ON CELLULAR SPACING SELECTION OF Cu-Mn ALLOYUNDER ULTRA-HIGH TEMPERATURE GRADIENT AND

RAPID SOLIDIFICATION CONDITION

Sen Yang, Weidong Huang, Xin Lin, Yunpeng Su and Yaohe ZhouState Key Laboratory of Solidification Processing, Northwestern Polytechnical University,

Xi’an 710072, People’s Republic of China

(Received September 16, 1999)(Accepted in revised form November 16, 1999)

Keywords:Ultra-high temperature gradient; Cellular spacing; Cu-Mn alloys; Rapid solidification

Introduction

Cellular/dendritic spacing, as one of the most important solidification microstructure scales, has beenextensively studied in the past three decades. Recently, both theoretical analyses and experimentalresearch found that there exists a wide allowable range of ultimate spacing for cellular or dendriticarrays under given growth condition. It was also found that the lower and upper limits of the allowablerange are very sharp at the same current growth condition, while average spacing for cellular/dendriticarrays is remarkably history-dependent on solidification parameters, i.e., growth rate and temperaturegradient [1–11]. Although some important progresses on cellular/dendrite spacing selection have beenmade, it should be noted that most of theoretical and experimental researches have been concentratedon the constrained growth at low or medium growth rate and temperature gradient. Up to now, therehave been few experiments on the cellular/dendrite spacing selection at rapid solidification andultra-high temperature gradient, andtheunderstanding on the cellular/dendrite spacing selection undersuch conditions is still very poor.

In order to study the cellular/dendritic spacing selection under ultra-high temperature gradient andrapid solidification condition, laser surface remelting technology have been adopted for its specialadvantages. During laser surface remelting, there is an extremely high temperature gradient (.106k/m)in the laser molten pool, which leads to directional growth of various microstructures. Two mainadvantages of the experiment are (1) no nucleation is involved, i.e. epitaxial growth; (2) the localgrowth rate and the corresponding microstructure can be determined directly.

In the present work, detailed experiments have been carried out to investigate the cellular/dendritespacing selection of Cu-Mn alloy under ultra-high temperature gradient and rapid unidirectionalsolidification condition, and the experiment results are compared with KGT model [12].

Experimental

Cu-27.3wt%Mn alloy was prepared by vacuum induction melting in an alumina crucible and pouredinto a 203 120 3 120 mm rectangular copper mould with alumina coatings. In order to removeinhomogeneities on the surface, the outer metal with 3mm thick was machined off and specimens with

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6mm square and 30mm long used for laser remelting were cut from the remaining ingot. In order tominimize the reflection for the laser beam and obtain a similar surface quality for each specimen, allthe specimens were ground by 800 grit SiC paper and cleaned in methanol prior to laser surfaceremelting.

Laser surface remelting experiments were performed on a 5kW CO2 Laser (Rofin-Sinar RS 850).The normally incident laser beam was focused to a spot with diameter of 0.3mm. During the laserremelting, a continuous flow of 51/min of helium was blown to the melted zone to prevent heavyoxidation. Laser beam scanning velocity (Vb) between 0.005m/s and 1.5m/s were used in this study. Bytaking the transverse section the cellular growth, the cellular spacing and their distribution range weremeasured by a Cambridge Quantimet 500 Image Processing and Analysis System. Local growth rate Vs

could be simply related to the known scanning velocity, Vb, via the relationship [13] Vs5 Vbcosu,whereu is the angle between Vs and Vb.

Results

Fig. 1 shows the variation of typical microstructures of Cu-27.3wt%Mn on the transverse section withincreasing growth rate in the range of 1.6;169.1mm/s. No dendrites appear within the whole rate rangeand fully cellular crystals are observed. This is qualitatively consistent with the prediction of Hunt-Lu’snumerical model [3]: under high temperature gradient condition, the microstructure will goplanar3cells3planar with the increase of growth rate. Table 1 gives the measurement results ofcellular spacing, wherelmax, lmin and l# is maximum, minimum and average cellular spacing,respectively. It can be obtained from Fig. 2, which is plotted from the data in Table 1, that there existsa large distribution range in primary spacing under rapid solidification conditions. The ratio ofmaximum primary spacing to the minimum value, as a function of growth rate, varies between 1.47 and2.46.

At relatively low growth rate, both the cellular spacing and the cellular trunk diameter are large [seeFig. 1a, b]. With the increase of growth rate, the average spacing tends to decrease. It is interesting tohave found that when the growth rate is above a certain value (approximate 90mm/s for the experi-mental alloy), the decreases in average cellular spacing is not significant, whereas the reduction in celltrunk diameter is remarkable [see Fig. 1g and Fig. 1h].

