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Note of use for calculations thermometallomecanic
Date:
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Author (S):
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:
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Organization (S): EDF-R & D/AMA
Handbook of Utilization
U2.03 booklet: Thermomechanical
Document: U2.03.04
Note of use for calculations
thermometallomecanic on steels
Summary
The objective of this note is to give information necessary so that a user can realize
easily a calculation thermo metal-worker-mechanics in Code_Aster. This type of calculation relates to steels which
undergo during a heating or of a cooling of structure transformations.
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
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Titrate:
Note of use for calculations thermometallomecanic
Date:
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Author (S):
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Count
matters
1 the broad outline of calculation thermo metal-worker-mechanics ..................................................................... 3
2 That to make to carry out a calculation thermo metal-worker-mechanics ............................................................... 3
2.1 Stage 1: which documents lira summarized ........................................................................................ 3
2.1.1 For the thermal part ......................................................................................................... 3
2.1.2 For the part metallurgical behavior ......................................................... 3 models
2.1.3 For the part mechanical behavior with effects of the transformations models
metallurgical ........................................................................................................................ 5
2.2 Stage 2: construction of the command file .............................................................................. 8
2.2.1 Parts thermics and metallurgical ......................................................................................... 8
2.2.2 Mechanical part .................................................................................................................... 8
2.2.3 Example of command file .......................................................................................... 9
3 Bibliography ........................................................................................................................................ 14
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
Version
8.1
Titrate:
Note of use for calculations thermometallomecanic
Date:
22/05/2006
Author (S):
V. CANO Key
:
U2.03.04-B Page
: 3/14
1
The broad outline of calculation thermo metal-worker-mechanics
In Code_Aster, calculations thermics, metallurgical and mechanical are uncoupled. Stages
successive of a complete calculation are as follows:
1) One carries out a thermal calculation which makes it possible to obtain the field of temperature in each node.
2) One realizes in post processing of thermal calculation, the metallurgical calculation which makes it possible to obtain
proportion of the various metallurgical phases in each node and possibly hardness
associated.
In Code_Aster, one can treat two different types of material, which undergo
metallurgical transformations: steels or the ZIRCALOY. One is interested here only in
materials of the steel type.
For a steel, one can take into account five different metallurgical phases: ferrite,
pearlite, the bainite, martensite, known as phase, and austenite, known as phase.
3) From the field of temperature and metallurgical phases, one carries out mechanical calculation
by choosing a model of behavior which takes into account the various possible effects
metallurgical transformations. One obtains the stress fields thus, of deformations
and of variables intern in each point of Gauss.
2
That to make to carry out a calculation thermo metal-worker-mechanics
2.1
Stage 1: which documents lira summarized
2.1.1 For the thermal part
The document [R5.02.02] contains information necessary to the comprehension of a calculation
nonlinear thermics.
In Code_Aster, for a nonlinear calculation, one treats the diffusion of heat with one
enthalpic formulation. One can provide is conductivity and the enthalpy according to
temperature, is conductivity and the specific heat C
P according to the temperature.
2.1.2 For the part models metallurgical behavior
The document [R4.04.01] of Code_Aster describes the various metallurgical models.
Brief summary:
When a material is heated, the phases are transformed into phase. When it is cooled
material, austenite is transformed, according to the speed of cooling, into ferrite and/or pearlite and/or
bainite and/or martensite. It is thus necessary to define for the heating the kinetics of transformation and
for cooling the nature and the kinetics of the possible transformations.
Kinetics of transformation to the heating:
The law of evolution of austenite is given by the equation:
Z
Z
Z
eq -
& =
0
if T
1
Ac
if T
1
1
Ac
1
TAC
1
TAC
with Z
=
eq
if
1
Ac T Ac
3 and = +
(-) if
1
Ac T Ac
3
1
3
1
Ac3
1
- Ac
Ac3
1
- Ac
1
if T Ac3
if
T Ac3
3
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
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Titrate:
Note of use for calculations thermometallomecanic
Date:
22/05/2006
Author (S):
V. CANO Key
:
U2.03.04-B Page
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where Z is the proportion of phase,
1
Ac the quasi-static temperature of beginning of transformation
phases, Ac3 the quasi-static temperature of end of transformation of the phases and 1, 3
two coefficients of material. Z eq corresponds to the evolution of the austenite rate transformed at the time
quasi-static evolutions. Initial temperatures
1
Ac and of end Ac3 of transformation
austenitic and parameters 1 and 3 can be identified starting from experimental data
providing for different heating rates, the proportion of austenite formed according to
the temperature. One will find in [bib1] precise details on the method of identification of the coefficients.
