metals
Article
Investigation on Hot Deformation Behavior and Hot
Processing Map of BSTMUF601 Super-Alloy
Chaoyang Sun *, Xun Zuo, Yu Xiang and Jing Yang
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China;
[email protected] (X.Z.); [email protected] (Y.X.); [email protected] (J.Y.)
* Correspondence: [email protected]; Tel.: +86-10-6233-4197; Fax: +86-10-6232-9145
Academic Editor: Johan Moverare
Received: 23 January 2016; Accepted: 15 March 2016; Published: 19 March 2016
Abstract: Isothermal compression tests of BSTMUF601 super-alloy in the temperature range of
950 ˝ C–1200 ˝ C and at the strain rates of 0.2 s´1 , 5 s´1 , 10 s´1 were performed on a Gleeble-1500D
thermo-mechanical simulator. Based on the hyperbolic sine function, the unified constitutive
equations and hot processing maps during the hot deformation process were established. The flow
stress predicted by the constitutive equations shows good agreement with the corrected stress.
Hot processing maps for hot working conditions were established based on exploring the effect
of power dissipation efficiency and the instability coefficient associated with various kinds of
temperatures and stain rates. Subsequently, power dissipation efficiency and the instability coefficient
were interpreted based on hot processing maps under a series of strains, temperatures and strain
rates. The results show that power dissipation efficiency increases gradually with the increasing
temperature and the decreasing stain rate, and instability domains reduce first, then increase with the
increase of true strain. The optimum hot working condition of BSTMUF601 super-alloy was obtained.
Keywords:
BSTMUF601 super-alloy;
deformation behavior
constitutive model;
hot processing map;
hot
1. Introduction
The nickel-based super-alloy used for the muffle furnace should provide good mechanical
properties, oxidation resistance and especially excellent, high temperature, creep-resistant
performance [1]. The BSTMUF601 super-alloy is a nickel-based super-alloy developed independently
by Baosteel and applied to produce plates for muffle furnaces, and it possesses great elevated
temperature performance at a less expensive cost. Under the working condition, when the temperature
is 1095 ˝ C and stress is 12.4 MPa, the steady creep rate of BSTMUF601 super-alloy is 10´6 s´1 , which is
close to that of Inconel601 super-alloy. The creep rupture strength at the elevated temperature obtained
through persistent tensile experiment is at the same level compared with similar foreign materials.
Additionally, BSTMUF601 super-alloy has excellent welding performance, and high temperature
strength of the welded joints is 100 MPa under 950 ˝ C and the room temperature strength is 630 MPa.
In the past years, research on the BSTMUF601 super-alloy was mainly focused on creep properties
and oxidation behavior [2,3]. However, little research has been carried out on investigating the
manufacturing technologies for this alloy, especially analyzing the processes to attain a fine and
uniform microstructure in a hot-wrought/rolled state. The flow stress is the most basic parameter
for characterizing plastic deformation properties of metals and alloys, and it determines the load
and energy needed during the plastic deformation [4]. In recent years, the processing map based
on the dynamic materials model (DMM) has been considered an important method for optimizing
hot working processes and controlling the microstructure in the forming process [5,6]. Based on
the processing map, the deformation mechanisms under different deformation conditions can be
Metals 2016, 6, 70; doi:10.3390/met6030070
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predicted, and then the deformation temperature and strain rate corresponding to the local peak
efficiency of power dissipation are chosen as the optimum processing parameters for the hot working
of materials [7,8].
The objective of this paper is to study the hot deformation behavior of BSMUF601 super-alloy
based on the results of isothermal compression tests. The processing maps of this alloy are constructed
in order to analyze the instability region and optimize the hot working parameters.
2. Materials and Methods
An experimental BSTMUF601 super-alloy was melted in vacuum in an electro-slag furnace
(Baosteel special steel, Shanghai, China), and then exposed to solid solution strengthening and hot
forging before specimen preparation, which was provided by Baosteel special steel. The chemical
composition (wt %) of the BSTMUF601 super-alloy is shown in Table 1. Cylindrical specimens
for compression tests (8 mm in diameter and 12 mm in height) were cut and machined from the
forged bar. To investigate the effects of the deformation temperature and flow stress, the isothermal
compression tests were performed on a Gleeble-1500D thermo-mechanical simulator (Dynamic Systems
Inc. Poestenkill, New York, NY, USA) at the temperature range of 950 ˝ C–1200 ˝ C with intervals of
50 ˝ C and at strain rate range of 0.2, 5 and 10 s´1 , respectively. A thermocouple was used to monitor
and control the temperature of the specimen during testing. Graphite foil pastes were used between
the specimens and the plate to minimize the friction during deformation [9].
