The Role of Acoustic Pressure during Solidiﬁcation of AlSi7Mg Alloy in Sand Mold Casting

: New alloy processes have been developed and casting techniques are continuously evolving. Such constant development implies a consequent development and optimization of melt processing and treatment. The present work proposes a method for studying the inﬂuence of acoustic pressure in the overall reﬁnement of sand cast aluminum alloys, using and correlating experimental and numerical approaches. It is shown that the reﬁnement / modiﬁcation of the α -Al matrix is a consequence of the acoustic activation caused in the liquid metal directly below the face of the acoustic radiator. Near the feeder, there is a clear homogeneity in the morphology of the α -Al with respect to grain size and grain circularity. However, the damping of acoustic pressure as the melt is moved away from the feeder increases and the inﬂuence of ultrasound is reduced, even though the higher cooling rate seems to compensate for this e ﬀ ect.

In the last decade, we have witnessed the development of highly efficient aluminum melt treatment techniques based on the use of acoustic energy [15][16][17][18][19]. The influence of ultrasound on the refinement/modification of the microstructure is based on physical phenomena due to the high acoustic intensity propagated through the liquid metal [17]. Two mechanisms have been proposed to explain the refinement of microstructures by ultrasound, dendritic fragmentation and cavitation induced heterogeneous nucleation [20,21]. However, the mechanism of heterogeneous nucleation induced by cavitation seems to be the most valid hypothesis, being supported by the majority of researchers who have worked in this field [22]. However, in order for this technique to be efficient, it is imperative that the ultrasonic system is correctly designed according to the specific needs of the casting process. This enhances the overall success of the technique and optimizes the casting component integrity.
For that purpose, the present work aimed to study the interaction between the requirements imposed by the melt conditions (i.e., the melt temperature/volume) and the constraints imposed by the manufacturing process (geometry of casting) in the optimization of an ultrasonic system and its impact on the overall microstructures [23]. Furthermore, considering their physical processing, a numerical model was used to investigate the associated acoustic pressure fields developed in the transmission medium and their role in the grain refinement.

Experimental Setup and Procedure
The excellent castability and ductility, combined with a reduced tendency to defect formation, have been crucial factors in increasing the application of AlSi7Mg based alloys in the production of structural castings cast by sand molding [24,25]. The mechanical properties of such castings can be improved by solubilizing and aging treatments, providing uniform distribution of Mg and Si precipitates in the aluminum matrix [26,27].
The melt charges used in this work were prepared from an AlSi7Mg0.3 alloy, with the composition presented in Table 1.  (2) (1) According to Aluminum Association, Inc. (2) Composition of the alloy used in the experimental work.
Melting charges weighing 10 kg were previously cut from a primary melt commercial ingot and later washed and dried to eliminate the cutting lubricant. After melting and overheating at the pre-established testing temperature (720 ± 5 • C), the melt was kept isothermal for a 30 min period for better homogenization. After this period, the melt was degassed for 5 min using ultrasound technology. The 5-minute period and the operational parameters were chosen according to works previously published by the authors [28]. After degassing, the melt was allowed to cool and was poured at 700 ± 5 • C into a sand mold, as shown in Figure 1. Immediately after pouring, the pre-heated acoustic radiator was positioned over the feeder with an immersion depth of 15 mm in the melt, to ensure the maximum transfer of acoustic energy to the melt from the thick zone (feeder) to the thin areas of the casting. Acoustic energy was supplied until the metal reached the solidus temperature +10 • C. Samples for microstructure characterization were taken from every cast sample by sectioning them perpendicularly to their vertical and horizontal axis (respectively, V#1 to V#3 and H#1 to H#3), according to Figure 1b. They were ground using 1200 μm SiC and polished down to 1 μm. An optical microscope (OM) (LEICA DM 2500M) and the ImageJ v1.46 computer application were used to determine the average grain size, d, and circularity, Rn, using Equations (1) and (2) where A corresponds to the area and P to the perimeter of the α-grains.

