Rheological behavior of semi-solid Al–Si alloys: Effect of morphology

Materials Science and Engineering A 454–455 (2007) 30–36

Rheological behavior of semi-solid Al–Si alloys: Effect of morphology Omid Lashkari, Reza Ghomashchi ∗ Advanced Materials and Processing Research Group, Department of Applied Sciences, University of Quebec at Chicoutimi, Quebec G7H 2B1, Canada Received 30 June 2006; received in revised form 21 October 2006; accepted 4 January 2007

Abstract Swirled enthalpy equilibration device (SEED) technology was used to cast semi-solid metal, SSM, billets of A356 Al–Si alloy. The deformation behavior of the SSM billets was studied using parallel plate compression viscometry. The compression tests were carried out at different applied pressures and solid phase morphologies. The rheological studies were conducted assuming the SSM slurry behaving like Newtonian or nonNewtonian fluid. The calculated viscosity numbers confirmed psuedoplastic behavior of the SSM billets and were correlated to the morphology, average aspect ratio, and shear rate to highlight the effect of metallurgical and process parameters on the viscosity and thus “rheological behavior” of SSM alloys. An empirical equation is proposed to correlate viscosity with average aspect ratio and shear rate: ◦

log η = −1.85 + 4.9AR − (0.255AR + 0.03)log γ ,

1.4 < AR < 1.8

This equation is valid for the shear rates less than 0.01 s−1 . © 2007 Elsevier B.V. All rights reserved. Keywords: Al–Si alloy; Semi-solid metal; Microstructure; Rheology; Viscosity

1. Introduction SEED is a novel rheocasting process developed by ALCAN international limited [1]. This process is based on off-center swirling of molten metal during solidification and partial decanting of the residual liquid from the slurry, “the mush”. The application of swirling is an important parameter to induce microstructures with the desirable morphology and distribution of the primary phase particles such as ␣-Al in hypo-eutectic Al–Si alloys. The variation of the microstructure of SSM alloys due to application of different swirling intensities may be characterized by rheological tests and measurement/calculation of the viscosity [2,3]. The viscosity value is an indication of the capability of the SSM slurry to fill-in the die cavity during casting and determines the required forces for injection, deformation and flow of SSM feed stock [4]. According to several recent review articles, viscometry is identified as an appropri∗ Corresponding author. Former Professor and NSERC-IRC Chair, Director, Advanced Materials and Processing Research Institute. Fax: +1 416 221 7530. E-mail address: [email protected] (R. Ghomashchi). URL: http://www.ampr-institute.com (R. Ghomashchi).

0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.01.003

ate route to study the rheological behavior of semi-solid metals [5–7]. The viscosity of SSM slurries is dependent on the process parameters and metallurgical characteristics of the alloy including pouring temperature and applied shear force, the fraction solid, and its morphology, dendritic or globular, and solid particle size and distribution, respectively. The effect of fraction solid as the key parameter to influence the viscosity of semisolid billets is already reported by the current authors elsewhere [8]. Parallel plate compression viscometry was initially used to study rheological behavior of the thixocast Pb–15% Sn alloy within low shear rate range [9]. Its suitability was further confirmed by other researchers for other alloys and composites [10,11], tested at different shear rates and fractions solid [12]. Despite the small aspect ratio of the samples, height (H) to diameter (D) ratio of H/D = 0.4 [9–12], frequently used in the literature, the current authors employed parallel plate compression viscometry directly on the commercial size rheocast SSM billets [2,3,13] and confirmed its reliability for billets with H/D ≈ 1.8. Rheological data was also used as the criterion to characterize the microstructure of SSM billets [2,3].

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The current article reports on the implication of rheological principles in characterizing the flow behavior of A356 Al–Si alloy billets cast by the “SEED” process [1] while treating the SSM billets as Newtonian and non-Newtonian fluids to highlight the differences between the two assumptions. Attempts were made to propose an empirical relationship to underline the correlation between the viscosity, morphology (average aspect ratio) of the primary ␣-Al particles and shear rate, respectively. 2. Experimental procedures The aluminum ingots of A356 alloy, Table 1, were melted in an electric resistance furnace and degassed with argon for 10 min before pouring. About 1.4 kg of the melt was poured at 695 ◦ C, 80 ◦ C superheat, into a refractory coated cylindrical metallic mold, held at 25 ◦ C, swirled off-center, while cooled down to temperatures below the liquidus, the mushy zone. A set of swirling speeds were employed to produce billets with different microstructures, ranging from fully dendritic (no swirling) to globular (high swirling intensity). The remaining liquid within the solidifying billet was partially drained out through the mold bottom orifice [1,14] to make a self-standing billet. The final billet temperature was registered at 600 ± 1 ◦ C with fraction solid of about 0.27, calculated according to the Scheil’s equation, and assuming linear liquidus and solidus lines having partition coefficient k = Cs /Cl = 0.13 [14]. The “liquid run-off” of about 25% of the initial melt weight, 1.4 kg, at this temperature changes the phase fraction and increases fraction solid, fs to 0.36 according to the following calculation [14]: fs (after-decanting) = =

