the effective partition coefficients of microalloing

METAL 2004
Hradec nad Moravicí
THE EFFECTIVE PARTITION COEFFICIENTS OF MICROALLOING
ELEMENTS IN CAST STEELS
EFEKTIVNÍ ROZDELOVACÍ SOUCINITELE MIKROLEGUJÍCÍCH
PRVKU V LITÝCH OCELÍCH
Petr Hásek a
Karel Macek b
a
b
BUT Brno, Faculty of Mechanical Engineering, IMSE, Technická 2, 616 69 Brno, CR
CTU in Prague, Faculty of Mechanical Engineering, DME, Karlovo nám. 13, 121 35
Prague 2, CR
Abstract
The effective partition coefficients were applied to assessment of heterogeneity of
distribution of microalloying elements in cast steels. Both the small castings from laboratory
heats and the heavy castings from pilot plant heats were investigated. The evaluation of
heterogeneity was based on the model of ideal dendrite. The effective partition coefficients
and the indexes of heterogeneity were derived from concentration profiles of aluminium,
titanium and vanadium. The effect of mean concentration of the above mentioned chemical
elements on their average partition coefficient was also studied. Close correlation between
partition coefficients and indexes of heterogeneity was confirmed. Small differences in
characteristics for laboratory heats or pilot plant heat were determined.
Abstrakt
Efektivní rozdelovací soucinitele byly použity pro hodnocení homogenity rozložení
legujících prvku v mikrolegovaných litých ocelích. Pri experimentu byly hodnoceny jednak
malé vzorky laboratorních taveb a jednak masivnejší vzorky z poloprovozních taveb. Pro
posouzení heterogenity byla použita metodika vycházející z modelu ideálního dendritu. Z
koncentracních profilu titanu, hliníku a vanadu byly stanoveny prubehy jejich efektivních
rozdelovacích soucinitelu a indexy heterogenity. Byl studován vliv prumerné koncentrace
legujících prvku na velikost jejich prumerného rozdelovacího soucinitele. Experimenty
potvrdily velmi tesnou závislost indexu heterogenity na efektivním rozdelovacím souciniteli.
Výsledky hodnocení laboratorních a poloprovozních taveb vykazují pouze malé rozdíly.
1. INTRODUCTION
The crystallization of steel is accompanied by segregation processes which cause various
concentration of any chemical element on different spots in the casting. This is due to the fact
that the solute element i, whether present as alloying element or impurity, is more soluble in
the liquid phase l than in the solid phase s. At definite temperature the relation between the
involved concentrations ci defines the partition coefficient ki = cis/cil. Because the liquid
becomes progressively richer in the solute as crystallization proceeds, the solute
concentrations in casting tend to rise in the areas that solidify last, i.e. in the centre of the
casting. This long-range concentration variations fall in the classification of
macrosegregation. In contrast to it, localized concentration variations on a scale smaller than
the crystal size are called microsegregation; it is caused by dendritic solidification in alloys
and therefore also called dendrite segregation. Segregation is an undesirable process that may
lead to complete impairment of the casting owing to foundry defects and to non-effective heat
treatment.
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An original method for assessment of dendritic segregation has been submitted in the
work ?1?. The concept of this work is based on the model of ideal dendrite that is an
imaginary dendrite characterizing the population of all actual dendrites in the casting. The
course of concentration ci of any chemical element i can be composed from a large number of
local concentrations of this element as measured in a sample by means of their rowing into
nondecreasing series. If the partition coefficient k i is less than unity, then the minimum
measured value of concentration cimin corresponds to the centre- line of the ideal dendrite,
whereas the maximum concentration cimax corresponds to its last frozen interface. These
critical locations are then labelled as gs = 0 (the beginning of solidification) and gs = 1 (the
end of solidification), where gs represents the fraction of the solidified phase. According to
the above mentioned concentration profile, it is possible to assess the course of effective
partition coefficient during the solidification. The latter has been therefore applied to the
evaluation of the degree of microsegregation in our castings.
Chemical homogeneity is of the utmost practical importance in cast low carbon
microalloyed steels since their yield strength and guaranteed weldability through carbon
equivalent are dependent on uniform distribution of small amounts of alloying elements.
