Code_Aster ®
Version
5.0
Titrate:
MTLP100 - Chauffage and hardening of an infinite bar


Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO Key
:
V4.61.100-C Page:
1/6

Organization (S): EDF/IMA/MN

Handbook of Validation
V4.61 booklet: Metallurgy
Document: V4.61.100

MTLP100 - Chauffage 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.

Handbook of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A

Code_Aster ®
Version
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Titrate:
MTLP100 - Chauffage and hardening of an infinite bar


Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO Key
:
V4.61.100-C Page:
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1
Problem of reference

1.1 Geometry
y
C
B
With
2L
O
X
2L


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)

CP = 5260000 J.m-3.°C1
= 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

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
Handbook of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A

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Titrate:
MTLP100 - Chauffage and hardening of an infinite bar


Date:
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Author (S):
F. WAECKEL, V. CANO Key
:
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1.3
Boundary conditions and loadings

T = 15 °C

H = 1675 W.m-2.°C1

1.4 Conditions
initial

T (X, y, 0) = 700°C.

Zf (X, y, 0) = 0.7
Zb (X, y, 0) = 0.3
Handbook of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A

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Titrate:
MTLP100 - Chauffage and hardening of an infinite bar


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:
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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,)
0 - T) + T

where:





- 2
T


- 2
T
I
I
(
)
CP
=


X y T
With E
X × A E
CP
,
cos
cos y
I
I
I
I

i=1
i=1

with I checking:


hL
I L
(
tg I L) =
=

.
5 00

and:

4 sin (L
I
)
Have =

2 L
I
sin (L
I
)

·
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.

Handbook of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A

Code_Aster ®
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Titrate:
MTLP100 - Chauffage and hardening of an infinite bar


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:
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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
L
C
B
With
O
L
X

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 grid

A number of nodes:
96
A number of meshs and types:
25 QUAD8, 20 SEG3

3.3 Functionalities
tested

Commands



Keys
DEFI_TRC HIST_EXT
VALE

[U4.23.05]
TEMP_MS
P



SEUIL



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


Handbook of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A

Code_Aster ®
Version
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Titrate:
MTLP100 - Chauffage and hardening of an infinite bar


Date:
04/09/99
Author (S):
F. WAECKEL, V. CANO Key
:
V4.61.100-C Page:
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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 steps of calculation from 0 to 410 S (40 steps of 5 S, then 40 steps of 1 S, then 85 steps 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 absolute 10­6
T = 140 S M13 (PG1) P
0.9505
0.9505
4.10 10­5 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



Obstruction 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 Code (not of reference solution).
Handbook of Validation
V4.61 booklet: Hi-75 metallurgy/01/010/A

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