Computational Modeling
In order to study the acoustic propagation in liquid metal, a simulation model was developed using the COMSOL v5.2a Multiphysics module-Acoustic Piezoeloectric Interaction, Frequency Domain, according to Figure 2. Considering that the acoustic wave propagation is linear, and the shear stresses are negligible for fluids, the acoustic pressure can be calculated by applying the following wave equation [6,7]: where ρ is the density of the liquid metal, c is the sound velocity in the liquid metal and t is time. For the case of a harmonic wave in time, the pressure varies according to: where, ω = 2πf is the angular frequency and p is the acoustic pressure. Assuming that the same harmonic is time dependent, in the same terms, Equation (3) can be reduced, through Equation (4), to the Helmholtz equation: Samples for microstructure characterization were taken from every cast sample by sectioning them perpendicularly to their vertical and horizontal axis (respectively, V#1 to V#3 and H#1 to H#3), according to Figure 1b. They were ground using 1200 µm SiC and polished down to 1 µm. An optical microscope (OM) (LEICA DM 2500M) and the ImageJ v1.46 computer application were used to determine the average grain size, d, and circularity, R n , using Equations (1) and (2) where A corresponds to the area and P to the perimeter of the α-grains.

Computational Modeling
In order to study the acoustic propagation in liquid metal, a simulation model was developed using the COMSOL v5.2a Multiphysics module-Acoustic Piezoeloectric Interaction, Frequency Domain, according to Figure 2. Considering that the acoustic wave propagation is linear, and the shear stresses are negligible for fluids, the acoustic pressure can be calculated by applying the following wave equation [6,7]: where ρ is the density of the liquid metal, c is the sound velocity in the liquid metal and t is time.
For the case of a harmonic wave in time, the pressure varies according to: where, ω = 2πf is the angular frequency and p is the acoustic pressure. Assuming that the same harmonic is time dependent, in the same terms, Equation (3) can be reduced, through Equation (4), to the Helmholtz equation: The Acoustic Piezoeloectric Interaction module in COMSOL Multiphysics was used to perform an analysis in the frequency domain. This combines the effects of (i) sound pressure and (ii) piezoelectric, linking the variations of acoustic pressure with the solids that are actuated by the piezoelectric effect of PZT. The physical interface also includes electrostatic elements to solve the electric field in the piezoelectric material. The Helmholtz equation is solved in the fluid domain and the structural equations in the solid domain, together with the constructive relations necessary for the piezoelectric modeling. The physical interface that solves the Helmholtz equation is suitable for the present study, in the domain of linear frequencies with harmonic variation of the pressure field.
In order to evaluate the profile of the acoustic pressure during the deformation of the solids actuated by the PZT piezoelectric effect, water was used since this is a suitable liquid medium to simulate the refinement / modification mechanism that occurs in melts of aluminum alloys at 660-700 °C [29]. With the appropriate boundary conditions, the Helmholtz equation can be solved through a range of numerical methods [6,8]. The accuracy of the numerical solution of the Helmholtz equation depends significantly on the wave number k(k = ω/c). The main boundary conditions are described as, (i) p = 0 (condition of total waves reflection, attributed to the liquid-air interfaces); (ii) p = p0 (interface of the acoustic radiator with the liquid metal); (iii) δp/δn = 0 (condition of "rigid walls" attributed to the lateral walls of the acoustic radiator); (iv) (1/ρ)(δp/δn) + iωp/Z = 0 (acoustic impedance limit condition Z attributed to the container walls).

Results and Discussion
Aluminum alloys are known for their high affinity to hydrogen at high temperature, promoting the appearance of numerous inclusions in the microstructure after solidification, with porosity being the most relevant and harmful defect compromising the strength of the component [4,30,31]. To assess the similarity of the porosity levels in samples, the melts were degassed before pouring at the desired temperature (700 ± 5 °C [31]), using the Multi-Mode Frequency, Modulated (MMM) ultrasonic technology, to ensure that the density of the bath was identical for every experiment. The average density reached in the experiments was 2.68 ± 0.1 (0.5% ± 0.07 porosity). Figure 3 shows the variation of the α-Al grain size and circularity of AlSi7Mg0.3 alloy processed by ultrasound, with an average frequency of 19.9 ± 0.2 kHz and 40% of the system power (400 W- The Acoustic Piezoeloectric Interaction module in COMSOL Multiphysics was used to perform an analysis in the frequency domain. This combines the effects of (i) sound pressure and (ii) piezoelectric, linking the variations of acoustic pressure with the solids that are actuated by the piezoelectric effect of PZT. The physical interface also includes electrostatic elements to solve the electric field in the piezoelectric material. The Helmholtz equation is solved in the fluid domain and the structural equations in the solid domain, together with the constructive relations necessary for the piezoelectric modeling. The physical interface that solves the Helmholtz equation is suitable for the present study, in the domain of linear frequencies with harmonic variation of the pressure field.
