Code_Aster ®
Version
7.4
Titrate:
Operator POST_FATI_ALEA


Date:
04/02/05
Author (S):
S. CAMBIER, A. Key M. DONORE
:
U4.84.03-E Page
: 1/6

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

Handbook of Utilization
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
constraints 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.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_FATI_ALEA


Date:
04/02/05
Author (S):
S. CAMBIER, A. Key M. DONORE
:
U4.84.03-E Page
: 2/6

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”,
/
“NIVEAU”
,

DUREE
=
/
duration
,
[R]
/
1.
,
[DEFAUT]


# Elastoplastic Coefficient of correction Ke

CORR_KE = “RCCM”
,


# Calculation of the elementary damage

DAMAGE = “WOHLER”,


MATER
=
to subdue
,
[to subdue]

TITER
=
titrate
,
[l_Kn]













)
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_FATI_ALEA


Date:
04/02/05
Author (S):
S. CAMBIER, A. Key M. DONORE
:
U4.84.03-E Page
: 3/6

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 command 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 constraints, 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 constraints, one emits an alarm when the calculation of the average damage
does not correspond to spectral concentrations of power homogeneous to constraints (DSP_CONT).

3.2 Operand
COMPTAGE

COMPTAGE =

To be able to calculate the damage undergone by a structure, the cycles should beforehand be extracted
elementary of the history of loading.

/
“PIC”
,

Allows to choose the method of counting of the peaks of constraints to determine them
elementary cycles of the random loading [R7.04.02].

/
“NIVEAU”
,

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
DUREE

DUREE
=
/
duration
,
[R]
/
1.
,
[DEFAUT]

Allows to introduce the data of the duration of the signal which intervenes in the expression of the damage
means [R7.04.02].
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_FATI_ALEA


Date:
04/02/05
Author (S):
S. CAMBIER, A. Key M. DONORE
:
U4.84.03-E Page
: 4/6

3.4 Operand
CORR_KE

CORR_KE =
“RCCM”,

This operand makes it possible to take account of an elastoplastic coefficient of concentration Ke, 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 = 1
if
< 3S
E
m

K = 1+ (1 - N)
E
(/3Sm -) 1/(N (m) 1) if 3S
< < 3m S
m
m
K = 1/N
if 3m S
E
m
<

where Sm is the acceptable maximum constraint, and N and m two constants depending on material.

Values of S
N
m
m,
and
are introduced into operator DEFI_MATERIAU [U4.43.01] under
key word FATIGUE and operands SM_KE_RCCM, N_KE_RCCM, and M_KE_RCCM.

3.5 Operand
DOMMAGE

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 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 FATIGUE, operand WOHLER),
·
analytical form of Basquin (key word FATIGUE, operands A_BASQUIN and
BETA_BASQUIN),
·
form “current zone” (key word FATIGUE, 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 106 cycles,
corresponding constraint, 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
constraint 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 Ke, it is necessary moreover
to have specified the data material (NR, M and SM) necessary to calculation of Ke.

3.7 Operand
TITER

TITER = title,

Titrate associated with the table.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_FATI_ALEA


Date:
04/02/05
Author (S):
S. CAMBIER, A. Key M. DONORE
:
U4.84.03-E Page
: 5/6

3.8 Count
produced

Operator POST_FATI_ALEA creates a table, TABL_POST_F_ALEA, which includes/understands 1 parameter:
DOMMAGE: value of the average damage over the duration of the signal.

Note:

If one used operand 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.

Command IMPR_TABLE [U4.91.03] makes it possible 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
,
COMPTAGE
=
“PIC”
,
DOMMAGE =
“WOHLER”
,
MATER
=
subdue,







)

Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

Code_Aster ®
Version
7.4
Titrate:
Operator POST_FATI_ALEA


Date:
04/02/05
Author (S):
S. CAMBIER, A. Key M. DONORE
:
U4.84.03-E Page
: 6/6

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Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A

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