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The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification
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Acta Materialia xxx (2013) xxx–xxx www.elsevier.com/locate/actamat
The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification Manas Paliwal, In-Ho Jung ⇑ Dept. Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, QC, Canada H3A 2B2 Received 3 January 2013; received in revised form 17 April 2013; accepted 21 April 2013
Abstract The comprehensive microstructural evolution of Mg–3, 6 and 9 wt.% Al alloys with respect to the solidification parameters such as thermal gradient (G), solidification velocity (V), cooling rate (GV) and solute (Al) content were investigated in the present study. Various solidification techniques, including directional solidification, wedge casting, sand and graphite mould casting, gravity casting in a Cu mould and water quenching, were employed in order to obtain wide ranges of cooling rates between 0.05 and 1000 K s–1. The microstructural length scales of Mg–Al alloys, such as secondary dendrite arm spacing and primary dendrite arm spacing, were determined experimentally and compared with published models. In addition, the solidification parameters of morphological transitions such as cellular to columnar dendrite and columnar to equiaxed dendrite were also determined. Based on all the experimental data and the solidification model, a solidification map was built in order to provide guidelines for the as-cast microstructural features of Mg–Al alloys. Crown Copyright Ó 2013 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Mg–Al alloy; Solidification; Growth morphology; Solidification map
1. Introduction As magnesium alloys are the lightest structural metallic materials, a great amount of research has been conducted recently relating to the transportation sector, with goals of improving fuel efficiency and reducing CO2 emissions. Most magnesium components are produced using melting and casting practices wherein as-cast products are finalized through thermo-mechanical processing or through small machining of the surface. Even in welding practices, the solidification microstructure of the alloy is retained in the welded zone. The characteristics of an as-cast microstructure, such as the size of the dendrite (grain), the nature of the dendrite (columnar or equiaxed), primary dendrite arm spacing (PDAS) and secondary dendrite arm spacing (SDAS), determine the mechanical properties of the as-cast products and the thermo-mechanical processing conditions ⇑ Corresponding author. Tel.: +1 514 398 2608; fax: +1 514 398 4492.
E-mail address: [email protected] (I.-H. Jung).
[1–3]. Therefore, understanding solidification microstructure evolution through both experimental and microstructural modelling studies is important. The evolution of a solidification microstructure in a metallic system can be characterized by different growth morphologies, such as cellular, columnar and equiaxed dendritic growth. The obtained microstructure is a result of the complex interplay between several solidification parameters. With this in mind, understanding the roles of different solidification parameters such as thermal gradient (G), solidification velocity (V), cooling rate (GV) and solute content is imperative in order to control the final microstructure of these alloys. To date, no comprehensive experimental work has been conducted on Mg alloys in order to understand the influences of the various solidification parameters and alloying elements on the evolution of different growth morphologies. The purpose of the present study is to experimentally investigate the microstructural evolution of Mg–3, 6 and 9 wt.% Al alloys, including cellular–columnar and colum-
1359-6454/$36.00 Crown Copyright Ó 2013 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.04.063
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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nar–equiaxed dendrite transitions, and to determine the important length scales, such as PDAS and SDAS, depending on the casting parameter and the solute content. This work is part of a comprehensive project that focuses on the experimental and numerical stimulation of the solidification microstructure of Mg alloys under various casting conditions. 2. Experimental The solidification experiments carried out in this study can be classified into two categories: steady-state and transient-state experiments. The schematics of the different solidification techniques employed in the present study are shown in Fig. 1. All the experiments were conducted for Mg–3, 6 and 9 wt.% Al alloys. 2.1. Steady-state experiment Directional solidification experiments have been widely used in order to investigate the columnar growth of various alloys [4]. This technique can induce heat extraction in a single direction with an established thermal gradient, which causes the solid phase to grow towards the opposite side of the heat extraction. The thermal gradient (G) and solidification velocity (V) can be varied independently, and the product of both gives the cooling rate. In the present study, the solidification process was carried out in an alumina cru-
cible of 300 mm length, 5.5 mm inner diameter and 1.5 mm thickness. An Mg alloy sample bar of 200 mm length was machined and placed in an alumina crucible, which was then loaded into an induction furnace column as shown in Fig. 1a. The furnace temperature was kept at 710 °C. After pulling out the sample about 100 mm from the induction furnace column, it was quenched by helium gas. The frozen solid–liquid solidification front was then examined using metallographic techniques for the further characterization of the as-cast microstructure. No noticeable chemical reaction between the alumina crucible and the Mg alloys was observed during the experiment. The thermal gradient (G) was measured by mounting a 1 mm diameter thin K-type sheath thermocouple in the alumina crucible. The temperature was recorded with a data logger attached to a computer when the sample was pulled down with the desired solidification velocity. The thermal gradient was determined from the slope of the temperature–distance curves at the liquidus temperature of each alloy. Cooling rates in the range of 0.05–9 K s–1 were achieved through the directional solidification experiments. The details are summarized in Table 1. 2.2. Transient-state experiment In order to obtain the solidification microstructure at intermediate and higher cooling rates, various gravity casting experiments were performed. In these experiments, the
Fig. 1. Schematics of the solidification techniques used in the present study. (a) Directional solidification, (b) water-cooled Cu wedge-shaped mould, (c) sand mould, (d) graphite mould and (e) water quenching. The dots in (b–d) represent the positions of thermocouple.
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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Table 1 The parameters of directional solidification and gravity casting experiments for Mg–Al (3, 6 and 9 wt.%) alloys. Casting
Thermal gradient (K mm–1)
Solidification velocity (mm s–1)
Cooling rate (K s–1)
Directional solidification
8.5 7.5 7.0 5.5 – – – – –
0.00625 0.05 0.17 0.50 – – – – –
0.05 0.38 1.16 2.75 30, 75, 100 20 1 175 687 ± 200
Wedge mould Graphite mould Sand mould Cu mould Water quenching
thermal gradient and solidification velocity were coupled time-dependent parameters which were difficult to determine. Therefore, the cooling rate was the only variable that could be experimentally measured. Casting in a watercooled wedge-shaped Cu mould (see Fig. 1b) is an efficient way to obtain different cooling rates in a single casting experiment. Experimental curves determined by thermocouples and heat flow simulations [5] showed that the cooling rate can be varied from over 250 K s–1 at the tip of wedge to just a few K s–1 near the top of the wedge. As shown in Fig. 1b, three K-type thermocouples were inserted at different positions from the tip of the wedge mould to record the cooling rate; as-cast samples were taken from these locations. Sand and graphite moulds were also employed for the casting at low and intermediate cooling rates, as shown in Fig. 1c and d, respectively. To obtain higher cooling rates, Mg alloys were cast in a 7 mm diameter Cu mould. A K-type sheath thermocouple with a 1 mm diameter was inserted at the center of the mould and connected to a CHINO KR3120 data acquisition system capable of recording at high frequencies (20 signals s–1). However, due to very fast cooling in the Cu mould, the liquidus temperatures for the Mg–Al alloys were hard to capture to determine the exact cooling rate for the alloys. In order to obtain the cooling rate of the samples, the experimental cooling curve obtained from the casting experiments was extrapolated to the liquidus temperatures of the Mg–Al alloys. To obtain more rapid cooling rates, direct water quenching experiments were performed (see Fig. 1e). The alloy samples were contained in a stainless steel tube (O.D. = 6.35 mm, I.D. = 5 mm) and the whole set-up was placed inside a resistance furnace at 700 °C. After holding the Mg–Al alloy sample for 1 h in an inert Ar atmosphere, the stainless tube was dropped in a cold water bath. A K-type sheath thermocouple was inserted in the tube wall to record the thermal history during the experiment. The cooling rates obtained with different casting techniques are summarized in Table 1. 2.3. Microstructural characterization The microstructural characterization of the directionally solidified alloy samples was performed both for the longi-
tudinal and transverse sections close to the quenched solid–liquid interface. Similarly, for the gravity cast experiments, the metallographic samples were taken from the sections close to the thermocouple tip. The samples were cold mounted and polished with 240, 400, 600 and 1200 grit SiC papers, then fine polished with 3 and 1 lm diamond pastes. The sample surfaces were cleaned with an ultrasonic bath for 20 min before etching with acetal–picral solution (4.2 g of picric acid, 10 ml of H2O, 10 ml of acetic acid and 70 ml of ethanol) before optical image analysis. The etching was performed by carefully immersing the samples in the etchant for 4–5 s, then cleaning the sample surface with running water and ethanol. The optical microscopy was performed using a CLEMEX optical image analyzer. The PDAS and SDAS were measured from the optical images of the solidified samples using the linear intercept method. 3. Results and discussion 3.1. General as-cast microstructure of Mg–Al alloys The as-cast microstructures of the directionally solidified Mg–Al alloys are shown in Fig. 2 and the microstructures obtained from gravity casting experiments are presented in Fig. 3. The microstructures for directionally solidified alloys showed columnar growth, with the primary dendrite stems growing against the heat extraction direction. Substantial side branching was seen for all the alloys, and the microstructures became finer as the solute content increased from 3 to 9 wt.% Al at the given cooling rate. Equiaxed dendrites were observed for all the gravity castings, as seen in Fig. 3. 3.2. SDAS of Mg–Al alloys SDAS is an important length scale in microstructural solidification as it can set the diffusion distance in solidification which directly affects the microsegregation of the final solidified alloy [6]. SDAS has been actively investigated for various Al alloys [4]. However, even for Al alloys, there has been no single comprehensive study on the evolution of SDAS encompassing a wide range of cooling rates
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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Fig. 2. The microstructure of directionally solidified Mg–Al alloys with different cooling rates (CR). G and V represent thermal gradient and solidification velocity, respectively. L and T represent longitudinal and transverse sections of samples, respectively.
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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Fig. 3. The microstructure of Mg–Al alloys solidified using different casting methods.
