Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
1/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
Organization (S):
EDF-R & D/AMA, CS IF
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
V7.22.126 document
HSNV126 - Thermo metal-worker-mechanics in traction
simple
Summary:
This test illustrates a mechanical calculation with nonlinear work hardening on a material (Zircaloy) undergoing
metallurgical transformations.
Concretely, initially, operator CALC_META calculates the metallurgical evolution associated with
a given thermal history. This metallurgical evolution is then provided to STAT_NON_LINE which goes
to carry out a mechanical calculation by taking of account metallurgical phases (in addition to loadings
mechanics). The material of mechanical calculation is defined with ELAS_META_FO and META_TRACTION.
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
2/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
1
Problem of reference
It is about a cylindrical bar in creep.
1.1 Geometry
Appear 1.1-a: Geometry and loading of the problem of reference
It is about a cylinder H= height 1000 m, and radius R=1000 Mr.
The square in fat corresponds to the axisymmetric modeling used with the §3.
1.2
Material properties
The properties materials are described by the following parameters:
For metal thermo calculation
(Steel 16MND5)
C
p
= 5260000 J.m
- 3
.°C
- 1
= 33.5 W.m
- 1
.°C
- 1
Coefficients for the metallurgy:
“Standard” TRC
AR3 = 830°C, alpha = - 0.0306
MS0 = 400°C, AC1 = 724°C, AC3 = 846°C
1
= 0.034,
3
= 0.034
For calculation thermo metal-worker-mechanics
· Young modulus: E= 200000 AP
· Poisson's ratio: = 0.3
y
X
F=30 NR
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
3/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
Definition of the elastic characteristics, dilation and elastic limits for
modeling of an undergoing material of the metallurgical transformations:
· T
ref.
= 20°C
· Thermal expansion factor average of the cold phases:
·
F
(T) = 10
E
- 6
· Thermal expansion factor average of the hot phase:
·
(T) = 0.0001
· Temperature of definition of the expansion factor:
· T
= 20°C
· Choice of the metallurgical phase of reference: cold
· Deformation of the phase not of reference compared to the phase of reference to
temperature T
ref.
:
= 1
E
- 2
· Elastic limit of the cold phase 1 for a plastic behavior:
F_sigm_f (T) = 100
· Elastic limit of the cold phase 2 for a plastic behavior:
F_sigm_f (T) = 100
· Elastic limit of the cold phase 3 for a plastic behavior:
F_sigm_f (T) = 100
· Elastic limit of the cold phase 4 for a plastic behavior:
F_sigm_f (T) = 100
· Elastic limit of the hot phase for a plastic behavior:
F_sigm_f (T) = 100
· Function used for the law of mixture on the elastic limit of multiphase material for
a viscous behavior:
0
0,2
0,4
0,6
0,8
1
1,2
0
0,2
0,4
0,6
0,8
1
1,2
META
SY_
M
E
L
With
NR
G
E
Appear 1.2-a: Law of mixture
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
4/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
Definition of the 5 traction diagrams used in the isotropic modeling of work hardening not
linear of an undergoing material of the metallurgical phase shifts:
· Isotropic curve work hardening R according to the cumulated plastic deformation p for
cold phase 1
to 20 °C
0,99
250
with 120°C
0,0105
90
0,032
160
0,064
220
0,1125
250
0,1815
270
· Isotropic curve work hardening R according to the cumulated plastic deformation p for
cold phase 2
idem preceding
· Isotropic curve work hardening R according to the cumulated plastic deformation p for
cold phase 3
idem preceding
· Isotropic curve work hardening R according to the cumulated plastic deformation p for
cold phase 4
idem preceding
· Isotropic curve work hardening R according to the cumulated plastic deformation p for
hot phase
idem preceding
1.3
Boundary conditions and loadings
The base of the cylinder is locked according to y:
Uy = 0 on the basis of cylinder.
A force of traction F=30 NR is imposed on the top of the cylinder.
The temperature is imposed on all the cylinder for:
T (X, y, T) = 120°C
1.4 Conditions
initial
The following variables are initialized:
Z
F
(X, y, 0) = 0.7
Z
p
(X, y, 0) = 0.0
Z
B
(X, y, 0) = 0.3
Z
m
(X, y, 0) = 0.0
D (X, y, 0) = 0.0
2
Reference solution
2.1
Results of reference
The results were obtained with a former version of aster. It is about a test of not-regression.
2.2
Uncertainty on the solution compared to the result of not-regression
Uncertainty is 1
E
- 10%.
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
5/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
3 Modeling
With
3.1
Characteristics of modeling
The modeling used in the case test is as follows:
Elements 2D “AXIS” (QUA8)
Appear 3.1-a: Geometry and mesh of modeling
Cutting: 1 meshs QUAD4 according to the x axis
1 meshs QUAD4 according to the y axis
Boundary conditions: Uy=0 on NO1 and NO2
F=30N on NO3 AND NO4
3.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 1 QUAD4, 4 SEG2.
