Article Type : Research Article
Authors : Xu R, Anh HJ and Kim K
Keywords : Gradient; Velocity; Radius; Primary dendrite space; Directionally solidification; TiAl
The
effects of the applied thermal gradient and pulling velocity, the spacing and
nucleation cooling are investigated in the present. The high value would be
found when G was7.8K/mm in contrast to that 0.12~0.06mm was observed when the
high G was 10K/mm. That would be caused upon high v. The value of measured and
literature has agreed with the curve of 10K/mm. The ?1 is about 140~40 ?m,
which might be caused by the low velocity approximately. The value ?Tn with 10K
is a little smaller than that of 1K. So the well choice is 10K for a bit high
v. The ?Tt are in the same relation to v proportionally. The reason for the big
varies is analysed as the nucleated temperature vary. The G with 10K/mm fit to
the large v, and the value of both G and ?Tt is smaller than 1K/mm. That might
be explained on the changed v that means the big v has large value.
TiAl alloys have had high strength and high
temperature strength compared with other high temperature (HT) alloys,
anti-oxidized and better creep properties, was dominant as very promising
material to substitute for Ti and Ni base alloys. In particular directionally
solidification (DS) TiAl alloys with an aligned lamellar microstructure (MS)
have a very good combination of strength and ductility over a wide temperature
range that columnar dendrite structures are desired. As for the mechanical mechanism,
Hunt developed the first analytical model to predict transition on the basis of
equiaxed grains nucleated in the constitutional undercooling region ahead of a
columnar front blocking the advance of the front if they occupy a sufficient
volume fraction [1]. It was estimated that the preferred growth directions of b
dendrite grown at HT near melting point was in the [001] b
direction at a growth rate of 30mm/h and in the [111] direction at a growth
rate of 90mm/h. The mechanical properties controlled by microstructures had
inverse relationship in them, which had been reported [2-3]. A b
solidified directional solidification (DS) method has used seed crystals, while
the initial solidification must be crossed into full transformation [4].
However in binary TiAl, Al contents with the full b
transus were low at RT?room
temperature) so that their mechanical properties were brittle. Adding elements
will move to b stabilization of Al rich was
confirmed. In the full b
transus the thermal gradients was low with Bridgman method and high with
Floating zone method (FZM) to be used. Using b
solidified
method, lamellar orientation of dendrites must be aligned to grow in the
direction [001]. The calculation results indicated that the columnar branch
spacing depends not only on the thermal gradient and the pulling velocity, but
also on number. A spacing adjustment can occur to develop to new columnar
grains. As for the effect of them on the thermal gradient and velocity,
qualitatively agrees well with the literature. By analysis it was evaluated
that the preferred growth directions of primary ? dendrite near the melting
point had been in the ? and ? primary phase at 2.77~50?m/s.
The thermal dynamic super ? cooling has been to avoid
or eliminate heterogeneous nucleation role, promote Gcr, hold back homogenous
nucleates making alloys or metal difficult to arrive cooling on the general
status. Super cooling method had changed thermal dynamic to obtain high
cooling. Herlach had demonstrated super cooling melt and rapid cool, liquid
alloys or metal had same mechanism being rapid solidification [5]. The solute
at the Solid/Liquid interface is distributed, at the local of the secondary
dendrite arm spacing by diffusion or convection [6]. It is to show the effect
of coarsening can be accounted for in a conventional segregation model by a
back-diffusion term. That results in a net diffusion process. The solidified
condition is for homogeneous nucleation, here DG
is change of system free energy and r is radius of nuclear crystal. The primary
dendrite arms space generally decreases with increasing cooling rate, and it is
crucial to take that effect into account. The relatively simple relationship
was found to be applicable to a wide range of DS [7, 8]. It is thought to be
ideal directional solidification. It is specified by the average temperature
gradient G, and a speed v, so the mean cooling rate is described as
Lg?1=-0.338lgC+2.16 (2-1)
?1 = AG-1/2v-1/4 (2-2)
The method of exponent would be used to the following
equation
?2 = A(1/C)1/3 (2-3)
R=?12G/(3?T) (2-5)
The proportional method was used as following
?2 = KR (2-4)
The extent of convection in the procedure is the
relation used to calculate the local permeability of the mushy zone as a
function of the liquid volume fraction and primary dendrite arm space l1.