(from a low cooling rate such as 0.05 K s–1 to a high cooling rate of several hundred K s–1). For Mg alloys, the SDAS has been specifically investigated for AZ91 cast alloy by many researchers [7–12] in the cooling rate ranging from 0.05 to 106 K s–1. Dube´ et al. [12] proposed a linear relationship between the cooling rate and SDAS (in a log–log scale) in this cooling rate range, which was mathematically expressed as: log k ¼ logð39:8Þ 0:32 log s
ð1Þ
where k is the measured SDAS (lm) and s is the cooling rate (K s–1). However, the experimental results by Pettersen et al. [7] and Tensi and Ro¨sch [8] using directional solidification experiments in the cooling rate range of 0.05– 0.17 K s–1 were found to deviate from this linear relationship. Although the SDAS can be more accurately determined in the directional solidification experiments, the measured SDAS at low cooling rates is found to be lower than that calculated from the linear relationship. A summary of the present experimental results for the SDAS of Mg–Al binary alloys is shown in Fig. 4 as a func-
tion of cooling rate and Al content. It is noted that the cooling rates were precisely determined for all the experimental points. Increasing the solute content decreased the SDAS of the Mg–Al alloys. Although it seems that the SDAS decreases linearly with cooling rate in logarithm scale, a closer look at the experimental data suggests a possibility that the log(SDAS) may not be a strictly linear function with log(cooling rate) in a wide range of cooling rates. It is interesting to note that the linearity relationship between SDAS and cooling rate can still be satisfied by a subset of SDAS data within each dendrite region (columnar dendrite growth below about 10 K s–1 and equiaxed dendrite growth above 20 K s–1), which may imply that the solidification mode may influence the relationship between SDAS and cooling rate or that the standard determination techniques of SDAS in the two different dendrite modes may not be equivalent. Interestingly, the same trend has been observed in the evolution of SDAS for Al–Si and Sn–Pb alloys in the directional solidification experiments performed by Okamoto and Kishitake [13]. It should be noted that the SDAS of these alloys also deviated from
100 80
SDAS (µm)
60 40
20
Al -2.8 wt. % Si [13] Al -5.0 wt. % Si [13] Sn -2.8 wt. % Pb[13] Sn -4.1 wt. % Pb[13]
10
-1
10
0
10
1
Cooling rate (K/sec) Fig. 4. The variation of SDAS for Mg–Al alloy with cooling rate and Al concentration.
Fig. 5. The variation of SDAS for Al–Si and Sn–Pb alloy [13] with cooling rate.
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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the linear logarithmic relationship at cooling rates below 0.5 and 1 K s–1, respectively, as shown in Fig. 5. The theoretical approach to the evolution of the SDAS implicates it as a function of cooling rate and alloy composition. The SDAS in the final solidified microstructure can be predicted by modelling the physics of different coarsening mechanisms that operate during solidification [6]. Kattamis and Flemings [14] proposed a model to predict the SDAS based on a coarsening mechanism similar to the Ostwald ripening phenomenon in which the growth of a dendrite takes place by the dissolution of smaller dendrites in the melt. Kattamis and Flemings’s model considered the cylindrical shaped (different radii) and two side branches (arms) of a growing columnar dendrite and assumed the presence of uniform temperature along the side branches. Furthermore, the different radii of the branches induce a difference in chemical potential between the neighbouring side branches which thermodynamically promotes the flow of solute from the smaller arm to the larger one via liquid between the branches. This process continues in the mushy zone until the smaller arm completely remelts. The proposed mathematical formulation by Kattamis and Flemings’s model can be written as: 0 k2 ¼ 5:5@
CDl ln
C eut Co
ml ð1 k o ÞðC eut C o Þ
1n A tn f
ð2Þ
where k2 is SDAS, C is the Gibbs–Thomson coefficient, Dl is the diffusivity of the solute in liquid phase, Ceut is the eutectic composition where the solidification terminates, Co is the solute composition, ml is the liquidus slope, ko is the equilibrium partitioning coefficient, tf is the time for solidification and n is the coarsening exponent. Several modifications of Kattamis and Flemings’s coarsening model are also available in the literature which address other possible coarsening mechanisms, such as remelting, the dissolution of the secondary branches from their roots or the coalescence between neighboring dendrite arms [15]. All the proposed coarsening mechanisms [14,15] tend to increase the final SDAS in the solidified microstructure, and these mechanisms are known to be valid for both columnar and equiaxed growth regimes [14]. The coarsening model of Kattamis and Flemings [14] was applied to predict the SDAS for Mg–Al alloys. The calculated results are shown in Fig. 6 and compared with experimental data. All the parameters for Eq. (2) were taken from a thermodynamic database [16] except D = 2 109 m2 s–1, C = 1 107 km and n = 1/3. It should be noted that the calculated SDAS were lower than experimental data at high cooling rates but were higher than the experimental data at low cooling rates. It should also be noted that the calculated SDAS were slightly lower than experimental data in the high cooling rate region but were slightly higher than the experimental data in the low cooling rate region. The coarsening exponent (n) in Eq.
(2) is generally accepted as 1/3. However, this value was changed slightly to confirm the influence of the coarsening exponent to the calculations of SDAS. As shown in Fig. 6, a small change in exponent can shift the curve up and down but hardly changes the slope of the curves. The calculated slope from the model is in excellent agreement with the experimental data for equiaxed dendrite, but is more negative than the experimental SDAS slope of columnar dendrite. This difference in slope for columnar dendrite becomes more significant with increasing Al concentration. It is unclear why this discrepancy should occur, but the possibility of it occurring is particularly high in the high solute alloy. The evolution of SDAS with cooling rate or solidification time is a complex process which is historically explained in the solidification theories within the framework of the coarsening phenomena. Kattamis and Flemings’s model describes the coarsening process as the dissolution of smaller secondary arms. However, there could be other coarsening processes, such as remelting or coalescence of secondary arms, that could possibly affect the final secondary arm spacing. The change in the SDAS from the quenched solid–liquid interface to the root of the columnar dendrite was measured, and is shown in Fig. 7. Interestingly, the SDAS increased noticeably with the distance from the quenched solid–liquid interface to the root of the dendrite, which implies that the distance between the secondary arms can increase during the coarsening process. Although the SDAS of the coarsened secondary arms became closer to the calculated results using Kattamis and Flemings’s model [14], they were still lower than the calculated values. For example, the most matured SDAS obtained at the dendrite roots for Mg–Al alloys solidified at the cooling rate of 0.375 K s–1 were compared with the calculated SDAS curves from Kattamis and Flemings’s model in Fig. 6. 3.3. Cellular–columnar dendrite transition (CDT) The CDT has been actively investigated both experimentally and numerically. Directional solidification experiments have aided significantly in understanding the mechanism of the CDT in a number of organic and metallic systems. The different growth morphologies, like planar, cellular, columnar and equiaxed, that occur during the solidification of alloys are a direct result of the thermodynamic and kinetic conditions prevailing at the dendrite tip. The growth parameters affecting the conditions of dendrite tip radius (rt) are the thermal gradient (G), solidification velocity (V) and solute composition (Co) of the alloy at the tip. Thus, any change in the growth morphology, specifically the transition between planar to cellular growth or the cellular to columnar growth should be reflected by a change in the tip radius, tip composition and tip temperature as a function of G, V and Co. Several researchers [17–20] have carried out the simultaneous measurements of tip radii, tip composition and PDAS for organic systems. Esaka and Kurz [17] carried
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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(b)
(a)
0.32
10
1 -1 10
n = 0.34 0.33
100
SDAS (µm)
SDAS (µm)
n = 0.34 0.33 100 0.32
7
10
Mg-3 wt. % Al
Mg-6 wt. % Al
Model
Model
0
10
1
2
10
3
10
10
1
-1
10
0
10
Cooling rate (K/sec)
(c)
2
10
3
10
Cooling rate (K/sec) n = 0.34
100
SDAS (µm)
1
10
0.33 0.32
10
Mg-9 wt. % Al Model 1 -1 10
0
1
10
10
2
10
3
10
Cooling rate (K/sec) Fig. 6. Comparison of experimental SDAS of Mg–Al alloys with the predicted SDAS curves from Kattamis and Flemings’s model [14] using different coarsening exponents (n). (a) Mg–3 wt.% Al, (b) Mg–6 wt.% Al and (c) Mg–9 wt.% Al. Half-filled symbols represent the SDAS obtained at the root of a columnar dendrite.
Fig. 7. Variation of SDAS of the Mg–Al alloys from the quenched solid– liquid interface to the root of the columnar dendrite directionally solidified at 0.375 K s–1.
out a directional solidification experiment on succinonitrile–1.3 wt.% acetone to measure the tip radius, tip temperature and initial SDAS. They found that the tip radius in the dendritic regime decreased with the growth rate at a constant thermal gradient; however, no results in the cel-
lular regime were obtained. Trivedi et al. [18] also conducted in situ measurements of tip radius and interdendrite spacing in a succinonitrile–salol system. They observed that cell spacing in the cellular regime decreased with growth velocity at a constant thermal gradient and the same happened for columnar dendritic spacing (PDAS) with growth velocity. However, they found a discontinuity in the change of the spacing between cell and columnar dendrite regimes. That is, they found that the PDAS was larger than the cell spacing at a given growth velocity where cells and columnar dendrites co-existed. Somboonsuk et al. [19] and Trivedi [20] also performed directional solidification experiments for succinonitrile– 5.5 mol.% acetone systems and reported the presence of a discontinuity in the spacing of cellular and columnar dendrites at CDT regions. Several researchers performed directional solidification experiments for other metallic systems (Al–Cu [21–23], Fe–Ni [24], Pb–Pd [25] and Pb–Au [25,26]). The primary dendrite arm and cell spacing in the final microstructure of these alloys were measured as a function of thermal gradient (G) and solidification velocity (V) for a fixed alloy
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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composition. A maximum in inter-dendrite spacing of columnar dendrites was observed at the CDT region. It can be extremely important to relate the behavior of PDAS with the dendrite tip radius. Relative to the in situ directional experiments for transparent organic materials [17– 20], obtaining accurate in situ measurement for tip radii in metallic systems is a challenging task. Tiwari [26] conducted careful measurements of tip radii in cellular, columnar and mixed regimes from directionally solidified samples of Pb–8 at.% Au. They reported that the tip radius decreases in the cellular and columnar region with increasing V. It subsequently increases in the region where the cells and columnar dendrites co-exist, then decreases again with increasing V in the columnar region. Similar observations were also reported by Miyata et al. [22] for an Al– 4.1 wt.% Cu alloy. The CDT of Mg–Al alloys can be deduced from the optical micrographs in Fig. 2. The critical cooling rate for the CDT changed with Al concentration. For example, the Mg–3 wt.% Al alloy has an entirely cellular structure at 0.05 K s–1 with no side branching at the growing primary dendrite stem. On the other hand, the Mg–9 wt.% Al alloy showed columnar growth with secondary branches at the same cooling rate. Interestingly, Mg–6 wt.% Al alloy showed a transition between cellular and columnar dendrite (there were no fully developed secondary branches) at 0.05 K s–1. The CDT of Mg–3 wt.% Al alloy occurred at a cooling rate higher than 0.05 K s–1 whereas that of Mg–9 wt.% Al occurred below the 0.05 K s–1 cooling rate. The present experimental results on the CDT of the Mg– Al alloys are summarized in Fig. 8. The PDAS of columnar dendrites for all Mg–Al alloys decreased linearly with increasing cooling rate in the logarithmic scale. Increasing Al concentration also slightly decreased the PDAS at the given cooling rate. In the literature, numerous studies have examined the influence of sol-
Fig. 8. Variation of PDAS of Mg–Al alloys with cooling rate. The dashed curve represents the expected cellular–dendrite transition in Mg–Al with respect to solute content in view of the current experiments and previous data on other alloy systems [21–26].
