Bainitic Ferrite Plate Thickness Evolution in Two Nanostructured Steels

Bainitic ferrite plate thickness evolution during isothermal transformation was followed at the same holding temperatures in two nanostructured steels containing (in wt.%) 1C-2Si and 0.4C-3Si. A dynamic picture of how the bainitic transformation evolves was obtained from the characterization of the microstructure present at room temperature after full and partial transformation at 300 and 350 °C. The continuous change during transformation of relevant parameters influencing the final scale of the microstructure, YS of austenite, driving force of the transformation and evolution of the transformation rate has been tracked, and these variations have been correlated to the evolution of the bainitic ferrite plate. Instead of the expected refinement of the plate predicted by existing theory and models, this study revealed a thickening of the bainitic ferrite plate thickness as the transformation progresses, which is partially explained by changes in the transformation rate through the whole decomposition of austenite into bainitic ferrite.

Nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies. Part 1. Resonance on difference frequency

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. As a preliminary task the investigation of only magnetic vibrations by two-frequency excitation is carried out. The possibility of description of forced linear vibrations on the basis of single nonuniform linear second order equation with arbitrary excitation is shown. It is found the analytical solution of task about excitation of oscillator by two signals which frequencies are distinguishes up and down from central frequency on the same frequency interval. It is shown the equivalency of representation of magnetic vibrations in linear regime and model vibrations on the basis of oscillator. It is found that in the general case the vibrations have view as beating which rounding frequency is equal to difference between excitation frequencies. The whole positing of task about excitation of nonlinear magnetoelastic vibrations in normal magnetized ferrite plate by two-frequency excitation is proposed. It is found that in conditions of large nonlinearity when the own elastic resonance of plate is equal to the difference frequency the powerful elastic vibrations are excited. It is found the nonlinear excitation of powerful non-resonance vibrations which take place also in the case of large elastic dissipation. It is shown that the non-resonance vibrations are determined precisely two-frequency character of excitation. It is found that the amplitude of non-resonance vibrations by increasing of plate thickness also is increased. By the small level of excitation, the low of increasing is linear, by middle – quadratic, by large – again approaches to linear with saturation and non-permanent sudden jumps. The character of excitation in conditions of resonance on difference frequency is investigated. It is shown that this resonance has powerful determined nonlinear character because it arises only by enough large excitation level. It is shown that the further increasing of resonance amplitude by the increasing the excitation level is realized by the low which is near to quadratic. But after this increasing when excitation level reaches determined value the resonance amplitude is saturated and remains constant. It is drawn attention to some discrepancy between the realization on nonlinearity by magnetic and elastic systems. For the de-scription of this discrepancy the empirical quadratic dependence is proposed. In brief is proposed some remarks about further development of work.

Nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies. Part 3. Variation of plate thickness

The task about nonlinear excitation of hypersound vibrations in ferrite plate in conditions of combine influence in two frequencies is investigated. As a most important parameter which is varied it is proposed the relative thickness of plate which is determined as relation of real thickness to the thickness which correspond to elastic resonance on the difference of excitation frequencies. It is established the necessity of choosing of character value of constant field which is determined by enough effective excitation of elastic vibrations. The system of nonlinear equations of motion of magnetization and elastic displacement is described. For solving of this system, the numerical Rounge-Cutta method is applied. The results of this calculation are the time-evolvent of vibrations, dependencies magnetic end elastic vibrations amplitudes and the spectra of vibrations in permanent conditions after end of relaxation processes. It is found the multi-regime character of elastic vibrations which takes place by variation of plate thickness. In the character of development of elastic vibrations in time by the increasing of plate thickness it is found four regimes: regime №1 – regular beatings, regime №2 – established resonance, regime №3 – displacement of center of established vibrations, regime №4 – gigantic oscillations. The intervals of thickness values which are necessary, or realization of these regimes are determined. The properties of each regimes taken separately are investigated. It is found that the regime №1 is realized when the thickness of plate is more less then the thickness of resonance on differential frequency. In this case the elastic vibrations in generally repeats the vibrations of magnetization which are realized as beating between two frequencies of excitation. The regime №2 takes place when the plate thickness is near to resonance on differential frequency. When thickness is corresponds to resonance on differential frequency it is found large raising of resonance character. In the vibrations of elastic displacement, the constant component is discovered. The regime №3 takes place when the plate thickness is exceeded of resonance on several (from two to seven) times. The vibrations of magnetization in this regime are the same as in regimes №1 and №2. The elastic displacement has two components: oscillatory on differential frequency and constant which value by increasing of thickness smoothly is increased. The displacement of center of oscillatory component by thickness is increased has quadratic character. The regime №4 takes place by plate thickness exceeds resonance thickness on the order and more. The vibrations of magnetization maintain the character of beating which are the same as in regimes №1, №2 and №3. The vibrations of elastic displacement are characterized by extremely large amplitude which is more then the amplitude in regime №3 on order and more and has extremely large period which is more then period of differential frequency vibrations on two-three order and more. The amplitude of vibrations and its period by the thickness is increases also increase by linear meaning. The some quality opinions about the nature of observed phenomena are proposed. It is established the specific character of two-frequency excitation in comparison to single-frequency excitation. As the possible task it is proposed the plan of singing the part of solution as dependence of vibration amplitude from plate thickness has quadratic character with necessary appreciation of two-frequency excitation. The mechanical analogy for vibrations of hard rod which is compressed on both ends by approaching forces is proposed. This analogy allows to interpret the displacement of vibrations center and gigantic oscillations regime.