Example:
For a steel 16MND5, the coefficients are worth
1
Ac = 716°C, Ac3 = 802°C,
12s
1 =
and
5
.
0 S
3 =
.
Kinetics of transformation to cooling:
For the ferritic, perlitic and bainitic transformations, the kinetics is given by the relation
following:
+
C
T
(- Ms)
Z & = F T
(, T&, Z, ms;D)
with Z = {Z F, ZP, ZB}
T
(- Ms)
where M S represents the martensitic initial temperature of transformation, C
D size of grain
austenitic and
+
(X) the positive part of X. For the functions of evolution F, one does not impose
particular forms and the identification of F is summarized with the definition of diagrams of the type TRC
(transformation into Refroidissement Continu). This diagram makes it possible to define the evolutions of
ferrite, pearlite and bainite associated with a thermal history with cooling and conditions
of austenitization given (for a size of grain C
D given).
For the martensitic transformation, one uses the kinetics of Koistinen-Marburger given by
the equation:
Z
= 1
(- Z - Z - Z)
M
F
P
B [1 - exp ((M
T) +
-
)
S
]
M
if Z
+ Z + Z threshold
M =
0
S
S
F
P
B
M + Akm (Z + Z + Z) + Bkm
if Z
+ Z + Z > threshold
s0
F
P
B
F
P
B
where M s0 represents the martensitic initial temperature of transformation when that Ci is total
and, Akm, Bkm and threshold are parameters materials.
In the simplest case, one can take the temperature M S constant and thus equalizes with M s0. For
a steel 16MND6, M s0 is worth 365°C.
Note:
Diagrams TRC relate to conditions of austenitization given to which
correspond a value of size of grain D. Cette cuts grain results from the history
thermics undergone with the heating and does not evolve/move any more with cooling. In Code_Aster, it
is possible to calculate starting from the thermal history with the heating, the evolution of
cut grain and to take account of its effect on the metallurgical behavior with
cooling (see case test of reference hsnv126a. COM, hsnv126b.comm and
mtlp102a. COM for the use).
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
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8.1
Titrate:
Note of use for calculations thermometallomecanic
Date:
22/05/2006
Author (S):
V. CANO Key
:
U2.03.04-B Page
: 5/14
Note:
It is possible in Code_Aster to calculate Hv hardness of the multiphase mixture
5
given by the Hv relation = Zk Hvk where Hvk is hardness associated with the phase K and
K =1
informed under operator DEFI_MATERIAU under key word “DURT_META”. Hardness
multiphase mixture is obtained by operator CALC_ELEM with the option
“DURT_ELNO_META” (hardness with the nodes by element).
2.1.3 For the part mechanical behavior with effects models of
metallurgical transformations
The reference document of Code_Aster is the note [R4.04.02].
Several models of behavior are available in the code. They make it possible to model them
various following phenomena: plastic behavior or viscous behavior, work hardening
isotropic linear or not linear or linear kinematic work hardening, plasticity of transformation,
restoration of metallurgical work hardening of origin, restoration of work hardening of viscous origin. One
can carry out a calculation in small deformations but also in great deformations (attention them
great deformations for a model with kinematic work hardening are not activated). For one
comprehension on the aspect great deformations, lira reference documents [R5.03.31]
(great deformations without metallurgical effect) and [R4.04.03] (great deformations with effects
metallurgical).
Brief summary:
The effects of structure transformations on the mechanical behavior are of 4 types:
·
the mechanical characteristics of the material which undergoes transformations are modified. In
private individual, plastic characteristics (elastic limits in particular) and the coefficient of
thermal dilation are strongly affected. For the elastic limit of the multiphase point, one
use a non-linear law of the mixtures given by:
4
Z
4
4
I there I
= 1
[- G (
y
Z)] + G (
I
y
i=
Z)
,
= 1
I
y
teststemyà
4
i=1
i=1
Zi
i=1
where Zi is the proportion of each phase and G a function of Zi.