ute on PDAS for Al- and Sn-based alloy systems with inconsistent results. Okamoto and Kishitake [13] performed unidirectional solidification under constant G and varying V for Al–Si, Al–Cu, Al–Sn, Al–Ni and Al–Ag alloys and observed that the PDAS increased with increasing solute concentration. Young and Kirkwood [27] observed the same trend in unidirectional solidified Al– Cu alloys. However, Peres et al. [28], Rosa et al. [29] and Cruz et al. [30] observed that solute concentration had no effect on PDAS in the directionally solidified microstructure of Al–Si, Pb–Sb and Al–Sn alloy systems under conditions of varying G and V. On the other hand, Rocha et al. [31] reported that PDAS decreases with increasing solute concentration for directionally solidified Al–Cu and Sn– Pb alloy systems; the present experimental results corroborated with this observation. In Fig. 8, cooling rate can be translated as V because the G was not varied significantly in the directional solidification experiments. Similar to previous studies [22,23], a discontinuity in the cell and columnar spacing occurred for the present Mg–Al alloys in the CDT region. That is, the maxima in PDAS were observed at a morphological transition from cellular to columnar dendrite growth. In the case of Mg–3 and 6 wt.% Al alloys, this transition was clearly observed. Unfortunately, as Mg–9 wt.% Al alloy showed columnar growth behavior across the entire cooling rate range of the present study, it was not possible to observe the maximum PDAS. However, from the trend of the cellular and columnar spacing of the Mg–3 and 6 wt.% Al alloys, the change in spacing for Mg– 9 wt.% Al alloy could be estimated as shown in Fig. 8. Zhang et al. [32] conducted directional solidification studies on an Mg–4 wt.% Al alloy and reported that the critical range of CDT for the alloy exists between 0.02 and 0.06 K s–1, which was also observed in the present study. The present experimental results imply that the critical cooling rate for the CDT of Mg–Al alloys increases with increasing solute Al concentration. To the authors’ knowledge, there is no comprehensive study in the literature that establishes the effect of solute content on the CDT for any alloy system. Also, the critical cooling rates for CDT for the present Mg–Al alloys and previous Al–Cu and Pb–Au alloys [22,23,26] were all found to be between 0.01 and 0.1 K s–1. The models for the prediction of PDAS developed by Kurz and Fisher [33] and Trivedi [34] are widely accepted in solidification studies because the previous model by Hunt [35] contained an inherent anomaly in the calculation of dendrite tip radius. Kurz and Fisher proposed a relationship in which the PDAS is related to the square root of the dendrite tip radius. They used the marginal stability criterion (the Langer and Muller-Krumbhaar theory [36] and the Mullins–Sekerka [37] stability criterion) to calculate the tip radius, which was related to the PDAS by assuming the shape of the dendrite to be ellipsoidal. The relationship is mathematically expressed as:
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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1=4 DC k1 ¼ V 1=4 G1=2 DT 0 k GD DT 0 DT 1 ¼ 1 V DT 0 1 k 1=2 4:3DT 1
9
ð3Þ
problem was also observed in the Al–Cu system [22] investigated previously.
ð4Þ
3.4. Columnar–equiaxed transition (CET)
where D is the diffusivity of the solute in the liquid phase, G is the thermal gradient, V is the solidification velocity, C is the Gibbs–Thomson coefficient, k is the equilibrium partition coefficient and DT0 is the solidification range. Trivedi [34] conducted a more rigorous analysis of the dendrite growth problem by modifying Hunt’s criterion [35]. The model predicted a minimum in the solute Peclet number as a function of V, which corroborated their experimental findings for organic materials [19,20]. The model can be mathematically expressed as: pffiffiffi k1 ¼ 2 2V 1=4 G1=2 ½LkDT o CD1=4 ð5Þ where L is a constant that depends on harmonic perturbations, and which Trivedi has stated is equal to 28 for the dendritic growth. The comparison of the present experimental PDAS data and predicted PDAS using the models of Kurz and Fisher [33] and Trivedi [34] are presented in Fig. 9. All the parameters for Eqs. (3)–(5) were taken from a thermodynamic database [16] except for D = 2 109 m2 s–1 and C = 1 107 km. Overall, the modelling results were found to be in reasonable agreement with the experimental results of PDAS of columnar dendrites. However, the predicted transition cooling rate of CDT of the Mg–Al alloys was much lower than the present experimental data. This
During solidification, columnar growth can often be terminated depending on thermal and solutal conditions at the advancing solid/liquid front and a band of equiaxed grains can appear in the solidified microstructure. Numerous theoretical [38–41] and experimental studies [42–50] have been conducted to understand the underlying mechanism of CET. Amongst the theoretical studies, Hunt’s approach [38] for the qualitative prediction of CET has been widely accepted. Based on Hunt’s model, the nucleation and growth of equiaxed dendrites in undercooled liquid ahead of a solid columnar front is a necessary condition for the formation of the equiaxed structure, and CET was assumed to occur when the volume fraction of equiaxed grains growing ahead of the advancing columnar front exceeded 0.66. Hunt’s criterion for CET is expressed as a critical steady-state thermal gradient (G) where the microstructure becomes fully equiaxed: ( 3 ) DT N 1=3 G < 0:617N o 1 DT ð6Þ DT where No is the number of equiaxed grains per unit volume, DTN is the undercooling required for nucleation of equiaxed grains and DT is the undercooling at the growing columnar dendrites. Although, DT can be calculated using
Fig. 9. Comparison of experimental PDAS of Mg–Al alloys with the predicted values from Kurz and Fisher’s [33] and Trivedi’s [34] models.
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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the Kurz–Giovanola–Trivedi (KGT) model [51], it was difficult to estimate accurate values of No and DTN for the given casting process. However, once the experimental ascast microstructure indicating the CET were obtained, Hunt’s model could be applied to the experimental CET results by varying the values of No and DTN. The model could then predict the CET across a wide range of casting conditions (G and V) for the given alloy compositions. Binary alloy systems like Al–Mg, Sn–Pb, Al–Cu, Al–Si, Al–Sn, Pb–Cu and Pb–Sn [42–50] have been investigated for CET using the directional solidification technique as a function of solidification parameters such as melt super heat, thermal gradient (G), solidification velocity (V) and solute content. The results of these experiments can be summarized as: (i) the critical G or V for CET is strictly dependent on the alloy composition and (ii) increasing solute concentration in alloys suppresses the columnar dendritic region by promoting the equiaxed mode of solidification. In most of the experimental studies, critical G and V at which the morphological transitions occur have been explained well by Hunt’s model (Eq. (6)) by adjusting the values of No and DTN. Fig. 10 shows the change of the solidification mode from columnar to equiaxed dendrites for the experimental Mg– Al alloys. In order to capture both solidification modes, the solidification speed (V) was changed during the directional solidification experiments with a constant thermal
gradient (G). Mg–9 wt.% Al was solidified with a V of 0.05 mm s–1 until 100 mm, after which the V was increased to 0.17 mm s–1. Mg–6 wt.% Al was directionally solidified by increasing V from 0.5 to 1 mm s–1. Similarly, Mg– 3 wt.% Al was solidified by increasing the V from 1 to 1.5 mm s–1. This solidification with two different values of V produced a microstructure with three distinct zones (columnar, columnar + equiaxed and equiaxed zones). The process parameters (G, V, cooling rate and Al content) and the resulting microstructure (columnar and equiaxed) from this study are listed in Table 2. It is noted in Fig. 10 that increasing the Al content in Mg alloy increased the region of equiaxed dendrites. That is, the CET occurred at a lower cooling rate when the Al concentration increased. Mg–9 wt.% Al showed CET in a cooling rate range of 0.38–1.17 K s–1, Mg–6 wt.% Al in the range of 2.75–5.5 K s–1 and Mg–3 wt.% Al in the range of 5.5– 8.25 K s–1. Previously, directional solidification experiments were conducted to establish the solidification parameters required for the CET in Al–Sn, Al–Ni, Al–Si and Al– Cu alloys [48–50]. The CET of these alloys occurred in the range of 0.2–1 K mm–1 (G) and 0.2–0.6 mm s–1 (V). The critical cooling rate at which the CET occurred in these alloys was about 0.15–0.8 K s–1, which is a very similar cooling rate for the present Mg–Al alloy. The present experimental results for the CET of Mg–Al binary alloys were analyzed using Hunt’s model [38]. The
Fig. 10. Microstructure for directionally solidified Mg–Al alloys with two different solidification velocities showing the columnar, equiaxed and mixed columnar–equiaxed growth modes. (a) 3 wt.% Al, (b) 6 wt.% Al and (c) 9 wt.% Al.
