Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_TRC
Date:
19/01/05
Author (S):
V. CANO
Key
:
U4.43.04-G
Page
:
1/6
Instruction manual
Booklet U4.4- Modeling
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA
Instruction manual
U4.4- booklet: Modeling
Document: U4.43.04
Operator
DEFI_TRC
1 Goal
To define a diagram TRC (Transformations into Continuous Cooling) of reference for
metallurgical calculations.
The diagram
trc
thus defined is necessary to the characterization of a law of behavior
metallurgical with cooling in the operator
DEFI_MATERIAU
(key word factor
META_ACIER
).
For the definition of the metallurgical data and the modeling which is made by it, one will refer to
document [R4.04.01].
Product a structure of data of the trc type.
Code_Aster
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Version
7.4
Titrate:
Operator
DEFI_TRC
Date:
19/01/05
Author (S):
V. CANO
Key
:
U4.43.04-G
Page
:
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Instruction manual
Booklet U4.4- Modeling
HT-66/05/004/A
2 Syntax
name [trc] = DEFI_TRC
(
HIST_EXP = _F
(
VALE = lval,
[l_R]
)
TEMP_MS = _F
(
THRESHOLD
=
zs,
[R]
AKM
=
akm
,
[R]
BKM
=
bkm
,
[R]
TPLM =
Vc, [R]
)
GRAIN_AUST = _F
(
DREF =
C, [R]
With =
has
,
[R]
)
)
Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_TRC
Date:
19/01/05
Author (S):
V. CANO
Key
:
U4.43.04-G
Page
:
3/6
Instruction manual
Booklet U4.4- Modeling
HT-66/05/004/A
3 Operands
3.1 Word
key
HIST_EXP
HIST_EXP
=
An occurrence of the key word factor
HIST_EXP
allows to define the ferrite evolutions, pearlite and
bainite associated with a thermal history with cooling and conditions with austenitization
data.
3.1.1 Operand
VALE
VALE = lval
List values defining the austenitization, the thermal history
()
T T
and ferrite evolutions,
pearlite and bainite.
The first value is the value of derived from the function
()
T T
(i.e. the speed of
cooling) when
T
700°C is worth.
The second value is the size of grain (i.e. their diameter) resulting from the conditions
of austenitization associated with the TRC.
The 6 following values define the thermal history enters
AR
3
and
TMF
(temperature of
beginning of decomposition of austenite in “quasi-static” cooling and temperature of end of
martensitic transformation respectively). These values are the respective coefficients of
students'rag processions of degree 0 to 5 such as the polynomial of a nature 5 thus built either the interpolation enters
AR
3
and
TMF
within the meaning of least squares of the function
()
F T
deduced from the thermal history and
such as:
()
()
(
)
F T
ln
T
=
T
If the experimental thermal history to define is a function closely connected of time
(i.e. where the speed of cooling is constant) one will inform these six values like
all equal to zero.
The following values (necessarily by group of 4) define the respective proportions of
ferrite, pearlite and bainite present at a temperature given for the thermal history
experimental defined by the first 8 values.
The ferritic, perlitic and bainitic transformations associated a thermal history are
defined by the whole of the final proportions of each phase (
Z
1
final,
Z
2
final,
Z
3
final) and corresponding temperatures, for each transformation with:
·
the temperature to which the transformation begins,
·
the temperature to which 1% of new phase are formed,
·
the temperature to which
Z
final
1% of new phase is formed,
·
the temperature to which the transformation is finished (with
Z
final
of formed phase).
Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_TRC
Date:
19/01/05
Author (S):
V. CANO
Key
:
U4.43.04-G
Page
:
4/6
Instruction manual
Booklet U4.4- Modeling
HT-66/05/004/A
The whole of the “points”
(
)
Z, Z, Z, T
1
2
3
defining an experimental history presents itself
thus as follows:
HIST_EXP = _F
(VALE =
(
- 8.784D-03, 1.100D-06, 8.563D+00,
- 2.760D-02
,
1.220D-04, - 2.955D-07, 3.402D-10, - 1.517D-13,
0.000D+00, 0.000D+00, 0.000D+00,
8.360D+02
,
0.000D+00, 0.000D+00, 0.000D+00,
7.897D+02
,
1.000D-02, 0.000D+00, 0.000D+00,
7.860D+02
,
7.039D-01, 0.000D+00, 0.000D+00,
6.568D+02
,
7.270D-01, 1.000D-02, 0.000D+00,
6.525D+02
,
7.370D-01, 2.728D-02, 0.000D+00,
6.488D+02
,
7.370D-01, 1.840D-01, 0.000D+00,
6.150D+02
,
7.370D-01, 1.940D-01, 0.000D+00,
6.107D+02
,
7.370D-01, 1.940D-01, 0.000D+00,
5.218D+02
,
7.370D-01, 1.940D-01, 1.000D-02,
4.900D+02
,
7.370D-01, 1.940D-01, 5.900D-02,
4.120D+02
,
7.370D-01, 1.940D-01, 6.900D-02,
3.802D+02
),)
Cut grain associated to the TRC
temperature corresponding
to formed bainite 1% and
proportion of ferrite
and pearlite formed with this
temperature
coefficients of the polynomial
P5 representing F (T)
such as F (T) = ln (T (T))
beginning of transformation
perlitic and proportion
of ferrite formed with this
temperature
U
N
E
occ
U
R
R
E
NCE of
m
O
T
Cl
E fact
E
U
R
HI
ST
_
E
X
P
horn
R
espo
N
D
with
U
hi
St
O
I
R
E
ex
EP
R
I
m
E
ntal
E
T (T) for T (T) = 700°C
.
temperature of
beginning of
transformation
ferritic
3.2 Word
key
TEMP_MS
TEMP_MS
This key word factor makes it possible to define the law of evolution of the temperature
Ms
according to
quantities of ferrite, pearlite and bainite already formed according to the law:
(
)
Ms
Z
Z
Z
Ms
Z
Z
Z
Z
Z
Z
1
2
3
1
2
3
1
2
3
=
+
+
=
+
+
+
+
+
+
>
Ms0
Ms0
AKM
BKM
if
if
THRESHOLD
THRESHOLD
where
Ms0
is the “conventional” temperature of martensitic beginning of transformation when the aforementioned
(it is total is defined under the key word factor
META_ACIER
of
DEFI_MATERIAU
.
Code_Aster
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Version
7.4
Titrate:
Operator
DEFI_TRC
Date:
19/01/05
Author (S):
V. CANO
Key
:
U4.43.04-G
Page
:
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Instruction manual
Booklet U4.4- Modeling
HT-66/05/004/A
3.2.1 Operand
THRESHOLD
THRESHOLD
= Z
S
,
Z
S
is the quantity of austenite transformed into on this side which
Ms
is
invariant.
3.2.2 Operand
AKM
AKM
= akm,
akm
is the factor of proportionality between the reduction in the temperature
Ms
and quantity of transformed austenite
(
)
Z
Z
Z
1
2
3
+
+
.
3.2.3 Operand
BKM
BKM
= bkm,
bkm
is the ordinate at the origin of the equation closely connected connecting the reduction in
Ms
with
quantity of transformed austenite.
3.2.4 Operand
TPLM
TPLM
=
Vc,
Vc
is the speed of cooling with 700°C of the experimental history more
slow, which makes it possible to form a little martensite.
These four key words define the values of the sizes
THRESHOLD
,
AKM
,
BKM
intervening in
law of evolution of
Ms
that one supposes independent of the size of grain.
3.3 Word
key
GRAIN_AUST
Allows to define the influence of the size of grain on the metallurgical transformations in
cooling defined by the diagram trc.
3.3.1 Operand
DREF
DREF =
C,
C is the size of grain (i.e. its diameter) associated the diagram defined under the key word
factor HIST_EXP.
3.3.2 Operand
With
With =
has
,
A is a parameter material which makes it possible to characterize the effect of the size of grain on
diagram TRC of a steel (cf [R4.04.01]).
Code_Aster
®
Version
7.4
Titrate:
Operator
DEFI_TRC
Date:
19/01/05
Author (S):
V. CANO
Key
:
U4.43.04-G
Page
:
6/6
Instruction manual
Booklet U4.4- Modeling
HT-66/05/004/A
Intentionally white left page.