OBRABOTKAMETALLOV Vol. 24 No. 2 2022 TECHNOLOGY Introducing vibrations into the system increases its free energy that characterizes the conversion of molten components from a liquid to a solid phase [28]. The total change in Gibbs energy ∆Gtot will be as follows: tot us, G S V G E where S is the total surface area of crystals, σ is the surface tension between the liquid metal and crystal, V is the nucleus volume, ΔG is the difference of Gibbs energy of metal in liquid and solid states, Eus is the energy of introduced ultrasonic vibrations. Eus means the kinetic energy imparted to the formed crystallization nuclei: 2 2 us (2 ) , 2 m m f E where m is the nuclei weight, f is the vibration frequency, and m is the vibration amplitude. As a result of a change in the energy balance, the work required for the formation of a stable nucleus increases, which leads to a decrease in the crystallization start temperature. The highest effect in the structural formation when applying vibrations is caused by cavitation, which includes the formation, growth, and collapse of bubbles, which is accompanied by an increase in pressure and temperature, the instantaneous values of which can reach several hundred MPa and several thousand degrees [29–37]. Shock waves and cumulative jets associated with that process disperse the formed nuclei. First of all, dendrites are fragmentized since they are the fi rst to start growing from the fusion boundary, which in this case is a surface that emits vibrations. Dispersed particles of dendrites will be new crystallization nuclei that will grow and then will be broken by cavitation. Acoustic streams occurring in the processed melt improve heat and weight transfer in the melt before crystallization begins. After the fragmentation of dendrites, the fl ows distribute new nuclei over the molten pool, some of which go into the active cavitation zone and are dispersed once again. Since all molten components in both liquid and solid phases move due to vibrations, acoustic streams, shock waves and cumulative jets, more complex conditions are created for the attachment of liquid phase atoms to nuclei. The weld crystallization process when applying vibrations can be schematically shown as follows (Fig. 8). Zone I: when the metal crystallizing without vibrations is cooled to the liquidus point Tliq, the fi rst dendrites start to grow. When applying vibrations, nuclei formation is not yet started due to an increase in the Gibbs energy. Cavitation and acoustic streams contribute to the uniform mixing of molten components in the liquid phase. Fig. 8. Crystallization scheme of the weld
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