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Table 2 The results of directional solidification experiments for CET of Mg–Al alloys. Alloy Mg–9 wt.% Mg–9 wt.% Mg–6 wt.% Mg–6 wt.% Mg–3 wt.% Mg–3 wt.%
Al Al Al Al Al Al
Thermal gradient (K mm–1)
Solidification velocity (mm s–1)
Cooling rate (K s–1)
Microstructure
7.0 7.0 5.5 5.5 5.5 5.5
0.05 0.17 0.50 1.00 1.00 1.50
0.38 1.16 2.75 5.5 5.5 8.25
Columnar Equiaxed Columnar Equiaxed Columnar Equiaxed
value of DT in Eq. (6) was calculated using the KGT model [51]. As mentioned above, the critical thermal gradient (G) for the equiaxed microstructure can be calculated from Eq. (6) by selecting different values of No and DTN. In the present study, DTN was set at 0.25 K and different values of No were used in the calculations. The results were superimposed with experimental data and can be seen in Fig. 11. The comparison with directional solidification experimental results revealed that the No value for CET of Mg–Al alloys increased with increasing Al concentration. For example, the No value for Mg–3 wt.% Al was about 1000–10,000 cm3, whereas that of Mg–9 wt.% Al was about 10,000–100,000 cm3. This means that increasing Al concentration requires an increase in the number of
nuclei in the liquid ahead of columnar dendrites to form equiaxed dendrites. The possibility of dendrite arm fragmentation could be ruled out because there was very limited thermo-solutal convection in the present directional solidification system. 3.5. Solidification map of Mg–Al alloys Solidification maps can be useful in predicting as-cast microstructural morphology depending on the solidification conditions and solute content. The calculated solidification map for the Mg–Al alloys is shown in Fig. 12. The transitions between different growth modes are marked by solid lines at a given Al content. The transition from
Fig. 11. The predictions of CET for Mg–Al alloys using Hunt’s model [39] at DTn = 0.25 K in comparison with the present directional solidification (DS) data for (a) 3 wt.% Al, (b) 6 wt.% Al and (c) 9 wt.% Al. The experimental data of Mg–4 wt.% Al data are from Zhang et al. [32].
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Solidification velocity (m/sec)
(a) 101 0
Equiaxed
10
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10
-2
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-3
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-4
Columnar
10
-5
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-6
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Cellular
-7
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Thermal gradient (K/m)
Solidification velocity (m/sec)
(b)
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0
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3 wt. %:Equiaxed-WC 3 wt. %:Equiaxed-DS 3 wt. %:Columnar-DS 3 wt. %:Cellular-DS 4 wt. %:Columnar-DS [32] 4 wt. %:Cellular-DS [32]
Equiaxed
4. Summary
Columnar
Cellular 3
10
4
10
5
increasing the cooling rate can induce more equiaxed microstructures, but the morphology can be changed depending on the changes of G and V even with the same cooling rate. That is, an equiaxed microstructure can be greatly promoted by increasing the solidification velocity at a given cooling rate. It should be noted that the present map in Fig. 12 is valid only for solidification conditions without significant stirring, as this causes dendritic fragmentation that facilitates equiaxed growth and without the addition of inoculants which promote the equiaxed dendrite formation. If the amount of dendritic fragmentation and inoculants are known, the expansion of the equiaxed area can be roughly calculated using Hunt’s model (Eq. (12)) by increasing No.
10
6
Thermal gradient (K/m) Fig. 12. Calculated solidification map for Mg–Al alloys in comparison to experimental data. (a) Solidification map for Mg–Al alloys. (b) Comparison to experimental data for Mg–3 wt.% Al map. WC and DS stand for wedge casting and directional solidification, respectively.
columnar to equiaxed dendrites was calculated as a function of thermal gradient (G) and solidification velocity (V) using Hunt’s model [38] (Eq. (6)) at fixed values of DTN = 0.25 K and No = 10,000 cm3 (an average of the results in Fig. 11). Similarly, the transition between columnar and cellular structures was calculated using the KGT model [51]. The constant cooling rates of 0.1, 10 and 1000 K s–1 are also marked in Fig. 12. The calculated SDAS using Kattamis and Flemings’s model [14] (Eq. (2)) is also marked on the map. Although SDAS can vary slightly with solute content, as seen in Fig. 6, the averaged values for the 3, 6 and 9 wt.% Al alloys at the given cooling rates were used in the map for the sake of simplicity. In order to validate the constructed solidification map, the present experimental data for the Mg–3 wt.% Al alloy and data from the previous study by Zhang et al. [32] for Mg–4 wt.% Al were compared with the map in Fig. 12b. All the growth morphologies were reasonably represented by the calculated map. As mentioned above with regard to Fig. 12, increasing Al concentration can promote the formation of equiaxed microstructures against a columnar structure. In general,
In order to investigate the growth morphology of the Mg–Al alloys, directional solidification and gravity casting experiments were performed across a wide range of cooling rates, between 0.05 and 1000 K s–1. The influence of the solute content (Al) on the growth morphology was also investigated by varying the Al content (3, 6 and 9 wt.% Al). The experimental results were also compared with available solidification models in the literature. The following results were obtained from the present study: (1) The SDAS decreases with increasing solute Al content, which is qualitatively reproduced by Kattamis and Flemings’s model. In the case of columnar dendrite growth, the value of SDAS increases with coarsening process from dendrite tip to dendrite root. Although the matured SDAS near columnar dendrite root is still lower than the calculated values, the SDAS of equiaxed dendrites can be reproduced well by Kattamis and Flemings’s model. (2) Experimental results on the logarithmic relationship between the cooling rate and SDAS of columnar and equiaxed dendrites show that the SDAS cannot be described as a linear relationship over the entire range of cooling rate. (3) Transitions from cellular to columnar dendrite and from columnar to equiaxed dendrite were experimentally determined. Increasing the Al content promotes the equiaxed dendrite over the columnar dendrite, and the columnar dendrite over cellular growth, respectively. (4) A solidification map for Mg–Al was calculated using Hunt’s model and the KGT model, and was validated using the present experimental data. Although the solidification morphology can be influenced by the cooling rate, the thermal gradient (G) and te solidification velocity (V) can independently influence the growth morphology of Mg–Al alloys even at a given cooling rate.
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Acknowledgements This research was supported by funding from the NSERC Magnesium Strategic Research Network (MagNET) grant, the Strategic Network Enhancement Initiative (SNEI) program and General Motors of Canada. The authors deeply thank Prof. Y.-B. Kang at GIFT, Postech, South Korea, Dr. E. Essadiqi at CANMET-MTL, Canada and Prof. K.-Y. Kim and Dr. B.-H. Kang at KUTECH, South Korea for the usage of a directional solidification, wedge casting, Cu mould casting and water quenching experiment equipment, respectively. References [1] Caceres CH, Davidson CJ, Griffithes JR, Newton CL. Mater Sci Eng 2002;325A:344. [2] Cai J, Ma GC, Liu Z, Zhang HF, Hu ZQ. J Alloys Compd 2006;422:92. [3] Park SS, Bae GT, Kang DH, Jung I-H, Shin KS, Kim NJ. Scripta Mater 2007;57:793. [4] Bouchard D, Kirkaldy JS. Metall Trans 1997;28B:631. [5] He Y, Javaid A, Essadiqi E, Shehata M. Can Met Quart 2009;48(2):145. [6] Kurz W, Fisher DJ. Fundamentals of solidification. Zurich: Trans Tech Publications; 1992. [7] Pettersen K, Lohne O, Ryum N. Metall Trans 1990;21A:230. [8] Tensi HM, Ro¨sch R. In: Magnesium alloys and their applications, DGM Verlag, Oberursel, Germany; 1992, p. 283. [9] Sasaki H, Adachi M, Sakamoto T, Takimoto A. In: Proceedings of the 53rd Annual World Magnesium Conference, McLean, Virginia, USA; 1996, p. 86. [10] Sequeira WP, Murray MT, Dunlop GL, St. John DH. TMS; 1997. p. 169. [11] Labrecque C, Angers R, Tremblay R, Dube´ D. Can Met Quart 1997;36:169. [12] Dube´ D, Couture A, Carbonneau Y, Fiset M, Angers R, Tremblay R. Int J Cast Metals Res 1998;11:139. [13] Okamoto T, Kishitake K. J Cryst Growth 1975;29:137. [14] Kattamis TZ, Flemings MC. AIME 1965;233:992. [15] Mortensen A. Metall Trans 1989;20A:247.
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[16] Bale CW, Be´lisle E, Chartrand P, Decterov SA, Eriksson G, Hack K, et al. CALPHAD 2009;31:295. [17] Esaka H, Kurz W. J Cryst Growth 1985;72:578. [18] Trivedi R, Shen Y, Liu S. Proc. ICAAMP; 2001. p. 42. [19] Somboonsuk K, Mason JT, Trivedi R. Metall Trans 1984;15A:967. [20] Trivedi R. Metall Trans 1984;15A:977. [21] Sharp RM, Hellawell A. J Cryst Growth 1970;6:253. [22] Miyata Y, Suzuki T, Uno JI. Metall Trans 1985;16A:1799. [23] McCartney DG, Hunt JD. Acta Metall 1981;29:1851. [24] Jin I, Purdy GR. J Cryst Growth 1974;23:37. [25] Mason JT, Verhoeven JD, Trivedi R. Metall Trans 1984;15A:1665. [26] Tiwari SN. Mater Sci Eng 1990;130A:219. [27] Young KP, Kirkwood DH. Metall Trans 1975;6A:198. [28] Peres MD, Siqueira CA, Garcia A. J Alloys Compd 2004;381:168. [29] Rosa DM, Spinelli JE, Ferreira IL, Garcia A. Metall Trans 2008;39A:2162. [30] Cruz KS, Spinelli JE, Ferreira IL, Garcia A. Mater Chem Phys 2008;109:87. [31] Rocha OL, Siqueira CA, Garcia A. Metall Trans 2003;34A:995. [32] Zhang C, Ma D, Wu K-S, Cao H-B, Kou S, Chang YA, et al. Intermetallics 2007;15:1395. [33] Kurz W, Fisher DJ. Acta Metall 1980;29:11. [34] Trivedi R. Metall Trans 1984;15:977. [35] Hunt JD. Solidification and casting of metals. London: The Metals Society; 1979. p. 3. [36] Langer JS, Muller-Krumbhaar H. J Cryst Growth 1977;42:11. [37] Mullins WW, Sekerka RF. J Appl Phys 1964;35:444. [38] Hunt JD. Mater Sci Eng 1984;65:75. [39] Flood SC, Hunt JD. J Cryst Growth 1987;82:552. [40] Fredriksson H, Olsson A. Mater Sci Technol 1986;2:508. [41] Lipton J, Kurz W, Heinemann W. Concast Technol News 1983;22:4. [42] Plaskett TS, Winegard WC. Trans ASM 1959;51:222. [43] Mahapatra RB, Weinberg F. Metall Trans 1987;18B:425. [44] Ziv I, Weinberg F. Metall Trans 1989;20B:731. [45] Suri VK, El-Kaddah N, Berry JT. Trans AFS 1991;99:187. [46] Ledgard LJ, McCartney DG. In: Proceedings of the 4th decennial international conference on solidification processing, Sheffield, UK; 1997. p. 227. [47] Kim S, Grugel RN. Metall Trans 1992;32A:1807. [48] Cante MV, Cruz KS, Spinelli JE, Cheung N, Garcia A. Mater Lett 2007;61:2135. [49] Siqueria A, Cheung N, Garcia A. J Alloys Compd 2003;351:126. [50] Siqueria A, Cheung N, Garcia A. Metall Trans 2002;33A:2107. [51] Kurz W, Giovanola B, Trivedi R. Acta Metall 1986;34:823.
