Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
1/24
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Organization (S):
EDF-R & D/AMA
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
Document: U4.83.01
Operator
POST_FATIGUE
1 Goal
To calculate, in a point, the damage of fatigue of a structure subjected to a history of loading.
With the difference of CALC_FATIGUE, POST_FATIGUE does not operate on a field but on a “signal”
extracted beforehand from a calculation or defines in addition.
The various methods available [R7.04.01] are:
·
methods based on uniaxial tests: methods of Wöhler, Manson-Whetstone sheath and Taheri.
These methods have as a common point to determine a value of damage from
evolution during the characterizing time of a scalar component, for the calculation of
damage, the state of stresses or structural deformations.
With this intention, it is necessary to extract, by a method of counting of cycles, the cycles
elementary of loading undergone by the structure, to determine the elementary damage
associated each cycle and to determine the total damage by a rule of linear office plurality,
·
method of Lemaître generalized.
This method makes it possible to calculate the damage (of Lemaître or Lemaître-Sermage) with
to leave the data of the tensor of the stresses and the cumulated plastic deformation,
·
criteria of Crossland and Dang Van-Papadopoulos.
These criteria apply to uniaxial or multiaxial loadings periodic. They
provide a value of criterion indicating if there is damage or not.
Product a concept of the type counts.
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
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HT-62/06/004/A
Count
matters
3.7.1
Methods based on uniaxial tests: method of Wöhler, method of Manson-
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
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HT-62/06/004/A
2 Syntax
tabl_post_fatig = POST_FATIGUE
(
# if purely uniaxial loading (or regarded as uniaxial)
/LOADING = “UNIAXIAL”,
HISTORY =
_F (
/SIGM = histsigm
/[function]
/
[formula]
/
EPSI
=
histepsi/
[function]
/
[formula]
),
COUNTING =/“RAINFLOW”
,
/
“RCCM”
,
/
“NATURAL”
,
DELTA_OSCI =
/
delta
, [R]
/
0.
, [DEFECT]
COEF_MULT = _F
(
KT
=
kt
),
[R]
CORR_KE = “RCCM”,
DAMAGE =/“WOHLER”
,
/
“MANSON_COFFIN”
,
/
“TAHERI_MANSON”
,
/
“TAHERI_MIXTE”
,
MATER
=
to subdue
,
CORR_SIGM_MOYE =/“GOODMAN”
,
/
“TO STACK”
,
TAHERI_NAPPE
=
fnappe
,
/
[tablecloth]
/
[formula]
TAHERI_FONC
=
ffonc
,
/
[function]
/
[formula]
OFFICE PLURALITY
=
“LINEAR”
,
# Finsi
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
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HT-62/06/004/A
# if loading periodic (for fatigue with great numbers of cycles and
for periodic cycles)
/LOADING = “PERIODIC”,
HISTORY = _F
(
SIGM_XX = fxx,/[function]/[formula]
SIGM_YY = fyy,/[function]/[formula]
SIGM_ZZ = fzz,/[function]/[formula]
SIGM_XY = fxy,/[function]/[formula]
SIGM_XZ = fxz,/[function]/[formula]
SIGM_YZ = fyz,/[function]/[formula]
)
CRITERION =/“CROSSLAND”
,
/
“PAPADOPOULOS”
,
DAMAGE = “WOHLER”
,
MATER
=
to subdue
,
[to subdue]
COEF_CORR
=
/
corr,
[R]
/d0/
0
,
[DEFECT]
# Finsi
# if loading unspecified (damage of Lemaitre or Lemaitre-
Sermage)
/LOADING = “UNSPECIFIED”,
HISTORY = _F
(
SIGM_XX = fxx,/[function]/[formula]
SIGM_YY = fyy,/[function]/[formula]
SIGM_ZZ = fzz,/[function]/[formula]
SIGM_XY = fxy,/[function]/[formula]
SIGM_XZ = fxz,/[function]/[formula]
SIGM_YZ = fyz,/[function]/[formula]
EPSP = p
,/[function]/[formula]
TEMP = temp,/[function]/[formula]
)
TOO BAD
= “LEMAITRE”,
MATER
=
to subdue
,
OFFICE PLURALITY
=
“LINEAR”
,
# Finsi
INFORMATION =
/
1,
[DEFECT]
/2,
TITRATE
=
titrate
[l_Kn]
)
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
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Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
3 Operands
3.1 Operand
LOADING
This key word makes it possible the user to specify the type of treated loading. The loading can be
“UNIAXIAL”, “PERIODIC” or “UNSPECIFIED”. With each loading corresponds its (or its)
method (S) of evaluation of the damage by fatigue.
3.2 Word
key
HISTORY
This key word gathers all the phase of definition of the history of loading.
According to the method of calculation of the damage, the history of loading can be the evolution:
·
of a value of stress or uniaxial deformation in the course of time,
Note:
That does not mean that the loading cannot be multiaxial, but only that
for the calculation of the damage, the loading is characterized by the evolution of one
scalar component, in the course of time (signed von Mises, invariant of a signed nature 2,…).
