Investigation of the Hydrostatic Pressure Effect on the Formation of Hot Tearing in the AA6111 Alloy During Direct Chill Casting of Rectangular Ingots

Abstract

The formation of hot tearing during direct chill casting of aluminum alloys, specifically AA6111, is a significant challenge in the production of ingots for industrial applications. This study investigates the role of hydrostatic pressure and tensile stress in the formation of hot tearing during direct chill casting of rectangular ingots. Combining experimental results and finite element modeling with ABAQUS/CAE 2022, the mechanical behavior of the semi-solid AA6111 alloy was analyzed under different cooling conditions. “Hot” (low water flow) and “Cold” (high water flow) conditions were the two types of cooling conditions that produced cracked and sound ingots, respectively. The outcomes indicate that high tensile stress and localized negative hydrostatic pressure in the hot condition are the main factors promoting the initiation and propagation of cracks in the mushy zone, whereas the improvement of the cooling conditions reduces these defects.

1. Introduction

1.1. The Direct Chill Casting Process

The semi-continuous direct chill (DC) casting method was introduced in 1935 to produce large aluminum ingots for rolling, extrusion, and forging applications. Since its inception, numerous improvements have been made to enhance both the quality and production speed of these ingots [1,2,3,4,5,6,7].

Figure 1 illustrates a schematic diagram of a typical DC casting process and some details about the heat transfer from the ingot. Initially, a bottom block is placed inside the water-cooled mold, and liquid metal is poured into the open mold from the top. Once the liquid metal reaches a certain height and the solid shell has achieved sufficient strength to support the liquid pool, the bottom block is lowered into a pit with a velocity referred to as the casting speed. Molten metal is continuously fed into the mold from the top. As the partially solidified ingot comes out of the mold, water spray directly contacts the cast surface.

During the operation, heat transfer occurs in direct chill casting through several mechanisms. Initially, heat is transferred from the liquid metal to the mold, which is known as primary cooling. Subsequently, heat is further transferred from the ingot surface to the water in contact with it, referred to as secondary cooling. During the start-up phase of the casting process, there is an additional mechanism of heat transport between the base of the ingot and the bottom block [8]. Typically, approximately 80 percent of the heat is removed through secondary cooling during steady-state operation [6]. Due to demands on lightweight construction and energy efficiency in the transportation industry, the utilization of aluminum alloys, especially 6xxx DC casting alloys, is on the rise. The industrial selection of 6xxx alloys is related to the high strength/weight ratio, good corrosion resistance, and reasonable formability of these alloys [9].

Among 6xxx series alloys, AA6111 alloys are widely used in the automotive industry as body sheets for the vehicle, as well as in structural applications. The main alloying elements present in AA6111 alloys include Mg, Si, Cu, and Mn. Given the multi-component nature of alloying elements, AA6111 alloys exhibit a large solidification interval, leading to the formation of as-cast microstructures with different intermetallic phases during solidification. As a result, these alloys are highly prone to hot tearing during DC casting.

1.2. Hot Tearing in DC Casting

The formation of hot tearing is one of the most important challenges in the DC casting process. This defect is caused by the limited ability of the mushy zone to be healed during the deformation when only a small fraction of the liquid phase is present in the semi-solid mush. These cracks have significant implications for the quality of products and lead to the rejection of the ingot [10]. Managing the thermal cooling conditions during the DC casting process for aluminum sheet ingots is a complex task. Understanding the mechanisms and the required conditions for hot-tearing formation is important for industrial-scale production, but it has not been well-established yet for some hot-tearing-prone alloys. Some investigations have shown that hot tearing and porosity originate from the same cause, but hot tearing additionally necessitates tensile deformation in the mushy zone [11,12]. Other research indicates that hot tears initiate from pores, while others show that hot tearing and porosity are interrelated. As a result, reducing and controlling the formation of porosity considerably improves the ductility of semi-solid materials [13].