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Acta Materialia xxx (2013) xxx–xxx www.elsevier.com/locate/actamat
The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification Manas Paliwal, In-Ho Jung ⇑ Dept. Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, QC, Canada H3A 2B2 Received 3 January 2013; received in revised form 17 April 2013; accepted 21 April 2013
Abstract The comprehensive microstructural evolution of Mg–3, 6 and 9 wt.% Al alloys with respect to the solidification parameters such as thermal gradient (G), solidification velocity (V), cooling rate (GV) and solute (Al) content were investigated in the present study. Various solidification techniques, including directional solidification, wedge casting, sand and graphite mould casting, gravity casting in a Cu mould and water quenching, were employed in order to obtain wide ranges of cooling rates between 0.05 and 1000 K s–1. The microstructural length scales of Mg–Al alloys, such as secondary dendrite arm spacing and primary dendrite arm spacing, were determined experimentally and compared with published models. In addition, the solidification parameters of morphological transitions such as cellular to columnar dendrite and columnar to equiaxed dendrite were also determined. Based on all the experimental data and the solidification model, a solidification map was built in order to provide guidelines for the as-cast microstructural features of Mg–Al alloys. Crown Copyright Ó 2013 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. Keywords: Mg–Al alloy; Solidification; Growth morphology; Solidification map
1. Introduction As magnesium alloys are the lightest structural metallic materials, a great amount of research has been conducted recently relating to the transportation sector, with goals of improving fuel efficiency and reducing CO2 emissions. Most magnesium components are produced using melting and casting practices wherein as-cast products are finalized through thermo-mechanical processing or through small machining of the surface. Even in welding practices, the solidification microstructure of the alloy is retained in the welded zone. The characteristics of an as-cast microstructure, such as the size of the dendrite (grain), the nature of the dendrite (columnar or equiaxed), primary dendrite arm spacing (PDAS) and secondary dendrite arm spacing (SDAS), determine the mechanical properties of the as-cast products and the thermo-mechanical processing conditions ⇑ Corresponding author. Tel.: +1 514 398 2608; fax: +1 514 398 4492.
E-mail address: [email protected] (I.-H. Jung).
[1–3]. Therefore, understanding solidification microstructure evolution through both experimental and microstructural modelling studies is important. The evolution of a solidification microstructure in a metallic system can be characterized by different growth morphologies, such as cellular, columnar and equiaxed dendritic growth. The obtained microstructure is a result of the complex interplay between several solidification parameters. With this in mind, understanding the roles of different solidification parameters such as thermal gradient (G), solidification velocity (V), cooling rate (GV) and solute content is imperative in order to control the final microstructure of these alloys. To date, no comprehensive experimental work has been conducted on Mg alloys in order to understand the influences of the various solidification parameters and alloying elements on the evolution of different growth morphologies. The purpose of the present study is to experimentally investigate the microstructural evolution of Mg–3, 6 and 9 wt.% Al alloys, including cellular–columnar and colum-
1359-6454/$36.00 Crown Copyright Ó 2013 Published by Elsevier Ltd. on behalf of Acta Materialia Inc. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2013.04.063
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nar–equiaxed dendrite transitions, and to determine the important length scales, such as PDAS and SDAS, depending on the casting parameter and the solute content. This work is part of a comprehensive project that focuses on the experimental and numerical stimulation of the solidification microstructure of Mg alloys under various casting conditions. 2. Experimental The solidification experiments carried out in this study can be classified into two categories: steady-state and transient-state experiments. The schematics of the different solidification techniques employed in the present study are shown in Fig. 1. All the experiments were conducted for Mg–3, 6 and 9 wt.% Al alloys. 2.1. Steady-state experiment Directional solidification experiments have been widely used in order to investigate the columnar growth of various alloys [4]. This technique can induce heat extraction in a single direction with an established thermal gradient, which causes the solid phase to grow towards the opposite side of the heat extraction. The thermal gradient (G) and solidification velocity (V) can be varied independently, and the product of both gives the cooling rate. In the present study, the solidification process was carried out in an alumina cru-
cible of 300 mm length, 5.5 mm inner diameter and 1.5 mm thickness. An Mg alloy sample bar of 200 mm length was machined and placed in an alumina crucible, which was then loaded into an induction furnace column as shown in Fig. 1a. The furnace temperature was kept at 710 °C. After pulling out the sample about 100 mm from the induction furnace column, it was quenched by helium gas. The frozen solid–liquid solidification front was then examined using metallographic techniques for the further characterization of the as-cast microstructure. No noticeable chemical reaction between the alumina crucible and the Mg alloys was observed during the experiment. The thermal gradient (G) was measured by mounting a 1 mm diameter thin K-type sheath thermocouple in the alumina crucible. The temperature was recorded with a data logger attached to a computer when the sample was pulled down with the desired solidification velocity. The thermal gradient was determined from the slope of the temperature–distance curves at the liquidus temperature of each alloy. Cooling rates in the range of 0.05–9 K s–1 were achieved through the directional solidification experiments. The details are summarized in Table 1. 2.2. Transient-state experiment In order to obtain the solidification microstructure at intermediate and higher cooling rates, various gravity casting experiments were performed. In these experiments, the
Fig. 1. Schematics of the solidification techniques used in the present study. (a) Directional solidification, (b) water-cooled Cu wedge-shaped mould, (c) sand mould, (d) graphite mould and (e) water quenching. The dots in (b–d) represent the positions of thermocouple.
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Table 1 The parameters of directional solidification and gravity casting experiments for Mg–Al (3, 6 and 9 wt.%) alloys. Casting
Thermal gradient (K mm–1)
Solidification velocity (mm s–1)
Cooling rate (K s–1)
Directional solidification
8.5 7.5 7.0 5.5 – – – – –
0.00625 0.05 0.17 0.50 – – – – –
0.05 0.38 1.16 2.75 30, 75, 100 20 1 175 687 ± 200
Wedge mould Graphite mould Sand mould Cu mould Water quenching
thermal gradient and solidification velocity were coupled time-dependent parameters which were difficult to determine. Therefore, the cooling rate was the only variable that could be experimentally measured. Casting in a watercooled wedge-shaped Cu mould (see Fig. 1b) is an efficient way to obtain different cooling rates in a single casting experiment. Experimental curves determined by thermocouples and heat flow simulations [5] showed that the cooling rate can be varied from over 250 K s–1 at the tip of wedge to just a few K s–1 near the top of the wedge. As shown in Fig. 1b, three K-type thermocouples were inserted at different positions from the tip of the wedge mould to record the cooling rate; as-cast samples were taken from these locations. Sand and graphite moulds were also employed for the casting at low and intermediate cooling rates, as shown in Fig. 1c and d, respectively. To obtain higher cooling rates, Mg alloys were cast in a 7 mm diameter Cu mould. A K-type sheath thermocouple with a 1 mm diameter was inserted at the center of the mould and connected to a CHINO KR3120 data acquisition system capable of recording at high frequencies (20 signals s–1). However, due to very fast cooling in the Cu mould, the liquidus temperatures for the Mg–Al alloys were hard to capture to determine the exact cooling rate for the alloys. In order to obtain the cooling rate of the samples, the experimental cooling curve obtained from the casting experiments was extrapolated to the liquidus temperatures of the Mg–Al alloys. To obtain more rapid cooling rates, direct water quenching experiments were performed (see Fig. 1e). The alloy samples were contained in a stainless steel tube (O.D. = 6.35 mm, I.D. = 5 mm) and the whole set-up was placed inside a resistance furnace at 700 °C. After holding the Mg–Al alloy sample for 1 h in an inert Ar atmosphere, the stainless tube was dropped in a cold water bath. A K-type sheath thermocouple was inserted in the tube wall to record the thermal history during the experiment. The cooling rates obtained with different casting techniques are summarized in Table 1. 2.3. Microstructural characterization The microstructural characterization of the directionally solidified alloy samples was performed both for the longi-
tudinal and transverse sections close to the quenched solid–liquid interface. Similarly, for the gravity cast experiments, the metallographic samples were taken from the sections close to the thermocouple tip. The samples were cold mounted and polished with 240, 400, 600 and 1200 grit SiC papers, then fine polished with 3 and 1 lm diamond pastes. The sample surfaces were cleaned with an ultrasonic bath for 20 min before etching with acetal–picral solution (4.2 g of picric acid, 10 ml of H2O, 10 ml of acetic acid and 70 ml of ethanol) before optical image analysis. The etching was performed by carefully immersing the samples in the etchant for 4–5 s, then cleaning the sample surface with running water and ethanol. The optical microscopy was performed using a CLEMEX optical image analyzer. The PDAS and SDAS were measured from the optical images of the solidified samples using the linear intercept method. 3. Results and discussion 3.1. General as-cast microstructure of Mg–Al alloys The as-cast microstructures of the directionally solidified Mg–Al alloys are shown in Fig. 2 and the microstructures obtained from gravity casting experiments are presented in Fig. 3. The microstructures for directionally solidified alloys showed columnar growth, with the primary dendrite stems growing against the heat extraction direction. Substantial side branching was seen for all the alloys, and the microstructures became finer as the solute content increased from 3 to 9 wt.% Al at the given cooling rate. Equiaxed dendrites were observed for all the gravity castings, as seen in Fig. 3. 3.2. SDAS of Mg–Al alloys SDAS is an important length scale in microstructural solidification as it can set the diffusion distance in solidification which directly affects the microsegregation of the final solidified alloy [6]. SDAS has been actively investigated for various Al alloys [4]. However, even for Al alloys, there has been no single comprehensive study on the evolution of SDAS encompassing a wide range of cooling rates
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Fig. 2. The microstructure of directionally solidified Mg–Al alloys with different cooling rates (CR). G and V represent thermal gradient and solidification velocity, respectively. L and T represent longitudinal and transverse sections of samples, respectively.
