Article Type : Research Article
Authors : Xu R, Lim S, Reddy NS, Nam T, Ahn HJ, Kim K and Hur B
Keywords : Modelling; TiAl; Dentrite; The secondary arm space; analysis; Temperature; Cooling rate; Composition difference; Gibbs free energy
According to the secondary dentrite arm
space L and composition at solid and liquid interface in solidification the
line model of temperature and composition in dentrite has been established. The
equation is gained as T=-44,260/L to follow last study on telationship between
temperature and composition. Meantime the cooling rate and the secondary arm
space has been discussed. In the intersection the cooling rate of solid and
liquid ?T is gained. According to dentrite therefore the composition can
determine temperature. According to Y changing from pure X to pure Y ie. The
temperature will change from maximum to minimum at Al composition in materials
like TiAl. The period one of cooling rate is from 10K/s to 77 K/s in speed of
4860mm/hr at the solidified length to be 50mm. For engineering use the speed is
better when the speed is higher like 8,860mm/h when the cooling rate attains
from 25K/s to 145K/s with the secondary arm space increasing with the maximum
value. When cooling rate is 8,860mm/hr the biggest one in these three
conditions will happen with 145K/s when it is 15?m. When DS is 2.4J/(mol·K) the
DG changes from 1200J to -1200J with the temperature increases same in TiAl.
The change of temperature
in the solid and liquid in solidification transformation can deduce the related
formula. The curve expresses its trend better. From this relation their
secondary dendrite arm space composition will change when the transformation
happens. It is known that the temperature in solidification can solve their
relationship. In this study in terms of these equations the deduction and
analysis is done and the error analysis to them is done. Here the solid and
liquid equation is explored within line and find the simple formula which make
us to calculate the cooling rate rapidly [1]. Therefore in this study the model
of temperature and composition has been established to observe the trend and
intrinsic relationship between them. Then the error is checked with variance to
both of constant. TiAl as a promise materials has been searched and developed
for many years. However the cooling rate with compositions is not much yet, so
in this study the equation is established through temperature and composition
according to the phase diagram. It is modelled with cooling rate and
composition difference too in directional solidification test. The detail value
is combined through phase equilibrium line and it is compared with thermal
dynamics. The research scope is from 0 to pure Al here [1,2]. On the other side
the relationship with cooling rate and energy difference & temperature has
been investigated according to varied speed and ?S respectively for the
application. According to the solidified crystalline and phase diagram the
application will be known. In addition relationship between cooling rate and
energy difference & temperature are drawn for further research in this
study. To calculate the cooling rate is our destination in the end in terms of
the composition in TiAl alloys. Therefore the establishment equation between
temperature and cooing rate in terms of the equilibrium diagram [3-6].
The
relationship between the secondary dendrtie space and temperature
I It is supposed that
T=C/L -- (1)
C is constant, L is the
second dendrite arm space.
Then C=TL
Since T=aCcom+b
[1]--(2)
Substitute (2) into (1)
it has
C= (aCcom+b) L
-- (3)
And supposed that
Ccom =0.06, L=20?m ---
(4)
Because it has
C=44260 K?m. --- (5)
So T=44260/L ---- (6)
This is the temperature
equation with L which is the secondary dentrite arm space.
At solidified length ls
it has
C rate=T/t --- (7)
And t=ls/v --- (8)
So the function between
cooling rate Crate and ls as below
C rate=T·v/ (3600·ls) ---
(9)
As seen in Figure 1 the
relationship between temperature and secondary dendrite space is exhibited
according to the equation above. When the temperature increases from 15 ?m to
110?m the temperature will decrease from 3000K to 400K in TiAl. The bigger
space expresses that low temperature. So the whole dendrite may be expressed in
terms of the whole space changing. Because it is supposed that Ccom
=0.06 and L=20?m the whole space and temperature will change a certain with the
two parameter changing. At the tip of dentrite the temperature attains high
value and then temperature will become low (Figure 1).
As seen in Figure 2 (a~e)
when the drawing speed increases from 4860~8860mm/hr the cooling rate will
increase from 75K/s, 95K/s, 110K/s, 130K/s and 145K/s at the place of 15?m to
10K/s, 15K/s, 18K/s,19K/s and 25K/s at the same one of 110?m in TiAl at the
solidified length to be 50mm. It expresses that the cooling rate decreases with
the drawing speed becomes bigger (Figure 2).
From Figure 3 DG
decreases with temperature increasing. It decreases with entropy DS increasing
from 2 to 2.4J/mol/K. It’s decreasing means cooling rate increases along the
dendrite. This is the result of
concentration of liquid and solid in terms of composition. When DS is 2J/
(mol·K) the DG changes from 1600J to 600J with the temperature increases from
850K to 1900K respectively. When DS is 2.4J/ (mol·K) the DG changes from1200J
to -1300J with the temperature increases same. It means that in TiAl when DS
becomes big the DG will decrease. G is Gibbs free energy and DH is enthalpy.
[3] It is supposed that enthalpy is constant in this study. It means that when
DS becomes big the Gibbs free energy DG will decrease.
In Ti-Al
Figure 1: The relationship between temperature and dentrite second space in TiAl.
(a) v=4,860mm/hr
(a) v=5,860mm/hr
(b) v=6,860mm/hr
(c) v=7,860mm/hr
(d) v=8,860mm/hr
Figure 2: The relationship between cooling rate and dentrite second space at the solidified length Ls= 50mmin TiAl.
(a) ?S=2J/(mol•k)
(a) ?S=2.4J/(mol•k)
Figure 3: The
relationship between ?G and temperature T in TiAl.
·
According to composition at solid and liquid
interface in solidification the line model of temperature and dentrite
secondary arm space in solidified course has been established. The equation is
gained as T=44260/L. Meantime the cooling rate and secondary arm space L has
been discussed. In the intersection the cooling rate of solid and liquid ?T is
gained. Composition difference has been deduced and analyzed according to
dentrite therefore the dentrite secondary arm space can determine temperature.
When the secondary arm space in dentrite is from 15 to 110?m the temperature
changes from 3,000K(2727?) to 450K(177?). Y changes from pure X to pure Y the
temperature will change from maximum to minimum with increasing secondary arm
space in materials like TiAl at solidified length to be 50mm.
·
The period one of cooling rate is from 25K/s
to 145 K/s in speed of 8,860mm/hr. For engineering use the speed is better when
the speed is higher like 7,860mm/h when the cooling rate attains from 20K/s to
77K/s with the secondary arm space increasing to minimum value 4860mm/hr. When
cooling rate is 8860mm/hr the biggest one in these three conditions will happen
with 145K/s mentioned above.
·
When DS is 2J/(mol·K) the DG changes
from1500J to -500J with the temperature increases same. It means that in TiAl
alloys when DS becomes big the DG will decrease. From diagram the concentration
of Al is measured to be 1.6at% in 46Al at%. The calculation value is thought to
be phase forming element due to the minus. That has been the low concentration
with solid solution in TiAl.