Hot Tear Formation During the Casting of Al–Zn Binary Alloys

The hot tearing susceptibility of Al–Zn binary alloys with solute contents of Al–0.5%Zn, Al–1%Zn, Al–2%Zn, and Al–4%Zn, with all compositions being in wt%, is investigated through physical experiments and numerical simulation. The temperature at the hot spot, the designed critical point for hot tearing, and the load at the end of the test bar are measured and compared with the simulation results. The test samples with 0.5 and 1.0% Zn show hot tears while those with 2.0 and 4.0% Zn have no sign of such tearing. The correlation between solid fraction, strain, stress, and hot tearing indicator is revealed using the simulation results of the Al–1%Zn and Al–4%Zn alloys. Just before solidification, the Al–1%Zn alloy is found to have not only a much higher strain rate at the hot spot of the test bar than that of the Al–4%Zn alloy, but also a higher strain gradient along the longitudinal direction. It is believed that both the high strain rate and high strain gradient are attributable to the formation of hot tears in the Al–1%Zn alloy.


Introduction
Due to the abundant availability and distinct material properties, aluminum alloys have found wide applications in transportation, packaging, and construction industries as the second industrial metal after steel. [1,2]Over the past two decades, there has been more than a doubling in the global production of aluminum alloys from 25 to 65 million tons per annum.Direct chill (DC) casting presents a good opportunity for the mass production of aluminum alloys to satisfy the rising demand.In fact, it has become the main production technique to produce wrought aluminum alloys.A challenge arises as there is a general trend of increased casting defects when casting speed, billet sizes, and alloy content interact.Billet casting facilities face the challenge of producing larger diameter and more highly alloyed billets without compromising productivity or experiencing a considerable rise in scrap rejection rates due to casting defects.
5][6] This phenomenon has been extensively investigated in both casting and welding processes from many perspectives since the 1950s.Hot tearing is often attributed to where insufficient feeding occurs in the mushy zone and/or where the internally generated stresses in the mushy zone exceed the strength of the partially solidified metal. [7,8]Past work has shown that hot tears initiate when the liquid flow through the mushy zone becomes insufficient to fill initiated cavities [9] and the localized zone at this stage is nearly 100% solidified. [10]Past work has also shown that solidification shrinkage and its implicit thermal contraction will generate stresses, these being concentrated at areas with sudden changes in cross section, at the hot spots where the casting solidifies last, or in adjacent areas to either. [11]o identify the practices necessary to minimize the occurrence of hot tearing in the day-to-day operations in a foundry, it is crucial to be able to understand the underlying physics behind hot tearing.The study of its behavior in alloys often involves both experiments and the use of hot tearing criteria.Numerous experiments have been developed using different configurations and various levels of complexity.Ring molds, [12,13] constrainedrod casting molds, [14,15] and cast hot tearing (CHT) test rigs [16][17][18] have been used to understand the relative hot tearing susceptibility (HTS) of various alloys.18][19] The advancement in computer and software technology has also driven the development of casting process simulation and commercial software tools.Many such tools have demonstrated their capability to investigate thermal-fluid transport phenomena, the effects of alloy chemistry, and the formation of some casting defects such as porosity and distortion.On the other hand, significant research and development work is still required to predict hot tearing because of the complexity of the material behavior in the mushy zone.
Based on the fundamental understanding of hot tearing formation, criteria proposed to predict hot tearing occurrence can been classified as either mechanical or nonmechanical. [9]The former are directly associated with the mechanical behavior of semisolid metals, including stress, strain, and strain rate.The latter include the vulnerable temperature range, phase diagram, and process parameters such as pouring temperature, mold temperature, and so on.Numerical models and criteria mainly address one of the main mechanisms, such as those previously mentioned: inadequate feeding during solidification or the excessive thermally induced deformation.From work done using models based on fundamental continuum mechanics that quantify thermally induced deformation and its associated stresses, the overcritical values of stress, strain, or strain rate have been proposed as the triggering factor for hot tearing.Hot tearing criteria have been implemented in commercial software such as ProCAST [20] and MAGMAsoft. [21]roCAST has been commonly used in foundries to simulate casting processes to help understand the physics behind those processes.Two modules are embedded in the software to predict hot cracking and hot tearing. [22]For steady-state conditions as would be encountered in DC casting, the hot cracking susceptibility (HCS) based on the Rappaz, Drezet, and Gremaud (RDG) criterion [13] is recommended.For normal casting processes, the hot tearing indicator (HTI) based on the Gurson constitutive model [20] is recommended.
Al-Si, Al-Mg, and Al-Cu binary alloys have been intensively investigated, and lambda curves have been used to describe the relationship of alloy content and HTS.The Al-Mg and Al-Cu systems exhibit a similar "lambda" shape in their composition HTS curves. [3]Increasing their Cu/Mg content extends the solidification range and thus increases the amount of linear contraction and the HTS, while further alloying beyond the solid solution limit generates more eutectics, thereby reducing the HTS. [3]n is used as the principal alloying element in 7000 series aluminum alloys.25] For nonrefined Al-xZn-2Mg-2Cu (x = 2-12) alloys, the minimum and maximum HTS values occurred at a Zn content of 4 and 12 wt%, respectively. [25]The HTS of Al-Zn binary alloys has also been studied.However, due to the inconsistency seen in the plots of composition against HTS observed by different researchers, [17,26] a lambda curve could not be constructed.This is explained by a significant change in the curvature of the solidus line in the Al-Zn phase diagram which manifests itself in significant changes in the partition coefficient of zinc.Bazhenov found that Al-Zn alloys exhibit no direct relationship between the effective solidification range and HTS.In that case, the Al-25%Zn alloy had the maximum HTS.The increase in the HTS at up to 25% Zn content was explained by a decrease in the solid fraction growth rate during non-equilibrium solidification at the end of the process.The decrease in the HTS at anything more than 25% Zn content was related to a significant fraction of the nonequilibrium eutectic and its predominant influence on the HTS. [26]Pumphrey and Lyons [27] tested alloys of 2-20% Zn using the ring test and found a peak in the HTS at 6%. Clyne and Davies [28] tested alloys of 5-50% Zn using a restrained bar mold, finding the percentage cracking to be constant over the range 5-40% before dropping dramatically between 40 and 50%.
Spittle and Brown [29] used a numerical model to predict the change in permeability as a function of fraction solid and composition in Al-Cu, Al-Si, and Al-Mg and Al-Zn binary alloy systems and highlighted that the permeability plays a significant role in the formation of hot tearing.There was fairly good correlation between the composition corresponding to minimum permeability and the composition corresponding to maximum HTS for Al-Si, Al-Cu, and Al-Mg binary systems.The only exception is the Al-Zn binary system, in which no correlation exists between data from different hot tear experiments and the predicted minimum permeability data.Viano et al. [17] reported the peak HTS at 0.5% Zn, a considerably lower solute concentration than previous other experimental studies, as well as correlation with Spittle and Brown's permeability model.
Using both physical experiments and numerical simulations, this article seeks enhanced insights into the mechanical aspect of the formation of hot tearing in Al-Zn alloys including the correlation between the development of stress and strain and the formation of hot tears.The experiments and numerical modeling are outlined in Section 2, results presented in section 3, and findings discussed in Section 4.