The most important processing parameters that influence the tendency for hot tearing are casting speed, casting temperature, and cooling water flow rate [14]. These factors affect melt flow and the cooling conditions of the ingot, which in turn impact the stresses caused by thermal contraction and solidification shrinkage. Researchers generally agree that in aluminum alloys, a higher melt temperature increases the thermal gradient during solidification, leading to the formation of columnar dendritic grains that are more prone to hot tearing compared to equiaxed globular grains [4,14]. Faster casting speeds result in a higher solidification rate and a deeper mushy zone, both of which raise the risk of hot tearing [4]. Additionally, a high cooling water flow rate can create uneven thermal contraction, causing the surface to cool faster than the center, which leads to stress and strain accumulation and ultimately contributes to hot tearing [4,15].

Various criteria for predicting hot tearing have been established [16]. These criteria are based on factors such as strain, strain rate, alloy composition, and solidification conditions [13,17]. One well-studied criterion, based on strain rate, is called the RDG (Rappaz–Drezet–Gremaud) criterion [11]. The RDG criterion focuses on how liquid metal flows between dendrites in the mushy zone. As the solid network becomes more interconnected deeper in the mush, feeding becomes challenging, and the risk of hot tears increases. A critical factor in hot tear development is the liquid pressure drop, which is the difference between metallostatic and local pressures in the mush. Hot tears form if the local pressure falls below the cavitation pressure. Both solid shrinkage and deformation contribute to this pressure drop, which is calculated using a mass balance over the mushy region [11,18].

1.3. Mathematical Simulations of DC Casting

Modeling of DC casting to investigate the formation of hot tearing has been the focus of researchers for decades. More investigations were done on round billets [13,19,20,21]. Suyitno [4] carried out a comprehensive study on hot tearing formation in the direct chill (DC) casting of aluminum alloys. The author used finite element modeling to simulate what happens in the mushy zone during casting. These simulations helped predict the stresses, strains, and temperature changes that are important for understanding when hot tearing happens. The findings showed that the highest stresses and strains occur at the center of the round cast billet. Some other researchers investigated rectangular ingots. As a result of the rectangular shape, the stresses and thus hot tearing concentrate on the ingot’s surface [2,22]. Sengupta et al. [23] developed a mathematical model to analyze heat transfer during the start-up phase of the DC casting process on rectangular aluminum ingots. In this study, they noted how water intrusion impacted heat transfer efficiency and focused on improving casting parameters during the start-up phase of DC casting. Their model results matched well with the experimental data from AA5182 direct chill ingots. Larouche et al. [24] investigated the tensile deformation of the Al-4.5 pct Cu aluminum alloy during solidification using a direct chill surface simulator (DCSS). They developed a constitutive model, focusing on grain boundary sliding as a key deformation mechanism. The model includes variables such as solid fraction and channel thickness, which are suitable for predicting the tensile behavior of semi-solid microstructures and addressing hot tearing during solidification.

Also, in recent years, some researchers have developed models to specifically predict hot tearing during DC casting [25,26]. Khodaei et al. [15] developed a multi-scale modeling approach to investigate hot tearing in the DC casting of aluminum alloys AA5182 and AA3104. They combined a macro-scale thermomechanical model with a meso-scale granular model. Their results revealed how casting speed, thermal gradients, and feeding coefficients affected hot tearing susceptibility. They accurately predicted hot tearing initiation, growth, and propagation in the mushy zone. Chen et al. [13] conducted a 2D model to predict the hot tearing susceptibility of the AA6111 alloy during the round DC casting of billets. The results showed that higher casting speeds and larger billet diameters resulted in greater hot tearing susceptibility, while better cooling conditions contributed to its reduction. Further, their study demonstrated the significance of pore fraction and its connection to the development of hot tearing. Also, some other researchers found that porosities and hot tearing are interlinked, and where there are more porosities, it is prone to form hot tearing [11,13]. In the high solid fraction, hydrostatic pressure plays a crucial role in the dynamics of the casting’s internal structure and the formation of porosities. It is calculated as the average of the normal stresses:

$$P_h=\left(S11+S22+S33\right)/3$$

(1)

where S11, S22, and S33 are the normal stress components in the X, Y, and Z directions, respectively. When the hydrostatic pressure is negative in any spot, this situation can initiate the nucleation of porosity within the casting in that spot. In this case, the remaining liquid metal may no longer be able to flow adequately into regions experiencing a pressure reduction, leading to localized shrinkage and porosity. Conversely, when the hydrostatic pressure is positive, it indicates that the pressure is directed inward, mitigating the risk of porosity formation and reducing the potential for defects like hot tearing.