Table 1. Chemical composition of the BSTMUF601 super-alloy (in wt %).
C
Si
Mn
S
P
Cr
Fe
Ni
0.013
0.02
0.21
0.002
0.005
29.19
9.49
balance
Considering the actual characteristics of hot working process, to obtain uniform microstructure,
each specimen was heated to the testing deformation temperature at a rate of 10 ˝ C/s, and held for
3 min. All the specimens were deformed with the desired deformation strain rate and 50% reduction
in height corresponding to a true strain of 0.69, and then quenched to room temperature immediately
in water.
3. Results and Discussion
3.1. Flow Stress-Strain Curves
The flow stress-strain curves of experimental BSTMUF601 super-alloy at the temperature range of
950 ˝ C–1200 ˝ C and at strain rates of 0.2, 5 and 10 s´1 are shown in Figure 1. As expected, the flow stress
is sensitively dependent on both the deformation temperature and strain rate. At the lower strain, the
flow stress increased rapidly with the increase of the strain, caused by the increase of the average value
of dislocation density which appears to have higher resistance to further compression. Some of the
stress curves showed a broad and flat peak, which indicates the occurrence of dynamic recrystallization
(DRX) and dynamic recovery (DRV) [10,11]. The flow stress decreases with the increase of deformation
temperature at the same strain rate, and increases with the decrease of the strain rate at the same
deformation temperature. This is easy to understand because the mobility of the grain boundary and
dislocation could be accelerated or improved at a higher temperature, while it would take a longer
time at a lower strain rate, according to the higher effect of the apparent activation energy of the
deformation and lower shearing stress. Additionally, higher deformation temperature and lower strain
rate could be beneficial for completing the DRX process including nucleation and growth.
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300
(b)
(a)
(c)
950oC
950oC
1000oC
1000oC
250
950oC
/MPa
200
1100oC
o
1100 C
1150oC
1200oC
150
1050oC
100
o
1100 C
1150oC
1200oC
50
0.0
1050oC
1050oC
1000oC
0.1
0.2
0.3
0.4
0.5
0.6

0.1
0.2
0.3
0.4
0.5
0.6
1150oC
1200oC
0.1
0.2
0.3
0.4
0.5
0.6


−1;;
Figure 1. Flow stress-strain curves of BSTMUF601
BSTMUF601 super-alloy
super-alloy under
underdifferent
differentstrain
strainrates:
rates:(a)
(a)0.2
0.2ss´1
´1
´1
(b) 5 s −1; ;(c)
(c)10
10s−1
s. .
3.2. Constitutive Model of Peak Stress
Among all
allthe
theflow
flow
stress
constitutive
equations,
the Arrhenius-type
equation
proposed
by
stress
constitutive
equations,
the Arrhenius-type
equation
proposed
by Sellars
Sellars
is thewidely
most widely
used [12,13].
These equations
are described
as follows:
et al. is et
theal.most
used [12,13].
These equations
are described
as follows:
Q
.
 exp(Q q )“ AA11 exp(
n11 σq
)
ε expp
exppn
RT
RT
.
Q
ε expp Qq “ A2 σnn22
 exp(RT )  A2
RT
.
Q
q “ A sinhpασqn
ε expp
RT
Q
(1)
(1)
(2)
(2)
(3)
.
 exp(
)  A sinh( )
(3)
where ε is the strain rate (s´1 ), Q is the
apparent
RT activation energy of deformation (J/mol), R is the
universal gas constant (8.314 J¨ mol´1 ¨ K´1 ), T is the absolute temperature (K), σ is the flow stress
−1), Q is the apparent activation energy of deformation (J/mol), R is the
where
strain
rate (sparameters
(MPa), n 1 ,isn2the
, n are
material
which are called the stress exponents, A, A1 , A2 , are material
−1·K−1), T is the absolute temperature (K), σ is the flow stress (MPa),
universal
gas
constant
(8.314
J·
mol
parameters which relate to the strain rate–sensitive parameter.
n1, n2Taking
, n arethe
material
are called
stress exponents, A, A1, A2, are material
naturalparameters
logarithm ofwhich
Equations
(1)–(3) the
yields:
parameters which relate to the strain rate–sensitive parameter.
.
