Mechanics |
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2001, No. 2
Y.N. Radayev
ON THREE-DIMENSIONAL EQUATIONS OF THE MATHEMATICAL THEORY OF PLASTICITY
A general analysis of three-dimensional static and kinematic equations of the theory of perfect elastoplasticity is given in an attempt to find approaches to analytical study of three-dimensional elastic-plastic problems. The Tresca yielding criterion and associated flow rule are used to formulate the equations. In the case of a stress state corresponds to an edge of the Tresca prism the stress field are determined via the maximal principal stress and unit vector field of the principal axes directions, thus allowing the static equilibrium equations to be considered independently of kinematic. In the most interesting cases the unit vector field of the principal axes directions is shown to be complex-lamelar. A complex-lamelar unit vector field, as it is obtained, determines a canonical curvilinear co-ordinate system. The latter is prooved generate a canonical transformation of spatial domains. The canonical transformation technique applicable to three-dimensional, plane strain and axially-symmetric problems is developed. Finally, the closed system of equations formulated in the local principal frame is obtained. The static and kinematic relations along the characterisric and principal stress lines are derived and analyzed.
L.V. Stepanova, M.E. Fedina
Asymptotic stress and damage fields for a growing crack under creep conditions for creep-damage coupled formulation of the problem are given. The self-similar variable proposed by Riedel is used for the analysis and a self-similar solution of the creep-damage coupled boundary value problem is obtained. It is shown that the totally damaged zone near the crack tip, where all stresses and scalar integrity parameter are equalled to zero, does exist. The geometry of the totally damaged zone for different values of material constants is investigated and presented.
V.S. Gluschenkov, L.A. Sarayev, A.Y. Sarantsev
With the aid of statistical averaging of the system of integral equations of composite material equilibrium, the effective constitutive relations of the visco-elastic-plastic flow of multi-component composite, which is chaotically reinforced by ellipsoidal inclusions, are analysed.
V.S. Gluschenkov, L.A. Sarayev, J.V. Khokhryakova
Elastic-plastic properties of composite material, containing chaotically oriented ellipsoidal inclusions, are in\-ves\-ti\-ga\-ted by meth\-ods of the mechanics of randomly inhomogeneous media. The effective constitutive equations of composite material are obtained and its macroscopic parameters are determined.
V.V. Bondarenko
AN ANALYSIS OF THE SUBCRITICAL CREEP CRACK GROWTH UNDER VARIABLE LOAD
By using the modified local fracture criterion the problem of creep crack growth increment under variable load is considered. The combined method of prediction of the crack growth process is developed. Numerical results of analysis of crack growth under variable load are presented in plots describing different types of crack propagation for different values of micro-structural parameters and external loads - initiation and subcritical crack growth, delayed fracture and instant fracture. To optimize the numerical analysis and predict the process of slow subcritical crack growth a computer program is developed.