Niobium, titanium and vanadium are commonly used in concentrations of hundredth percent
by weight. Aluminium also plays an important role, however, it is not usually considered as a
typical microalloyer. Sufficient level of microalloying is necessary in order to promote
precipitation strengthening and to control the grain growth. On the other hand, toughness is
reduced if microalloying is excessive. It follows that the optimisation of valid chemical
composition in this class of steels is relevant.
The aim of this contribution is to evaluate dendritic segregation of aluminium, titanium
and vanadium in cast microalloyed steels and work out an appraisal of optimum concentration
of these elements with respect to their uniform distribution.
2. EXPERIMENTAL MATERIAL
Chemical composition of chosen experimental steels is given in tab. 1. Laboratory
heats of steels 15MnTi4 and 14MnNb52 were cast into small ingots having mass aprox. 1,5
kg. After solidification these ingots were normalized at 900 °C for 3 h and cooled with rate
100 °C/h. Pilot-plant heats of the other steels were cast into blocks with dimensions 400 x 400
x 250 mm. The blocks were cut into prismatic balks 250 x 100 x 100 mm and homogenized at
1050 °C for 8 h, cooled down 100 °C/h and then normalized like ingots of laboratory heats.
Tabulka 1. Chemické složení sledovaných taveb stanovené chemickou analýzou [hm.%]
Steel
15MnTi4
14MnNb52
27MnTiV4
12MnTi4
26MnTi4
14MnTi8
28Mn8
C
0,15
0,14
0,27
0,12
0,26
0,14
0,28
Mn
1,11
1,16
1,20
1,12
1,12
2,00
2,00
Si
V
Nb
0,36
0,42
0,19
0,30 0,13
0,28
0,27
0,28
0,29
-
Ti
0,035
0,003
0,017
0,025
-
Al
0,042
0,070
0,003
0,005
0,006
0,002
0,002
S
0,009
0,012
0,013
0,009
0,010
0,010
0,010
P
0,018
0,019
0,020
0,016
0,018
0,017
0,019
Table 1. Chemical composition of investigated heats measured by chemical analysis [wt.%]
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3. METHODS OF MEASUREM ENT AND COMPUTATION
Measurements of local concentrations of chemical elements were conducted by wave
dispersion microanalysis by means of apparatus CAMEBAX-MICRO. Lineal method was
applied when the electron beam was directed perpendicularly to the prime arms of dendrites.
The number of analysed spots n varied from 30 to 50, as well as spacing between
neighbouring spots that ranged from 1 to 9 ? m. The programme of quantitative analysis ran
with simultaneous correction of measured values regarding atomic number Z, absorption A
and fluorescence F. Energy-dispersion analyser of characteristic X-ray radiation EDAX was
used in connection with analytical electron microscope JEOL CM200.
Local concentrations c of definite chemical elements were sequentially rowed into
nondecreasing series, where the i-th number of the progression was labelled as c(i). In
accordance with the procedure introduced in ?1?, concentrations c(i) were converted into the
sequential effective partition coefficient k ef(i) using the formula (1):
c( i)
k ef (i ) ?
(1)
n
1
?? c j
n ? i ? 1 j? i
Arithmetic mean of all values k ef(i) was called as effective partition coefficient k ef.