Taking the natural logarithm ofln
Equations
yields:
ε “ ln A2 (1)–(3)
` n1 σ ´
Q{pRTq
(4)
n
.ln   ln A n  - Q / ( RT )
ln ε “ ln A1 `2 n2 1ln σ ´ Q{pRTq
.
ln ε “lnln
` An1 ln
´ Q{pRTq
 Aln
 nsinhpασq
2 ln  - Q / ( RT )
(4)
(5)
(6)
(5)
Generally, the different descriptions of the Arrhenius-type equations are used for different regions.
ln could
 ln Apredict
 n ln sinh(
) - Qstress
/ ( RT )for the high stress level while(6)
The exponential law in Equation (5)
the
flow
the
power
law
in
Equation
(4)
could
only
be
used
for
the
low
stress
level.
However,
the
hyperbolic
sine
law
Generally, the different descriptions of the Arrhenius-type equations are used for different
in Equation
is applicable
low stress
and high
stress
In the
thestress
flow stress
regions.
The(6)
exponential
lawforinboth
Equation
(5) could
predict
thelevels
flow [8].
stress
for study,
the high
level
ranges
from
50
to
300
MPa;
therefore,
the
hyperbolic
sine
law
in
Equation
(6)
is
the
most
optimum
while the power law in Equation (4) could only be used for the low stress level. However,
the
constitutive
equation.
Obviously,
the
material
parameters
α,
n,
n
,
n
and
Q
should
be
identified
at
1
2
hyperbolic sine law in Equation (6) is applicable for both low stress and high stress levels [8]. In the
first
to
analyze
the
flow
behavior
of
the
studied
steel,
and
according
to
reference
[14],
α
=
n
/n
.
1
2
study, the flow stress ranges from 50 to 300 MPa;. therefore, the hyperbolic sine law in Equation (6) is
By linear
fitting
and plotting
σ against
ln ε, n1 the
could
be obtained
fromα,the
of the linear
the most
optimum
constitutive
equation.
Obviously,
material
parameters
n, nslope
1, n2 and Q should
regression
astoshown
inthe
Figure
The of
average
valuesteel,
of nand
calculated
to be 0.0562.
1 was
be
identifiedlines,
at first
analyze
flow 2a.
behavior
the studied
according
to reference
[14],
Additionally,
n
=
9.01
could
be
obtained
from
the
slope
of
the
linear
regression
lines,
as shown
2
α = n1/n2.
in Figure
2b. Then,
α =and
n1 /n
2 = 0.111/17.807
 , n1 could be obtained from the slope of the linear
By linear
fitting
plotting
σ against =
ln0.00623.
regression lines, as shown in Figure 2a. The average value of n1 was calculated to be 0.0562.
Additionally, n2 = 9.01 could be obtained from the slope of the linear regression lines, as shown in
Figure 2b. Then, α = n1/n2 = 0.111/17.807 = 0.00623.
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(a)
(b)
950oC
5.6
17.807
1000 C
250
200
o
1100 C
1150oC
150
1200oC
100
1050 C
o
1100 C
5.2
o
1150 C
o
1200 C
4.8
4.4
-2
-1
0
1
-1
ln(stain rate,s )
2
3
-2
-1
.
1.2
1050oC
0.4
1100oC
1150oC
0.0
1200oC
-0.4
-2
-1
0
1
.
-1
ln(strain rate,s )
2
3
1 -1
2
0.8
3
10s-1
5s-1
(d)
1000oC
ln(sinh()),MPa
ln(sinh()),MPa
950oC
0.148
0
ln(strain rate,s )
.
1.2
(c)
0.8
o
1000 C
o
1050oC
,MPa
o
950 C
0.111
o
ln（ ,MPa）
300
0.838
0.2s-1
0.4
0.0
-0.4
8.5
9.0
9.5
10.0
10.5
-1
10000/T， K
.
.
lnε;. ;(b)
;
Figure
(b)lnσ
lnσagainst
againstlnln
; (c)
lnsinh(ασ)
against
Figure 2.
2. The
The linear
linear regression
regression (a)
(a) σσ against
against ln
ε; (c)
lnsinh(ασ)
against
lnε;lnand
and
(d)
lnsinh(ασ)
against
(10000/T).
(d) lnsinh(ασ) against (10000/T).
The value of n was calculated to be 6.757, obtained from the slope of the linear regression lines,
The value of n was calculated to be 6.757, obtained from the slope of the linear regression lines,
as shown in Figure 2c. To calculate the apparent activation energy Q, Q = 1000 × n × R × K, where
as shown in Figure 2c. To calculate the apparent activation energy Q, Q = 1000 ˆ n ˆ R ˆ K, where
K   ln sinh( ) / (10000 / T ) , R is the universal gas constant, T is the deformation temperature, by
K “ Blnsinhpασq{Bp10000{Tq|ε. , R is the universal gas constant, T is the deformation temperature, by
plotting
the lnsinh(ασ)
lnsinh(ασ) against
against 1000/T
1000/T at
plotting the
ataa constant
constant strain
strain rate,
rate, K
K could
could be
be obtained
obtained from
from the
the slope
slope of
of
the
linear
regression
lines,
as
shown
in
Figure
2d.
