Mechanics |
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2004, No. 2
Y.N. Radayev
The equations of plane-strain and axially-symmetric problems of the mathematical theory of plasticity are considered in the case when a stress state corresponds to an edge of the Tresca prism. The consideration is based on an approach developed in a number of previous discussions devoted to three-dimensional problem of the mathematical plasticity. This approach employes the isostatic co-ordinate net and the three stress principal line invariants. The latter permits the separation of a space variable in the three-dimensional static equilibrium equations of the mathematical plasticity, thus allowing to develop a new treatment of the plane-strain and axially-symmetric equations. A number of new theorems related to the geometry of the stress principal lines, static and kinematic equations valid along the slip lines are obtained as a complement contribution to the plane-strain and axially-symmetric analysis.
L.V. Stepanova, M.E. Phedina
FAR FIELD STRESS ASYMPTOTIC BEHAVIOR IN GROWING CREEP CRACK PROBLEMS FOR A DAMAGED MATERIAL
symptotic fields of stresses, strain rates and damage of a mode I creep crack in steady-state growth under plane stress and plane strain conditions are analyzed on the basis of Continuum Damage Mechanics. The Kachanov-Rabotnov creep - damage theory is utilized and the scalar continuity parameter is incorporated into the power stress-strain rate constitutive relations. Asymptotic analysis of the kinetic law of damage evolution shows that it is necessary to study the eigenspectrum of the stress field at large distances from the crack tip in a creeping damaged body with a growing crack. The new eigenvalue problem formulated is numerically solved. The new far stress field determining the geometry of the totally damaged zone is found and analyzed. It can be concluded that the new far field asymptotic stress found differs from the well-known Hutchinson-Rice-Rosengren (HRR)-solution and the HRR-solution can't be used as the remote boundary condition. It is shown that the configuration of the totally damaged zone is entirely determined by the far field stress obtained.