·
the expansion or the voluminal contraction which accompanies structure transformations
translated by a spherical deformation “of transformation” which is superimposed on
thermal deformation. In general, one gathers this effect with that due to the modification of
thermal dilation coefficient. The thermal deformation is given by:
4
HT
= Z [
R
Tref
T
(- T
ref.) - 1
(- Z)
+ Z T
(- T
) + Z
F
]
I [
R
Tref
F
ref.
F
]
i=1
where and F are the dilation coefficients of the austenitic and ferritic phases,
respectively.
Tref
F translates the difference in compactness between the two phases with
temperature of reference. There are R
Z = 1
when the phase of reference is the phase
austenitic and R
Z = 0
when the phase of reference is the ferritic phase.
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
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Note of use for calculations thermometallomecanic
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·
a transformation proceeding under constraints can give rise to a deformation
irreversible and this, even for levels of constraints much lower than the elastic limit
material. One calls this phenomenon the plasticity of transformation. Into small
deformations, this additional term appears in the expression of the total deflection.
The law of evolution of the deformation which accompanies this phenomenon writes:
4
Pt
& = 3 ~ K F (
I I Z). Z&
2
I
i=1
where ~ is the diverter of the tensor of the constraints, X the positive part of X, Ki and I
F,
coefficients of the 4 ferritic phases. It is considered that this phenomenon does not exist at the time
austenitic transformations.
·
finally, one can have at the time of the transformation a phenomenon of restoration of work hardening:
the work hardening of the mother phase (or not completely) is not transmitted to the phases
lately created. The phases lately created can is to be born with a state
of virgin work hardening, either to inherit only part of work hardening of the mother phase or or
to inherit the totality of the work hardening of the mother phase.
In the case of an isotropic work hardening, the plastic deformation p is not characteristic any more
state of work hardening and it is necessary to define other variables for each phase, noted K
r.
Isotropic work hardening is written then:
4
F Z
4
R = 1
(- F (Z))R + ()
Z .R
I
I, Z = Z
Z
I
i=1
i=1
where Rk is the variable of work hardening of the phase K which can be linear or not linear by
report/ratio with K
R and F (Z) a function depending on Z such as F (Z) []
1
,
0.
The laws of evolution of the ir variables are given by:
4
- Z & (R - R)
I
I I
I 1
R & = p & + =
- (Cr
) m
if
Z > 0
moy
Z
4
1
4
2 3
only
viscosity
in
Z & (R - R)
R & = p & + I
I
I
- (Cr
) m
if
Z > 0
I
moy
I
Zi
4
1
4
2 3
only
viscosity
in
5
R
=
moy
Zk Kr
k=1
5
C = ZkCk
k=1
5
m = Zkmk
k=1
Ck and mk are the coefficients of viscous restoration associated the phase K, I and I
characterize the proportion of work hardening transmitted at the time of the transformation and of
transformation, respectively. The memory is non-existent if = 0, supplement if = 1.
Handbook of Utilization
U2.03 booklet: Thermomechanical
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Code_Aster ®
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Date:
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In an equivalent way, a kinematic work hardening in the case of is written:
4
4
X =
F Z
1
(- F (Z))X + ()
Z .iXi, Z = Z
Z
I
i=1
i=1
where X K is the kinematic variable of work hardening of the phase K which is linear compared to
variable K:
2
X K = Hkk
3
The laws of evolution of the variables kinematics K are given by:
4
Z & (-)
I
I I
p
3
I 1
& = & + =
+ (C) m
if
Z > 0
Z
2
eq
eq
1 4
4 2 4
4 3
only
viscosity
in
Z & (-)
p
I
I
I
3
& = & +
+ (C) m
if
> 0
I
Z
Z
2
eq
I
I
eq
1 4
4 2 4
4 3
only
viscosity
in
~
p
3
(-)
& =
X
p&
2 (- X) eq
where HK are the slopes of work hardening associated with each phase K.
For a model of plasticity, the plastic multiplier is obtained by writing the condition of
coherence &f = 0 and one a:
p &,
0 F 0
and &f
p = 0
In the viscous case, p & is written:
N
F
p & =
where F is the threshold of plasticity given by:
F = eq - R - y in the case of an isotropic work hardening
F =
(- X) eq - y in the case of a kinematic work hardening
Handbook of Utilization
U2.03 booklet: Thermomechanical
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Note of use for calculations thermometallomecanic
Date:
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2.2
Stage 2: construction of the command file
2.2.1 Parts thermics and metallurgical
1) Definition of diagram TRC: to see command DEFI_TRC in the document [U4.43.04].