1.4. Study Intent

This study focuses on modeling and analyzing the mechanical behavior of an Al AA6111 alloy during the DC casting process for rolling ingots with rectangular cross-sections. The evolution of hydrostatic pressure, stress, and strain near the solidus temperature was examined and correlated with hot tears in real DC-cast ingots. This approach provides insights into the link between casting conditions and defect formation, aiming to improve the quality of the final product.

2. Experimental Section

2.1. Materials

Two AA6111 ingots with a rectangular cross-section area of 200 mm × 600 mm and 400 mm in length were provided by the Arvida Research and Development Center of Rio Tinto Aluminum (Saguenay, QC, Canada).

Table 1. Chemical composition of AA6111 alloy used in this study (weight%).

Elements	Cu	Si	Mg	Mn	Fe	Al
	0.5	0.6	0.5	0.1	0.19	Balance

shows the chemical composition of the AA6111 alloy, as determined by optical emission spectroscopy immediately before casting. Each ingot was cast with different water flow rates, called ‘Hot’ and ‘Cold’ conditions, in which the hot condition involved lower water flow rates and the cold condition used higher water flow rates (see Figure 2). Two thermocouples were embedded into the molten metal within the ingot near the base of the casting to record metal temperatures during the DC casting process. The thermocouples were placed in the ingot adjacent to the rolling and narrow faces at heights of 170 mm above the ingot and bottom block interface and 25 mm inside the surfaces and were hauled by the solidified metal. Figure 3 illustrates the thermocouple position in the ingot.

2.2. Model Description

The model was adapted based on a previous model developed by Sengupta et al. [27]. Due to the two planes of symmetry of the ingot, only a quarter section of the ingot and the bottom block were modeled. The symmetry planes are indicated in Figure 3. To better monitor the formation of the gap between them, both objects were meshed, ensuring that the nodes at the interface were aligned. The model geometry was meshed with cuboid elements, with a size range from 1.6 mm to 20 mm. The calculation was implemented in ABAQUS/CAE 2022 using the built-in FORTRAN user subroutines. ABAQUS was selected for this analysis due to its flexibility in handling user-defined heat transfer coefficients and temperature-dependent constitutive models. A FIELD subroutine was employed to monitor the formation of the gap between the ingot and the bottom block. Also, a FILM subroutine was used to calculate the complex heat transfer coefficients between the ingot and its immediate surroundings—air, water, and the bottom block. The results were extracted from the simulation using Python scripts. The computational regions and the thermal boundary conditions are depicted in Figure 4. The initial heat loss occurs at the direct contact between the molten metal and the water-cooled mold (primary cooling, A1), and at the interface between the bottom block and the ingot (A4), which includes the effects of gap formation during casting. In area A2, the water spray hits the ingot surface, while the water, free falling is observed in area A3. The heat loss along A6 is assumed to be zero due to the symmetry of the face, and area A7 is also assumed to have zero heat loss, as new material is continuously fed into the mold. In the simulation, the bottom block and ingot are kept in a fixed position. Consequently, the thermal boundary moves upward by following changes in casting speed. A continuous flow of liquid metal is simulated by gradually activating horizontal layers of elements (see Figure 4b). The initial temperature of the liquid metal was set at 670 °C, representing the pouring temperatures of the casting of AA6111. The ambient temperature was presumed to be 25 °C.

To prevent convergence difficulties caused by rigid body motion, applying appropriate mechanical boundary conditions is crucial. As a result, the lowest node at the ingot’s center was constrained by a virtual spring to prevent any separation between the bottom block and the ingot at that surface and center. Stresses, strains, and temperatures were determined based on the position of the ingot and how much time had passed. The focus was on the early stage of the process, known as the start-up phase. This start-up stage lasted up to 350 s.

2.3. Material Properties

DC casting models necessitate the incorporation of the alloy’s specific solidification path relevant to the simulation. Precisely identifying the start and end of solidification, as well as predicting the evolution in solid fraction with temperature, are extremely important. These parameters are closely intertwined with the mechanical properties in the semi-solid state. Consequently, to achieve reliable predictions of semi-solid stress–strain behaviors, an accurate representation of the alloy’s solidification path must be included in the model.