In order to evaluate the profile of the acoustic pressure during the deformation of the solids actuated by the PZT piezoelectric effect, water was used since this is a suitable liquid medium to simulate the refinement / modification mechanism that occurs in melts of aluminum alloys at 660-700 • C [29]. With the appropriate boundary conditions, the Helmholtz equation can be solved through a range of numerical methods [6,8]. The accuracy of the numerical solution of the Helmholtz equation depends significantly on the wave number k(k = ω/c). The main boundary conditions are described as, (i) p = 0 (condition of total waves reflection, attributed to the liquid-air interfaces); (ii) p = p 0 (interface of the acoustic radiator with the liquid metal); (iii) δp/δn = 0 (condition of "rigid walls" attributed to the lateral walls of the acoustic radiator); (iv) (1/ρ)(δp/δn) + iωp/Z = 0 (acoustic impedance limit condition Z attributed to the container walls).

Results and Discussion
Aluminum alloys are known for their high affinity to hydrogen at high temperature, promoting the appearance of numerous inclusions in the microstructure after solidification, with porosity being the most relevant and harmful defect compromising the strength of the component [4,30,31]. To assess the similarity of the porosity levels in samples, the melts were degassed before pouring at the desired temperature (700 ± 5 • C [31]), using the Multi-Mode Frequency, Modulated (MMM) ultrasonic technology, to ensure that the density of the bath was identical for every experiment. The average density reached in the experiments was 2.68 ± 0.1 (0.5% ± 0.07 porosity). Figure 3 shows the variation of the α-Al grain size and circularity of AlSi7Mg0.3 alloy processed by ultrasound, with an average frequency of 19.9 ± 0.2 kHz and 40% of the system power   The experimental results suggest that the feeder (central zone of the feeder and directly below the acoustic radiator) presents a microstructure with a well-defined globular morphology. Overall, the variation of grain size and circularity apparent was minimal, as can confirmed by the standard deviations presented in Figure 3. Indeed, the average grain size and circularity for all characterized positions were, respectively, 120 μm and 0.8. As demonstrated by Puga et al. [32] and Eskin et al. [29]    The experimental results suggest that the feeder (central zone of the feeder and directly below the acoustic radiator) presents a microstructure with a well-defined globular morphology. Overall, the variation of grain size and circularity apparent was minimal, as can confirmed by the standard deviations presented in Figure 3. Indeed, the average grain size and circularity for all characterized positions were, respectively, 120 μm and 0.8. As demonstrated by Puga et al. [32] and Eskin et al. [29]  The experimental results suggest that the feeder (central zone of the feeder and directly below the acoustic radiator) presents a microstructure with a well-defined globular morphology. Overall, the variation of grain size and circularity apparent was minimal, as can confirmed by the standard deviations presented in Figure 3. Indeed, the average grain size and circularity for all characterized positions were, respectively, 120 µm and 0.8. As demonstrated by Puga et al. [32] and Eskin et al. [29] the zone below the flat acoustic radiator is able to promote extremely intense cavitation, being able to promote nucleation and further to this, an increase in the quantity of α-Al grains, and consequently, the reduction of their diameter and a globular morphology. Figure 5 shows the variation of the α-Al grain size and circularity of AlSi7Mg0.3 alloy processed by ultrasound, at the average frequency of 19.9 ± 0.2 kHz (resonance frequency at high temperature), with the distance to the acoustic radiator in the feeder (H#1 to H#3 samples, according to Figure 1). The respective microstructures are shown in Figure 6a the zone below the flat acoustic radiator is able to promote extremely intense cavitation, being able to promote nucleation and further to this, an increase in the quantity of α-Al grains, and consequently, the reduction of their diameter and a globular morphology. Figure 5 shows the variation of the α-Al grain size and circularity of AlSi7Mg0.3 alloy processed by ultrasound, at the average frequency of 19.9 ± 0.2 kHz (resonance frequency at high temperature), with the distance to the acoustic radiator in the feeder (H#1 to H#3 samples, according to Figure 1). The respective microstructures are shown in Figure 6a-c.    the zone below the flat acoustic radiator is able to promote extremely intense cavitation, being able to promote nucleation and further to this, an increase in the quantity of α-Al grains, and consequently, the reduction of their diameter and a globular morphology. Figure 5 shows the variation of the α-Al grain size and circularity of AlSi7Mg0.3 alloy processed by ultrasound, at the average frequency of 19.9 ± 0.2 kHz (resonance frequency at high temperature), with the distance to the acoustic radiator in the feeder (H#1 to H#3 samples, according to Figure 1). The respective microstructures are shown in Figure 6a-c.   The results presented suggest that with increasing distance to the acoustic radiator the α-Al grain size tends to increase, and the grain circularity tends to decrease. Although the grain size tends to increase, the matrix continues to present a quasi-globular morphology with some indications of rosette grains. This is an opposite tendency compared to what happens with the traditional processes of sand casting, where the matrix tends to present a dendritic morphology, even after chemical melt treatments.
