Modelling of Creep and Oscillations in Material Described by Armstrong-Frederick Equations - Breslavsky, Dmitry; Altenbach, Holm; Naumenko, Konstantin; Tatarinova, Oksana (NTU "KhPI", 2016)
Different 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.