Article Type : Research Article
Authors : Xu R and Jun Ahn H
Keywords : Modeling; TiAl; Dentrite; The secondary arm space; Analysis; Temperature; Cooling rate; Composition; Solidificational speed
The parameters simulation of
solidificational speed and cooling rate and secondary & composition has
been established for the sake of searching their intrintic relationship. It is observed
that the cooling rate will with increasing speed of solidification. The detail
is that Cr changes from 0 to 23K/s when the solidificaition changes from 0 to
1800mm/hr. For the making TiAl intermetallic compounds the fit cooling rate and
secondary arm space will be determined in advance to proceed the experiment
which is necessary for us to regulate. The dentrite secondary arm space will
increase from 33mm to 0.1mm when the solidificational speed increases from 5 to
1800mm/hr. The dendrite secondary arm space will increase from 698?m to 0?m
when the solidificational speed increases from 0 to 1800mm/hr. The arm space is
big which is bigger than 100?m in low solidificational speed like 30mm/hr. The
cost will be high in less than 30mm/hr so in order to acquire low cost the
bigger one than 30mm/hr will be chosen in manufacture. The temperature will
decrease from 1584K to 4K with the increasing solidificational speed from 0 to
1800mm/hr in terms of calculation.
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. Meanwhile the solidificational speed is main parameter to search
for its property in this study because it affects directly to the cooling rate
and secondary arm space etc. On the other side the relationship with cooling
rate and energy difference & temperature has been investigated according to
varied speed 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 [1-3]. 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 [3-8]. 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.
From the secondary arm space in dendrite the cooling rate will be checked out and it can be convenient for us to use in practice and experiment. On the contrary from the cooling rate the secondary arm space the cooling rate is also seen in this study. It is said again the bigger secondary arm space creates lower cooling rate and the higher cooling rate creates the lower arm space. It is seen evidently in this study. For the decreasing making cost the high cooling rate is effective to compare with low one so the secondary arm space will be low too. This is the valuable data computed and shown in this study. For the making TiAl intermetallic compounds the fit cooling rate and secondary arm space will be determined in advance to proceed the experiment which is necessary for us to regulate. For the cost down the high solidified speed is needed on the other side the single crystal is not neglected for the science experiment and high quality. This is the final destination in this paper to look for (Figure 1,2).
Figure 1: The graph between the cooling rate and solidificational speed in TiAl.
Figure 2: The graph between the temperature and solidificational speed in TiAl.
As seen in Figure 1 the Cr increases with increasing speed of solidification. The detail is that Cr changes from 0 to 23K/s when the solidificaition changes from 0 to 1800mm/hr. They are proportional to each other. As seen in Figure 2 the temperature will decrease from 1584K to 4K with the increasing solidificational speed from 0 to 1800mm/hr (Figure 3).
(a) 0~1800mm/hr
(a) 0~400mm/hr
(c)30~400mm/hr
Figure 3: The graph between the dentrite secondary arm space and solidificational speed within different speeds in TiAl.
As seen in Figure 3(a,b,c) the dendrite secondary arm space will increase from 698?m to 0?m when the solidificational speed increases from 0 to 1800mm/hr. The arm space is big which is bigger than 100?m in low solidificational speed like 30mm/hr. The cost will be high in less than 30mm/hr so in order to acquire low cost the bigger one than 30mm/hr will be chosen in manufacture. In Figure 3(b) is the one part of Figure 3(a) the detail graph is seen there the 30mm/hr is the critical value with 100?m of solidification arm space. The curve will change stable one which means that low arm space happens later. In Figure 3(c) the secondary arm space is from 110?m to 10?m within increasing speed from 30mm/hr to 400mm/hr. It fits to the principle well. If the destination is 180mm/hr the secondary arm space occupies 22?m in TiAl alloys. The predict value is very precise to compare with literature in this study. On the other hand below 30mm/hr the cell will be formed only more than this value the dendrite is formed. So for the sake of decreasing the cost the dendritic one is been needed in materials direction. The higher speed will produce more production in one time with low cost in fighter jet of aerospace (Figure 4).
Figure 4: The graph between the solidificational speed and composition Al in TiAl.
As seen in Figure 4 when
composition increase from 0 to 1 the solidificational speed will increase too
from 3.4mm/hr to 6.3 mm/hr. It is a low value so it means that composition
affection is weak to solidificational speed which can be neglected somewhat.
The modelling equation is
as below
Cr=45V --- (1)
T=2.2/V --- (2)
L=0.009/V --- (3)
V=2.2/ (-1000Com+2273)
--- (4)
Here Cr is the cooling rate K/s; V is
solidificational speed m/s; L is dendrite secondary arm space mm; Com is
composition of Al.
When composition increase
from 0 to 1 the solidificational speed will increase too from 3.4mm/hr to 6.3
mm/hr. It is a low value so it means that composition affection is weak to
solidificational speed which can be neglected somewhat. The secondary arm space
is from 110?m to 10?m within increasing speed from 30mm/hr to 400mm/hr. It fits
to the principle well.