Furthermore, the results presented in Figures 5 and 6 suggest that the cooling rate influences the grain morphology. Although the effect of ultrasound promotes a globular matrix, the fast cooling rates in thinner sections (e.g., position H#3 with a section solidification module 0.41) tends to overlap the effect of ultrasound. However, this effect also allows the formation of a thinner but non-dendritic microstructure, which is beneficial for the mechanical properties. However, in sections directly affected by the acoustic radiator (e.g., feeder- Figures 3 and 4), it is suggested that the morphology of the Al matrix (grain size and circularity) may be directly affected by the cavitation mechanism.
Contrary to the traditional process of refinement, where the addition of the master alloy Al-Ti-B is generally used, in the present approach this issue is not considered. Overall, the applied acoustic intensity is sufficient for: (i) converting the displacement of piezoelectric into kinetic energy in the liquid; (ii) creating acoustic cavitation and acoustic streams able to promote the nucleation and homogenization in the melt; (iii) increasing the temperature of the medium due to bubble collapse, which can promote and accelerate the α-Al grains.
A numerical simulation study was performed to validate the aforementioned hypothesis and experimental results. Figure 7 presents the numerical results of the axial displacement (evaluated in solid parts and the acoustic pressure in the melt), for the whole system, when the acoustic radiator was immersed in water at a depth of 15 mm, according to the boundary conditions represented in Figure 2. The results presented suggest that with increasing distance to the acoustic radiator the α-Al grain size tends to increase, and the grain circularity tends to decrease. Although the grain size tends to increase, the matrix continues to present a quasi-globular morphology with some indications of rosette grains. This is an opposite tendency compared to what happens with the traditional processes of sand casting, where the matrix tends to present a dendritic morphology, even after chemical melt treatments.
Furthermore, the results presented in Figures 5 and 6 suggest that the cooling rate influences the grain morphology. Although the effect of ultrasound promotes a globular matrix, the fast cooling rates in thinner sections (e.g., position H#3 with a section solidification module 0.41) tends to overlap the effect of ultrasound. However, this effect also allows the formation of a thinner but non-dendritic microstructure, which is beneficial for the mechanical properties. However, in sections directly affected by the acoustic radiator (e.g., feeder- Figures 3 and 4), it is suggested that the morphology of the Al matrix (grain size and circularity) may be directly affected by the cavitation mechanism.
Contrary to the traditional process of refinement, where the addition of the master alloy Al-Ti-B is generally used, in the present approach this issue is not considered. Overall, the applied acoustic intensity is sufficient for: (i) converting the displacement of piezoelectric into kinetic energy in the liquid; (ii) creating acoustic cavitation and acoustic streams able to promote the nucleation and homogenization in the melt; (iii) increasing the temperature of the medium due to bubble collapse, which can promote and accelerate the α-Al grains.
