Code_Aster
®
Version
5.0
Titrate:
MTLP100 - Heating and hardening of an infinite bar
Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO
Key
:
V4.61.100-C
Page:
1/6
Manual of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A
Organization (S):
EDF/IMA/MN
Manual of Validation
V4.61 booklet: Metallurgy
Document: V4.61.100
MTLP100 - Heating and hardening of an infinite bar
with square section
Summary:
The purpose of this test is to provide a metallurgy calculation of reference, in postprocessing of an evolutionary calculation of
thermics planes linear which one knows the analytical solution. More concretely, this test validates calculations
two-dimensional of linear thermics with conditions of exchange and provides values of reference for
the austenitic model of transformation to the heating, like for the model of decomposition of
austenite with cooling.
Code_Aster
®
Version
5.0
Titrate:
MTLP100 - Heating and hardening of an infinite bar
Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO
Key
:
V4.61.100-C
Page:
2/6
Manual of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A
1
Problem of reference
1.1 Geometry
y
X
O
2L
2L
With
B
C
Infinite bar with square section:
side 2L = 0,10 m
Co-ordinates of the points (in m):
With
B
C
O
X 0.026
0.350
0.041 0.0
y 0.026
0.350
0.041 0.0
1.2
Properties of material
(Steel 16MND5)
C
p
= 5260000 J.m
- 3
.°C
1
= 33.5 W.m
- 1
.°C
- 1
Coefficients for the metallurgy:
TRC
“standard”
AR3 = 830°C, alpha = - 0.0306
MS0 = 400°C, AC1 = 724°C, AC3 = 846°C
1
= 0.034,
3
= 0.034
Microhardness of the différenres metallurgical phases:
for ferrite D = 200. HV
for the pearlite D = 200. HV
for the bainite D = 300. HV
for martensite D = 400. HV
for austenite D = 100. HV
Code_Aster
®
Version
5.0
Titrate:
MTLP100 - Heating and hardening of an infinite bar
Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO
Key
:
V4.61.100-C
Page:
3/6
Manual of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A
1.3
Boundary conditions and loadings
T
= 15 °C
H = 1675 W.m
- 2
.°C
1
1.4 Conditions
initial
T (X, y, 0) = 700°C.
Zf (X, y, 0) = 0.7
Zb (X, y, 0) = 0.3
Code_Aster
®
Version
5.0
Titrate:
MTLP100 - Heating and hardening of an infinite bar
Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO
Key
:
V4.61.100-C
Page:
4/6
Manual of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
·
On the heating, one imposes a rise in uniform temperature of 700 on 900°C into 200 S.
·
Analytical solution for thermal calculation (with cooling since 900°C).
(
)
(
) (
)
(
)
T X y T
X y T T X y
T
T
,
,
,
=
-
+
0
where:
(
)
X y T
With E
X
With E
y
I
I
C T
I
I
I
C T
I
I
p
I
p
,
cos
cos
=
×
=
-
=
-
1
1
2
2
with
I
checking:
()
I
I
L
L
hL
tg
.
=
= 5 00
and:
()
()
With
L
L
L
I
I
I
I
=
4
2
sin
sin
·
The values of reference for the metallurgical evolutions depend on the model and on
integration in time of the relations of behaviors. One does not have values of
reference.
·
The hardness of a material point depend on the metallurgical proportions of each phase, one
do not have values of reference.
2.2
Results of reference
(Thermal Calculation):
·
temperature at the points A, B, C at the moment T = 300 S,
·
proportion of bainite at the items A, B, C at the moment T = 410, 300 and 300 S, respectively,
·
proportion of martensite at the points A, B, C at the moment T = 410 S,
·
proportion of austenite at point A at the moment T = 30 S and 140 S.
·
hardness at the point O at the moment T = 30 S, 140 S, 300 S and 410 S.
2.3
Uncertainty on the solution
Lower than 1% with 30 modes for each nap.
2.4 References
bibliographical
[1]
F.P. INCROPERA, D.P. OF WITT, J. WILEY. Fundamentals off heat and farmhouse transfer. Third
Edition. 1990.
Code_Aster
®
Version
5.0
Titrate:
MTLP100 - Heating and hardening of an infinite bar
Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO
Key
:
V4.61.100-C
Page:
5/6
Manual of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
Elements “PLANE” 2D
By reason of symmetry, one nets only one quarter of square section and one refines in X = L and y = L.
y
X
O
L
With
B C
L
Cutting:
5 meshs QUAD8 according to the x axis
5 meshs QUAD8 according to the y axis
Boundary conditions:
on X = 0 and y = 0
= 0
on X = L and y = L
(
)
(
)
-
=
-
T N H T X y T
T
,
Points of Gauss:
A:
net m13 point 1
B:
net m19 point 1
C:
net m19 point 3
Node:
O:
N1 node
3.2
Characteristics of the mesh
A number of nodes:
96
A number of meshs and types:
25 QUAD8, 20 SEG3
3.3 Functionalities
tested
Controls
Keys
DEFI_TRC HIST_EXT
VALE
[U4.23.05]
TEMP_MS
P
THRESHOLD
AKM
BKM
TPLM
DEFI_MATERIAU META_THER TRC
[U4.23.01]
AR3
ALPHA AC1 AC3
MS0 TAUX_1 TAUX_3
DURT_META
F_DURT
P_DURT
B_DURT
M_DURT
A_DURT
Code_Aster
®
Version
5.0
Titrate:
MTLP100 - Heating and hardening of an infinite bar
Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO
Key
:
V4.61.100-C
Page:
6/6
Manual of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A
THER_LINEAIRE OPTION
“META_ELGA_TEMP”
[U4.23.05]
TEMP_INIT
META_INIT
CALC_ELEM OPTION “DURT_ELGA_META”
[U4.61.02]
“DURT_ELNO_META”
3.4 Remarks
165 pitches of calculation from 0 to 410 S (40 pitches of 5 S, then 40 pitches of 1 S, then 85 pitches of 2 S).
4
Results of modeling A
4.1 Values
tested
Identification Sizes
Reference
Aster %
difference
T = 30 S M13 (PG1) P
0.0489
0.0489
1.64 10
6
absolute
T = 140 S M13 (PG1) P
0.9505
0.9505
4.10 10
5
absolute
T = 300 S M13 (PG1) TPG
464.1
464.37
0.058
T = 300 S M19 (PG1) TPG
338.5
338.79
0.086
T = 300 S M19 (PG3) TPG
245.4
245.68
0.116
T = 410 S M13 (PG1) ZB
0.7828
T = 300 S M19 (PG1) ZB
0.5873
T = 300 S M19 (PG3) ZB
0.3113
T = 410 S M13 (PG1) ZM
0.2156
T = 410 S M19 (PG1) ZM
0.4103
T = 410 S M19 (PG3) ZM
0.6846
T = 30 S N1
HV
223.643
T = 140 S N1
HV
106.430
T = 300 S N1
HV
100.000
T = 410 S N1
HV
308.248
TPG:
temperature at the point of GAUSS,
ZB:
proportion of bainite,
ZM:
proportion of martensite,
P:
proportion of austenite.
HV
hardness of Vickers
4.2 Parameters
of execution
Version: 5.00.15
Machine: SGI - Origin 2000
Overall dimension memory:
64 Mo
Time CPU To use:
31.54 seconds
5
Summary of the results
The temperatures calculated at points A, B and C are obtained with a margin of 0.1%. Proportions
of austenite are perfectly given.
The proportions of bainites, martensite and the calculation of hardness are results allowing of
to check nonthe regression of the Code (not of reference solution).