L
L
O
X
y
NO3
NO2
NO1
NO4
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
6/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
3.3 Functionalities
tested
Controls
DEFI_TRC HIST_EXP VALE
TEMP_MS
THRESHOLD
AKM
BKM
TPLM
GRAIN_AUST
DREF
With
DEFI_MATERIAU THER
RHO_CP
LAMBDA
META_ACIER
TRC
AR3
ALPHA
MS0
AC1
AC3
TAUX_1
TAUX_3
CALC_META ETAT_INIT
COMP_INCR
META_INIT_ELNO
RELATION
“STEEL”
DEFI_MATERIAU ELAS_META_FO E
NAKED
F_ALPHA
C_ALPHA
TEMP_DEF_ALPHA
PHAS_REFE
EPSF_EPSC_TREF
F1_SY
F2_SY
F3_SY
F4_SY
C_SY
SY_MELANGE
META_TRACTION
SIGM_F1
SIGM_F2
SIGM_F3
SIGM_F4
SIGM_C
MODEL AFFE_CHAR_MECA
TEMP_CALCULEE
MODEL STAT_NON_LINE
CHAM_MATER
EXCIT
CHARGE
FONC_MULT
COMP_INCR
RELATION
“META_P_INL”
RELATION_KIT
“STEEL”
INCREMENT
LIST_INST
NEWTON
STAMP
“TANGENT”
REAC_ITER
CONVERGENCE
RESI_GLOB_RELA
ITER_GLOB_MAXI
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
7/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
4
Results of modeling A
4.1 Functionalities
tested
Controls
DEFI_TRC HIST_EXP VALE
TEMP_MS
THRESHOLD
AKM
BKM
TPLM
GRAIN_AUST
DREF
With
DEFI_MATERIAU THER
RHO_CP
LAMBDA
META_ACIER
TRC
AR3
ALPHA
MS0
AC1
AC3
TAUX_1
TAUX_3
CALC_META ETAT_INIT
COMP_INCR
META_INIT_ELNO
RELATION
“STEEL”
DEFI_MATERIAU ELAS_META_FO E
NAKED
F_ALPHA
C_ALPHA
TEMP_DEF_ALPHA
PHAS_REFE
EPSF_EPSC_TREF
F1_SY
F2_SY
F3_SY
F4_SY
C_SY
SY_MELANGE
META_TRACTION
SIGM_F1
SIGM_F2
SIGM_F3
SIGM_F4
SIGM_C
MODEL AFFE_CHAR_MECA
TEMP_CALCULEE
MODEL STAT_NON_LINE
CHAM_MATER
EXCIT
CHARGE
FONC_MULT
COMP_INCR
RELATION
“META_P_INL”
RELATION_KIT
“STEEL”
INCREMENT
LIST_INST
NEWTON
STAMP
“TANGENT”
REAC_ITER
CONVERGENCE
RESI_GLOB_RELA
ITER_GLOB_MAXI
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
8/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
4.2 Values
tested
Identification Size Reference
Aster %
difference
t=1.1s NO3
SIYY
60.
59.99
- 1.28E-12
t=1.4s NO3
SIYY
142.
142.
- 1.62E-12
t=2.0s NO3
SIYY
218.
218
- 1.14E-13
t=1.1s NO3
DY
4.
3.999
- 6.04E-14
t=1.4s NO3
DY
13.
13.
- 2.52E-13
t=2.0s NO3
DY
31.
31.
3.55E-15
t=1.1s NO3
V1
0.
0
0%
t=1.4s NO3
V1
4.9E-3
4.899E-3
- 3.79E-12%
t=2.0s NO3
V1
1.91E-2
1.91E-2
- 2.54E-13%
t=1.1s NO3
V7
0.
0
0%
t=1.4s NO3
V7
41.1
41.099
- 3.96E-12%
t=2.0s NO3
V7
117.58
117.58
- 1.72E-12%
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
9/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
5
Results of modeling B
5.1 Functionalities
tested
Controls
MODEL STAT_NON_LINE
CHAM_MATER
EXCIT
CHARGE
FONC_MULT
COMP_INCR
RELATION
“META_P_INL”
RELATION_KIT
“STEEL”
DEFORMATION
“SIMO_MIEHE”
INCREMENT
LIST_INST
NEWTON
STAMP
“TANGENT”
REAC_ITER
CONVERGENCE
RESI_GLOB_RELA
ITER_GLOB_MAXI
Modeling B is the exact equivalent one of modeling A by taking into account the large ones
deformations via key word DEFORMATION=' SIMO_MIEHE'.
5.2 Values
tested
Identification Size
Reference
Aster %
difference
t=1.1s NO3
SIYY
59.72
5.9724891293860E+01
0.005
t=1.4s NO3
SIYY
141.
1.4099749961110E+02
- 0.003
t=2.0s NO3
SIYY
215.66
2.1566273036229E+02
0.003
t=1.1s NO3
DY
4.
3.9975135788390
- 0.002
t=1.4s NO3
DY
13.
1.2997513578839E+01
- 0.002
t=2.0s NO3
DY
31.
3.0997513578839E+01
- 0.002
t=1.1s NO3
V1
0.
0.
0
t=1.4s NO3
V1
4.8787000000000E-03
4.8787703363334E-03
0.001
t=2.0s NO3
V1
1.8866000000000E-02
1.8866871352412E-02
0.005
t=1.1s NO3
V7
0.
0.
0
t=1.4s NO3
V7
41.82
4.1818031454286E+01
- 0.005
t=2.0s NO3
V7
117.2
1.1724097649622E+02
0.035
Code_Aster
®
Version
8.1
Titrate:
HSNV126 - Thermo metal-worker-mechanics in simple traction
Date:
05/09/05
Author (S):
V. CANO, S. VANDENBERGHE
Key
:
V7.22.126-A
Page:
10/10
Manual of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A
6 Comments
This case test of not-regression makes it possible to check the coherence of Code_Aster of a version on the other
with regard to the metallurgy.