It is the evolution of this scalar component which the user must provide to the control
POST_FATIGUE
.
·
tensor of stresses in the course of time,
·
tensor of stresses, cumulated plastic deformation and temperature with the course
time.
3.2.1 Operand
SIGM
SIGM = histsigm,
Name of the function or the formula describing the history of the loading in stresses in a point.
It is a function or a formula of the parameter
INST
, which gives the evolution in the course of time
of a scalar component characterizing the state of stresses of the structure.
This operand is obligatory for the calculation of the damage by a method of WOHLER.
3.2.2 Operand
EPSI
EPSI = histepsi,
Name of the function or the formula describing the history of the loading in deformations in one
not. It is a function or a formula of the parameter
INST
, which gives the evolution to the course
time of a scalar component characterizing the state of structural deformations.
This operand is obligatory for the calculation of the damage by the methods of
MANSON_COFFIN or TAHERI_MANSON or TAHERI_MIXTE.
3.2.3 Operands
SIGM_XX/SIGM_YY/SIGM_ZZ/SIGM_XY/SIGM_XZ/
SIGM_YZ
Names of the functions or the formulas describing the history of each component of the tensor of
stresses in the course of time. Each function or formula depends on the parameter
INST
. All them
functions or formulas must be defined for the same moments.
In 2D the operands are obligatory
SIGM_XX, SIGM_YY, SIGM_ZZ
and
SIGM_XY
.
In 3D the operands are obligatory
SIGM_XX, SIGM_YY, SIGM_ZZ, SIGM_XY, SIGM_XZ
and
SIGM_YZ
.
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
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3.2.4 Operand
EPSP
EPSP = p,
Name of the function describing the history of the plastic deformation cumulated in the course of time,
only for the calculation of the damage of LEMAITRE.
This function or formula depends on the parameter
INST
and must be defined for the same moments
that functions or formulas describing the history of the components of the tensor of the stresses.
The operand
EPSP
must be used jointly with the operands
SIGM_XX
,…
3.2.5 Operand
TEMP
TEMP = temp,
Name of the function or the formula describing the history of the temperature in the course of time,
only for the calculation of the damage of LEMAITRE. It is used in this case to determine
value of the mechanical characteristics (Young modulus
E
, Poisson's ratio
and
parameter material
S
) at the moments of calculation of the damage.
This function or formula depends on the parameter
INST
and must be defined for the same moments
that functions or formulas describing the history of the components of the tensor of the stresses.
The operand
TEMP
must be used jointly with the operands
EPSP
,
SIGM_XX
,…
3.3 Operand
DELTA_OSCI
DELTA_OSCI = delta,
Filtering of the history of the loading. In all the cases, if the function remains constant or
decreasing on more than two consecutive points one removes the intermediate points for
to keep that two extreme points. Then, one removes history of loading the points
for which the variation of the value of the stress is lower than the value
delta
. By defect
delta
is equal to zero, which amounts keeping all the oscillations of the loading, even those
of low amplitude.
Example: Let us consider the following history of loading:
N°
not
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Moment
0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Loading 4. 7. 2. 10. 9.6 9.8
5. 9. 3. 4. 2. 2.4.2.2 12. 5.
N°
not
16 17 18 19 20 21 22 23 24 25 26 27 28 29
Moment 15.
16.
17.
18.
19.
20.
21. 22. 23. 24. 25. 26. 27. 28.
Loading 11. 1. 4. 3. 10. 6. 8. 12. 4. 8. 1. 9. 4. 6.
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
7/24
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
The extraction of the peaks of this history of loading, with a value of
delta
of 0.9 conduit with
to destroy all the oscillations of amplitude lower than 0.9. What leads to the history of loading
following:
N°
not
1 2 3 4 7 8 9 10 11 14 15 16 17 18 19
Moment
0. 1. 2. 3. 6. 7. 8. 9. 10. 13. 14. 15. 16. 17. 18.
Loading 4. 7. 2. 10. 5. 9. 3. 4. 2. 12. 5. 11. 1. 4. 3.
N°
not
20 21 23 24 25 26 27 28 29
Moment 19.
20.
22.
23.
24.
25.
26. 27. 28.
Loading 10. 6. 12. 4. 8. 1. 9. 4. 6.
One removed:
·
item 5 bus
9
.
0
)
4
(
)
5
(
<
-
=
,
·
item 6 bus
9
.
0
)
4
(
)
6
(
<
-
=
,
·
item 12 bus
9
.
0
)
11
(
)
12
(
<
-
=
,
·
the point 13 bus
9
.
0
)
11
(
)
13
(
<
-
=
.
In the same way one removes the point 22 bus the history of loading is increasing between the items 21, 22 and
23 and thus one keep only the extreme points.
3.4 Word
key
COEF_MULT
COEF_MULT = _F
This key word factor gathers the coefficients of performance of the history of loading. For
the moment, only one multiplying coefficient of the history of loading is available: the coefficient
of stress concentration
KT
.
Values of the coefficient of stress concentration are available in the RCC_M.