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Fig. 3. The microstructure of Mg–Al alloys solidified using different casting methods.
(from a low cooling rate such as 0.05 K s–1 to a high cooling rate of several hundred K s–1). For Mg alloys, the SDAS has been specifically investigated for AZ91 cast alloy by many researchers [7–12] in the cooling rate ranging from 0.05 to 106 K s–1. Dube´ et al. [12] proposed a linear relationship between the cooling rate and SDAS (in a log–log scale) in this cooling rate range, which was mathematically expressed as: log k ¼ logð39:8Þ 0:32 log s
ð1Þ
where k is the measured SDAS (lm) and s is the cooling rate (K s–1). However, the experimental results by Pettersen et al. [7] and Tensi and Ro¨sch [8] using directional solidification experiments in the cooling rate range of 0.05– 0.17 K s–1 were found to deviate from this linear relationship. Although the SDAS can be more accurately determined in the directional solidification experiments, the measured SDAS at low cooling rates is found to be lower than that calculated from the linear relationship. A summary of the present experimental results for the SDAS of Mg–Al binary alloys is shown in Fig. 4 as a func-
tion of cooling rate and Al content. It is noted that the cooling rates were precisely determined for all the experimental points. Increasing the solute content decreased the SDAS of the Mg–Al alloys. Although it seems that the SDAS decreases linearly with cooling rate in logarithm scale, a closer look at the experimental data suggests a possibility that the log(SDAS) may not be a strictly linear function with log(cooling rate) in a wide range of cooling rates. It is interesting to note that the linearity relationship between SDAS and cooling rate can still be satisfied by a subset of SDAS data within each dendrite region (columnar dendrite growth below about 10 K s–1 and equiaxed dendrite growth above 20 K s–1), which may imply that the solidification mode may influence the relationship between SDAS and cooling rate or that the standard determination techniques of SDAS in the two different dendrite modes may not be equivalent. Interestingly, the same trend has been observed in the evolution of SDAS for Al–Si and Sn–Pb alloys in the directional solidification experiments performed by Okamoto and Kishitake [13]. It should be noted that the SDAS of these alloys also deviated from
100 80
SDAS (µm)
60 40
20
Al -2.8 wt. % Si [13] Al -5.0 wt. % Si [13] Sn -2.8 wt. % Pb[13] Sn -4.1 wt. % Pb[13]
10
-1
10
0
10
1
Cooling rate (K/sec) Fig. 4. The variation of SDAS for Mg–Al alloy with cooling rate and Al concentration.
Fig. 5. The variation of SDAS for Al–Si and Sn–Pb alloy [13] with cooling rate.
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the linear logarithmic relationship at cooling rates below 0.5 and 1 K s–1, respectively, as shown in Fig. 5. The theoretical approach to the evolution of the SDAS implicates it as a function of cooling rate and alloy composition. The SDAS in the final solidified microstructure can be predicted by modelling the physics of different coarsening mechanisms that operate during solidification [6]. Kattamis and Flemings [14] proposed a model to predict the SDAS based on a coarsening mechanism similar to the Ostwald ripening phenomenon in which the growth of a dendrite takes place by the dissolution of smaller dendrites in the melt. Kattamis and Flemings’s model considered the cylindrical shaped (different radii) and two side branches (arms) of a growing columnar dendrite and assumed the presence of uniform temperature along the side branches. Furthermore, the different radii of the branches induce a difference in chemical potential between the neighbouring side branches which thermodynamically promotes the flow of solute from the smaller arm to the larger one via liquid between the branches. This process continues in the mushy zone until the smaller arm completely remelts. The proposed mathematical formulation by Kattamis and Flemings’s model can be written as: 0 k2 ¼ 5:5@
CDl ln
C eut Co
ml ð1 k o ÞðC eut C o Þ
1n A tn f
ð2Þ
where k2 is SDAS, C is the Gibbs–Thomson coefficient, Dl is the diffusivity of the solute in liquid phase, Ceut is the eutectic composition where the solidification terminates, Co is the solute composition, ml is the liquidus slope, ko is the equilibrium partitioning coefficient, tf is the time for solidification and n is the coarsening exponent. Several modifications of Kattamis and Flemings’s coarsening model are also available in the literature which address other possible coarsening mechanisms, such as remelting, the dissolution of the secondary branches from their roots or the coalescence between neighboring dendrite arms [15]. All the proposed coarsening mechanisms [14,15] tend to increase the final SDAS in the solidified microstructure, and these mechanisms are known to be valid for both columnar and equiaxed growth regimes [14]. The coarsening model of Kattamis and Flemings [14] was applied to predict the SDAS for Mg–Al alloys. The calculated results are shown in Fig. 6 and compared with experimental data. All the parameters for Eq. (2) were taken from a thermodynamic database [16] except D = 2 109 m2 s–1, C = 1 107 km and n = 1/3. It should be noted that the calculated SDAS were lower than experimental data at high cooling rates but were higher than the experimental data at low cooling rates. It should also be noted that the calculated SDAS were slightly lower than experimental data in the high cooling rate region but were slightly higher than the experimental data in the low cooling rate region. The coarsening exponent (n) in Eq.
(2) is generally accepted as 1/3. However, this value was changed slightly to confirm the influence of the coarsening exponent to the calculations of SDAS. As shown in Fig. 6, a small change in exponent can shift the curve up and down but hardly changes the slope of the curves. The calculated slope from the model is in excellent agreement with the experimental data for equiaxed dendrite, but is more negative than the experimental SDAS slope of columnar dendrite. This difference in slope for columnar dendrite becomes more significant with increasing Al concentration. It is unclear why this discrepancy should occur, but the possibility of it occurring is particularly high in the high solute alloy. The evolution of SDAS with cooling rate or solidification time is a complex process which is historically explained in the solidification theories within the framework of the coarsening phenomena. Kattamis and Flemings’s model describes the coarsening process as the dissolution of smaller secondary arms. However, there could be other coarsening processes, such as remelting or coalescence of secondary arms, that could possibly affect the final secondary arm spacing. The change in the SDAS from the quenched solid–liquid interface to the root of the columnar dendrite was measured, and is shown in Fig. 7. Interestingly, the SDAS increased noticeably with the distance from the quenched solid–liquid interface to the root of the dendrite, which implies that the distance between the secondary arms can increase during the coarsening process. Although the SDAS of the coarsened secondary arms became closer to the calculated results using Kattamis and Flemings’s model [14], they were still lower than the calculated values. For example, the most matured SDAS obtained at the dendrite roots for Mg–Al alloys solidified at the cooling rate of 0.375 K s–1 were compared with the calculated SDAS curves from Kattamis and Flemings’s model in Fig. 6. 3.3. Cellular–columnar dendrite transition (CDT) The CDT has been actively investigated both experimentally and numerically. Directional solidification experiments have aided significantly in understanding the mechanism of the CDT in a number of organic and metallic systems. The different growth morphologies, like planar, cellular, columnar and equiaxed, that occur during the solidification of alloys are a direct result of the thermodynamic and kinetic conditions prevailing at the dendrite tip. The growth parameters affecting the conditions of dendrite tip radius (rt) are the thermal gradient (G), solidification velocity (V) and solute composition (Co) of the alloy at the tip. Thus, any change in the growth morphology, specifically the transition between planar to cellular growth or the cellular to columnar growth should be reflected by a change in the tip radius, tip composition and tip temperature as a function of G, V and Co. Several researchers [17–20] have carried out the simultaneous measurements of tip radii, tip composition and PDAS for organic systems. Esaka and Kurz [17] carried
Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063
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(b)
(a)
0.32
10
1 -1 10
n = 0.34 0.33
100
SDAS (µm)
SDAS (µm)
n = 0.34 0.33 100 0.32
7
10
Mg-3 wt. % Al
Mg-6 wt. % Al
Model
Model
0
10
1
2
10
3
10
10
1
-1
10
0
10
Cooling rate (K/sec)
(c)
2
10
3
10
Cooling rate (K/sec) n = 0.34
100
SDAS (µm)
1
10
0.33 0.32
10
Mg-9 wt. % Al Model 1 -1 10
0
1
10
10
2
10
3
10
Cooling rate (K/sec) Fig. 6. Comparison of experimental SDAS of Mg–Al alloys with the predicted SDAS curves from Kattamis and Flemings’s model [14] using different coarsening exponents (n). (a) Mg–3 wt.% Al, (b) Mg–6 wt.% Al and (c) Mg–9 wt.% Al. Half-filled symbols represent the SDAS obtained at the root of a columnar dendrite.
