic analyses, and the rate-sensitive constitutive equation is derived under the model. With the adoption of the rate-sensitive constitutive relationship, it is asymptotically investigated the propagating tip fields of plane stress mode I crack, and the quasi-static equations are obtained governing the stress fields at the crack-tip. Numerical calculations of governing equations are carried out with selections of appropriate values of characteristic parameter by combinations of 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 each parameter.We can see that poisson's ratio doesn't exist in the quasi-static equations of plane stress I model crack governing the stress field, which is different from that of plane strain. The crack-tip field has power singularity, and is continues and self-rule. Near the crack interface, the particles are transferred from compression to tension. The amplitude of crack-tip stress field decreases when the coefficient of hardening becomes bigger, and increases when viscosity increases. Furthermore, viscosity dominates the structure of crack-tip field. The material turns to the ideal-plastic material when the hardening coefficient is zero. The solutions are the same with that of quasi-static HR solutions under the condition of quasi-static propagation.