This command is made up of three parts: a part where the ferrite evolutions are defined,
pearlite and bainite associated with a unit with thermal history to cooling and
conditions of austenitization given (size of grain), one second part which defines them
parameters related to the change of temperature ms and a third part which defines the influence of
size of grain on the metallurgical transformations with cooling by diagram TRC.
This last part is not obligatory.
2) Definition of the initial metallurgical phases: to see command CREA_CHAMP in
document [U4.72.04]. This command makes it possible to define the initial metallurgical phases
present in material.
3) Definition of material: to see command DEFI_MATERIAU (document [U4.43.01]). For
thermal part, it is necessary to inform the key word THER_NL which contains the values of conductivity
thermics and those of the enthalpy, functions possibly of the temperature. For the part
metallurgical, it is necessary to inform the key word META_ACIER of which the structure is as follows:
META_ACIER:(
TRC: name of diagram TRC defines into 1)
AR3: quasi-static temperature of beginning of decomposition of austenite to cooling.
ALPHA: coefficient has law of Koïstinen-Marbürger
MS0: martensitic initial temperature of transformation when this one is total.
AC1: quasi-static temperature of beginning of transformation into austenite with the heating.
AC3: quasi-static temperature of end of transformation into austenite.
TAUX_1: parameter intervening in the kinetics with the heating.
TAUX_3: parameter intervening in the kinetics with the heating.
LAMBDA: parameter material intervening in the model of evolution of size of grain.
QSR_K: parameter energy of activation intervening in the model of evolution of size of grain.
D10: parameter material intervening in the model of evolution of size of grain.
WSR_K: parameter energy of activation intervening in the model of evolution of size of grain.
4) Realization of thermal calculation: to see documentation of Utilization and Référence of
thermal operators: THER_LINEAIRE and THER_NON_LINE.
5) Realization of metallurgical calculation: to see command CALC_META (document [U4.85.01]).
This command makes it possible to obtain starting from preceding thermal calculation, the proportions of
various metallurgical phases. It is on this level that the initial metallurgical state is informed
(command CREA_CHAMP).
2.2.2 Part
mechanics
1) Definition
material: to see command DEFI_MATERIAU (document [U4.43.01]). According to
phenomena which one wishes to model, several key words must be indicated.
In all the cases, the user must supplement the key words:
·
ELAS_META (_FO) which contains information on the elastic characteristics, of
thermal dilations and of elastic limits,
·
META_ECRO_LINE to define an isotropic or kinematic work hardening linear and
META_TRACTION to define a nonlinear isotropic work hardening.
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
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Titrate:
Note of use for calculations thermometallomecanic
Date:
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The other possible phenomena (nonobligatory) are as follows:
·
viscoplasticity + restoration of viscous origin: key word factor META_VISC (_FO)
·
plasticity of transformation: key word factor META_PT
·
metallurgical restoration of origin: key word factor META_RE
Note:
_FO means that the coefficients can possibly depend on the temperature.
2) Realization of mechanical calculation: order STAT_NON_LINE (document [U4.51.03]). Under
key word COMP_INCR, one must specify under RELATION, the name of the model chosen among the 24
models below and under RELATION_KIT, material “ACIER”.
The various models are:
/“META_P_IL”
/“META_P_INL”
/“META_P_IL_PT”
/“META_P_INL_PT”
/“META_P_IL_RE”
/“META_P_INL_RE”
/“META_P_IL_PT_RE”
/“META_P_INL_PT_RE”
/“META_P_CL”
/“META_P_CL_PT”
/“META_P_CL_RE”
/“META_P_CL_PT_RE”
/“META_V_IL”
/“META_V_INL”
/“META_V_IL_PT”
/“META_V_INL_PT”
/“META_V_IL_RE”
/“META_V_INL_RE”
/“META_V_IL_PT_RE”
/“META_V_INL_PT_RE”
/“META_V_CL”
/“META_V_CL_PT”
/“META_V_CL_RE”
/“META_V_CL_PT_RE”
Significance of the letters:
P = plasticity, V = viscoplasticity, IT = linear isotropic work hardening, INL = work hardening
isotropic nonlinear, linear CL = kinematic work hardening, Pt = plasticity of
transformation, RE = restoration of metallurgical work hardening of origin.