Alloy Preparation and Test Apparatus
The Al-Zn alloys were prepared from commercially pure aluminum (99.7%) and pure zinc (99.999%) using an induction furnace in a 5 kg batch.ThermoCalc software was used to calculate liquidus and solidus temperatures.Table 1 presents the chemical composition of the Al-Zn alloys.
The details of the CHT rig used have been reported elsewhere. [16,17]For this work, as illustrated in Figure 1, the CHT rig was used with modifications to the load measurement unit to investigate the hot tearing of Al-Zn alloys: the casting had two restrained bars fed by a center sprue.One bar was fully restrained from both ends and was used to quantify hot tearing, while the other bar was used to measure the temperature and tensile load.In the measurement bar, one end was restrained, and the other end of the bar contained a sliding end that was attached to the load cell via a connecting rod.The load cell had a 2 kN capacity, rated output 1.5 mV V À1 , and 24 VDC excitation.A type K thermocouple was placed at the hot spot as indicated by T/C in the Figure1a to record the hot spot temperature.Chill blocks on the ends combined with ceramic fiber insulation along the side walls of the mold promoted directional solidification toward the center of the casting.A 1.5 kg quantity of the prealloyed material for each composition was remelted and preheated to 750 °C inside a graphite clay crucible for 15 min.The melt was poured into the mold cavity (preheated to 250 °C).A data acquisition system with eight channels (Toprie TP700) was used to record temperature and load development.

