Nonlinear Dynamics–2016
Постійне посилання колекціїhttps://repository.kpi.kharkov.ua/handle/KhPI-Press/24522
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Документ Modelling of Creep and Oscillations in Material Described by Armstrong-Frederick Equations(NTU "KhPI", 2016) Breslavsky, Dmitry; Altenbach, Holm; Naumenko, Konstantin; Tatarinova, OksanaDifferent structural elements at high temperatures and cyclic loading demonstrate essential creep behavior. Due to variety of materials which are used in modern industrial applications the different forms of creep response have to be analyzed. The one of them presents in materials are characterized by creep processes with essential recovery, which is expressed by strain decreasing after the unloading. Such material behavior is described by well-known Armstrong-Frederick model. The case of cyclic loading leading to forced oscillations at high temperature is studied. The Armstrong- Frederick creep model contains two equations: first for creep strain rate function as well as the second for socalled backstress evolution. The problem is solved by two time scales methods with subsequent averaging in a period of oscillations. The solution was performed for the hyperbolic creep strain rate function which satisfactory describes the high-temperature behavior of advanced steel with primary creep conditions. The stress function is presented by expansion in Fourier series. Asymptotic solution of creep equations was obtained and by use of the procedure of averaging in the period the new model describing ‘slow’ creep motion has been derived. The analytical forms of influence functions for both equations of the model expressing the role of cyclical loading were obtained. Numerical examples which demonstrate the cyclic creep behavior in advanced steel X20CrMoV12-l are presented and discussed.Документ Asymptotic Solution of Anisotropic Cyclic Creep Problem(NTU "KhPI", 2016) Breslavsky, Dmitry; Mietielov, Volodymyr; Morachkovsky, Oleg; Tatarinova, Oksana; Pashchenko, SergeyThin-walled structural elements made from rolled metal usually demonstrate anisotropic creep behavior. Very often the model of transversally-isotropic material is suitable for its description. Due to the difficulties in direct numerical integration the case of cyclic loading demands the development of suitable method of the creep problem’s solution when the material behavior isn’t isotropic. The general problem statement as well as the constitutive equations for two-dimensional creep problem are presented. Transversally-isotropic creep material model developed by O.Morachkovsky is used. The case of substantial stress values which are greater than yield limit is studied. Addition of cyclic loading, which is essentially varying the creep response, is analyzed. Deriving of resolving system of creep equations was performed by use of the method of asymptotic expansions jointly with the method of averaging in a period of stress cycle. This system allows simulation of only the problem of static loading with constitutive equations of special type, in which the values of cyclic parts of loading are included in so-called influence functions. These equations are derived from the general form by use of asymptotic expansions of creep strain functions with further averaging in a period of oscillations. Developed method is realized as an applied C+ + software. The Finite Element Method is used for solution of boundary-value problem jointly with Finite Difference Scheme for initial one. The results of experimental investigations of creep in specimens and plates with holes made from rolled steel are discussed. The anisotropic creep curves in three directions were obtained and constants for creep flow rule were determined. Additional number of experiments was performed for the case of cyclic loading. The comparison between experimental and numerical data shows the satisfactory agreement. Due to this a number of numerical examples for cyclic creep simulation in thin plates were performed and their results are discussed.