**4. Results and Discussion**

At a frequency of 60 Hz and the angle of off-center block *θ* = 20◦ (amplitude of 0.53 mm), the density of samples cut from the lower part of an ingot increases in comparison with the density obtained at 50 Hz (Table 2).

° Increasing the density of samples may be linked to the facilitated gas (hydrogen) release during melt vibration that decreases gas and shrinkage porosity [5,28]. A further increase in the vibration frequency up to 80 Hz leads to a decrease in the density of an ingot. A similar trend is observed at the angle of off-center block *θ* = 10◦ (amplitude of 0.38 mm), i.e., the increased frequency 80 Hz slightly reduces the density of the samples.

These measurements correlate well with the modeling (Figure 5a): the integral of mechanical stresses increases with the vibration frequency up to 60 Hz and then slightly decreases to 80 Hz. This is due to the reduction in the solidification time with increasing frequency as a result of intensified thermal processes in the melt, which consequently reduces the effective time of vibration and for degassing.

The observation of the macrostructure of the obtained A356 ingots without (Figure 7a) and with vibration (Figure 7b) shows that vibration processing (frequency of 60 Hz and amplitude of 0.5 mm) leads to a significant grain refinement.


**Table 2.** Measurements of the density of A356 aluminum alloy.

**Figure 7.** Macrostructure of an A356 ingot: (**a**) obtained without vibration; (**b**) obtained with vibration during solidification (frequency of 60 Hz and amplitude of 0.5 mm).

The microstructures of the A356 alloy samples (Figure 8) show that significant structural changes occurred during the vibration. The average grain size reduces from 208 μm in the alloy produced without vibration to 89 μm for the alloy cast with vibration (Figure 9).

**Figure 8.** Microstructure of an A356 aluminum alloy: (**a**) without vibration; (**b**) after vibration during solidification (frequency of 60 Hz and amplitude of 0.5 mm).

**Figure 9.** Grain size distribution in an A356 aluminum alloy (**a**) without vibration and (**b**) after vibration during solidification (frequency of 60 Hz and amplitude of 0.5 mm).

Based on the obtained experimental and theoretical results, we can conclude that the optimal frequency for vibration processing for the given mold geometry and the range of parameters is 60 Hz. The calculations also showed that the higher the amplitude, the better the result of the treatment. The experimental study showed a similar trend with the maximum density of the samples obtained at the highest amplitude used (0.53 mm, angle of 20◦).

The improvement of the structure in the castings obtained with vibration is related to intensive heat transfer in the melt. The vibration energy is spent on the fragmentation of dendritic branches, and this process results in grain multiplication. The alloy structure obtained by vibration shows the presence of very small grains (Figure 8b) which represent preserved dendrite fragments.

Mechanical testing of the as-cast A356 aluminum alloy shows that yield strength σ0.2 increases from 67 ± 6 to 121 ± 7 MPa after vibration of the melt with a frequency of 60 Hz and an amplitude of 0.53 mm compared to the sample without vibration. This result can be associated with the decrease in the grain size and porosity and the increased density of the samples. Meanwhile, the tensile strength remains unchanged at the level σ<sup>B</sup> = 182 ± 7 MPa and the elongation δ remains at the level δ = 3.4 ± 0.2% (Table 3, Figure 10).


**Table 3.** Mechanical testing of A356 aluminum alloy.

**Figure 10.** Stress-strain diagrams of the A356 aluminum alloy without vibration and after vibration during solidification (frequency of 60 Hz and amplitude of 0.5 mm).

Our results agree well with the work of Murakami et al. [17] who studied the effect of vibration frequency, acceleration amplitude, velocity amplitude, and displacement amplitude on the size and shape of the grains in an JIS AC4CH aluminum alloy (A356 analog). They used the frequencies of 10, 20, 50,100,150 and 200 Hz and found that the smallest grains (132 μm) were obtained at a frequency of 50 Hz and an amplitude of 0.49 mm, which is close to our result. However, their work did not cover the frequency range of our interest, i.e., 50 to 80 Hz.

It is important to note that in the frequency range 50–80 Hz and amplitudes up to 1 mm there are no conditions for cavitation and turbulent fluid flow [15]. At the same time, there are no conditions for entrapment of atmospheric gases and oxide films, which leads to extremely undesirable porosity in the ingot. When implementing more intensive and high-frequency process conditions, both the positive effects of turbulence and cavitation (better mixing, higher stresses, efficient degassing) and the negative ones (entrapment of gases and oxides leading to pores and cavities in the metal) should be considered.