pri(fs ) pri(fs ) + [pri(fl ) − decanted(fl )] 0.27 = 0.36 0.27 + [0.73 − 0.25]

The as-cast billets were quickly transferred and compressed uniaxially and isothermally in a parallel plate compression test machine, designed and constructed in our labs [15], for applications of 1–100 kg dead weights. The dead weight motion is controlled pneumatically and the applied force and resulting displacement are monitored using a 300 kg maximum capacity load cell of <0.02% precision and a displacement transducer (0–255 mm), precision of ±(0.1–0.2)% full stroke, respectively. A cylindrical furnace is installed on the press bed to keep the billet temperature constant during the course of the compression tests. The furnace is equipped with two quartz heat resistant Table 1 Chemical analysis of the melts (wt.%) Si Mg Fe Mn Cu Ti Al

6.9–7.1 0.3–0.31 0.09 0.001 0.001 0.13 Balance

Fig. 1. Schematic diagram of the parallel plate compression test machine.

windows to view the billet from front and back of the furnace. There are two K-type thermocouples positioned within the furnace to control the chamber temperature. Fig. 1 shows the schematic diagram of such machine, but detailed information is given elsewhere [15]. The temperature of the furnace was the same as the billet temperature at the end of casting, 600 ± 2 ◦ C. The applied dead weight varied between 3 to 8 kg and the changes in the billet height was registered versus time using a national instrument data acquisition unit, SCXI-1102TM . The billets were taken out of the furnace immediately after deformation and quickly quenched in cold water. The microstructure of the as-cast billets was characterized on the specimens prepared by sectioning the billets transversely at the tip of thermocouple and examining the regions between the center and wall. The average aspect ratio, AR, as an indication of morphology, was measured on 80 randomly selected fields of view with a total scanned area of 255 mm2 for each specimen. 3. Results and discussion 3.1. Microstructure Fig. 2 shows the resulting microstructures of the SEED billets, ranging from dendritic morphology due to no swirling, to globular structure at high swirling intensity [16]. The application of swirling induces uniform temperature distribution with shallow temperature gradient across the semi-solid slurry. It further breaks up the dendrites secondary and tertiary branches to eventually promote the formation of equiaxed primary ␣-Al particles. That is to transform the dendritic structure to globular morphology. This is in line with previous studies where fluid flow was reported to promote remelting, fragmentation and generally disrupting dendritic solidification [17,18]. The resulting equiaxed structure is expected to improve deformation behavior of the SSM billets at any given temperature and fraction solid, fs , and renders lower viscosity values as discussed later. In order to characterize the morphology of the primary ␣Al particles, the average aspect ratio, AR, was obtained from image analysis measurements as explained in Section 2. The

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Fig. 2. Microstructural features obtained in SEED process poured at 695 ◦ C: (a) dendritic (no swirling); (b) rosette (low swirling intensity); (c) globular (high swirling intensity).

AR value changes from one (1) for fully isolated globular particles and increases slowly depending on the complexity of the morphology and agglomeration of the primary particles. It is important to emphasize that although there is not much difference in the magnitude of AR for dendritic and globular structures as measured by image analysis of as-cast billets, in realty the distinction is considerable even with AR changing only by one-tenth of one. This is because of the nature of image analysis measurement where it only distinguishes between the isolated and continuous particles and treats the detached secondary or tertiary dendrite branches, generated due to sectioning and polishing, as isolated and individual globular particles. Therefore, the resulting average aspect ratio values are expected to be quite close for both dendritic and globular structures. In other words, it would be misleading to use the AR values alone as a means to characterize particle morphology in SSM structures. For instance, the average aspect ratios measured for the microstructures in Fig. 2a and c are 1.7 and 1.5, respectively, while as can be seen there are huge and distinctive differences between the two structures.

where h0 and h are the initial and instantaneous heights (mm) of the specimen during compression test, respectively. The graphs presented in Fig. 3 are typical strain–time behavior of the SEED billets cast at different swirling speeds. The difference in the morphology of primary ␣-Al particles has a distinct effect on the engineering strain. The dendritic structure shows the lowest deformation rate while globular morphology deforms at much higher rate, flows with less resistance. The applied pressure appears to be an important parameter in differentiating between the structures, since its increase from 3.55 to 7.54 kPa has improved the flow behavior of all structures, Fig. 3. The overall resulting data for the morphologies, initial pressures and the total engineering strain are presented in Table 2. The values of fraction solid were calculated by including the 25% drainage of the residual liquid as explained in Section 2. 3.3. Rheological analysis The values of viscosity are calculated for the SEED billets, assuming them behaving like Newtonian and non-Newtonian fluids, respectively.