Solid phase precipitation during solidification was calculated with a model proposed by Larouche [28], which accounts for both back-diffusion and micro-segregation. The results are shown in

Table 2. Solidification path of AA6111 alloy predicted by Larouche’s model [28].

Solidification Path	Temperature (°C)
$l\to \alpha -\mathrm{Al}+\alpha -\mathrm{Al}\left(\mathrm{Fe},\mathrm{Mn}\right)\mathrm{Si}$	620
$l\to \alpha -\mathrm{Al}+\beta -\mathrm{Al}\left(\mathrm{Fe},\mathrm{Mn}\right)\mathrm{Si}$	581.25
$l\to \alpha -\mathrm{Al}+\mathrm{Si}$	557
$l\to \alpha -\mathrm{Al}+\mathrm{Q}-$ Phase (Al5Cu2Mg8Si6)	541.75
$l\to \alpha -\mathrm{Al}+\theta -{\mathrm{Al}}_2\mathrm{Cu}$	514.5

. As can be seen, the microstructure of the AA6111 alloy consists of α-Al dendrite cells and several intermetallic phases, including primary Mg₂Si, two Fe-rich intermetallics (α-Al₁₅(Fe,Mn)₃Si₂ and β-Al₅(Fe,Mn)Si), and two Cu-bearing intermetallics (Q-Al₅Mg₈Si₆Cu₂ and θ-Al₂Cu) [29]. Figure 5 illustrates the calculated fraction solid versus temperature curve for the AA6111 alloy as predicted by [28]. The liquidus and solidus temperatures of this alloy are seen to be 652 and 510 °C, respectively.

Thermophysical properties for AA6111 alloy were extracted from references [13,30,31]. The thermophysical properties utilized in this model are provided in

Table 3. Material properties used in DC casting simulation.

Temperature (°C)	Thermal Expansion Coefficient × 10−6 (K−1) [31]	Specific Heat Capacity (J.kg−1·K−1) [13]	Thermal Conductivity (W·m−1·K−1) [13]
20	22.4147	909.2	196.8
100	23.1396	950.4	202.1
200	24.1860	999.6	204.6
300	25.2453	1044.8	204.1
400	26.3176	1090	201.7
500	27.4027	1135.2	198.1
510	27.5120	1170	197.6
550	29.4292	1217	190.1
600	32.4869	1112	177
630	38.9769	1023	151.5
660	67.8313	1003	88

. The density of the material is held constant at 2400 kg/m³ to avoid altering the mass, since the volume of the computational domain is held constant. Poisson’s ratio was considered to be 0.3.

The plastic stress data, used as input in the coupled temperature–displacement analysis to simulate the alloy’s behavior during solidification, were calculated based on the tensile test results of Qassem et al.’s work on AA6111 [29], which were obtained near the solidus temperature. The creep stress was calculated with the model proposed by Larouche et al. [24]. According to this model, when sufficient liquid is present between grains, fully lubricated sliding can occur. To apply this concept to stress, a parameter κ was used, which represents the fraction of grain boundaries where sliding does not occur. In other words, this parameter determines how much of the applied stress contributes to plastic deformation. If σ_yield is the nominal stress required to activate plastic deformation through these boundaries, then by combining a portion of the yield stress with the stresses induced by the two mechanisms, which are ${\sigma }_{creep}$ (non-lubricated) and ${\sigma }_{visc}$ (lubricated), the average stress can be expressed as follows [24]:

$$\langle \sigma \rangle =\kappa ·{\sigma }_{yield}+\left(1-\kappa \right)·\left({{\displaystyle \int }}_0^{h_{trans}}{\sigma }_{creep}\cdot {\psi }_{in}\cdot dh+{{\displaystyle \int }}_{h_{trans}}^{\infty }{\sigma }_{visc}\cdot {\psi }_{in}\cdot dh\right)$$