2.2.3 Example of command file
The example that we present now is that of a thin steel 16MND5 disc which is
heated on its face higher by a laser beam then cooled than the ambient air. Modeling is
axisymmetric. The imposed loading is a flow on part of the higher face, the remainder of
faces undergoing of the conditions of natural convection and radiation. Initially the disc is
composed of 61% of ferrite and bainite 39%. With the heating, ferrite and the bainite change into
austenite. With cooling, austenite is transformed into bainite and martensite (it thus does not have there
pearlite). This study is presented in detail in document HI-74/99/002.
One presents Ci below the command file of this simulation. One gives only them
principal commands which refer to a metallurgical calculation.
Handbook of Utilization
U2.03 booklet: Thermomechanical
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Code_Aster ®
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Titrate:
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Date:
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Command file
# CALCULATION ON A STEEL 16MND5 DISC
# I - THERMAL AND METALLURGICAL PART
# I.1 - DEFINITION OF THE GRID
# I.2 - DEFINITION OF THE MODEL
moth=AFFE_MODELE (
MAILLAGE=mail,
AFFE=_F (
TOUT=' OUI',
PHENOMENE=' THERMIQUE',
MODELISATION=' AXIS',),);
# I.3 - DEFINITION OF MATERIAL
# I.3.1 - DEFINITION OF DIAGRAM TRC
TRC = DEFI_TRC (
HIST_EXP= (
_F (VALE = (
- 1.000D+00 1.000D+01 0.000D+00 0.0000D+00
0.000D+00 0.000D+00 0.000D+00 0.0000D+00
0.000D+00 0.000D+00 0.000D+00 8.3000D+02
0.000D+00 0.000D+00 0.000D+00 5.6520D+02
0.000D+00 0.000D+00 1.000D-02 5.6000D+02
0.000D+00 0.000D+00 2.400D-02 5.5062D+02
0.000D+00 0.000D+00 7.600D-02 5.3670D+02
0.000D+00 0.000D+00 12.00D-02 5.2960D+02
0.000D+00 0.000D+00 22.70D-02 5.1380D+02
0.000D+00 0.000D+00 32.50D-02 5.0155D+02
0.000D+00 0.000D+00 41.80D-02 4.8748D+02
0.000D+00 0.000D+00 52.80D-02 4.6595D+02
0.000D+00 0.000D+00 57.60D-02 4.5422D+02
0.000D+00 0.000D+00 60.00D-02 4.4531D+02
0.000D+00 0.000D+00 69.00D-02 4.0712D+02
0.000D+00 0.000D+00 72.20D-02 3.9157D+02
0.000D+00 0.000D+00 7.500D-01 3.6600D+02
0.000D+00 0.000D+00 7.600D-01 3.6080D+02)),
_F (VALE = (
- 3.400D+00 1.000D+01 0.000D+00 0.0000D+00
0.000D+00 0.000D+00 0.000D+00 0.0000D+00
0.000D+00 0.000D+00 0.000D+00 8.3000D+02
0.000D+00 0.000D+00 0.000D+00 5.6530D+02
0.000D+00 0.000D+00 1.000D-02 5.6000D+02
0.000D+00 0.000D+00 5.980D-02 5.4326D+02
0.000D+00 0.000D+00 35.00D-02 5.0750D+02
0.000D+00 0.000D+00 44.00D-02 4.9711D+02
0.000D+00 0.000D+00 52.50D-02 4.7641D+02
0.000D+00 0.000D+00 65.00D-02 4.2853D+02
0.000D+00 0.000D+00 6.840D-01 3.8393D+02
0.000D+00 0.000D+00 6.800D-01 3.8200D+02