3.2. Engineering strain The instantaneous changes in the billet height was registered during parallel plate compression test and converted into engineering strain using the following simple equation: e=1−

h h0

(1)

3.3.1. Newtonian assumption The simplest way to analyze the results of the compression tests is to assume the squeezed semi-solid alloy behaving like a Newtonian fluid. This is a reasonable assumption if the shear rate value is low, less than 0.01 s−1 , and does not vary greatly across the billet during compression [8,19]. In this case the resulting

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Fig. 3. The effect of primary ␣-Al morphology on the engineering strain–time behavior for SEED billets poured at 695 ◦ C with fs = 0.36: (a) P0 = 3.55 kPa and (b) P0 = 7.54 kPa.

engineering strain–time graphs could be treated mathematically with the following equations to calculate the viscosity of the semi-solid cylindrical billets [9,20–22]. According to the Newton’s first law, the applied shear stress (τ yx ) is given as: τyx = −η

dvx dy

(2)

Eq. (2) may be rewritten in terms of the applied force, F, for a cylindrical sample squeezed between two parallel plates (assuming the billet does not fill the space between the two parallel plates during the course of deformation) [19]: 3ηV 2 F =− 2πh5



dh dt

 (3)

Integrating Eq. (3) for h = h0 at t = 0 and h = h at t = t (Eq. (4)), and knowing the initial applied pressure, P0 = Fh0 /V, at the onset of deformation, the viscosity–time relationship is given in Eq. (5): 1 1 8πFt − 4 = 2 h4 3ηV h0 3Vh0 8πP0



1 1 − 4 h4 h0

(4)

 =

t η

(5)

The viscosity is calculated as the inverse slope of a graph where the left hand side of Eq. (5), [(3Vh0 /8πP0 )(1/ h4 − 1/ h40 )], is plotted against time (t). For Newtonian fluids, the average shear ◦ rate, γ av , at any instant during compression test is calculated as [19]: 

◦

γ av = −

V π



dh/dt 2h2.5

 (6)

where the variables in Eqs. (2)–(6), vx , η, V, h0 , h, F, P0 , and t are deformation speed (ms−1 ), viscosity (Pa s), volume of specimen (mm3 ), initial height (mm), instantaneous height (mm), initial applied dead weight (N), initial applied pressure (Pa) and deformation time (s), respectively. Fig. 4 is the developed graphs from Eq. (5), using the instant height values during the quasi steady-state condition of deformation [23], the segment of the strain–time graphs in Fig. 3 having nearly constant slope, which is about 50 s after the beginning of each compression test in this study. Viscosity is calculated through the inverse slope of such graph. The calculated values of viscosity, and shear rates together with the average aspect ratios, AR, are listed in Table 3. The results support previous findings for the viscosity of semi-solid alloys of A356 [2,12], Pb–15% Sn [9] and Al–SiC particulate composite [24] having similar morphology and tested within the same range of shear rates.

Table 2 Experimental data for SEED trials Experiment number (different morphology 695 ◦ C, SEED)

Temperature (◦ C)

1 2 3 4 5 6 7 8 9

599 599 599 599 599 599 599 599 599

Dendritic (D), rosette (R) and globular (G).

± ± ± ± ± ± ± ± ±

1 1 1 1 1 1 1 1 1

Fraction solid, fs , after 25% drainage 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36

± ± ± ± ± ± ± ± ±

0.01 D 0.01 R 0.01 G 0.01 D 0.01 R 0.01 G 0.01 G 0.01 G 0.01 G

Initial pressure (kPa)

Total strain, e, after 200 s

3.55 3.55 3.55 7.54 7.54 7.54 14.32 14.32 14.32

0.105 0.117 0.273 0.293 0.476 0.521 0.576 0.59 0.583

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squeezed between two parallel plates is as follows: 2n/(3n+5)    3n + 5 h0 (n+1)/n t = 1+ kh0 h 2n where k is given as:   1/n n  2n 4(n + 3) k= F 2n + 1 πmd0n+3

Fig. 4. The right hand side of Eq. (5), [3Vh0 /8πP0 (1/ h4 − 1/ h40 )] (Pa−1 ) is plotted against time for the quasi steady-state part of the deformation, to calculate the viscosity for different morphologies.

