Download DETERMINATION OF ACTIVATION ENERGY IN HOT

18. - 20. 5. 2011, Brno, Czech Republic, EU
DETERMINATION OF ACTIVATION ENERGY IN HOT FORMING OF ALLOY Fe-40Al TYPE
Ivo SCHINDLER a, Václav ŠUMŠAL a, Michal CAGALA a,
Hana KULVEITOVÁ a, Marcin KNAPIŃSKI b
a
VŠB – Technical University of Ostrava, Faculty of Metallurgy and Materials Engineering, 17. listopadu 15,
708 33 Ostrava, Czech Republic, [email protected], [email protected], [email protected]
b
Czestochowa University of Technology, Faculty of Materials Processing Technology and Applied Physics,
Al. Armii Krajowej 19, 42-200 Częstochowa, Poland, [email protected]
Abstract
Low density and comparatively favourite price of the Fe – 40 at. % Al type intermetallic compounds
predestine them for various technical applications, but their promising potential is used only in a limited way
as yet, mainly due to their high brittleness. Conventional techniques of processing of the coarse-grained
structure by hot forming, which are accompanied by the repeated recrystallization and progressive grain
refining, are feasible only with great difficulty in the case of this material. With regard to attraction of the
given type material, the plastometric research at temperatures 800 °C to 1200 °C was carried out as a basic
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one, namely using the compression tests on plastometer Gleeble at strain rates 0.05 s to 30 s . Cylindrical
specimens with diameter 10 mm and height 15 mm were manufactured with great difficulty from laboratory
castings of the cross section ca 20 x 33 mm, gained by means of the vacuum induction furnace. The very
coarse-grained material contained 25.1 wt. % Al and 0.013 % wt. C. From the obtained stress-strain curves
the values of peak stress were determined, which were used for determination of the values of activation
energy in hot forming according to the classical equation of the hyperbolic sine type. Enumeration of its
coefficients led at the same time to a chance to predict maximum deformation resistance characteristics of
the investigated alloy in dependence on temperature and strain rate.
Keywords:
iron aluminides; hot compression; stress-strain curves; activation energy; deformation resistance
1.
INTRODUCTION
Iron aluminides have been considered as potential candidates for high temperature structural applications
primarily due to their attractive physical, oxidative, and mechanical properties [1]. Intermetallic compounds of
Fe – 40 at. % Al type are formed by B2 FeAl phase. Their low density, comparatively favourite price and
other beneficial service properties predestine them for various technical applications, but their promising
potential is used only in a limited way as yet, mainly due to their considerable brittleness. Conventional
techniques of processing of the coarse-grained structure by hot forming (rolling and/or extrusion), which are
accompanied by the repeated static recrystallization and progressive grain refining, are feasible only with
great difficulty in the case of this material. Issues connected with the low formability can be improved to a
certain degree by selected ternary additions, as for instance Mn or B. Another type of solution represents
then the application of casting with using the method of lost wax moulding or powder metallurgy – see e.g.
[2]. Using special protective capsules [3], laboratory castings made of the brittle intermetallic alloys were
successfully hot rolled [4]. The rolling was performed from thickness 20 to 13 mm with 6 or 4 passes, using
afterheating of the intermediate rolled product in the furnace heated to temperature 1200 °C after eve ry even
pass [5]. Even the symptoms of superplasticity of the given alloys in conditions of the slow tensile
deformation [6] or compression deformation [7] are known.
The main target of the work was to obtain stress-strain curves for this type of the material in a wide range of
strain, strain rate and temperature and determine the activation energy during hot forming from the peak
18. - 20. 5. 2011, Brno, Czech Republic, EU
stress values. The plastometric tests should enable to determine the basic characteristics of formability in
relation to thermomechanical conditions of forming.
2.
EXPERIMENTAL PROCEDURES
Cylindrical specimens with diameter 10 mm and height 15 mm were manufactured with great difficulty from
laboratory castings of the cross section ca 20 (thickness) x 33 (width) mm, gained by means of the vacuum
induction furnace. It was necessary to use i.a. water jet cutting and fine grinding because machinability of the
coarse-grained material, containing 25.1 % Al, 0.014 % C and 0.16 % Mn (all in wt. %, remainder Fe) was
reduced very much. Figure 1 documents the very heterogeneous and coarse-grained microstructure of the
laboratory casting over its height (or thickness 20 mm). Similarly the cylindrical specimens were oriented,
where the areas with the as small as possible occurrence of the internal cavities were chosen, which
complicated the preparation of specimens and their following hot forming.
