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Elasticviscoplastic Analysis of the Asymptotic Stress Field Near the Tip of a Quasistatic Propagating Crack under Plane Stress Condition
Author: WangXingGang
Tutor: PangBaoJun
School: Harbin Institute of Technology
Course: Mechanics
Keywords: elasticviscoplastic quasistatic propagation plane stress cracktip field
CLC: O346.1
Type: Master's thesis
Year: 2008
Downloads: 89
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Abstract
The research of cracktip 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 cracktip 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 cracktip 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 cracktip. 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 stressstrain relation of the material at the cracktip. With a rational assumption of the viscosity coefficient of the material, the exponent of singularity is determined through asymptotic analyses, and the ratesensitive constitutive equation is derived under the model. With the adoption of the ratesensitive constitutive relationship, it is asymptotically investigated the propagating tip fields of plane stress mode I crack, and the quasistatic equations are obtained governing the stress fields at the cracktip. 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 stressstrain fields are obtained at the cracktip. 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 quasistatic equations of plane stress I model crack governing the stress field, which is different from that of plane strain. The cracktip field has power singularity, and is continues and selfrule. Near the crack interface, the particles are transferred from compression to tension. The amplitude of cracktip stress field decreases when the coefficient of hardening becomes bigger, and increases when viscosity increases. Furthermore, viscosity dominates the structure of cracktip field. The material turns to the idealplastic material when the hardening coefficient is zero. The solutions are the same with that of quasistatic HR solutions under the condition of quasistatic propagation.

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory
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