A numerical simulation study was performed to validate the aforementioned hypothesis and experimental results. Figure 7 presents the numerical results of the axial displacement (evaluated in solid parts and the acoustic pressure in the melt), for the whole system, when the acoustic radiator was immersed in water at a depth of 15 mm, according to the boundary conditions represented in Figure 2. According to the eigenfrequency results of the acoustic radiator, the first longitudinal compression mode was located at 20.23 kHz. This matches well with the operation frequency of the transducer, as can be proved by the experimental electrical impedance results measured by the authors. Thus, in order to numerically quantify the acoustic pressure in the medium, a domain frequency study was performed at f0 = 20.20 kHz. Figure 8a,b presents the numerical values of acoustic pressure along the horizontal section with the distance to the acoustic radiator in the feeder (H#1 to H#2) and the vertical component beneath the feeder (V#1 to V#3). According to the eigenfrequency results of the acoustic radiator, the first longitudinal compression mode was located at 20.23 kHz. This matches well with the operation frequency of the transducer, as can be proved by the experimental electrical impedance results measured by the authors. Thus, in order to numerically quantify the acoustic pressure in the medium, a domain frequency study was performed at f 0 = 20.20 kHz. Figure 8a,b presents the numerical values of acoustic pressure along the horizontal section with the distance to the acoustic radiator in the feeder (H#1 to H#2) and the vertical component beneath the feeder (V#1 to V#3). As can be observed in Figure 8a, a sinusoidal curve with a positive and negative acoustic pressure of at least 5 MPa in the vertical component is reached in the melt. According to Eskin's work [29] the threshold of acoustic pressure to verify cavitation is around 2 MPa. Indeed, according to experimental results for parameters numerically evaluated, the level of cavitation and acoustic streams at 40% system power (using the same acoustic radiator that numerically simulated) is totally defined, as can be observed in Figure 9. It may be clearly observed that in corresponding conditions (i.e., similar fluid and boundary conditions) that are initially resting (Figure 9a), it is possible to promote streaming and cavitation effects by the use of the detailed ultrasonic system. Contrary to high values of acoustic pressure measured along the longitudinal section of the feeder (V#1 to V#3), in the horizontal cylindrical section (H#1 to H#2) the maximum acoustic pressure registered was 1 MPa (Figure 8b). Considering the high level of cavitation and acoustic streams created below the flat surface of the acoustic radiator, as well as the long interval time of solidification, it is suggested that a mixing and distribution of nuclei can travel along the cylindrical shape and contribute to the refining of Al grain reported in results of Figures 5 and 6. Furthermore, according to Figure 10, there is a correlation between the acoustic pressure and the grain size. It is shown that as the pressure increases, the grain size tends to decrease by an exponential decay function. As can be observed in Figure 8a, a sinusoidal curve with a positive and negative acoustic pressure of at least 5 MPa in the vertical component is reached in the melt. According to Eskin's work [29] the threshold of acoustic pressure to verify cavitation is around 2 MPa. Indeed, according to experimental results for parameters numerically evaluated, the level of cavitation and acoustic streams at 40% system power (using the same acoustic radiator that numerically simulated) is totally defined, as can be observed in Figure 9. It may be clearly observed that in corresponding conditions (i.e., similar fluid and boundary conditions) that are initially resting (Figure 9a), it is possible to promote streaming and cavitation effects by the use of the detailed ultrasonic system. As can be observed in Figure 8a, a sinusoidal curve with a positive and negative acoustic pressure of at least 5 MPa in the vertical component is reached in the melt. According to Eskin's work [29] the threshold of acoustic pressure to verify cavitation is around 2 MPa. Indeed, according to experimental results for parameters numerically evaluated, the level of cavitation and acoustic streams at 40% system power (using the same acoustic radiator that numerically simulated) is totally defined, as can be observed in Figure 9. It may be clearly observed that in corresponding conditions (i.e., similar fluid and boundary conditions) that are initially resting (Figure 9a), it is possible to promote streaming and cavitation effects by the use of the detailed ultrasonic system. Contrary to high values of acoustic pressure measured along the longitudinal section of the feeder (V#1 to V#3), in the horizontal cylindrical section (H#1 to H#2) the maximum acoustic pressure registered was 1 MPa (Figure 8b). Considering the high level of cavitation and acoustic streams created below the flat surface of the acoustic radiator, as well as the long interval time of solidification, it is suggested that a mixing and distribution of nuclei can travel along the cylindrical shape and contribute to the refining of Al grain reported in results of Figures 5 and 6. Furthermore, according to Figure 10, there is a correlation between the acoustic pressure and the grain size. It is shown that as the pressure increases, the grain size tends to decrease by an exponential decay function. Contrary to high values of acoustic pressure measured along the longitudinal section of the feeder (V#1 to V#3), in the horizontal cylindrical section (H#1 to H#2) the maximum acoustic pressure registered was 1 MPa (Figure 8b). Considering the high level of cavitation and acoustic streams created below the flat surface of the acoustic radiator, as well as the long interval time of solidification, it is suggested that a mixing and distribution of nuclei can travel along the cylindrical shape and contribute to the refining of Al grain reported in results of Figures 5 and 6. Furthermore, according to Figure 10, there is a correlation between the acoustic pressure and the grain size. It is shown that as the pressure increases, the grain size tends to decrease by an exponential decay function.