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Автор: Yurii Maksymiuk, Doctor of Science (Engineering), Associate Professor, Kyiv National University of Construction and Architecture, Kyiv; Vitalii Didok, Postgraduate student, Department of Structural Mechanics, Kyiv National University of Construction and Architecture, Kyiv; Yevhenii Polishchuk, Postgraduate student, Department of Structural Mechanics, Kyiv National University of Construction and Architecture, Kyiv; Mykola Chernenko, Postgraduate student, Department of Structural Mechanics,
Kyiv National University of Construction and Architecture, Kyiv
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Most elements of power equipment, which are axisymmetric bodies of revolution (parts of steam and gas turbines, pipelines), are subjected to prolonged exposure to significant force loads and high temperatures during operation, which leads to the development of creep deformations, and disruption of material integrity. Under these conditions, the period of accumulation of scattered damage in the material is 50-80 per cent of its service life, therefore, the development of reliable methods for modelling the processes of deformation and destruction of structural elements, taking into account the accumulation of damage, is a pressing task in the mechanics of deformable solids.
Due to the complexity of the processes occurring in the material during the accumulation of scattered damage, the theory of continuous material damage, based on the use of the damage parameter, has been widely used for their modelling.
Mathematical modelling of the deformation processes of the objects under consideration under creep conditions leads to the formulation of viscoelasticity problems, which can only be solved using numerical methods, the leading one being the finite element method (FEM).
In solving the problem, the initial relations of the spatial problem of viscoelasticity are used without taking into account instantaneous plastic deformations. The description of the process of material deformation beyond the elastic limit is carried out in accordance with the associated law of plastic flow under the condition of Mises flow. Creep deformations are determined by the equation of one of the known phenomenological theories of creep, which includes damage as a structural parameter. The most general approach that allows taking into account the simultaneity of deformation and destruction processes is the application of Sosnin's energy theory of creep. The damage value is calculated using the corresponding kinetic equation; the use of different strength criteria to determine the equivalent stress allows taking into account the anisotropic nature of damage accumulation and failure under complex stress conditions.
The problem is solved using the finite element method according to an algorithm based on a combination of the parameter integration method and the block iteration method. At each step in time, the values of creep deformations and corresponding stresses, the value of the damage parameter growth, and its total value are calculated. When the damage parameter reaches a critical value, in order to take into account the presence of damaged material, the tensor of elastic constants of the material is corrected by reducing the elastic modulus of the material by several orders of magnitude.
The developed methodology was tested by solving several test problems. When solving the example of one-dimensional stretching of thin-walled tubes at different stress levels, the results closely matched the experiment and the reference result. The solution of the problem of deformation of a thick-walled pipe under the influence of internal pressure was carried out for different initial data on the geometric dimensions and material of the pipe, which are given by different authors. In both cases, good agreement was obtained between the data on the evolution of the stress-strain state and the time to the onset of failure with the reference result. A study was conducted on the initial location of the failure area, which largely depends on the characteristics of the construction material, in particular the material's ability to accumulate damage and creep deformations [1]. Thus, in the case of failure at a relatively low level of deformation, failure begins along the inner contour of the pipe [2], while at significant values of creep deformation, failure begins from the outer contour of the pipe [1].
The developed methodology was applied to study the evolution of stress-strain state parameters and determine the service life of a steam turbine rotor. Thus, an effective methodology was developed and tested, which is focused on the specifics of the operational load process of power equipment components.
List of references
1. Bazhenov V.A., Gulyar O.I., Piskunov S.O., Sakharov O.S. Semi-analytical finite element method in problems of continuous destruction of spatial bodies - Kyiv, Karavela, 2014. 236 p.
2. Bazhenov V.A., Piskunov S.O., Maksymiuk Yu.V. Finite element method in problems of deformation and destruction of bodies of revolution under thermo-mechanical loading - Kyiv, Karavela, 2018. – 316 p.
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