Evidently, the magnitude of viscosity increases with introduction of more dendritic structure or reduction of applied pressure. The reverse trend has been seen for globular morphology or higher applied pressure, Fig. 4. Increasing the pouring temperature induces directional heat flow and encourages the formation of columnar dendritic structure with a resistible character against flow [3]. The shear thinning behavior, psuedoplasticity, where viscosity decreases with increasing shear rate is seen for the SSM samples having different morphologies, Table 3. In other words, the SSM billets are non-Newtonian fluids by nature: “the viscosity changes with shear rate”. This is treated in more details in the following section. 3.3.2. Non-Newtonian assumption The non-Newtonian power law model is widely used to study rheological behavior of SSM slurries [9,12,20,21,24]. The model expresses viscosity changes in terms of applied stress and resulting shear rates as: ◦ n−1

η = mγ

(7)

where m and n are the consistency and power law indices, respectively [19]. If the SSM billets are treated as non-Newtonian fluids, the solution to the flow equations for cylindrical samples

(8)

(9)

Eq. (8) is only valid for deformation under quasi steady-state condition where the engineering strain changes linearly with time. Eq. (8) could be further treated mathematically to include engineering strain (e) as given in the following equation:   2n log t log(1 − e) = − 3n + 5     2n 3n + 5 (n+1)/n − (10) log kh0 3n + 5 2n In order to calculate the values of m and n, the logarithmic of engineering strain, log(1 − e), should be plotted against time, log t, and the slope of such graph and its intercept with strain axis should provide the necessary means to calculate m and n [19]. The calculated viscosity values, shear rates, m and n, are listed in Table 4 for different morphologies of the primary ␣Al particles. The viscosity numbers for the billets when treated as non-Newtonian fluids are close to those of the results with Newtonian fluid assumption given in Table 3. The almost similar viscosity values for billets tested with the same shear rate and morphology confirm the validity of Newtonian fluid assumption to simplify the viscosity calculation within low shear rates range. In order to highlight the effect of primary phase morphology on the materials constants, m and n, the aspect ratio is plotted against m and n in Fig. 5. Eqs. (11) and (12) show the resulting relationships for m and n obtained from the trend fitted to these graphs: m = 10(1.85−4.9AR)

for 1.5 < AR < 1.7

(11)

Table 3 Logarithm of viscosity numbers (Pa s), at different shear rates (s−1 ) and morphologies (Newtonian analysis) ◦

◦

◦

Average aspect ratio, AR

log γ

log η

log γ

log η

log γ

log η

1.5 1.6 1.7

−3.36 −3.6 −3.68

7.09 7.69 8

−2.82 −2.89 −3.25

6.5 6.8 7.09

−2.6 – –

6.3 – –

Table 4 Logarithm of viscosity numbers (Pa s), n and m at different shear rates (s−1 ) and morphologies (non-Newtonian analysis) ◦

Average aspect ratio, AR

log γ

1.5 1.6 1.7 1.5 1.6 1.7

−3.36 7.10 −3.6 7.62 −3.68 7.72 n = 0.410, log m = 5.12 n = 0.350, log m = 5.3 n = 0.332, log m = 6

log η

◦

log γ

log η

−2.82 6.39 −2.89 6.64 −3.25 7.09 n = 0.593, log m = 5.53 n = 0.553, log m = 5.93 n = 0.542, log m = 6.51

◦

log γ

log η

−2.6 6.20 – – – – n = 0.634, log m = 5.22 – –

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Fig. 6. The predicted effect of shear rate on the viscosity of SSM billets for different morphologies of the solid particles, Eq. (13) (lines). The points are the values from conventional cast tests reported by Lashkari and Ghomashchi [2].