Through regression analysis, we obtain:

lmax 5 4.88VS20.26 (1)

lmin 5 2.35VS20.22 (2)

l# 5 3.66VS20.25 (3)

Discussion

There is no available analytical model for the cellular/dendritic primary spacing under rapid solidifi-cation conditions, in order to compare our experimental results with theoretical model, the KGT model[12] for rapid cellular/dendritic growth was used, in spite of the fact that the tip radius (R), instead ofprimary spacing, can be predicted by the model. Since the tip radius in metal can’t be obtained frommicrographs, for the purpose of comparison, the relation between tip radius and primary spacing mustbe firstly defined. Recently, the numerical model of cellular/dendritic array growth in the high velocityregion by Luet al [14] has shown that the tip radius predicted by KGT model and primary spacing

CELLULAR SPACING SELECTION OF Cu-Mn ALLOY544 Vol. 42, No. 6

Figure 1. Variation of the directional growth dendrites/cells on transverse section with the increasing growth rateVs, (a)Vs 53.9mm/s, (b)Vs 5 11mm/s, (c)Vs 5 17mm/s, (d)Vs 5 28.1mm/s, (e) Vs 5 45.3mm/s, (f) Vs 5 90.3mm/s, (g) Vs 5 127.5mm/s,(h) Vs 5 169.1mm/s.

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calculated by numerical model follow a similar tendency with growth rate, in which primary spacingis a factor of approximately 2 larger than tip radius. Therefore, we assumed here that this relationshipis valid for the present case, which makes it feasible to compare theoretical prediction with experimentalresult.

The cellular spacings, as a function of growth rate, are given by KGT model in Fig. 3. Thethermophysical parameters used for calculations are listed in Table 2. It can be concluded from Fig. 3that the experimental results are in reasonable agreement with KGT model. However, it is worth notingthat there exist some discrepancies between theoretical predictions and experimental results. One is thatthe absolute stability predicted by M-S theory [15] doesn’t agree with the observations very well. Thislimit also corresponds to the theoretical maximum growth rate above which dendrites or cells can notform according to the KGT model, as shown in Fig. 3. Another is that the significant increase of cellularspacing in the vicinity of absolute stability predicted by KGT model is not observed due to theappearance of the absolute stable planar. The third is that the experimental results are larger than thatpredicted by the model. On the one hand, these discrepancies may be due to the inaccuracy of thethermophysical parameters of alloy, on the other hand, KGT model only dealt with constant temperature

TABLE 1Experimental Results of Primary Spacing as the Function of Growth Rate under Laser Rapid

Solidification Condition

Growth rate(mm/s)

lmin

(mm)lmax

(mm)

#l(mm)

lmax

lmin

1.6 2.37 4.33 3.24 1.833.9 2.08 3.57 2.41 1.727.5 1.77 3.01 2.04 1.7511 1.5 2.67 1.99 1.7817 1.49 2.43 1.92 1.6128.1 1.48 2.21 1.83 1.4945.3 1.37 2.00 1.69 1.4790.3 0.64 1.57 1.11 2.45127.5 0.62 1.50 1.05 2.41169.1 0.52 1.28 0.9 2.46

Figure 2. Selection of primary spacing as a function of growth rate, under laser rapid solidification conditionF - the maximumcellular spacing;E - the minimum cellular spacing;Π- the average cellular spacing.

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gradient and growth rate, while the growth rate and temperature gradient varied in the molten poolduring laser surface remelting, which makes the formed microstructure obvious history-dependent. It isshown that much theoretical research must be done to describe rapid solidification process and topredict the cellular/dendritic spacing selection.

Conclusions

There exists a large distribution range in cellular spacing of Cu-27.3wt%Mn alloy under rapidsolidification condition. With the increase of growth rate, both the average spacing and the distributionrange tend to decrease. It is worthwhile to note that when growth rate is beyond a certain value, theaverage spacing is nearly constant, however, the reduction in the cell trunk diameter is remarkable. Theaverage, maximum and minimum primary spacing of Cu-27.3wt% Mn, as functions of growth rate, canbe given as,lmax54.88VS

20.26, lmin52.35VS20.22 and l#53.66VS

20.25 respectively. Our experimentalresults agree with the KGT model reasonably.

Figure 3. A comparison between the experimentally measured average cellular spacing with two times the tip radius,R,calculated by KGT model. The arrow indicates the limit of absolute stability by M-S theory [15].

TABLE 2Thermophysical Parameters of Cu-27.3wt%Mn Alloy

Property Symbol Unit Value Ref.

Gibbs-Thomson coefficient G mK 3 3 1027 [16]Distribution coefficient K 0.88 [16]Diffusion coefficient (liq.) DL m2S21 1.753 1029 [16]Slope of liquidus line M K(wt.%)21 21.81 [16]Thermal conductivity (sol.) lS Jm21K21l21 34 [16]Thermal conductivity (liq.) lL Jm21K21l21 16 [16]Thermometric conductivity (sol.) aS m2S21 8.83 1026 [16]Thermometric conductivity (liq.) aL m2S21 4.03 1026 [16]Latent heat DH Jmol21 7.143 103 [16]Thermal gradient G K/m 2.23 106 [17]*

* Calculated by heat-flow model [17].

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Acknowledgments

The financial aid of the National Natural Science Foundation of China under grant No. 59771054 isgratefully acknowledged.

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