It implies a lower space leads to lower permeability and a higher resistance to
flow in the mush zone. A best fit of calculated data was for parallel and
perpendicular to l1. The value of l1
generally decreases with increasing cooling rate. It was found to apply to a
range of DS alloys inspite of preciser’ done no bad. The procedure to solve the
conservation equations. A phase equilibrium in this zone offers a way to
calculate the solid volume fraction. Some modifications necessary to the use of
equilibrium instead of a relation between lquidus temperature and
concentration. In the evolution of the morphology of solid liquid, growth
velocities have made important and complicated roles. In the low velocity zone,
with the growth v increased, make plane interface unstable, however, in the
high velocity zone, the increasing of v it promoted interface to develop
absolutely stability. It has increased the effect of composition undercooling
and curvature [9]. With raising growth rate v mushy zone length shrink, which
shorten to a certain mushy length. That is a factor of Dendritic-cellular
change.
At a relatively high thermal gradient, increasing pulling velocity decreases the space of the crystal. It occurs after introduce of the seeds and nucleation of new columnar grains. Nucleation of seeds is not likely to be impeded by solutal interactions. As for low pulling velocity the solute diffusion length is so large that many the seeds never reach the specified nucleation undercooling. It can be found that a gradient in solute concentration had given a slope of 1.22at.%/?m, which agrees well with the predicted values. It can be shown that increasing the thermal gradient decreases the maximum undercooling in the liquid along the central dendrite axis from 2K to 0.5K as (Figure. 1). If the nucleation undercooling DT is greater than 2K, no equiaxed grains could form. If the nucleation undercooling is 1K nucleation would take place as the thermal gradient is smaller than 30K/mm. The maximum undercooling varies between 1K and 2K depending on the thermal gradient. They all are behind the columnar tips. The G was appropriated proportion to v in the condition of 1K/mm. on the other hand larger variation was occurred in 10K. DTt are both similar proportional relation with v. The reason for the bigger varies is analysized as nucleated temperature vary. G=10K/mm fit to large v, and the value of both G and DTt is smaller than 1K/mm. It might be explained on changed v that means big v has large value. It was found that the equiaxed growth generally occurs under condition of high pulling velocity and low thermal gradient. Conversely columnar growth is trend to low velocity or high thermal gradient. Equiaxed growth occurs if the thermal gradient is less than the value by Hunt’s model. In terms of Hunt’s model, the tip undercooling is thought to as a function of the velocity. The constant is a function of the material properties only. From further models, the tip temperature depends on the thermal gradient too and not exactly relation to v. It should be viewed as an attempt to better understand the present predictions relative to Hunt’s model. The approximate agreement indicates that the dependence on the thermal gradient and pulling velocity. Furthermore at low Gl it occurs at a constant v, and at high Gl it separates the two grain structures. Here 1.33 and 3.5×108 /m2 of N was used for 0.5 and 2.5K. Compared with literature approaching trend would be seen. It was found that the same slope and curve had been occurred. The big velocity had high gradient in terms of the results. Tip temperature was proportional to v, it would reach about 50 as v is 0.03mm/s, and 130 as v is 1mm/s. G is 60K/mm when v is 0.4, while 50 and 40K/mm respectively when v is 0.01.The value G of 10 is a little smaller than that of 1. So the well choice is 10 for a bit higher v above 0.01mm/s. There is line relation in the liquid phase temperature gradient G and interface velocity v. It is a function between interface velocity and drawing velocity v. From the curve in the Fig. 2 the exponent function relation can be found. It was formed to be decreasing proportion. K is analysed to about 0.25. Using the equation of (2-1) it is determinates upon measured values. The equation of C=Gv was used to calculate. The original value was of 0.25 and 0.16 mm in terms of the 0.025 and 0.1 mm/s respectively. The mother G is 7.8K/mm and has gained the state of 24K/mm. The trend is shown in Figure 2, the calcultional results is good fit to measure in the case of the 7.8-24K/mm (Figure 2). The value of 74K/mm is lightly higher than the literature [10]. The varies will be thought with G. The process of TiAl-3Si would be done by Directional solidification used seeding material as reference. The k = 1.4 and A for 0.157 were used to taken proportional and exponent method for n = 0.5 respectively, seen in Fig. 4. They were corresponded to each other and measured data well [11]. As seen in Fig. 3 higher value would be found when G=8.8K/mm scope of ?1 is 0.8~0.12mm (Figures 3,4). In contrast to that 0.12~0.06mm was observed when high G=24K/mm. That would be caused upon high v. The value of measured and litre. Has agreed with the curve of 24K/mm. Maybe there was a difference in A= 0.292. That was derived from (2-1). In the right condition G is 24 being little bigger than 7.8. In terms of formula (3-4), ?1 is AG-1/2v-1/4.