The
average
value
of
K
is
0.53
from
the
slope
of
the
the linear regression lines, as shown in Figure 2d. The average value of K is 0.53 from the slope of the
three
at different
different strain
strain rates.
rates. Therefore,
three linear
linear regression
regression lines
lines at
Therefore, the
the apparent
apparent activation
activation energy
energy was
was
calculated
to
be
470.5
kJ/mol.
In
the
same
way,
the
value
of
lnA
=
Q/(RT)
–
h
×
n
can
be
obtained
from
calculated to be 470.5 kJ/mol. In the same way, the value of lnA = Q/(RT) – h ˆ n can be obtained from
.
11
ln sinh( )´
- lnlnε,
the
, and
and lnA
lnA is
is 25.64.
25.64. Therefore,
Therefore, A
A is
is 1.37
1.37 ˆ
× 10
the intercept
intercept hh of
of the
the lnsinhpασq
1011ininthe
thepresent
presentstudy.
study.
By filling the obtained material parameters (α, n, Q and A) into Equation (3), the hyperbolic sine
equation for the peak stress of BSTMUF601 super-alloy is developed as
as following:
following:
  1.37 1011 [sinh(6.23 10-3  )]6.757
exp[-4.705 105 / ( RT5 )]
.
6.757
ε “ 1.37 ˆ 1011 rsinhp6.23 ˆ 10´3 σqs
expr´4.705 ˆ 10 {pRTqs
(7)
(7)
3.3. Unified
Unified Constitutive
Constitutive Model
Model
3.3.
At higher
higher deformation
deformation temperature
temperature and
and lower
lower strain
strain rate,
rate, flow
flow stress
stress decreases
decreases with
with the
the increase
increase
At
of
the
true
strain,
which
declares
flow
stress
is
sensitive
to
true
strain
at
the
material
hot
deformation
of the true strain, which declares flow stress is sensitive to true strain at the material hot deformation
process [15].
[15]. Therefore,
Therefore, effects
effects of
of the
the strain
strain on
on flow
flow stress
stress should
should be
be considered
in the
process
considered in
the established
established
constitutive
model
process.
In
order
to
achieve
a
primitive
estimation
of
the
flow
stress
in the
the plastic
plastic
constitutive model process. In order to achieve a primitive estimation of the flow stress in
deformation, the
(α, (α,
n, Qn,and
were obtained
individually
at 12 different
deformation,
thematerial
materialparameters’
parameters’
Q A)
andvalues
A) values
were obtained
individually
at 12
true
strains
between
0.05
and
0.6
with
0.05
intervals,
similar
to
the
method
used
for
establishing
different true strains between 0.05 and 0.6 with 0.05 intervals, similar to the method used the
for
constitutive model
of peak stress.
The
parameters
(α, n, Qparameters
and A) have
establishing
the constitutive
model
of material
peak stress.
The material
(α,functional
n, Q and relations
A) have
with true strain;
furthermore,
relations
between the
materialbetween
parameters
and trueparameters
strain couldand
be well
functional
relations
with true strain;
furthermore,
relations
the material
true
fitted
with
six-order
polynominal
functions
[16],
shown
as
Equation
(8),
plotting
material
parameters
strain could be well fitted with six-order polynominal functions[16], shown as Equation (8), plotting
against true
strain, asagainst
shown true
in Figure
3. as
The
material
parameters
n, Q and
A) could be
material
parameters
strain,
shown
in Figure
3. The(α,
material
parameters
(α,accurately
n, Q and
calculated
by
Equation
(8);
hence,
flow
stress
could
be
obtained
through
Equation
(3).
A) could be accurately calculated by Equation (8); hence, flow stress could be obtained through
$
Equation
(3).