Finite-Element Model
In this study, the commercial virtual casting software tool ProCAST was used to simulate stress and strain development and hot tear formation.Figure 2 shows the computer-aided design model of the CHT rig.The model was assembled from three separate parts to splice the H-shaped casting cavity to accommodate different castings to mold interfacial heat transfer conditions in different parts of the mold.

Heat Transfer Coefficient
As shown in Figure 2a, two sets of interfacial heat transfer coefficients were assigned to the interface between the mold and casting to duplicate the designed rig setup.For the far end of the bars (as shown in white), the interfacial HTC1 was set as 500 w m À2 ⋅k, and in the center part of the bars (as shown in red), the interfacial HTC2 was set as 200 w m À2 ⋅k.

Restrained Surfaces for Stress Simulation
As shown in Figure 2b, to reflect the actual casting process, only one end was attached to a dynamometer for load measurement while the other three ends were displacement restrained.

Material Model
An elastic-plastic model was used to simulate the stress and strain in this study.Its properties included the Young's modulus, the Poisson's ratio, and the thermal expansion coefficients in the elastic range, the last being temperature dependent.These were defined for the four alloys.The hardening coefficient and yield stress for the plastic model were defined as temperature dependent, with the latter corresponded to the slope of the stress-strain curve in the plastic range.The linear hardening is defined as follows. [22]¼ σ 0 þ Hε pl (1)  where: σ 0 is yield stress, ε pl is plastic strain, and H is the plastic modulus.
The material properties for the four alloys were calculated using ThermoCalc.A back diffusion model [30] was used to calculate the thermal properties data for the four alloys.The fraction solid profile for each alloy was determined from JMatPro using Thermotech TT-Al database assuming back diffusion conditions.

Hot Tearing Criteria
To predict the HTS, HTI was used.This model was based on the total strain occurring during solidification, that is, it is "strain driven".It computes the elastic and plastic strain at a given location when the solid fraction is between 50 and 99%.The HTI is defined by the accumulated plastic strain in the mushy zone that corresponds to the void nucleation described in the Gurson model. [22]I ¼ where έp ht is the critical accumulated effective plastic strain for the initiation of hot tearing, έp is the effective plastic strain rate, t c denotes the time when the coherency temperature is reached, and t s is the time when the solidus temperature is reached.The coherency temperature refers to the state of a solidifying alloy at which a coherent dendrite network is established during the formation of grains. [31]

Model Validation
The model was validated using temperature and load data measured from physical experiments.Unlike the high level of agreement obtained between the measured and simulated temperature evolution, the load data from the measurement and the stress from a selected location in the simulation cannot be compared since they are different quantities.Nevertheless, load development through the experimental measurement showed a similar trend to the simulated stress development.A minor deviation can be noted in the trend of simulated stress evolution compared to the observed load development.As shown in Figure 3a-d, the simulated stress steadily built up during the isothermal solidification process, reaching about 10 MPa by the end.Subsequently, the simulated load exhibited a sharp rise, which is nearly inversely proportional to the temperature decrease.On the other hand, the progression of load obtained through experimental measurements did not exhibit a pronounced increase until the latter stages of the isothermal solidification process.As depicted in Figure 4, load measurement initiation was delayed, commencing around 60-80 s into the test.It is likely that the friction between the load cell block and the mold wall may have caused the delayed responses.Despite this delayed start, the measured load rapidly increases at the latter stages of the isothermal solidification process, subsequently displaying a sharp increase.

Results
It is worth noting that the Zn content in the studied Al alloys indicated the opposite effect on the load/stress build up through experimental measurement and simulation.As the Zn content increases, the simulated stress at 150 s showed a descending trend from %75 MPa in the Al-0.5%Znalloy to %72 MPa, 68 MPa, and 64 MPa, respectively, in the Al-1%Zn, Al-2%Zn, and Al-4%Zn alloys.The measured load steadily decreased from 880, 860, 830, and 750 N in the Al-0.5%Zn,A-1.0%Zn, Al-2% Zn, and Zn-4%Al alloy respectively.Figure 4a 2 -d 2 shows the distribution of HTI on the cast bar at the end of the solidification process of the studied Al alloys.It can be seen that the Zn content in the studied alloys has a direct influence on the distribution of HTI.In all instances, the peak HTI value can be found at the center of the cast bar.However, in the low-alloyed Al alloys (Al-0.5%Zn), the peak HTI (%0.020) is highly concentrated and rapidly drops off as it moves away from the center.Additional secondary peaks occur at a distance of onethird of a half-bar length away from the center, both to the left and right sides.The value associated with these peaks is %0.0058.