The variation will fit to TiAl-3Si in the scope of 0.1~1?m/s well. The ones of measured Ni base CMSX-2 and TiAl-3Si would be slightly above the line calculated. The solid-liquid interface had relation with ?1, R and v to alloy Al-2%Cu. That of Al-2%Cu would be referring to 8], that was 100K/cm. The method of exponent would be used to the following equation (2-3). Here v was 10 to 70mm/s as G=10K/mm. Exponent 1/3 was used by 1/2 in order to simplify the equation. According to (2-4) the proportional method was used as follow. Here K=1.12.;
From Fig. 3.3 the cooling
rate would be arranged to be 1~2.5~6 K/s with raised v 20~240 ?m/s. That may
agree well with principle of solidified course. A negative proportion between R
and v shown in total. R will be changed from 2 to 55 ?m. On the basis of (2-5)
the result was obtained. The curve for v-R relation had been seen in Fig. 1 R
will be decreased in accordance with increasing v. The maximum value could
reach above 400 mm. The value of ?1 is higher than that of ?2 through measured and
calculated shown as Figure 3 & 4. The measured and literature was not much
varies. They may be the same cooling condition ie. The same G. Discussion
detailed will be done as below. ?1 was computed under 7.8~24K/mm the fit more
to approaching 24K/mm. That is about 0.1mm which had less than measured. The
high C had low G under a certain v. That means high G caused slow
solidification. In the state of high G the low ?1 could be formed. Here series
had been computed by using on ?2=A(?T/(RG))1/3. On the basis of equation R= ?22*G/(3
DT?), the G was 25K/mm and DT?was 10K. As seen in calculation
higher value would be found as G=7.8K/mm scope of ?1 is 800~120?m. According to
G = (Ttip-Tbase)/L it could calculate the G. In contrast to that 120~60 ?m was
observed when high G=24K/mm. That would be caused upon high v. The value of measured
and liter. Has agreed with the curve of 24K/mm. Maybe there was a difference in
A= 0.292. In the right condition G is 24 being little bigger than 7.8. In terms
of formula (3-4), ?1 is AG-1/2v-1/4. The variation will fit to TiAl-3Si in the
scope of 0.1~1micm/s well. That may be explained upon the raising vG. The value
of v is 10~1250 ?m/s. Here l1 is the dendrite space which is
regulated by A. As the G is 10K/mm the data in reference has agreed with it
well. That l1 will reduce to 100 mm with reducing v to 0.1mm/s. below
10mm that would be beyond 200
mm. It has followed the
below equation. Thermal equilibrium equation in DS is obtained according to
(2-2).
In this study an influence on solidification behaviors of DS in g had been obtained. The main results were as follow.
This
work was supported in part by the Korea of Science and Engineering Fund, under
the Specified Base program Granted as 96-0300-11-01-3.