Fig. 5. Effect of primary ␣-Al particle aspect ratio on the power law (n) and consistency (m) indices.

n = 0.97 − 0.255(AR)

for 1.5 < AR < 1.7

(12)

It is noteworthy that the equations for m and n do not include the applied pressure and the resulting shear rate. This is because of the negligible effect that applied pressure has on m and n values as seen in Fig. 5 where the points, each representing a specific applied pressure for each fraction solid, do not vary much. As for the effect of primary phase morphology, the graphs in Fig. 5 together with the respective Eqs. (11) and (12) show the reducing and increasing trends for n and m, respectively, with increasing the average aspect ratio at a constant fraction solid, 0.36. The effect of morphology is not reported before; probably due to the fact that all tested SSM slurries were fully globular. The validity of Eqs. (11) and (12) is therefore verified using the results of conventional cast billets [2] as discussed later for viscosity numbers. Having established the effect of morphology on the materials constants, the resulting Eqs. (11) and (12) are substituted in Eq. (7) for m and n, to generate an empirical relationship for the power law model incorporating the morphology of the primary ␣-Al particles. Such Eq. (13) is useful to predict the viscosity of semi-solid materials within a specific average aspect ratio: ◦

log η = −1.85 + 4.9AR − (0.255AR + 0.03)log γ , 1.4 < AR < 1.8

(13)

The resulting Eq. (13) was plotted in Fig. 6 to emphasize the importance of solid phase morphology on the viscosity value. This equation also justifies the concept of rheology, where the viscosity of slurries could be altered by changing the morphology of solid phase [3,12]. The authors could not find other

reports to substantiate the validity of the empirical relationship given here, Eq. (13). This is because of the lack of an effective method to quantify the particle morphology and associated theoretical model to account for the effect of particle morphology. To the best of our knowledge, Fan and Chen [25] and Zoqui et al. [26] who have recently reported the effect of morphology on the rheology of SSM alloys, used fractal dimension and rheocast quality index, respectively, not aspect ratio. In other words, there is not any report where aspect ratio is correlated to viscosity. Therefore, Eq. (13) is plotted for SEED billets having different morphologies but substantiated with the results previously reported for conventionally cast billets having globular, AR = 1.4, or dendritic, AR = 1.8, morphologies [2]. Fig. 6 further shows the pseudoplastisity of SEED prepared SSM A356 billets within low shear rates range, where the viscosity decreases with increasing shear rate. 4. Conclusions The effect of primary ␣-Al particles morphology on the viscosity of A356 SSM billets is studied for billets cast by SEED process. The application of various swirling intensities as one of the process parameters of the SEED technology resulted in the formation of a range of primary ␣-Al morphologies in hypoeutectic Al–Si SSM billets. Parallel plate compression test was used to study the rheological behavior of SSM billets and to calculate their viscosities. It was confirmed at low shear rate values, the SSM billets can be treated as Newtonian fluid even though the two-phase fluids are basically non-Newtonian. The calculated viscosity values at different applied pressures confirmed the SEED billets behaving as pseudoplastic materials where the viscosity numbers decreased with increasing applied pressure. The SSM billets were also treated as non-Newtonian fluids and the materials constant m and n were calculated and presented as an empirical relationship for different morphologies. These equations were then substituted in the power law model equation to generate an empirical relationship to correlate the SSM viscosity, the morphology of the primary ␣-Al particles and shear rate. The empirical relationships were further confirmed with experimental results reported in the literature.

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Acknowledgements The work reported here is supported by the NSERC-ALCANUQAC industrial research chair, grant no. IRCPJ268528-01, on the “Solidification and Metallurgy of Al-alloys”. The authors would like to gratefully acknowledge financial support from Natural Sciences and Engineering Research Council of Canada, and ALCAN International Limited. References [1] D. Doutre, G. Hay, P. Wales, US Patent 6,428,636 (2002). [2] O. Lashkari, R. Ghomashchi, J. Mater. Sci. 41 (18) (2006) 5958–5965. [3] O. Lashkari, S. Nafisi, R. Ghomashchi, Mater. Sci. Eng. A 441 (1–2) (2006) 49–59. [4] M. Su´ery, Mise en forme des alliages m´etalliques a` l’´etat semi-solide, Herm`es Science Pub., Lavoisier, 2002, ISBN 2-7462-0453-3. [5] M.C. Flemings, Metall. Trans. A 22 (1991) 952–981. [6] Z. Fan, Int. Mater. Rev. 47 (2) (2002) 49–85. [7] D.H. Kirkwood, Int. Mater. Rev. 39 (5) (1994) 173–189. [8] O. Lashkari, R. Ghomashchi, Rheol. Acta, submitted for publication. [9] V. Laxmanan, M.C. Flemings, Metall. Trans. A 11 (1980) 1927–1937. [10] M. Mada, F. Ajersch, Mater. Sci. Eng. A 212 (1996) 157–170. [11] S. Jabrane, B. Clement, S. Ajersch, in: S.B. Brown, M.C. Flemings (Eds.), Proceedings of the Second International Conference on Semi-solid Processing of Alloys and Composites, MIT, Cambridge, MA, 1992, pp. 223–236.

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