(2)

where h is the channel thickness between solidified particles, h_trans is the critical channel thickness, and${\psi }_{in}$ is the log-normal distribution of h. The values for σ_visc and ${\psi }_{in}$ are calculated via the following:

$${\sigma }_{visc}={\displaystyle \frac{\mu \dot{\epsilon }}{9}}\left[{\left(1-g_s^m-{\displaystyle \frac{\epsilon }{2}}\right)}^{-3}+2{\left(1-g_s^m+\epsilon \right)}^{-3}\right]$$

(3)

$${\psi }_{ln}={\displaystyle \frac{1}{h\sqrt{2\pi }·\mathit{ln}{\varphi }_g}}\exp \left[-{\displaystyle \frac{1}{2}}{\left({\displaystyle \frac{\mathit{ln}h-\mathit{ln}{h}_{med}}{\mathit{ln}{\varphi }_g}}\right)}^2\right]$$

(4)

where g_s is the solid volume fraction, m is a microstructure factor, µ is the viscosity of the liquid phase, ε is the uniaxial strain, and $\dot{\varepsilon }$ is the uniaxial strain rate. In Equation (3), ${\varphi }_g$ is the standard geometric deviation, and h_med is the median value of h. The standard geometric deviation is a key parameter in the log-normal distribution that describes the dispersion or spread of the channel thickness distribution.

The influence of temperature and strain rate on material deformation is expressed as below [30]:

$$\dot{\epsilon }=A{\left[\sinh \left(\alpha \sigma \right)\right]}^n\exp \left(-{\displaystyle \frac{Q}{RT}}\right)$$

(5)

where σ is the flow stress (MPa); T is the temperature (K); R is the gas content; Q is the thermal deformation activation energy (J.mol⁻¹); and A, n, and α are material constants. The flow stress was used to describe the non-lubricated creep behavior at high temperatures.

Table 4. Constants used in this investigation [24,30].

Constants	Value
m	1/2 for a columnar structure
µ	0.001 Pa·s
a	100 µm
Q	148,616 KJ/mol

gives the value of the constants required for these equations that were taken from the references [24,30]. Based on Equation (2) and the relevant parameters, the values of ${\varphi }_g$ and κ were adjusted to optimize the fit between the experimental results and the curve generated by the model.

Table 5. The ${\varphi }_g$, κ, and other values adjusted to fit with experimental results.

Strain Rate (s−1)	Temp (°C)	Fraction Solid	${\mathit{\varphi }}_{\mathit{g}}$	κ	Yield Stress (MPa)
0.0001	510	0.988	7	0.5	5
	535	0.971	17	0.65	5
	552	0.96	55	0.63	4
	564	0.947	27	0.75	4
0.001	535	0.971	19	0.45	6
	552	0.96	25	0.4	4
	564	0.947	15	0.45	4

shows the value of ${\varphi }_g$, κ, and σ_yield used with strain rates of 0.0001 and 0.001 s⁻¹ and temperature between 510 and 564 °C. The stress was interpolated between the pre-determined values of strain, strain rates, and temperature. Figure 6 illustrates the modeled and experimental curves at temperatures of 535 and 564 °C. The graph in Figure 7 demonstrates how the calculated flow stress changes with the plastic strain and temperature when the strain rate is 0.0001 s⁻¹. The reader is referred to [24] for a complete description of the constitutive model.

The Young’s modulus for this study was taken from the reference [31] for the solid state up to 500 °C. At higher temperatures, Young’s modulus is observed to decrease progressively, with a pronounced drop just above the solidus temperature [32]. This trend aligns well with previous research findings. Figure 8 shows the evolution of Young’s modulus with temperature used in this study. Young’s modulus values for higher temperatures were obtained from reference [13].

3. Results and Discussion

3.1. Macro Cracks in the Cast Ingots

Upon visually inspecting the cracked ingot cast under the hot condition, shown in Figure 9, it is observed that the first transverse cracks (perpendicular to the casting direction) emerge at approximately 8 cm above the ingot and bottom block interface. Following this, more severe and deeper longitudinal cracks begin to form, starting 15 cm above the mentioned interface. These two types of cracks differed in their appearance and characteristics. Evidence of remelting in the last stage of solidification and deformation was seen in the longitudinal cracks in the higher position of the ingot. In contrast, the transverse cracks in the lower position were generally thin and small and exhibited minimal deformations on the crack surfaces. The longitudinal cracks seem to have been produced by hot tearing, while the transverse cracks resulted most likely from another defect, cold cracking.

