| The studying of crack-tip asymptotical field is one of the important subjects of fracture mechanics. After determining the stress, strain and other physical quantity in crack-tip field, the related theoretical reference may be put forward to discuss material parameter's influence to crack-tip field and found the fracture rule of material breakage. The propagating of dynamic crack has extensive application in materials science, geology and structural engineering field, therefore the study of dynamic propagation of crack in viscoelastic material possess theoretical meaning and broad application foreground.With the continuous development of science and technology, coming forth much new type material, the common feature of them is possessing obvious viscoelastic character, which not only influences the rigidity of structure, but also the intensity. Then when studying the asymptotic crack-tip field, viscous effects of material should be considered, which not only accords with reality, but also can solve some problem existing in asymptotic solution of rate irrelated material, therefore the research of viscoelastic character's influence on fracture capability of material attracts much more recognition.Adopting separately a rather simple but practicable viscoelastic model and rigid-viscoelastic Bi-material interface model in the dissertation, it has been asymptotically analyzed and calculated that the stress, strain and displacement of dynamic propagating crack-tip fields of plane strain mode I, II mode crack under the condition of incompressibility; and further adopting viscoelastic model to analyze and calculate the stress, strain and displacement of mixed mode crack under the condition of incompressibility. With regard to this problem, the main research items in this dissertation are as follows:1. Through the asymptotical analyzing of singular crack-tip field, it is determined that the same exponent of singularity of stress and strain in dynamic propagating crack-tip field, namely,2. By analyzing to the constitutive theory of viscoelastic material, the constitutive equations of viscosity and elasticity with the same dominant effect is obtained in the stable creep stage, and combining the movement and harmonization equations, the governing equations in dynamic growing crack-tipfield is deduced.3. Numerical solutions of governing equations are obtained in combination with boundary conditions of each problem, and the fully continuous stress, strain and displacement in crack-tip field is found.4. Having analyzed the nature of each dynamic solution, the laws of variation of stress, strain and displacement in crack-tip field according to each parameter are discussed and the influence of physical constant, such as creep exponent, creep coefficient and the Mach number on asymptotical crack-tip field is pointed out further.5. By deducing and analyzing the basic equations of two models, it is obtained that when creeping exponent is close to infinitude, the solution of dynamic crack-tip field of viscoelastic power-hardening material in the dissertation is close formally to the solution of elastic-ideally plastic material given by Freund, in addition, when the Mach number is close to zero and creeping exponent is close to infinitude, the asymptotical solution of viscoelastic material is close formally to the static solution of elastic-ideally plastic material.6. Through the asymptotical analyzing of dynamic propagation crack-tip field, the result is produced that the hoop strain reaches to maximum in the front of mode I crack of viscoelastic material, and the shearing strain reaches to maximum in the front of mode II and mixed mode crack of viscoelastic material, mode I and mode II interfacial crack of rigid-viscoelastic material, so local fracture rules may be founded from the point of view of strain.In conclusion, by consideration of elasticity and viscosity effect of material in propagation crack-tip field, it is established that the mechanics model of viscoelasti...
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