Fig. 7. Variation of SDAS of the Mg–Al alloys from the quenched solid– liquid interface to the root of the columnar dendrite directionally solidified at 0.375 K s–1.
out a directional solidification experiment on succinonitrile–1.3 wt.% acetone to measure the tip radius, tip temperature and initial SDAS. They found that the tip radius in the dendritic regime decreased with the growth rate at a constant thermal gradient; however, no results in the cel-
lular regime were obtained. Trivedi et al. [18] also conducted in situ measurements of tip radius and interdendrite spacing in a succinonitrile–salol system. They observed that cell spacing in the cellular regime decreased with growth velocity at a constant thermal gradient and the same happened for columnar dendritic spacing (PDAS) with growth velocity. However, they found a discontinuity in the change of the spacing between cell and columnar dendrite regimes. That is, they found that the PDAS was larger than the cell spacing at a given growth velocity where cells and columnar dendrites co-existed. Somboonsuk et al. [19] and Trivedi [20] also performed directional solidification experiments for succinonitrile– 5.5 mol.% acetone systems and reported the presence of a discontinuity in the spacing of cellular and columnar dendrites at CDT regions. Several researchers performed directional solidification experiments for other metallic systems (Al–Cu [21–23], Fe–Ni [24], Pb–Pd [25] and Pb–Au [25,26]). The primary dendrite arm and cell spacing in the final microstructure of these alloys were measured as a function of thermal gradient (G) and solidification velocity (V) for a fixed alloy
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composition. A maximum in inter-dendrite spacing of columnar dendrites was observed at the CDT region. It can be extremely important to relate the behavior of PDAS with the dendrite tip radius. Relative to the in situ directional experiments for transparent organic materials [17– 20], obtaining accurate in situ measurement for tip radii in metallic systems is a challenging task. Tiwari [26] conducted careful measurements of tip radii in cellular, columnar and mixed regimes from directionally solidified samples of Pb–8 at.% Au. They reported that the tip radius decreases in the cellular and columnar region with increasing V. It subsequently increases in the region where the cells and columnar dendrites co-exist, then decreases again with increasing V in the columnar region. Similar observations were also reported by Miyata et al. [22] for an Al– 4.1 wt.% Cu alloy. The CDT of Mg–Al alloys can be deduced from the optical micrographs in Fig. 2. The critical cooling rate for the CDT changed with Al concentration. For example, the Mg–3 wt.% Al alloy has an entirely cellular structure at 0.05 K s–1 with no side branching at the growing primary dendrite stem. On the other hand, the Mg–9 wt.% Al alloy showed columnar growth with secondary branches at the same cooling rate. Interestingly, Mg–6 wt.% Al alloy showed a transition between cellular and columnar dendrite (there were no fully developed secondary branches) at 0.05 K s–1. The CDT of Mg–3 wt.% Al alloy occurred at a cooling rate higher than 0.05 K s–1 whereas that of Mg–9 wt.% Al occurred below the 0.05 K s–1 cooling rate. The present experimental results on the CDT of the Mg– Al alloys are summarized in Fig. 8. The PDAS of columnar dendrites for all Mg–Al alloys decreased linearly with increasing cooling rate in the logarithmic scale. Increasing Al concentration also slightly decreased the PDAS at the given cooling rate. In the literature, numerous studies have examined the influence of sol-
Fig. 8. Variation of PDAS of Mg–Al alloys with cooling rate. The dashed curve represents the expected cellular–dendrite transition in Mg–Al with respect to solute content in view of the current experiments and previous data on other alloy systems [21–26].
ute on PDAS for Al- and Sn-based alloy systems with inconsistent results. Okamoto and Kishitake [13] performed unidirectional solidification under constant G and varying V for Al–Si, Al–Cu, Al–Sn, Al–Ni and Al–Ag alloys and observed that the PDAS increased with increasing solute concentration. Young and Kirkwood [27] observed the same trend in unidirectional solidified Al– Cu alloys. However, Peres et al. [28], Rosa et al. [29] and Cruz et al. [30] observed that solute concentration had no effect on PDAS in the directionally solidified microstructure of Al–Si, Pb–Sb and Al–Sn alloy systems under conditions of varying G and V. On the other hand, Rocha et al. [31] reported that PDAS decreases with increasing solute concentration for directionally solidified Al–Cu and Sn– Pb alloy systems; the present experimental results corroborated with this observation. In Fig. 8, cooling rate can be translated as V because the G was not varied significantly in the directional solidification experiments. Similar to previous studies [22,23], a discontinuity in the cell and columnar spacing occurred for the present Mg–Al alloys in the CDT region. That is, the maxima in PDAS were observed at a morphological transition from cellular to columnar dendrite growth. In the case of Mg–3 and 6 wt.% Al alloys, this transition was clearly observed. Unfortunately, as Mg–9 wt.% Al alloy showed columnar growth behavior across the entire cooling rate range of the present study, it was not possible to observe the maximum PDAS. However, from the trend of the cellular and columnar spacing of the Mg–3 and 6 wt.% Al alloys, the change in spacing for Mg– 9 wt.% Al alloy could be estimated as shown in Fig. 8. Zhang et al. [32] conducted directional solidification studies on an Mg–4 wt.% Al alloy and reported that the critical range of CDT for the alloy exists between 0.02 and 0.06 K s–1, which was also observed in the present study. The present experimental results imply that the critical cooling rate for the CDT of Mg–Al alloys increases with increasing solute Al concentration. To the authors’ knowledge, there is no comprehensive study in the literature that establishes the effect of solute content on the CDT for any alloy system. Also, the critical cooling rates for CDT for the present Mg–Al alloys and previous Al–Cu and Pb–Au alloys [22,23,26] were all found to be between 0.01 and 0.1 K s–1. The models for the prediction of PDAS developed by Kurz and Fisher [33] and Trivedi [34] are widely accepted in solidification studies because the previous model by Hunt [35] contained an inherent anomaly in the calculation of dendrite tip radius. Kurz and Fisher proposed a relationship in which the PDAS is related to the square root of the dendrite tip radius. They used the marginal stability criterion (the Langer and Muller-Krumbhaar theory [36] and the Mullins–Sekerka [37] stability criterion) to calculate the tip radius, which was related to the PDAS by assuming the shape of the dendrite to be ellipsoidal. The relationship is mathematically expressed as:
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1=4 DC k1 ¼ V 1=4 G1=2 DT 0 k GD DT 0 DT 1 ¼ 1 V DT 0 1 k 1=2 4:3DT 1
9
ð3Þ
problem was also observed in the Al–Cu system [22] investigated previously.
ð4Þ
3.4. Columnar–equiaxed transition (CET)
where D is the diffusivity of the solute in the liquid phase, G is the thermal gradient, V is the solidification velocity, C is the Gibbs–Thomson coefficient, k is the equilibrium partition coefficient and DT0 is the solidification range. Trivedi [34] conducted a more rigorous analysis of the dendrite growth problem by modifying Hunt’s criterion [35]. The model predicted a minimum in the solute Peclet number as a function of V, which corroborated their experimental findings for organic materials [19,20]. The model can be mathematically expressed as: pffiffiffi k1 ¼ 2 2V 1=4 G1=2 ½LkDT o CD1=4 ð5Þ where L is a constant that depends on harmonic perturbations, and which Trivedi has stated is equal to 28 for the dendritic growth. The comparison of the present experimental PDAS data and predicted PDAS using the models of Kurz and Fisher [33] and Trivedi [34] are presented in Fig. 9. All the parameters for Eqs. (3)–(5) were taken from a thermodynamic database [16] except for D = 2 109 m2 s–1 and C = 1 107 km. Overall, the modelling results were found to be in reasonable agreement with the experimental results of PDAS of columnar dendrites. However, the predicted transition cooling rate of CDT of the Mg–Al alloys was much lower than the present experimental data. This
During solidification, columnar growth can often be terminated depending on thermal and solutal conditions at the advancing solid/liquid front and a band of equiaxed grains can appear in the solidified microstructure. Numerous theoretical [38–41] and experimental studies [42–50] have been conducted to understand the underlying mechanism of CET. Amongst the theoretical studies, Hunt’s approach [38] for the qualitative prediction of CET has been widely accepted. Based on Hunt’s model, the nucleation and growth of equiaxed dendrites in undercooled liquid ahead of a solid columnar front is a necessary condition for the formation of the equiaxed structure, and CET was assumed to occur when the volume fraction of equiaxed grains growing ahead of the advancing columnar front exceeded 0.66. Hunt’s criterion for CET is expressed as a critical steady-state thermal gradient (G) where the microstructure becomes fully equiaxed: ( 3 ) DT N 1=3 G < 0:617N o 1 DT ð6Þ DT where No is the number of equiaxed grains per unit volume, DTN is the undercooling required for nucleation of equiaxed grains and DT is the undercooling at the growing columnar dendrites. Although, DT can be calculated using
Fig. 9. Comparison of experimental PDAS of Mg–Al alloys with the predicted values from Kurz and Fisher’s [33] and Trivedi’s [34] models.
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the Kurz–Giovanola–Trivedi (KGT) model [51], it was difficult to estimate accurate values of No and DTN for the given casting process. However, once the experimental ascast microstructure indicating the CET were obtained, Hunt’s model could be applied to the experimental CET results by varying the values of No and DTN. The model could then predict the CET across a wide range of casting conditions (G and V) for the given alloy compositions. Binary alloy systems like Al–Mg, Sn–Pb, Al–Cu, Al–Si, Al–Sn, Pb–Cu and Pb–Sn [42–50] have been investigated for CET using the directional solidification technique as a function of solidification parameters such as melt super heat, thermal gradient (G), solidification velocity (V) and solute content. The results of these experiments can be summarized as: (i) the critical G or V for CET is strictly dependent on the alloy composition and (ii) increasing solute concentration in alloys suppresses the columnar dendritic region by promoting the equiaxed mode of solidification. In most of the experimental studies, critical G and V at which the morphological transitions occur have been explained well by Hunt’s model (Eq. (6)) by adjusting the values of No and DTN. Fig. 10 shows the change of the solidification mode from columnar to equiaxed dendrites for the experimental Mg– Al alloys. In order to capture both solidification modes, the solidification speed (V) was changed during the directional solidification experiments with a constant thermal
gradient (G). Mg–9 wt.% Al was solidified with a V of 0.05 mm s–1 until 100 mm, after which the V was increased to 0.17 mm s–1. Mg–6 wt.% Al was directionally solidified by increasing V from 0.5 to 1 mm s–1. Similarly, Mg– 3 wt.% Al was solidified by increasing the V from 1 to 1.5 mm s–1. This solidification with two different values of V produced a microstructure with three distinct zones (columnar, columnar + equiaxed and equiaxed zones). The process parameters (G, V, cooling rate and Al content) and the resulting microstructure (columnar and equiaxed) from this study are listed in Table 2. It is noted in Fig. 10 that increasing the Al content in Mg alloy increased the region of equiaxed dendrites. That is, the CET occurred at a lower cooling rate when the Al concentration increased. Mg–9 wt.% Al showed CET in a cooling rate range of 0.38–1.17 K s–1, Mg–6 wt.% Al in the range of 2.75–5.5 K s–1 and Mg–3 wt.% Al in the range of 5.5– 8.25 K s–1. Previously, directional solidification experiments were conducted to establish the solidification parameters required for the CET in Al–Sn, Al–Ni, Al–Si and Al– Cu alloys [48–50]. The CET of these alloys occurred in the range of 0.2–1 K mm–1 (G) and 0.2–0.6 mm s–1 (V). The critical cooling rate at which the CET occurred in these alloys was about 0.15–0.8 K s–1, which is a very similar cooling rate for the present Mg–Al alloy. The present experimental results for the CET of Mg–Al binary alloys were analyzed using Hunt’s model [38]. The
Fig. 10. Microstructure for directionally solidified Mg–Al alloys with two different solidification velocities showing the columnar, equiaxed and mixed columnar–equiaxed growth modes. (a) 3 wt.% Al, (b) 6 wt.% Al and (c) 9 wt.% Al.
