| 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 these problems. 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.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. High strain rate will occur at the tip of a growing crack,whether quasi-static or dynamic growth,due to the existence of strain singularity. Furthermore,the highly 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. While the influence of viscosity is often ignored in previous researches,which bring on some unresolved contradictions in whether quasi-static or dynamic solutions,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 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 of hardening principle,it is shown that,under the condition of linear-hardening,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 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 boundary conditions of each problem,and the fully continuousstress-strain fields are obtained at the crack-tip. The nature of each asymptotic solution is analyzed and the variations of solutions are discussed according to each 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 problems are 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 the dissertation.The material turns to the visco-elastic power-hardening 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.In conclusion,by consideration of viscosity effect of material at propagating crack-tip,it is established in the paper the unified continuous singular crack-tip field in linear-hardening m...
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