Under the cold condition, the rolling face of the ingot exhibited no cracks, while two large cracks were found on the ingot bottom touching the bottom block (see Figure 10). This region is not included in the final ingot as it is typically cut off at the beginning of downstream processing. The presence of these cracks in the cold ingot and hot tearing in the hot ingot suggests that the relaxation of stresses caused by cracking was different.

3.2. Modeling and Its Analysis

Figure 11 shows a contour plot of the ingot temperatures after 209 s, with (a) showing the rolling face and (b) the symmetry faces. As can be seen, the metal was in direct contact with the mold and water spray on the external surfaces, which rapidly cooled. However, the cooling process was slower in the center of the ingot and along the symmetry faces. Figure 12a displays calculated and measured temperature variations during the casting of the ingot at the positions corresponding to the embedded thermocouples for each ingot under hot and cold conditions. Figure 12b provides a magnified view of the temperature range where hot tearing is likely to occur. The experimental hot condition curve displays a different pattern that shows a change in the slope and reheating phenomenon. This is likely due to the infiltration of molten metal into hot tearing cracks, which raises the temperature around the cracked areas. Since the tip of the embedded thermocouple was close to the severe hot tearing crack, it captured this change in heat flow. Of course, the mathematical simulation cannot consider localized reheating caused by hot tearing. As expected, the cold simulated curve during solidification and cooling has a lower temperature than the hot condition simulated curve. An overall observation reveals a satisfactory agreement between the simulation and experimental results when cracking does not occur.

Figure 13 and Figure 14 illustrate the evolution of temperature, hydrostatic pressure, and the S22 stress component during solidification at specific points and near the solidus temperature (A and B in Figure 11). It is necessary to mention that, since hot tearing cracks occur in a longitudinal orientation, the stress (S22), which is perpendicular to the crack along the rolling face in the Y direction (Figure 11a), plays a key role in their formation. Since the model combines the material properties as one phase, it was assumed that the pressure within a finite element remains the same in both the liquid and solid phases. The values of S22 and hydrostatic pressure were taken from the finite elements located along the rolling face. At a temperature of 530 °C and a liquid percentage of 2.4% at both points A and B under the hot conditions, the hydrostatic pressure values were negative: −4.3 MPa for point A and −1.6 MPa for point B. The corresponding stress in the y-direction (rolling face) was 1.8 MPa for point A and 8.7 MPa for point B. In the cold conditions, the hydrostatic pressures at both points were positive, 2.1 MPa at point A and 9.45 MPa at point B, while the stresses were negative, at −4.7 MPa for point A and −3.06 MPa for point B, respectively. In both positions A and B, there are negative hydrostatic and positive S22 values in the hot condition that promote the formation and propagation of porosities and hot tearing. In both images, the blue lines represent the stress and pressure values at a temperature of 530 °C and a liquid fraction of 2.4%.

To better link the stress predictions with hot tearing, results were extracted for a specific line positioned 16 cm above the bottom block on the rolling face to compare the hot and cold conditions. Figure 15a,b show the temperature and solid fraction profile along the mentioned line. As expected, the temperature profile on the surface of the ingot in the hot condition shows a higher temperature and lower solid fraction compared to the cold condition.

Figure 16 illustrates the evolution of stress (S22) and pressure along a line on the rolling faces that is located 16 cm above the interface of the ingot and bottom block for both hot and cold conditions (red line in Figure 3). For the hot condition, the hydrostatic pressure in the molten metal close to the solidus temperature along the mentioned line is negative. At the same time, the stress S22 is highly positive and prone to form porosities and hot tearing, while in the cold condition along that line, the situation is completely different. Localized negative hydrostatic pressure in a semi-solid state creates a suitable area for hot tearing formation. When positive stress in the appropriate direction occurs in this region, the possibility of hot tearing formation will increase.

The combination of negative hydrostatic and positive stress, close to the solidus temperature, is likely the cause of hot tearing [11]. After a complete investigation of stress and pressure on the surface of the ingot, it is identified that the zone, 12.8 cm above the ingot and bottom block interface, is the initial region where the hydrostatic pressure becomes negative, and S22 exhibits positive and considerably high values under hot conditions. In contrast, this situation was not observed on the surface of the ingot under cold conditions.

