Code_Aster
®
Version
7.4
Titrate:
Operator
POST_FATI_ALEA
Date:
04/02/05
Author (S):
S. CAMBIER, A.M. DONORE
Key
:
U4.84.03-E
Page
:
1/6
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Organization (S):
EDF-R & D/AMA
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
Document: U4.84.03
Operator
POST_FATI_ALEA
1 Goal
To calculate the damage of fatigue undergone by a structure subjected to a stress of the random type.
With this intention
POST_FATI_ALEA
allows starting from the data of the spectral moments characterizing
entirely the random signal:
·
to extract by a statistical method of counting of cycles (method of counting of peaks
stresses or method of goings beyond of a level given) the number of cycles
elementary of loading undergone by the structure,
·
to determine the elementary damage associated with each elementary cycle using
curve of Wöhler of material,
·
to determine the average damage throughout signal.
In addition, it is possible to take account of the influence of the coefficient of concentration
elastoplastic.
The average damage is stored in a table:
tabl_post_f_alea
.
Code_Aster
®
Version
7.4
Titrate:
Operator
POST_FATI_ALEA
Date:
04/02/05
Author (S):
S. CAMBIER, A.M. DONORE
Key
:
U4.84.03-E
Page
:
2/6
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
2 Syntax
tabl_post_f_alea = POST_FATI_ALEA
(
# Introduction of the random loading
/
MOMENT_SPEC_0
=
0
,
[R]
MOMENT_SPEC_2
=
2
,
[R]
MOMENT_SPEC_4
=
4
,
[R]
/
TABL_POST_ALEA
=
count
,
[tabl_post_alea]
# Method of counting of cycles
COUNTING =/“PEAK”,
/
“LEVEL”
,
DURATION
=
/
duration
,
[R]
/
1.
,
[DEFECT]
# Elastoplastic Coefficient of correction Ke
CORR_KE = “RCCM”
,
# Calculation of the elementary damage
DAMAGE = “WOHLER”,
MATER
=
to subdue
,
[to subdue]
TITRATE
=
titrate
,
[l_Kn]
)
Code_Aster
®
Version
7.4
Titrate:
Operator
POST_FATI_ALEA
Date:
04/02/05
Author (S):
S. CAMBIER, A.M. DONORE
Key
:
U4.84.03-E
Page
:
3/6
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
3 Operands
3.1 Operands
TABL_POST_ALEA
/
MOMENT_SPEC_0
/
MOMENT_SPEC_2
/
MOMENT_SPEC_4
These operands make it possible to introduce the three spectral moments value of command 0, 2 and 4 which
can be determined by the control
POST_DYNA_ALEA
[U4.84.04].
These values completely characterize the random signal for the statistical methods of
counting of the cycles:
·
method of counting of peaks of stresses, which uses
0
,
2
and
4
,
·
method of counting of going beyond of a given level, which only requires
data of
0
and
2
.
/
MOMENT_SPEC_0
=
0
,
[R]
MOMENT_SPEC_2
=
2
,
[R]
MOMENT_SPEC_4
=
4
,
[R]
One provides the value of the spectral moment following the operand corresponding.
/
TABL_POST_ALEA
=
count
,
[tabl_post_alea]
Allows to specify the name of a table created by
POST_DYNA_ALEA
[U4.84.04], in which are
stored values of spectral moments
(
0
,
2
,
4
), for various modes or various nodes.
The values are read again and one calculates a value of average damage for each triplet of moments
spectral met in the table.
However, method of calculation of the average damage being valid only for loadings
homogeneous with stresses, one emits an alarm when the calculation of the average damage
does not correspond to spectral concentrations of power homogeneous to stresses (
DSP_CONT
).
3.2 Operand
COUNTING
COUNTING =
To be able to calculate the damage undergone by a structure, the cycles should beforehand be extracted
elementary of the history of loading.
/
“PEAK”
,
Allows to choose the method of counting of the peaks of stresses to determine them
elementary cycles of the random loading [R7.04.02].
/
“LEVEL”
,
Allows to choose the method of counting of the goings beyond of a level given for
to determine the elementary cycles of the random loading [R7.04.02].
3.3 Operand
DURATION
DURATION
=
/
duration
,
[R]
/
1.
,
[DEFECT]
Allows to introduce the data of the duration of the signal which intervenes in the expression of the damage
means [R7.04.02].