’
Q{10000 “ 48.58 ´ 123.81ε ` 3462.54ε2 ´ 24542.6ε3 ` 72972.3ε4 ´ 98514.7ε5 ` 49872.3ε6
’
’
& lnA “ 41.01 ´ 82.34ε ` 2752.32ε2 ´ 19910.79ε3 ` 59299.40ε4 ´ 79801.05ε5 ` 40202.88ε6
’
n “ 10.07 ´ 52.99ε ` 651.71ε2 ´ 3811.26ε3 ` 10556.13ε4 ´ 13879.26ε5 ` 7007.21ε6
’
’
%
α “ 0.014 ´ 0.110ε ` 0.795ε2 ´ 3.258ε3 ` 7.515ε4 ´ 8.939ε5 ` 4.248ε6
(8)
Q
 48.58 -123.81
  3462.54
 - 24542.6
  72972.3
- 98514.7
 49872.3
ln /10000
A  41.01-82.34
  2752.32
 -19910.79
  59299.40
 - 79801.05
  40202.88


2
3
4
5
 41.01-82.34
 2752.32
 -19910.79
  59299.40
 - 79801.05
 7.21
 40202.88
6
ln
n A10.07
- 52.99 651.71
 2 - 3811.26
 3  10556.13
 4 -13879.26
 5  700
6

2
3
5
6
n 10.07
3811.26
 10556.13
 4 -13879.26

0.014--52.99
0.110651.71
0.7952 --3.258
 3  7.515
 4 -8.939
 5  4.248 6  7007.21
  0.014 - 0.110  0.795 2 - 3.258 3  7.515 4 -8.939 5  4.248 6

Metals 2016, 6, 70
(8)
(8)
5 of 8
9
0.010
Mesured
Regressed
Mesured
Regressed
0.010
0.009
Mesured
Regressed
Mesured
Regressed
9
8
7
n
-1
0.008
7
n
0.008
6
(a)
(a)
0.1
0.1
0.2
0.2
0.3
0.3
560000


0.4
0.4
0.5
0.5
0.6
-1
520000
480000
480000
440000
(b)
0.1
0.2
0.3
0.1
0.2
0.3
48


0.4
0.4
44
44
0.5
0.6
0.5
0.6
Mesured
Regressed
Mesured
Regressed
48
lnA/slnA/s
-1
520000
(b)
5
Mesured
Regressed
Mesured
Regressed
560000
440000
5
0.6
-1
0.007
Q/Jmol
Q/Jmol
6
0.007
-1
/MPa
/MPa
-1
8
0.009
40
40
(c)
(c)
(d)
0.1
0.1
0.2
0.2
0.3
0.3


0.4
0.4
0.5
36
0.6
0.5
(d)
36
0.6
0.1
0.2
0.3
0.1
0.2
0.3


0.4
0.5
0.6
0.4
0.5
0.6
Figure 3. Relations between material parameters and (a) α; (b) n; (c) Q; (d) lnA.
Figure 3.
3. Relations
Relations between
between material
material parameters
parameters and
and (a)
(a) α;
α; (b)
(b) n;
n; (c)
(c) Q;
Q; (d)
(d) lnA.
lnA.
Figure
300
(a)
300
250
(a)
- - - -Predicted
___Experiment
- - - -Predicted
___Experiment
950oC
950ooC
1000
C
250
200
o
1000
1050 C
1100oC
1050
200
150
1150oC
1100oC
1200oC
1150oC
150
100
1200oC
100
50
50
0
0.0
0
0.0
0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.2
True strain
0.3
0.4
0.5
0.6
True strain
Predicted
flow stress,MPa
Predicted
flow stress,MPa
True stress,MPa
True stress,MPa
Comparing flow stress calculated from the unified constitutive model to experimental values
Comparing
flow
calculated
constitutive
whenComparing
the strain rate
is stress
5 s−1, ascalculated
shown in from
Figurethe
4a,unified
it is easy
to see that model
flow stress
calculated from
the
flow
to experimental
values
´1 , as shown in Figure 4a, it is easy to see that flow stress calculated from
−1
when
the
strain
rate
is
5
s
unified
constitutive
well in
with
the experimental
values.
The
correlation
betweenfrom
the flow
the
strain rate model
is 5 s ,isasfits
shown
Figure
4a, it is easy to
see that
flow
stress calculated
the
the unified
constitutive
model
fits calculated
well
the
experimental
The correlation
between
stress
ofconstitutive
experimental
values
values
was values.
fine,values.
asThe
shown
in Figure
4b,
andflow
the
unified
model
is fitsisand
well
withwith
the experimental
correlation
between
the
flow stress
of
values
values
fine,
as
shown
Figure
4b, and
and
correlation
is experimental
0.995. Additionally,
thecalculated
average
relative
error
(AARE)
was
calculated
at the
stress
of experimental
values
and and
calculated
values
waswas
fine,
as
shown
ininFigure
4b,
isis0.995.
Additionally,
average
error
(AARE)
calculated
the
experimental
experimental
conditions,
and thethe
value
therelative
AARE
is 2.78%.