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Table 2 The results of directional solidification experiments for CET of Mg–Al alloys. Alloy Mg–9 wt.% Mg–9 wt.% Mg–6 wt.% Mg–6 wt.% Mg–3 wt.% Mg–3 wt.%
Al Al Al Al Al Al
Thermal gradient (K mm–1)
Solidification velocity (mm s–1)
Cooling rate (K s–1)
Microstructure
7.0 7.0 5.5 5.5 5.5 5.5
0.05 0.17 0.50 1.00 1.00 1.50
0.38 1.16 2.75 5.5 5.5 8.25
Columnar Equiaxed Columnar Equiaxed Columnar Equiaxed
value of DT in Eq. (6) was calculated using the KGT model [51]. As mentioned above, the critical thermal gradient (G) for the equiaxed microstructure can be calculated from Eq. (6) by selecting different values of No and DTN. In the present study, DTN was set at 0.25 K and different values of No were used in the calculations. The results were superimposed with experimental data and can be seen in Fig. 11. The comparison with directional solidification experimental results revealed that the No value for CET of Mg–Al alloys increased with increasing Al concentration. For example, the No value for Mg–3 wt.% Al was about 1000–10,000 cm3, whereas that of Mg–9 wt.% Al was about 10,000–100,000 cm3. This means that increasing Al concentration requires an increase in the number of
nuclei in the liquid ahead of columnar dendrites to form equiaxed dendrites. The possibility of dendrite arm fragmentation could be ruled out because there was very limited thermo-solutal convection in the present directional solidification system. 3.5. Solidification map of Mg–Al alloys Solidification maps can be useful in predicting as-cast microstructural morphology depending on the solidification conditions and solute content. The calculated solidification map for the Mg–Al alloys is shown in Fig. 12. The transitions between different growth modes are marked by solid lines at a given Al content. The transition from
Fig. 11. The predictions of CET for Mg–Al alloys using Hunt’s model [39] at DTn = 0.25 K in comparison with the present directional solidification (DS) data for (a) 3 wt.% Al, (b) 6 wt.% Al and (c) 9 wt.% Al. The experimental data of Mg–4 wt.% Al data are from Zhang et al. [32].
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Solidification velocity (m/sec)
(a) 101 0
Equiaxed
10
-1
10
-2
10
-3
10
3
-4
Columnar
10
-5
10
-6
10
Cellular
-7
10
10
3
10
4
10
5
10
6
Thermal gradient (K/m)
Solidification velocity (m/sec)
(b)
10
1
10
0
10
-1
10
-2
10
-3
10
-4
10
-5
10
-6
10
-7
10
3 wt. %:Equiaxed-WC 3 wt. %:Equiaxed-DS 3 wt. %:Columnar-DS 3 wt. %:Cellular-DS 4 wt. %:Columnar-DS [32] 4 wt. %:Cellular-DS [32]
Equiaxed
4. Summary
Columnar
Cellular 3
10
4
10
5
increasing the cooling rate can induce more equiaxed microstructures, but the morphology can be changed depending on the changes of G and V even with the same cooling rate. That is, an equiaxed microstructure can be greatly promoted by increasing the solidification velocity at a given cooling rate. It should be noted that the present map in Fig. 12 is valid only for solidification conditions without significant stirring, as this causes dendritic fragmentation that facilitates equiaxed growth and without the addition of inoculants which promote the equiaxed dendrite formation. If the amount of dendritic fragmentation and inoculants are known, the expansion of the equiaxed area can be roughly calculated using Hunt’s model (Eq. (12)) by increasing No.
10
6
Thermal gradient (K/m) Fig. 12. Calculated solidification map for Mg–Al alloys in comparison to experimental data. (a) Solidification map for Mg–Al alloys. (b) Comparison to experimental data for Mg–3 wt.% Al map. WC and DS stand for wedge casting and directional solidification, respectively.
columnar to equiaxed dendrites was calculated as a function of thermal gradient (G) and solidification velocity (V) using Hunt’s model [38] (Eq. (6)) at fixed values of DTN = 0.25 K and No = 10,000 cm3 (an average of the results in Fig. 11). Similarly, the transition between columnar and cellular structures was calculated using the KGT model [51]. The constant cooling rates of 0.1, 10 and 1000 K s–1 are also marked in Fig. 12. The calculated SDAS using Kattamis and Flemings’s model [14] (Eq. (2)) is also marked on the map. Although SDAS can vary slightly with solute content, as seen in Fig. 6, the averaged values for the 3, 6 and 9 wt.% Al alloys at the given cooling rates were used in the map for the sake of simplicity. In order to validate the constructed solidification map, the present experimental data for the Mg–3 wt.% Al alloy and data from the previous study by Zhang et al. [32] for Mg–4 wt.% Al were compared with the map in Fig. 12b. All the growth morphologies were reasonably represented by the calculated map. As mentioned above with regard to Fig. 12, increasing Al concentration can promote the formation of equiaxed microstructures against a columnar structure. In general,
In order to investigate the growth morphology of the Mg–Al alloys, directional solidification and gravity casting experiments were performed across a wide range of cooling rates, between 0.05 and 1000 K s–1. The influence of the solute content (Al) on the growth morphology was also investigated by varying the Al content (3, 6 and 9 wt.% Al). The experimental results were also compared with available solidification models in the literature. The following results were obtained from the present study: (1) The SDAS decreases with increasing solute Al content, which is qualitatively reproduced by Kattamis and Flemings’s model. In the case of columnar dendrite growth, the value of SDAS increases with coarsening process from dendrite tip to dendrite root. Although the matured SDAS near columnar dendrite root is still lower than the calculated values, the SDAS of equiaxed dendrites can be reproduced well by Kattamis and Flemings’s model. (2) Experimental results on the logarithmic relationship between the cooling rate and SDAS of columnar and equiaxed dendrites show that the SDAS cannot be described as a linear relationship over the entire range of cooling rate. (3) Transitions from cellular to columnar dendrite and from columnar to equiaxed dendrite were experimentally determined. Increasing the Al content promotes the equiaxed dendrite over the columnar dendrite, and the columnar dendrite over cellular growth, respectively. (4) A solidification map for Mg–Al was calculated using Hunt’s model and the KGT model, and was validated using the present experimental data. Although the solidification morphology can be influenced by the cooling rate, the thermal gradient (G) and te solidification velocity (V) can independently influence the growth morphology of Mg–Al alloys even at a given cooling rate.
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Acknowledgements This research was supported by funding from the NSERC Magnesium Strategic Research Network (MagNET) grant, the Strategic Network Enhancement Initiative (SNEI) program and General Motors of Canada. The authors deeply thank Prof. Y.-B. Kang at GIFT, Postech, South Korea, Dr. E. Essadiqi at CANMET-MTL, Canada and Prof. K.-Y. Kim and Dr. B.-H. Kang at KUTECH, South Korea for the usage of a directional solidification, wedge casting, Cu mould casting and water quenching experiment equipment, respectively. References [1] Caceres CH, Davidson CJ, Griffithes JR, Newton CL. Mater Sci Eng 2002;325A:344. [2] Cai J, Ma GC, Liu Z, Zhang HF, Hu ZQ. J Alloys Compd 2006;422:92. [3] Park SS, Bae GT, Kang DH, Jung I-H, Shin KS, Kim NJ. Scripta Mater 2007;57:793. [4] Bouchard D, Kirkaldy JS. Metall Trans 1997;28B:631. [5] He Y, Javaid A, Essadiqi E, Shehata M. Can Met Quart 2009;48(2):145. [6] Kurz W, Fisher DJ. Fundamentals of solidification. Zurich: Trans Tech Publications; 1992. [7] Pettersen K, Lohne O, Ryum N. Metall Trans 1990;21A:230. [8] Tensi HM, Ro¨sch R. In: Magnesium alloys and their applications, DGM Verlag, Oberursel, Germany; 1992, p. 283. [9] Sasaki H, Adachi M, Sakamoto T, Takimoto A. In: Proceedings of the 53rd Annual World Magnesium Conference, McLean, Virginia, USA; 1996, p. 86. [10] Sequeira WP, Murray MT, Dunlop GL, St. John DH. TMS; 1997. p. 169. [11] Labrecque C, Angers R, Tremblay R, Dube´ D. Can Met Quart 1997;36:169. [12] Dube´ D, Couture A, Carbonneau Y, Fiset M, Angers R, Tremblay R. Int J Cast Metals Res 1998;11:139. [13] Okamoto T, Kishitake K. J Cryst Growth 1975;29:137. [14] Kattamis TZ, Flemings MC. AIME 1965;233:992. [15] Mortensen A. Metall Trans 1989;20A:247.
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Please cite this article in press as: Paliwal M, Jung I-H. The evolution of the growth morphology in Mg–Al alloys depending on the cooling rate during solidification. Acta Mater (2013), http://dx.doi.org/10.1016/j.actamat.2013.04.063