Code_Aster
®
Version
7.4
Titrate:
Operator
POST_FATI_ALEA
Date:
04/02/05
Author (S):
S. CAMBIER, A.M. DONORE
Key
:
U4.84.03-E
Page
:
4/6
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
3.4 Operand
CORR_KE
CORR_KE =
“RCCM”,
This operand makes it possible to take account of an elastoplastic coefficient of concentration
K
E
, which
is defined by the RCC-M as being the relationship between the amplitude of real deformation and
the amplitude of deformation determined by an elastic analysis.
(
)
(
)
(
)
(
)
K
S
K
N
S
N m
S
m S
K
N
m S
E
m
E
m
m
m
E
m
=
<
= + -
-
-
<
<
=
<
1
3
1 1
3
1
1
3
3
1
3
if
if
if
/
/
/
where
S
m
is the acceptable maximum stress, and
N
m
and
two constants depending on material.
Values of
S
N
m
m
,
and
are introduced into the operator
DEFI_MATERIAU
[U4.43.01] under
key word
TIRE
and operands
SM_KE_RCCM
,
N_KE_RCCM
, and
M_KE_RCCM
.
3.5 Operand
TOO BAD
DAMAGE = “WOHLER”,
This operand makes it possible to specify the method of calculation of the damage, which in the case of one
stress of the random type is the method of Wöhler.
To calculate the damage, the user must introduce into the operator
DEFI_MATERIAU
[U4.43.01], the curve of Wöhler of the material which can be given in three forms
distinct mathematics [R7.04.02]:
·
point by point discretized function (key word
TIRE
, operand
WOHLER
),
·
analytical form of Basquin (key word
TIRE
, operands
A_BASQUIN
and
BETA_BASQUIN
),
·
form “current area” (key word
TIRE
, operands
E_REFE
,
A0
,
A1
,
A2
,
A3
and
SSL
and
key word
ELAS
operand
E
).
Notice on the curves of fatigue:
For the small amplitudes, the problem of the prolongation of the curve of fatigue can
to pose: for example, for the curves of fatigue of the RCC-M beyond 10
6
cycles,
corresponding stress, 180 MPa is regarded as limit of endurance, i.e.
that very forced lower than 180 MPa must produce a factor of null use or a number
cycles acceptable infinite.
The method adopted here corresponds to this concept of limit of endurance: if the amplitude of
stress is lower than the first X-coordinate of the curve of fatigue, then one takes one
factor of null use i.e. an infinite number of cycles acceptable.
3.6 Operand
MATER
MATER = to subdue,
Allows to specify the name of the MATER material created by
DEFI_MATERIAU
[U4.43.01].
The MATER material must at least contain the definition of the curve of Wöhler of material
[R7.04.02].
If one wishes to take account of an elastoplastic coefficient of concentration
K
E
, it is necessary moreover
to have specified the data material (
NR
,
M
and
SM
) necessary to the calculation of
K
E
.
3.7 Operand
TITRATE
TITRATE = title,
Titrate associated with the table.
Code_Aster
®
Version
7.4
Titrate:
Operator
POST_FATI_ALEA
Date:
04/02/05
Author (S):
S. CAMBIER, A.M. DONORE
Key
:
U4.84.03-E
Page
:
5/6
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
3.8 Count
produced
The operator
POST_FATI_ALEA
create a table,
TABL_POST_F_ALEA
, which includes/understands 1 parameter:
TOO BAD
: value of the average damage over the duration of the signal.
Note:
If the operand were used
TABL_POST_ALEA
to introduce the values of
spectral moments, one stores in the table, the value of the average damage over the duration of the signal,
for each triplet of spectral moments present in the table.
The control
IMPR_TABLE
[U4.91.03] allows to print the produced table.
4 Example
= DEFI_MATERIAU subdue
(
TIRE = _F (A_BASQUIN
= 1.001730939 E14,
BETA_BASQUIN
=
4.065)
)
count = POST_FATI_ALEA (
MOMENT_SPEC_0
= 182.5984664,
MOMENT_SPEC_2
= 96098024.76,
MOMENT_SPEC_4
= 6.346193569E+13
,
COUNTING
=
“PEAK”
,
DAMAGE =
“WOHLER”
,
MATER
=
subdue,
)
Code_Aster
®
Version
7.4
Titrate:
Operator
POST_FATI_ALEA
Date:
04/02/05
Author (S):
S. CAMBIER, A.M. DONORE
Key
:
U4.84.03-E
Page
:
6/6
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
Intentionally white left page.