0.000D+00 0.000D+00 6.900D-01 3.7670D+02)),
_F (VALE = (
- 8.000D+00 1.000D+01 0.000D+00 0.000D+00
0.000D+00 0.000D+00 0.000D+00 0.000D+00
0.000D+00 0.000D+00 0.000D+00 8.300D+02
0.000D+00 0.000D+00 0.000D+00 5.570D+02
0.000D+00 0.000D+00 1.000D-02 5.500D+02
0.000D+00 0.000D+00 1.800D-02 5.4746D+02
0.000D+00 0.000D+00 10.80D-02 5.2087D+02
0.000D+00 0.000D+00 27.00D-02 4.8780D+02
0.000D+00 0.000D+00 37.30D-02 4.5920D+02
0.000D+00 0.000D+00 44.40D-02 4.2560D+02
0.000D+00 0.000D+00 49.70D-02 3.7440D+02
0.000D+00 0.000D+00 5.115D-01 3.6400D+02
0.000D+00 0.000D+00 5.215D-01 3.5660D+02))),
TEMP_MS = _F (
SEUIL = 1.000D+00
AKM = 0.000D+00
Handbook of Utilization
U2.03 booklet: Thermomechanical
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Author (S):
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U2.03.04-B Page
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BKM = 0.000D+00
TPLM = - 5.000D-01));
# I.3.3 DEFINITION OF MATERIAL
ACIER=DEFI_MATERIAU (
THER_NL=_F (
LAMBDA= conductivity,
BETA=enthalpie,),
META_ACIER=_F (
TRC=TRC,
AR3=830.0,
ALPHA=-0.0247,
MS0=365.0,
AC1=716.29,
AC3=802.58,
TAUX_1=12.0,
TAUX_3=0.5,),);
# I.3.4 - ASSIGNMENT OF MATERIAL
# I.4 - BOUNDARY CONDITIONS AND LOADING
# I.5 - CALCULATION THERMAL
# I.5.1 - LIST D URGENT
# I.5.2 - RESOLUTION WITH THE HEATING AND COOLING
TEMPE=THER_NON_LINE (
MODELE=moth,
CHAM_MATER=matc,
EXCIT=_F (CHARGE=char_c,),
INCREMENT=_F (
LIST_INST=list,
NUME_FIN=70,),
TEMP_INIT=_F (VALE=28.0,),
CONVERGENCE=_F (
RESI_GLOB_RELA=5.E-05,
ITER_GLOB_MAXI=40,),);
TEMPE=THER_NON_LINE (
reuse =tempe,
MODELE=moth,
CHAM_MATER=matr,
EXCIT=_F (CHARGE=char_r,),
INCREMENT=_F (
LIST_INST=list,
NUME_INIT=70,),
TEMP_INIT=_F (
EVOL_THER=tempe,
NUME_INIT=70,),
NEWTON=_F (REAC_ITER=1,),
CONVERGENCE=_F (
RESI_GLOB_RELA=5. E-05,
ITER_GLOB_MAXI=40,),);
# I.6 - CALCULATION METALLURGICAL
# I.6.1 - STATE METALLURGICAL STARTING
# “v1” = ferrite Proportion
# “v2” = Proportion of pearlite
# “v3” = bainite Proportion
# “v4” = martensite Proportion
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
Version
8.1
Titrate:
Note of use for calculations thermometallomecanic
Date:
22/05/2006
Author (S):
V. CANO Key
:
U2.03.04-B Page
: 12/14
PHASINIT=CREA_CHAMP (
OPERATION=' AFFE',
TYPE_CHAM=' CART_VAR2_R',
MAILLAGE=MAIL,
AFFE=_F (
ALL = “YES”,
NOM_CMP = (“V1”, “V2”, “V3”, “V4”,),
VALE = (0.61, 0.0, 0.39, 0.0,)))
# I.6.2 - RESOLUTION METALLURGICAL
TEMPE=CALC_META (
reuse =TEMPE,
MODELE=moth,
CHAM_MATER=matr,
RESULTAT=tempe,
ETAT_INIT=_F (META_INIT_ELNO=phasinit,),
COMP_INCR=_F (RELATION=' ACIER',),);
# II - MECHANICAL CALCULATION WITH AN ELASTOPLASTIC MODEL INTO LARGE
DEFORMATIONS WHICH TAKES INTO ACCOUNT THE PLASTICITY OF TRANSFORMATION AND
