Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
1/10

Organization (S): EDF-R & D/AMA, CS IF

Handbook 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.

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
2/10

1
Problem of reference

It is about a cylindrical bar in creep.

1.1 Geometry

y
F=30 NR
X

Appear 1.1-a: Géométrie 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)
CP = 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 Pa
· Poisson's ratio: = 0.3
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
3/10

Definition of the elastic characteristics, dilation and elastic limits for
modeling of an undergoing material of the metallurgical transformations:
· Tref= 20°C
· Thermal dilation coefficient average of the cold phases:
· F (T) = 10th-6
· Thermal dilation coefficient average of the hot phase:
· (T) = 0.0001
· Temperature of definition of the dilation coefficient:
· 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
Tref temperature:
= 1E-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:

1,2
1
0,8
E
G
NR
With
L 0,6
E
M
SY_
0,4
0,2
0
0
0,2
0,4
0,6
0,8
1
1,2
META

Appear 1.2-a: Loi of mixture

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
4/10

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 blocked 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:

Zf (X, y, 0) = 0.7
Zp (X, y, 0) = 0.0
Zb (X, y, 0) = 0.3
Zm (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 of 1E- 10%.
Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
5/10

3 Modeling
With

3.1
Characteristics of modeling

The modeling used in the case test is as follows:

Elements 2D “AXIS” (QUA8)

y
NO4
NO3
L
NO1
NO2
X
O
L
Appear 3.1-a: Géométrie and grid 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 grid

A number of nodes: 4
A number of meshs and types: 1 QUAD4, 4 SEG2.

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
6/10

3.3 Functionalities
tested

Commands




DEFI_TRC HIST_EXP VALE

TEMP_MS
SEUIL


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 META_INIT_ELNO

COMP_INCR
RELATION
“ACIER”
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
“ACIER”

INCREMENT
LIST_INST


NEWTON
MATRICE
“TANGENTE”

REAC_ITER


CONVERGENCE
RESI_GLOB_RELA

ITER_GLOB_MAXI

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
7/10

4
Results of modeling A

4.1 Functionalities
tested

Commands




DEFI_TRC HIST_EXP VALE

TEMP_MS
SEUIL


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 META_INIT_ELNO

COMP_INCR
RELATION
“ACIER”
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
“ACIER”

INCREMENT
LIST_INST


NEWTON
MATRICE
“TANGENTE”

REAC_ITER


CONVERGENCE
RESI_GLOB_RELA

ITER_GLOB_MAXI

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
8/10

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%

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
9/10

5
Results of modeling B

5.1 Functionalities
tested

Commands




MODEL STAT_NON_LINE



CHAM_MATER



EXCIT
CHARGE


FONC_MULT


COMP_INCR
RELATION
“META_P_INL”

RELATION_KIT
“ACIER”

DEFORMATION
“SIMO_MIEHE”

INCREMENT
LIST_INST


NEWTON
MATRICE
“TANGENTE”

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

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

Code_Aster ®
Version
8.1
Titrate:
HSNV126 - Thermo- metal-worker-mechanics in simple traction

Date:
05/09/05
Author (S):
V. CANO, Key S. VANDENBERGHE
:
V7.22.126-A Page:
10/10

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.

Handbook of Validation
V7.22 booklet: Thermomechanical nonlinear statics of the voluminal structures
HT-66/05/005/A

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