Heterogeneity index was determined as a quotient of standard deviation sn-1 of the population
and the mean concentration cm :
s
I H ? n? 1
(2)
cm
Tabulka 2. Strední koncentrace cm vypoctené z merení mikrosondou [hm.%], efektivní
rozdelovací soucinitele k ef a jejich smerodatné odchylky sn-1 (cm ) a sn-1 (k ef)
Steel
cm
15MnTi4 sn-1(cm)
kef
sn-1(kef )
cm
27MnTiV4 sn-1(cm)
kef
sn-1(kef )
cm
26MnTi4 sn-1(cm)
kef
sn-1(kef )
cm
sn-1(cm)
28Mn8
kef
sn-1(kef )
V
Al
Ti
Steel
0,041 0,02
cm
±0,041 ±0,015
14MnNb52 sn-1(cm)
0,416 0,528
kef
±0,358 ±0,267
sn-1(kef )
0,194 0,004 0,068
cm
±0,039 ±0,007 ±0,022
12MnTi4 sn-1(cm)
0,841 0,232 0,778
kef
±0,078 ±0,336 ±0,193
sn-1(kef )
0,017 0,003 0,013
cm
±0,014 ±0,004 ±0,013
14MnTi8 sn-1(cm)
0,487 0,262 0,394
kef
±0,360 ±0,380 ±0,268
sn-1(kef )
0,012 0,004 0,004
±0,013
±0,006
±0,007
0,363
0,25
0,241
±0,325
±0,368
±0,287
V
Al
Ti
0,108 0,006
±0,030 ±0,010
0,791 0,222
±0,116 ±0,324
0,015 0,005 0,014
±0,015
±0,008
±0,016
0,404 0,228 0,354
±0,320
±0,286
±0,285
0,009 0,003 0,088
±0,013
±0,004
±0,016
0,282 0,248 0,875
±0,359
±0,330
±0,108
Table 2. Mean concentrations cm calculated from microanalyzer measurement [wt.%],
effective partition coefficients k ef and their standard deviations sn-1 (cm ) or sn-1 (k ef)
4. RESULTS AND DISCUSSION
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METAL 2004
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1
0,8
0,6
0,4
Ti
0,2
0
0
0,2
0,4
0,6
0,8
1
S. e. p. coefficient kef(i) [-]
Solidified
phase
part
Podíl ztuhlé
fáze
gs g[-]s [-]
S. e. p. coefficient kef(i) [-]
S. e. p. coefficient kef(i) [-]
Heterogenity index I H [-]
Heterogeneity index IH [-]
In tab.2, there are collected mean concentrations, effective partition coefficients, and their
standard deviations of investigated chemical elements that were computed as arithmetic
means from experimental data obtained by microanalyzer measurements.
By comparing the
Ti
mean concentrations
2,0
V
given in tab.1 and
Al
tab.2, one can see
1,5
15MnTi4
fairly good agreement
14MnNb52
between
1,0
27MnTiV4
corresponding values
IH = -1,087.ln(k ef ) + 0,0306
2
12MnTi4
within
standard
R = 0,9983
0,5
26MnTi4
deviations. There are
14MnTi8
only two exceptions
0,0
28Mn8
concerning the content
0,1
0,2
0,3 0,4 0,5 0,6 0,8 1
0,7 0,9
of aluminium in steel
Effective partition coefficient kef [-]
14MnNb52
and
vanadium in steel
Obr. 1. Korelace indexu heterogenity IH a efektivního rozdelovacího
27MnTiV4,
which
soucinitele k ef
might be ascribed to
macrosegregation in
Fig. 1. Correlation between heterogeneity index IH and effective
the ingot.
partition coefficient k ef
Fig.1 represents
the
relation
of
heterogeneity index and effective partition coefficient. Drawing symbols distinguish both the
chemical elements (by shape of symbol) and steels (by colour of symbol). Even at first glance
one can see very tight correlation between the two characteristics of microsegregation. It also
follows that there are no relevant differences between laboratory heats and pilot-plant heats.
1
0,8
0,6
0,4
V
0,2
0
0
0,2
0,4
0,6
0,8
Solidified
phase
part
Podíl ztuhlé
fáze
gs g[-]s [-]
1
0,8
Obr. 2. Závislost sekvencního
efektivního rozdelovacího soucinitele
k ef(i) na podílu ztuhlé fáze gs
0,6
Al
0,4
0,2
0
0
0,2
0,4
0,6
0,8
1
Solidified
Podíl ztuhlé
phase
fáze
part
gs g[-]s [-]
4
Fig. 2. Dependence of sequential
effective partition coefficient k ef(i) on
solidified phase part gs
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METAL 2004
Hradec nad Moravicí
1,0
S. e. p. coefficient kef(i) [-]
However, it is worth to note, that
effective partition coefficients,
Increasing mean
[-] 0,8
complying the applied method of
Ro
concentration of
zde
computation and heat treatment of
chem.
(i) lov
ací 0,6
samples, involve not only
element
[1]so
uci
ef nit
processes
running
during
k el k0,4
d
solidification,
but
also
c
a
concentration
changes
related
to
b
0,2
cooling of the casting and its heat
treatment. Smaller ingots of
0,0
0
0,2
0,4
0,6
0,8
1
laboratory heats should exhibit
g s fáze
[1]g [-]
Podíl ztuhlé
lower heterogeneity than massive
Solidified phase part gs [-]
blocks of pilot-plant heats, but the
Obr. 3. Závislost sekvencního efektivního
were
subjected
to
rozdelovacího soucinitele k ef(i) na podílu ztuhlé fáze gs – latter
homogenisation
treatment
and
the
obecné schéma
former did not.