Uniaxial hot compression (flow stress) tests of the cylindrical specimens were performed on the dynamic
testing machine Gleeble 3800, after the unified preheating to temperature 1200 °C. The forming
temperatures were chosen 800 °C, 900 °C, 1000 °C, 1 100 °C or 1200 °C, the strain rate values were 0. 05
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s , 0.4 s , 4 s or 30 s . The
formability
was
favourably
influenced by heated tools –
a) influence of strain rate at constant temperature 1100°C
b) influence of temperature at constant strain rate 0.05 s
Fig. 1 Microstructure of the
casting
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Fig. 2 Selected examples of determined stress-strain curves
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swages. Most of the tests could be finished after reaching the true (logarithmic) height reduction ca 0.5.
The result of experiments was stress-strain curves, recalculated from the recorded values of the forming
force and compression of the specimen – see e.g. the comparative graphs in Fig. 2. The situation was
complicated from time to time by premature fracture of the material.
3.
MATHEMATICAL PROCESSING OF RESULTS
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Apparent activation energy for hot deformation Q [J·mol ] is a constant dependent on the chemical
composition and microstructure of the hot formed material whose deformation behaviour is largely influenced
by this quantity. Knowledge of its value is very useful, e.g. for description of dynamic recrystallization kinetics
or stress-strain curves at continuous deformation. For finding out the Q-value, it is obvious to use a solution
of modified equation [8]
 −Q 
e& = C ⋅ exp
 ⋅ [sinh(α ⋅ σmax )] n
R ⋅ T 
(1)
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where e& [s ] is strain rate; C [s ], α [MPa ] and are another material constants; R = 8.314 J·mol ·K ; T [K]
is deformation temperature; σmax [MPa] is deformation resistance associated with the maximum (peak)
stress. This relationship was originally developed for mathematical description of strain rate corresponding to
the steady-state stress σss [MPa] and therefore it is basically possible to use both the σmax- and σss-values for
computation of activation energy. Nevertheless, the peak stress is applied much more often because the σss
-values are hardly accessible at wide range of strain rates and temperatures. The traditional way of
assessing the constants in Eq. 1 was described e.g. in [9]. It can be solved by a graphic method using
multiple linear regression analysis. The computing program ENERGY 4.0 in language Turbo Pascal 5.0 was
developed [10] which has made more sophisticated work with the input data set (T – e& – σmax) possible.
Brainless automated advance of the calculation often leads to strange results, mostly due to definite scatter
of experimental data. The procedure described above is largely sensitive to the position of every point in
regression coordinates, especially if the number of data points is low (which is practically always the case
due to limited resources
for experiments) [11].
Hence the capability to
plot selected data and
individually evaluate it is
so
important.
The
possibility of separation
of some points from
further
calculation
seems to be absolutely
basic.
Software
ENERGY 4.0 makes it
possible in the first
stage the evaluation
and
selection
of
experimental data and a
rough estimate of the
particular
material
constants in Eq. 1,
Fig. 3 Example of work with programme ENERGY 4.0 – hardcopy of monitor
afterwards
in
the
during final regression (before more precise automatic recalculation)
second stage they are
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specified more precisely by means of the computer-aided application of the least squares method during the
non-linear regression, the result of which is among others the model σmax = f(T, e& ). One of the job stages
within the framework of programme ENERGY 4.0 is demonstrated in Fig. 3. The final regression analysis
resulted in gaining the following constants in Eq. 1 for the investigated iron aluminide of type Fe – 40 at. %
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Al: activation energy Q = 235 kJ·mol , n = 2.68, α = 0.0033 MPa , C = 2.17·10 s .
4.
DISCUSSION
The obtained values of the activation energy and further material constants enable - based on the modified
Eq. 1 – to predict the maximum deformation resistance of the investigated material in dependence on the
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temperature-compensated strain rate, defined by Zener-Hollomon parameter Z [s ] [12]:
 Q 
Z = e& ⋅ exp

R⋅T 
σ max =
(2)
1
Z
⋅ arg sinh n
α
C
(3)
The graph in Fig. 4 compares the experimentally measured and the according to Eq. 1 calculated values
σmax. Although the accuracy of plastometric tests was adversely affected by the structural heterogeneity of
specimens and sometimes also by their premature fracture, the resulting mathematical description of the
dependence σmax = f(T,γ) may be regarded as very successful. So, it was not necessary to modify parameter
Z, as it did e.g. the authors of works [13,14]. In technical literature sufficient pieces of information may be
found
concerning
apparent
activation energy for hot working,
or flow activation energy during
superplastic deformation of alloys
on the basis of iron aluminides.