Thatwas
declared
that at
the
predicted
correlation
0.995.
Additionally,
theof average
relative
error
(AARE)
was
calculated
at flow
the
conditions,
the
valueconstitutive
of the
isof2.78%.
Thatwell
declared
predicted
stress
from
the
stress
from and
the
unified
model
agreed
with that
the the
experimental
results.
It is
worth
experimental
conditions,
and
theAARE
value
the
AARE
is
2.78%.
That
declared
thatflow
the predicted
flow
unified
constitutive
model
agreed
well
with
the
experimental
results.
It
is
worth
mentioning
that
the
mentioning
thatunified
the predicted
flow stress
a great
difference
experimental
flowItstress
at a
stress
from the
constitutive
modelhas
agreed
well
with thewith
experimental
results.
is worth
predicted
flow
stress
hasitashould
greatflow
difference
flow with
stress
atadiabatic
a higher flow
stress,
it
higher
flow
stress,
be attributed
softening
caused
by the
temperature
rise
mentioning
that
theand
predicted
stress with
has to
aexperimental
great
difference
experimental
flow
stressand
at
a
should
bestrain
attributed
to softening
caused
by thetoadiabatic
temperature
rise adiabatic
at a high strain
rate. rise
at
a high
rate.and
higher
flow
stress,
it should be
attributed
softening
caused by the
temperature
at a high strain rate.
300
(b)
300
250
(b) R=0.995
250
200
AARE=2.78%
R=0.995
AARE=2.78%
200
150
150
100
___
100
50
50
Best linear fit
th
6 predicted data point
Best linear fit
th
O 6 predicted data point
100
150
200
250
300
Experimental flow stress/MPa
100
150
200
250
300
Experimental flow stress/MPa
O
___
50
50
Figure
4. (a)
Comparisons between
Correlation between
between
Figure 4.
(a) Comparisons
between predicted
predicted and
and experimental
experimental flow
flow stress;
stress; (b)
(b) Correlation
predicted
and
experimental
flow
stress.
Figure
4.
(a)
Comparisons
between
predicted
and
experimental
flow
stress;
(b)
Correlation
between
predicted and experimental flow stress.
predicted and experimental flow stress.
4. Hot Processing Map
4.1. Approach Processing Map
The processing maps have been proved to be useful tools for understanding the hot deformation
behavior of metals and alloys over a wide range of temperatures, strains, and strain rates [17–21].
According to the dynamic materials model (DMM), processing maps are composed of two
superimposed power efficiency and instability maps at a constant strain [22]. The dynamic materials
Metals 2016, 6, 70
6 of 8
model assumes that the total instantaneous power P absorbed from the equipment is dissipated through
the temperature rise and microstructure change. The dissipated powers caused by the temperature rise
and microstructure change are named content G and co-content J. Most of the instantaneous power P
absorbed by the work-piece is dissipated by the dissipater content G, which is the power dissipated via
plastic deformation. The dissipater co-content J, which is the work related to metallurgical evolution
via various mechanisms such as DRV, DRX and phase transition, occurs dynamically to dissipate
power. The total power absorbed P can be expressed as:
żσ
.
P “ σε “ G ` J “
.
żσ
σdε `
0
.
εdσ
(9)
0
The ratio of dJ/dG is equivalent to the strain rate sensitivity exponent m. For an ideal linear
.
dissipater, m = 1 and Jmax “ σε{2. By normalizing the instantaneous J with the maximum value, the
efficiency of power dissipation η can be expressed as:
η“
J
2m
“
Jmax
m`1
(10)
The power dissipation map is obtained by plotting the parameter η against temperature and
strain rate for different strains in the form of a contour map.
A continuum criterion for the occurrence of flow instability is obtained by utilizing the principle
of the maximum rate of entropy production, which was proposed by Ziegler, and is given as:
` . ˘ B lnrm{pm ` 1qs
`m ă 0
ξ ε “
.
B ln ε
(11)
.
where ξ(ε) is the instability coefficient. The instability map can be obtained by plotting the instability
coefficient against the temperature and strain rate for different strains where the negative values of the
instability coefficient indicate domains of instability.
The processing map can not only be used to provide optimum deformation conditions but it
also can be used to describe the flow instability domains. The processing map is obtained through
superimposing an instability map on a power dissipation map.
4.2. Processing Map of BSTMUF601 Super-Alloy
.