Hot Tearing Formation and the Prediction Using HTI
The HTI distribution became dispersed with increasing Zn content in the Al-1%Zn, Al-2%Zn, and Al-4%Zn alloys, as shown in Figure 4b 2 -d 2 .Despite this, the primary HTI peaks remained at the center of the cast bars, maintaining a value of %0.020.Two major changes in the HTI distribution can be observed with the increasing Zn content in these alloys.First of all, the tails of the major peak appear to be significantly wider and flatter with the increasing Zn concentration.On the other hand, the secondary peaks also indicated higher values and wider distribution under the same effect.

Development of Stress and Strain and Formation of Hot Tearing
Figure 5 shows the two extreme cases, with the evident hot tearing phenomenon (Figure 5   than the Al-4%Zn alloy at 94 s.The build-up of effective stress begins from the far end of the cast bar at the onset of solidification and propagates into the center.After 48 s, when the right half of the studied bar achieved full solidification, the effective stress in Al-1%Zn and Al-4%Zn alloys indicated distinctive respective peaks in the 55-80 mm and 60-75 mm regions.As the solidification proceeds, the effective stress in Al-1%Zn continued to build up with no additional change in pattern and eventually settled with an evident peak in the 55-75 mm region with a value of 19.5 MPa. Additional effective stress peak build-up can be observed at the 40 mm region in the Al-4%Zn alloy after 68 s, and the effective stress distribution is shown to be wider (40-75 mm) with a lower peak value at 16 MPa.
As the initial solidification (0-58 s) progresses from the end of the cast bar toward the center, the effective strain gradually builds up toward the solidification direction in both alloys with the first peak value of 0.15 observed at the most recently solidified site (around 35-40 mm).After 58 s, effective strain saw a slight drop at around 25-35 mm.As solidification proceeds toward the central region of the casting, the effective strain reached the peak, measuring 0.225 and 0.210 for the Al-1%Zn and Al-4%Zn alloys, respectively.There is a substantial increase in effective strain at the midpoint of the bar when the solid fraction surpasses 60%.In the case of the Al-1%Zn alloy, the effective strain experiences a sharp increase from 0.00225 to 0.02225 as the solid fraction increased from 60% to 100%.In contrast, the rise in the effective strain at the center of the Al-4%Zn alloy is more gradual, with an increase from 0.00725 to 0.020 as the solid fraction increased from 60% to 100%.
The progress of HTI over different sites follows a similar pattern to the effective strain, which starts with a gradual increase to a weak peak in the 35-40 mm region, followed by a slight drop until 10 mm.After that, the HTI increased rapidly when the center of the bar reached the final stage of solidification (above 60% solid fraction).A distinct difference in terms of the HTI distribution along the solidification direction can be noted between the Al-1%Zn and Al-4%Zn alloys.The major HTI peak at the center of the cast Al-1%Zn bar is characterized by its narrow distribution.This peak, initially measuring 0.0225, swiftly diminishes to 0.0005 within a 10 mm distance from the center.A secondary HTI peak appears at the 35 mm location in the Al-1%Zn alloy, reaching 0.010 and then diminishing to 0 at 72 mm.The secondary peak HTI in Al-1%Zn alloy is found at 35 mm, with a peak value of 0.010, and drops to 0 at 72 mm.On the other hand, the peak HTI distribution is significantly wider in the Al-4%Zn alloy, with a peak value of 0.022, and drops to 0.008 at 10 mm away from the center.The secondary peak also indicated a wide distribution with a relatively high peak value of 0.015, which gradually dropped to 0 at 80 mm.The above findings suggest that the relatively uniform HTI distribution along the solidification length may be the key to reducing the HTS of Al-Zn alloys.