Fig.2 shows the dependences
Fig. 3. Dependence of sequential effective partition
of
sequential effective partition
coefficient k ef(i) on solidified phase part gs – generalized
coefficient
of
microalloying
scheme
element on the fraction of
solidified phase. The dependences differ mutually for every single steel. If we now compare
the course of these dependences with mean concentration of chemical element concerned
(tab.2), we obtain ge neralized scheme for influence of the latter magnitude on discussed
relationship (fig.3). The effect of concentration on partition coefficient of any chemical
element is able to contribute to explanation of unusual scatter for values of these coefficients
reported in literature, e.g. 0,12 ? 0,92 for Al and 0,05 ? 0,62 for Ti ?2??3?.
From fig.2 also follows different rate of increase of chemical homogeneity (uniformity of
distribution) with increasing content of microalloying element. It can be better seen on fig.4,
where effective partition coefficients are plotted against mean concentrations of elements
detected
by
microanalyzer. Drawing
1,0
symbols
used
are
0,9
identical with those in
0,8
fig.1. For titanium and
vanadium
the
curve
0,7
seems to have logarithmic
0,6
character,
whereas
0,5
straight line approximates
0,4
the
dependence
for
0,3
aluminium. The level of
0,2
segregation of chemical
0,1
element must be assessed
0,0
not only with respect to
0,00
0,05
0,10
0,15
0,20
value of its effective
Mean concentration cm [wt.%]
partition coefficient, but
also
its
mean
Obr. 4. Závislost efektivního rozdelovacího soucinitele k ef
concentration shell be
na strední koncentraci prvku cm
taken into account. If we
row investigated elements
Fig. 4. Dependence of effective partition coefficient k ef on
according
to
their
elements mean concentration cm
e
x
Ef. partition coefficient k ef [-]
s
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METAL 2004
Hradec nad Moravicí
concentration needed for attaining k ef = 0,5, we shall obtain lower mean concentration for
titanium and vanadium as compared to aluminium.
For optimisation of content of microalloying elements in cast low carbon steels from the
point of view of their uniform distribution, it would be necessary to define some critical value
of effective partition coefficient, e.g. 0,95. Our present results (fig.4) do not permit to apply
such approach.
5. CONCLUSIONS
Presented assessment of dendritic segregation of selected chemical elements in cast
microalloyed steels based the model of ideal dendrite resulted in following conclusions:
1. Laboratory heats as compared to pilot-plant heats do not exhibit relevant differences in
chemical heterogeneity of investigated elements. The reason for this unexpected
experimental fact is probably concerned with opposite effect of solidification conditions
and heat treatment.
2. Very tight correlation between effective partition coefficients and heterogeneity indexes
was confirmed for all steels investigated.
3. Previously suggested generalized scheme for effect of mean concentration of chemical
element in steel on its sequential effective partition coefficient was approved.
4. Titanium and vanadium attain the value 0,5 of effective partition coefficient at lower mean
concentration as compared to aluminium.
5. Our present results are insufficient for optimising the contents of microalloying elements
with respect to dendritic segregation.
Acknowledgement
Authors gratefully appreciate the financial support provided by Grant Agency of the
Czech Republic to project No.106/03/0473.
REFERENCES:
[1] DOBROVSKÁ,J., DOBROVSKÁ,V., MILLION,B., STRÁNSKÝ,K.: Estimation of the
partition coefficients of elements from the distribution curves their dendritic segregation
(theory). In: Proceedings Diffusion and thermodynamics of materials. Brno: IPM AS CR,
1998, p. 25.
[2] LEVÍCEK,P., STRÁNSKÝ,K.: Metalurgické vady ocelových odlitku. Prague: SNTL,
1984.
[3] DÁPALA,J., KUCHAR,L.: Solidus and liquidus curves and distribution coefficients of
admixtures in iron and prediction of the solidification interval in low-alloyed steels.
Hutnické listy, 2000, vol. LV, is. 4-7, p. 61.
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