The function relationship between lnσ and ln ε is obtained by cubic curve fitting, and then the
strain rate sensitivity exponent m can be obtained. According to Equation (10), the efficiency of power
dissipation η was obtained. The power dissipation map is obtained by plotting the parameter η
against temperature and strain rate for different strains in the form of a contour map. According
to Equation (11), the value of the instability coefficient was calculated. The instability map can be
obtained by plotting the instability coefficient against temperature and strain rate for different strains
where the negative values of the instability coefficient, gray areas, indicate flow instability regions.
The processing maps for BSTMUF601 super-alloy obtained in the temperature range of 950 ˝ C–1200 ˝ C
and at the strain rate range of 0.2, 5 and 10 s´1 at true strains of 0.2, 0.4 and 0.6, through superimposing
the instability maps on the power dissipation maps are shown in Figure 5, respectively.
Metals 2016, 6, 70
Metals 2016, 6, 70
7 of 8
7 of 8
(b)
(a)
0.14
2 0.020
0.17
0.19
0.23
0.23
0.13
0.060
(c)
0.31
0.11
ln(strain rate)
0.27
0.10
0.20
0.15
0.15
0.18
0.090 0.030
0.12
0.090
0.24
1
0.030 0.060
0.21
0.12
0.15
0.18
0.14
0
0.24
0.17
-1
0.14
0.24
0.28
0.19
0.20
0.20
950
0.19
1000
1050
1100
temperature(OC)
1150
1200
1000
0.27
0.31
0.35
0.40
0.45
0.17
1050
1100
temperature(OC)
1150
1200
0.27
0.36
0.39
0.33
0.30
1000
1050
0.420.45
0.48
0.51
1100
1150
1200
temperature(OC)
Figure 5.
5. Hot
Hotprocessing
processingmaps
mapsatatdifferent
different
strains
BSTMUF601
super-alloy.
strain
is 0.2;
Figure
strains
of of
BSTMUF601
super-alloy.
(a) (a)
TheThe
strain
is 0.2;
(b)
(b)
the
strain
is
0.4;
and
(c)
the
strain
is
0.6.
the strain is 0.4; and (c) the strain is 0.6.
Generally,
the maximum
Generally, the
maximum ηη represents
represents the
the optimal
optimal processing
processing window.
window. From
From Figure
Figure 5,
5, the
the power
power
dissipation
efficiency
will
be
elevated
with
the
increase
of
the
deformation
temperature
dissipation efficiency will be elevated with the increase of the deformation temperature and
and the
the
decrease
decrease of
of the
the strain
strain rate;
rate; the
the safety
safety regions
regions are
are in
in the
the low
low strain
strain rate
rate regions,
regions, and
and furthermore,
furthermore,
instability
instability domains
domains reduce
reduce first,
first, then
then increase
increase with
with the
the increase
increase of
of the
the true
true strain,
strain, implying
implying that
that the
the
true
strain
has
a
significant
effect
on
the
instability
domains.
true strain has a significant effect on the instability domains.
At
peak efficiency
efficiency appears
appears at
at strain
strain rate
rate 0.2
0.2ss´−11 and
At true
true strain
strain 0.2,
0.2, the
the peak
and deformation
deformation temperature
temperature
−1
˝
of
about
1150
°C;
as
also,
the
instability
regions
appeared
at
the
strain
rate
range
of
2–10
of about 1150 C; as also, the instability regions appeared at the strain rate range of 2–10 ss´1 and
and
˝ C–1170
˝ C,inas
deformation
950–1040
°C and˝ C
1140–1170
as shown
Figure
5a.in
It should
deformationtemperature
temperaturerange
rangeofof
950 ˝ C–1040
and 1140°C,
shown
Figure be
5a.
noted
that
the
space
between
the
contour
lines
becomes
close
in
the
temperature
range
of
1100–1150
It should be noted that the space between the contour lines becomes close in the temperature range of
˝ C–1150
˝ C rate
°C
and
the strain
of 0.2–0.35
s−1, of
implying
value isthat
relatively
sensitive
to the sensitive
changes
1100
and range
the strain
rate range
0.2–0.35that
s´1the
, implying
the value
is relatively
of
temperature
andtemperature
strain rate. At
true
strains
0.4At
and
0.6,strains
the peak
appeared
at strain
to both
the changes
of both
and
strain
rate.
true
0.4efficiency
and 0.6, the
peak efficiency
−1 and deformation´
1
˝
rate
0.2
s
temperature
of
about
1200
°C,
as
shown
in
Figure
5b,c.