Discussion
Previous studies have found that it is difficult to use the lambda curve to describe the correlation of HTS with the Zn content for Al-Zn binary alloys since there is no agreement between the experimental data sets from different research groups.Viano found the peak HTS to be at 0.5% Zn, a much lower solute concentration than other experimental studies, and the compositional range affected by hot tearing was significantly narrower, something which emphasizes the importance of good feeding. [17]he current study shows hot tearing in 0.5% Zn and 1.0% Zn, and no hot tearing for 2.0 and 4.0% Zn, supporting Viano's findings.
Two mechanisms have been proposed for hot tearing.1) The void mechanism which only occurs when feeding is unable to compensate for shrinkage and contraction before tensile coherency.Once the void has formed, the adjacent grains are free to grow and complete solidification unconstrained.It is proposed that this is the dominant failure mechanism for low-solute alloys to the left of the peak in the lambda curve.2) The classic tear mechanism is observed when feeding is unable to compensate for shrinkage and contraction after tensile coherency occurs.The amount of tearing, and how localized it is, depends upon how early tensile coherency occurs and how long afterward feeding becomes insufficient.It is proposed that this is the dominant failure mechanism for high-solute alloys to the right of the peak in the lambda curve.
The imposed strain on the hot spot region from thermal contraction contributes to the hot tearing formation.The imposed strain is attributed to a few factors such as the length of the restrained bar, mold preheat, and a melt superheat.Campbell [32] quantifies the strain theory of hot tearing (ε) as where α is the coefficient of thermal expansion, ΔT is the change in temperature, L is the length of the casting, and I is length of the hot spot.
From Equation ( 3), the strain on the hot spot region increases with increase in both the length of the casting and the cooling rate.The experimental rig and the cooling conditions in the current study determine the level of strain imposed on the hot spot region.
To understand the strain differences between two alloys, the solid fraction and effective strain profiles in the center of the test bars in the last six seconds before it is solidified are plotted in Figure 6.The fraction solid profile longitudinally along the cast bar at a later stage of solidification is seen in Figure 6a.In the Al-1%Zn alloy, the solid fraction increased quicker along the longitudinal distance, with a narrower semisolid pool at 9 mm and a faster increase of solid fraction from 0.48 to 1 in 6 s at the center point.Most of the solidification of the Al-1%Zn is concentrated in a narrower band at the center of the test bar with a higher rate of solidification.The rapid increase in fraction solid translates into an order of magnitude drop in permeability in the last stages of solidification.By comparison, Al-4.0%Zn shows a wider semisolid region of 12.5 mm and the solid fraction increases much more slowly (from 0.63 to 1.0 in 6 s).The solidification of the Al-4%Zn proceeds at a slower rate across a wider area of the hot spot.The broader region of slower solidification growth of the Al-4%Zn alloy leads to a higher permeability in the mushy zone.A good permeability is associated with a high ability to heal micropores and therefore to reduce the hot tears.
Changes of the effective strain in the center zone for the two alloys are also quite different as shown in Figure 6b.The adjacent zone located 15 mm away from the center point for Al-1%Zn alloy is slightly lower than that of the Al-4%Zn alloy at the same location.The gradients of the effective strain for both Al-1%Zn and Al-4%Zn were calculated as 0.0026 mm À1 and 0.0012 mm À1 respectively, and the strain gradient of Al-1%Zn alloy was much higher than that of the Al-4%Zn alloy.The effective strain at the center point increases much faster from 0 to 0.021 for the Al-1% Zn alloy, while the effective strain at the center point increases from 0.075 to 0.20 for the Al-4%Zn alloy.
It was seen that the Al-4%Zn alloy had a much wider solidification range (23 °C) that that of the Al-1%Zn (11 °C).This results in a broader hot spot and a slower solidification rate, both of which would contribute to a small strain in the hot spot.While the simulation results showed only a minor reduction of the effective strain in the hot spot, there is a significantly higher strain rate in the last moments of solidification at the hot spot in the Al-1%Zn alloy and a higher strain gradient, and these may be the main mechanisms for the formation of the hot tearing.