Upon further investigation of data extracted from nodes located 20 mm inside the external surfaces for both conditions, it was found that negative pressure and positive stress were obtained at some points under hot and cold conditions. These conditions are conducive to porosity formation. It is normal to have porosities inside the cracked ingot, but more investigation was required for the sound ingot. As shown in Figure 17a, a sample was extracted and prepared from the sound ingot at the exact location where hot tearing occurred in the cracked ingot, 20 mm beneath the external surface. Figure 17b shows an SEM image of the sample, confirming the presence of microporosities in the specific area under investigation. Even though this microporosity was generated because of the negative pressure and high positive stress (S22), the situation was reversed near the surface of the ingot cast under the cold condition because the hydrostatic pressure was positive and the tensile stress was negative there, preventing the propagation of a large macroscopic crack.

3.3. Crack Surfaces Analysis

To better understand the hot tearing phenomenon in DC-cast rolling ingots, the longitudinal central crack in the hot ingot (Figure 9) was cut and opened for examination. The optical image in Figure 18 shows the complex topography of the crack surface, including bridges between the two opposite sides of the crack and multiple crack initiation locations that merged during crack propagation. The topography of both sides of the crack does not match in most areas, indicating that the crack has not propagated along a continuous path, but that many small cracks have merged with a severe deformation of bridges to form this topography. Also, there is a smooth and meandering area (black rectangular) close to the ingot surface, which is supposed to be where the crack emerged at the surface. This topographic diversity on the fracture surface indicates that the fracture occurred in different regions at various temperatures. The SEM images of the crack surfaces are presented in Figure 19. These SEM images show a (a) directional and layered structure, (b) dendrites and liquid on the microstructure, (c) round and glassy-like zones that indicate liquid between the dendrites and reheating of the metal during solidification, (d) ductile areas, and (e) some sharp and pointy structures that are related to the bridges remaining during the formation of crack. Other studies [33,34] have thoroughly investigated the bridges between the two crack surfaces and the liquid in the fracture surface.

Figure 20 shows an X-ray tomography image of a hot-tearing crack on the opposite rolling face of the sample shown in Figure 9. The 3D image was acquired using a Nikon M2 system at 220 kV, with a 2850 × 2850 flat-panel detector, yielding a voxel size of 33.6 µm (Nikon Corporation, Tokyo, Japan). The AA6111 sample, measuring 10 cm × 10 cm × 10 cm, was cut from the near-surface region of the ingot. This crack was located in the center of the surface, 15 cm above the tip of the bottom block. It is noteworthy that the crack is thinner near the surface and thicker within the ingot, indicating that the crack initially formed inside the ingot and propagated towards the surface. This observation supports the hypothesis that cracking was facilitated by pore formation due to reduced pressure. The crack path shows discontinuity within the interior of the ingot. These observations may indicate the presence of multiple distinct crack initiation sites inside the ingot and their subsequent coalescence during crack propagation. This agrees with the simulation results, revealing that initiation of hot tearing cracks was favorable in both conditions below the surface, and likely beyond 20 mm from the surface. The extensive presence of the liquid phase on the fracture surface confirms the infiltration of the molten metal into the formed cracks.

4. Conclusions

This study examined the influence of hydrostatic pressure in the semi-solid state, leading to the development of hot tears during the DC casting of AA6111 alloy. Simulations were conducted with ABAQUS and used a modified constitutive equation. Industrial trials were carried out to create a hot cast, filled with hot tears, and a cold cast, without hot tears. The findings reveal that, under hot conditions leading to the cracked ingot, in some points of the ingot surface, the ingot experiences negative hydrostatic pressure within the temperature range of 530 to 540 °C in the semi-solid state, accompanied by high enough positive S22 stress. These situations and stress direction are completely suitable for forming hot tearing. In comparison, such a combination of negative hydrostatic pressure and a positive high amount of stress was not calculated in the surfaces of the ingot under cold conditions. That leads to producing a sound ingot under cold conditions and the formation of hot tearing under hot conditions.