The
optimum
hot
appeared at strain rate 0.2 s and deformation temperature of about 1200 C, as shown in Figure 5b,c.
working
condition
of
BSTMUF601
super-alloy
for
all
the
true
strains
occurs
in
the
strain
rate
range
The optimum hot working condition of BSTMUF601 super-alloy for all the true strains occurs in the
−1, the temperature
of
0.2–0.4
of 1100–1130
°C and
the ˝temperature
range
1170–1200 range
°C as
strain
ratesrange
of 0.2–0.4 s´1 ,range
the temperature
range
of 1100
C–1130 ˝ C and
theof
temperature
˝
˝
well.
The
power
dissipation
efficiency
of
these
two
domains
is
higher
than
that
in
the
other
regions.
of 1170 C–1200 C as well. The power dissipation efficiency of these two domains is higher than that
in the other regions.
5. Conclusions
5. Conclusions
Hot deformation behavior of BSTMUF601 super-alloy was studied in the temperature range of
−1. The following conclusions were drawn.
950–1200
°C and the strain
rate range
of 0.2–10 ssuper-alloy
Hot deformation
behavior
of BSTMUF601
was studied in the temperature range of
˝
˝
1 . The following
The material
parameters
(α,range
n, Q and
A) have
polynominal
functional
950 (1)
C–1200
C and the
strain rate
of 0.2–10
s´six-order
conclusions
wererelations
drawn. with
the true
strain,
and
the
unified
constitutive
equations
of
BSTMUF601
super-alloy
were
established.
(1) The material parameters (α, n, Q and A) have six-order polynominal functional relations
with
The
apparent
activation
energy for
hot deformation
is 470.5
kJ/mol.
the true
strain,
and the unified
constitutive
equations
of BSTMUF601
super-alloy were established.
(2) The activation
power dissipation
will beis 470.5
elevated
with the increase of deformation
The apparent
energy forefficiency
hot deformation
kJ/mol.
temperature
and the
decrease of
strain rate;
safety regions
areincrease
in the low
strain rate regions,
and
(2) The power
dissipation
efficiency
will the
be elevated
with the
of deformation
temperature
the
domains
reduce
first,safety
then regions
increaseare
with
the low
increase
theregions,
true strain,
that
andinstability
the decrease
of strain
rate; the
in the
strainofrate
and implying
the instability
the
true strain
hasfirst,
a significant
effectwith
on the
domains
reduce
then increase
theinstability
increase ofdomains.
the true strain, implying that the true strain
The BSTMUF601
super-alloy
has a(3)
significant
effect on the
instabilitypossesses
domains.a large instability region and limited hot-working
region
large
strain. Thesuper-alloy
optimum hot
working
conditions
of BSTMUF601
were the
(3)atThe
BSTMUF601
possesses
a large
instability
region and super-alloy
limited hot-working
−1, and the temperature ranges of 1100–1130 °C and 1170–1200 °C.
strain
rate
range
of
0.2–0.4
s
region at large strain. The optimum hot working conditions of BSTMUF601 super-alloy were the strain
rate range of 0.2–0.4 s´1 , and the temperature ranges of 1100 ˝ C–1130 ˝ C and 1170 ˝ C–1200 ˝ C.
Acknowledgments: The authors would like to thank the financial support of “High-end CNC Machine Tool and
Acknowledgments:
The authors
would
to thank Major
the financial
“High-end
Machine Tool and
and
Manufacturing
Equipment”
Science
and like
Technology
Specialsupport
Project of China
(NO.CNC
2014ZX04014-051)
Manufacturing Equipment” Science and Technology Major Special Project of China (NO. 2014ZX04014-051) and
Open Research Fund of Key Laboratory of High Performance Complex Manufacturing, Central South University
Open Research Fund of Key Laboratory of High Performance Complex Manufacturing, Central South University
(NO.
(NO. Kfkt2015-01).
Kfkt2015-01).
Chaoyang Sun
Sun and
and Xun
Xun Zuo
Zuo conceived
conceived and
and designed
designed the
the experiments;
experiments; Chaoyang
Chaoyang Sun,
Sun,
Author Contributions: Chaoyang
Xun
Zuo
and
Yu
Xiang
performed
the
experiments;
Chaoyang
Sun,
Xun
Zuo,
Yu
Xiang
and
Jing
Yang
analyzed
Xun Zuo and Yu Xiang performed the experiments; Chaoyang Sun, Xun Zuo, Yu Xiang and Jing Yang analyzed
the data; Chaoyang Sun and Xun Zuo contributed to writing and editing of the manuscript.
the data; Chaoyang Sun and Xun Zuo contributed to writing and editing of the manuscript.
Conflicts of Interest: The authors declare no conflict of interest.
Metals 2016, 6, 70
8 of 8
Conflicts of Interest: The authors declare no conflict of interest.
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© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
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