Conclusion
The HTS of Al-Zn binary alloys has been investigated through physical experiments and numerical simulation.The test samples with 0.5 and 1.0% Zn solute contents showed hot tears while those with 2.0 and 4.0% Zn solute contents had no sign of such tearing.The simulation results have been used to investigate in detail the evolution of the solid fraction, effective stress, effective strain, and HTI to reveal the correlation between these and provide insight into what is happening.A detailed comparison has been made between the Al-1%Zn and Al-4%Zn alloys to reveal the mechanism of the hot tearing formation.
In the last moments before the alloy solidified, most of the solidification of the Al-1%Zn is concentrated in a narrower band at the center of the test bar with a higher rate of solidification.The rapid increase in fraction solid translates into an order of magnitude drop in permeability in the last stages of solidification.By comparison, the solidification of the Al-4% Zn proceeds at a slower rate across a wider area of the hot spot.The broader region of slower solidification growth of the Al-4%Zn alloy leads to a higher permeability in the mushy zone and therefore a higher ability to heal micropores and reduce HTS.
No notable difference in effective strain between Al-1%Zn and Al-4%Zn alloys has been found.Interestingly, the Al-1% Zn alloy showed not only a much higher strain rate at the hot spot of the test bar than that of the Al-4%Zn alloy, but also a higher strain gradient along the longitudinal direction.
It is believed that the formation of hot tears in the Al-1%Zn alloy is caused by the low permeability, high strain rate, and high strain gradient generated in the last moments of solidification.

Figure 1 .
Figure 1.a) Schematic view of the mold and b) casting with mold.

Figure 2 .
Figure 2. The heat transfer coefficient setting separately of the four end regions and the central region: a) two interfacial heat transfer coefficients, b,c) restricted surfaces (T refers to the node at which the hot spot temperature was measured and similarly S refers to the node at which the end stress of the bar was measured).

3. 1 .
Stress and Load Development at the End of the Test Bar

Figure 3
Figure3presents the measured temperature/load evolution and the associated simulation of temperature/stress as seen at the nodes T and S during the solidification process of the studied Al-Zn alloys.The simulated temperature evolution closely aligned with the measured data, indicating a high level of agreement for all of the four alloys studied.At the start of the measurement, the alloy melt underwent a rapid cooling process from 700 to 650 °C for 20 s.Following this, isothermal solidification began at around 650 °C and continued until %85 s from the onset of the measurement.Subsequently, the continuous cooling of the alloy melt started at around 2 °C s À1 until 150 s after the start of the experiment when the temperature dropped below the region of interest to 525 °C.Unlike the high level of agreement obtained between the measured and simulated temperature evolution, the load data from the measurement and the stress from a selected location in the simulation cannot be compared since they are different quantities.Nevertheless, load development through the experimental measurement showed a similar trend to the simulated stress development.A minor deviation can be noted in the trend of simulated stress evolution compared to the observed load development.

Figure 4
Figure 4 shows the hot tearing phenomena observed in the studied Al-Zn alloys and the associated simulation of the HTI distribution on the cast bars.According to Figure 4a 1 ,b 1 , the Al-0.5%Zn and Al-1.0%Zn alloys underwent hot tearing damage.The cracks observed in these figures appear to have penetrated perpendicularly to the length of the cast bar and extended toward the center of the casting.On the other hand, the Al alloy with Zn contents of 2% and 4% did not indicate any hot tearing damage, as shown in Figure 4c 1 ,d 1 .
Figure5shows the two extreme cases, with the evident hot tearing phenomenon (Figure5left-side, Al-1%Zn) and no hot tearing defect (Figure5right-side, Al-4%Zn), and the evolution of the solid fraction, effective stress, effective strain, and HTI profile longitudinally along the cast bar over time.Due to the symmetric nature of the cast bar design and load-stress distribution, only the right-side half of the cast bar was analyzed and presented.As shown in Figure5b1 ,b 2 , the solidification of Al-1%Zn and Al-4%Zn both commenced at the far end of the cast bar and propagated toward the center, indicating a good sequence of directional solidification.The Al-1%Zn alloy achieved complete solidification after 86.5 s into the test, which was slightly earlier

Figure 5 .
Figure 5. Simulated solid fraction, stress, strain, and HTI versus the bar length and time a) Al-1.0Zn and b) Al-4.0Zn.

Figure 6 .
Figure 6.a) Solid fraction and b) effective strain in the later stage of solidification for the Al-1%Zn and Al-4%Zn alloys.