The problem with the comparability
of results consists in very different
testing conditions of particular
authors – e.g. during torsion or
tensile tests, when the different
order strain rate values and ranges
of the applied temperatures, very
different initial grain size etc. may
occur. For the materials of FeAl
type (containing ca 40 at. % Al)
e.g. the following values of
Fig. 4 Comparison of measured and according to Eq. 3 calculated
activation energy are mentioned
values σmax
(all data about the chemical
composition in at. %):
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Gas atomized FeAl (Fe-39.6Al-0.19Mo-0.05Zr) [15]: Q = 465 kJ·mol
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Water atomized FeAl (Fe-39.4Al-0.18Mo-0.05Zr-0.86O2) [15]: Q = 430 kJ·mol
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Large-grained Fe-36.5Al [16]: Q = 370 kJ·mol
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Large-grained Fe-36.5Al-1Ti [16]: Q = 290 kJ·mol
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Large-grained Fe-36.5Al-2Ti [16]: Q = 260 kJ·mol
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Fe-40Al-5Cr-0.2Mo-0.2Zr-0.02B [17]: Q = 343 kJ·mol
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It is obvious that our value Q = 235 kJ·mol is in comparison with the above mentioned activation energy
values very low. This discrepancy may also be influenced by a different methodology of determination of the
variable Q. While we start from the complex hyperbolic sine relation of type given in Eq. 1, other authors use
the equation
 −Q 
e& = A ⋅ σ n ⋅ exp

R⋅T 
(4)
where stress σ [MPa] is on the pertinent stress-strain curve localized differently. It is evident that Eq. 4
corresponds to a simplified shape of Eq. 1 and is suitable for the description of deformation behaviour only at
the low stress values [9,13]. Of course, its advantage consists in the easy conversion into a shape
appropriate for the linear regression analysis.
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From the literature analysis it is obvious that the derived value Q = 235 kJ·mol
deformation behaviour of some alloys of Fe3Al type:
corresponds rather to
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Fe-27.5Al [15]: Q = 260 kJ·mol
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Fe-28Al [18]: Q = 263 kJ·mol
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Fe-28Al-2Ti [15]: Q = 191 kJ·mol
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Fe-28.7Al-2.3Cr [15]: Q = 340 kJ·mol
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Fe-29.6Al-2.7Mn [15]: Q = 350 kJ·mol
Considering the complicating effect of internal cavities in the investigated cast material on its plastic
properties, we succeeded in defining the basic trends of influence of deformation conditions on formability of
the material in conditions of the compression test. The occurrence of cracks at surface of the compressed
specimen subject to free spread was evaluated. The formability lowered with decreasing temperature and
increasing strain rate, which corresponds with data about the superplastic behaviour of the iron aluminides at
very low forming speeds [6,18].
5.
SUMMARY
In an indirect way the key role of cooling of surface layers in formability of the Fe – 40 at. % Al type
intermetallic compounds was confirmed. If we manage to avoid the heat removal from these areas into the
tool during the plastic working, the hot technological formability of these and similarly hardly workable
materials is increasing – see e.g. the application of protective capsules in rolling, indicia of superplasticity
during the tensile test or the effect of heated swages during the compression tests, applied in this work. The
plastic properties of the studied alloy are positively influenced by a higher temperature and lower strain rate.
Based on plastometric tests, a relatively low value of the apparent activation energy for hot deformation of
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the investigated alloy Q = 235 kJ·mol was determined. Thanks to this value the equation precisely
describing the relation between the maximum deformation resistance and Zener-Hollomon parameter at
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temperatures 800 to 1200 °C and strain rates of the order 10 to 10 s could be derived.
ACKNOWLEDGEMENTS
This work was carried out in the framework of the project P107/10/0438 (Czech Science Foundation),
with utilization of the procedures developed at solving of Project No. CZ.1.05/2.1.00/01.0040 (within
the frame of the operation programme "Research and Development for Innovations" financed by the
Structural Funds and from the state budget of the Czech Republic) and Research Plan
MSM6198910015 (Ministry of Education of the Czech Republic).
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