RESTORATION D WORK HARDENING
# II.1 DEFINITION OF THE MODEL
MOMECA=AFFE_MODELE (
MAILLAGE=MAIL,
AFFE=_F (
TOUT=' OUI',
PHENOMENE=' MECANIQUE',
MODELISATION=' AXIS',),);
# II.2 - DEFINITION OF MATERIAL
# II.2.1 DEFINITION OF THE COEFFICIENTS ACCORDING TO THE TEMPERATURE
# Modulus Young E
# Coefficient Naked fish
# Limit D elasticity of Sy_a austenite, Sy_f ferrite, the Sy_b bainite and Sy_m martensite
# function of multiphase plasticity for the elastic limit mixes
# Slopes D work hardening for H_a austenite and ferrite, bainite and H_f martensite
# Dilation coefficients for AlphaA austenite
# and for ferrite, bainite and AlphaF martensite
# Functions of plasticity of transformation for bainite and FzBM martensite, FzF ferrite
# II.2.2 - DEFINITION OF MATERIAL
ACIERM=DEFI_MATERIAU (
ELAS_META_FO=_F (
E=E,
NU=NU,
F_ALPHA=ALPHAF,
C_ALPHA=ALPHAA,
PHASE_REFE=' FROID',
EPSF_EPSC_TREF=1.E-2,
F1_SY=SY_F,
F2_SY=SY_F,
F3_SY=SY_B,
F4_SY=SY_M,
C_SY=SY_A,
SY_MELANGE=MELANGE,),
META_ECRO_LINE=_F (
F1_D_SIGM_EPSI=H_F,
F2_D_SIGM_EPSI=H_F,
F3_D_SIGM_EPSI=H_F,
F4_D_SIGM_EPSI=H_F,
C_D_SIGM_EPSI=H_A,),
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
Version
8.1
Titrate:
Note of use for calculations thermometallomecanic
Date:
22/05/2006
Author (S):
V. CANO Key
:
U2.03.04-B Page
: 13/14
META_PT=_F (
F1_K=7.E-11,
F2_K=7.E-11,
F3_K=7.
E-11,
F4_K=7.
E-11,
F1_D_F_META=FZF,
F2_D_F_META=FZF,
F3_D_F_META=FZBM,
F4_D_F_META=FZBM,),
META_RE=_F (
C_F1_THETA=0.0,
C_F2_THETA=0.0,
C_F3_THETA=0.0,
C_F4_THETA=1.0,
F1_C_THETA=0.0,
F2_C_THETA=0.0,
F3_C_THETA=0.0,
F4_C_THETA=0.0,),);
# II.2.3 - ASSIGNMENT OF MATERIAL
CHMATM=AFFE_MATERIAU (
MAILLAGE=MAIL,
AFFE=_F (
TOUT=' OUI',
MATER=ACIERM,
TEMP_REF=28.0,),);
# II.3 - LIMITING CONDITION AND LOADING
# ONE IMPOSES THE FIELD OF TEMPERATURE AND THE METALLURGICAL CARD OBTAINED OUT OF I
# II.4 - MECHANICAL CALCULATION
# II.4.1 - LIST D URGENT
# II.4.2 - MECHANICAL RESOLUTION
U=STAT_NON_LINE (
MODELE=MOMECA,
CHAM_MATER=CHMATM,
EXCIT=_F (CHARGE=CHMECA,),
COMP_INCR=_F (
RELATION=' META_P_IL_PT_RE',
RELATION_KIT=' ACIER',
DEFORMATION=' SIMO_MIEHE',
TOUT=' OUI',),
INCREMENT=_F (LIST_INST=LISTM,),
NEWTON=_F (
REAC_INCR=1,
MATRICE=' TANGENTE',
REAC_ITER=5,),
RECH_LINEAIRE=_F (ITER_LINE_MAXI=3,),
CONVERGENCE=_F (
RESI_GLOB_RELA=5.E-06,
ITER_GLOB_MAXI=34,),);
FIN ();
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Code_Aster ®
Version
8.1
Titrate:
Note of use for calculations thermometallomecanic
Date:
22/05/2006
Author (S):
V. CANO Key
:
U2.03.04-B Page
: 14/14
3 Bibliography
[1]
WAECKEL F.: Modeling of the austenitic transformation in Code_Aster.
Note EDF/DER/IMA, note HI-74/95/017/0
Handbook of Utilization
U2.03 booklet: Thermomechanical
HT-62/06/004/A
Outline document