Analysis On The Singular In The Field At The Tip Of A Dynamic Propagating 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. In all stress analysis's problem, there is no problem just like crack's problem that get perpetual attention and elaborate analysis. In crack analysis, we will feel more and more complicate and difficult. Discuss its reason, we will find crack's problem is tightly contact with the engineer's problem, the main motive to drive crack's problem is the mighty and practical need on the engineer.Many engineering materials such as polymer, soil, metal and rock et. al., often exhibit the features of elasticity, viscosity and plasticity at the same time under certain circumstances, for example, high strain-rate or high temperature. More error may arise if the theory of viscoelasticity or plasticity is employed solely to discuss the stress ,strain and other physical quantum and be used to confirm material parameter bring influence to crack-tip field and material fracture principle. The elastic-viscoplastic model should be considered in order to solve them better which possesses the features of elasticity, viscosity and plasticity as well as correlations to time and loading history.At the tip of a growing crack, some unresolved contradictions is existed whether quasi-static or dynamic growth, e.g. the existence of discontinuity of stress or strain at the crack-tip field, the unability of transformation from dynamic solution to quasi-static solution, et al. The reason is the influence on the viscosity of material is ignored. In propagating process, due to high strain rate will occur and a great amount of energy of irreversible deformation will be caused at the tip of crack, a part of energy will be released by form of heat, which will cause local temperature rise at the tip of crack, material possess the features of viscosity, Thus, the study of influence of material's viscosity property on fracture performance of material has aroused more and more recognition.The viscosity is considered in the dissertation, with the adoption of a rather simple but practicable elastic-viscoplastic model to describe the stress-strain relation of the material at the crack-tip. With a rational assumption of the viscosity coefficient of the material, namely it has a inverse ration to the plastic strain rate raised to some power, the exponent of singularity is determined through asymptotic analyses, and the rate-sensitive constitutive equations is derived under the model. With the aid of further analyses, the elasticity, viscosity and plasticity of material can be logically matched on magnitude.With the adoption of the rate-sensitive constitutive relationship, it is asymptotically investigated the propagating tip fields of plane strain mode I,II and compress-shear mixed mode propagating 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...