3.4.1 Operand
KT
KT = kt
kt
is the coefficient of stress concentration which depends on the geometry of the part, of
geometry of a possible defect and type of loading. This coefficient is used to apply
with the history of loading “filtered” a homothety of report/ratio
kt
.
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
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HT-62/06/004/A
3.5 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. For that of many methods are available.
In Code_Aster, three methods were programmed.
/
“RAINFLOW”
,
Method of counting of extended in cascade or method of RAINFLOW
(recommendation AFNOR A03-406 of November 1993) for the extraction of the cycles
elementary of the history of loading [R7.04.01].
/
“RCCM”
,
Method of the RCC-M [R7.04.01].
/
“NATURAL”
,
Method known as natural which consists in generating the cycles in the order of their application
[R7.04.01].
3.6 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
S N
m
m
,
and
are provided in the operator
DEFI_MATERIAU
[U4.43.01] under the word
key factor
TIRE
and operands
SM_KE_RCCM
,
N_KE_RCCM
and
M_KE_RCCM
.
3.7 Operand
TOO BAD
To calculate the damage undergone by a structure in a point, various methods are available
[R7.04.01].
3.7.1 Methods based on uniaxial tests: method of Wöhler, method of
Manson-whetstone sheath, methods of Taheri
These methods have as a common point to determine a value of damage starting from the evolution with
run from the time of a scalar component characterizing the state of stress or deformation of
structure.
That does not mean that the state of stresses cannot be multiaxial, but only that for
calculation of the damage one chose a uniaxial component characterizing the state of stress or of
deformation (forced of von Mises signed, invariant of a nature 2 signed of the tensor of
deformations,…).
The methods of Manson-Whetstone sheath and Taheri use the deformations generated by
loading.
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
9/24
Instruction manual
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HT-62/06/004/A
The method of Wöhler uses the stresses generated by the loading.
DAMAGE = “WOHLER”,
For a history of stresses associated with a uniaxial loading, the number of cycles with
rupture is given using the curve of Wöhler of material
NR
rupt
=
WOHLER
2
.
The curve of Wöhler of material must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] under one of the three possible mathematical forms [R7.04.01]:
·
point by point discretized function (key word factor
TIRE
, operand
WOHLER
),
·
analytical form of Basquin (key word factor
TIRE
, operands
A_BASQUIN
and
BETA_BASQUIN
),
·
form “current area” (key word factor
TIRE
, operands
E_REFE
,
A0
,
A1
,
A2
,
A3
and
SSL
and key word factor
ELAS
operand
E
).
Notice on the curves of fatigue:
For the small amplitudes of stresses, the problem of the prolongation of the curve of
fatigue can be posed: for example, for the curves of fatigue of the RCC-M beyond 10
6
cycles, the corresponding stress, 180 MPa is regarded as limit of endurance,
i.e. very forced lower than 180 MPa must produce a factor of null use or
an infinite number of cycles acceptable.
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.
DAMAGE = “MANSON_COFFIN”,
For a uniaxial history of loading of type deformations, the number of cycles to the rupture
is given using the curve of Manson-Whetstone sheath of material
NR
rupt
=
MANSON_ WHETSTONE SHEATH
2
.
The curve of Manson-Whetstone sheath of material must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] (key word factor
TIRE
, operand
MANSON_COFFIN
).
DAMAGE = “TAHERI_MANSON”,
This method of calculation of the damage applies only to loadings in deformations.
Are
N
elementary cycles (extracts by a method of counting) of half-amplitude
1
2
2
,
,
K
N
.
The value of the elementary damage of the first cycle is determined by interpolation on
curve of Manson-Whetstone sheath of material.
The calculation of the elementary damage of the following cycles is carried out by the algorithm described Ci
below:
·
If
I
I
+
1
2
2
the calculation of the elementary damage of the cycle
(
)
I
+1
is determined by interpolation on
curve of Manson-Whetstone sheath of material,
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
10/24
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
·
If
I
I
+
<
1
2
2
one determines:
=
=
+
+
<
+
+
2
2
2
,
2
2
1
* 1
1
1
I
I
J
I
J
I
I
Max
Ffonc
Fnappe
where:
Fnappe
is a tablecloth introduced under the operand
TAHERI_NAPPE
,
Ffonc
is a function introduced under the operand
TAHERI_FONC
.
The value of the damage of the cycle
()
I
+ 1
is obtained by interpolation of
I
+ 1
2
*
on the curve of
Manson-whetstone sheath of material.
1
+
I
rupt
NR
is the number of cycles to the rupture of the cycle
()
I
+ 1
1
+
I
rupt
NR
=
MANSON_COFFIN
I
+
1
2
and
1
+
I
Dom
is the damage of the cycle
(
)
I
NR
rupt
I
+ =
+
1
1
1
/
.
The curve of Manson-Whetstone sheath of material must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] (key word factor
TIRE
, operand
MANSON_COFFIN
).
DAMAGE = “TAHERI_MIXTE”,
This method of calculation of the damage applies only to loadings in deformations.
Are
N
elementary cycles (extracts by a method of counting) of half-amplitude
2
,
,
2
1
N
L
.
The value of the elementary damage of the first cycle is determined by interpolation on
curve of
Manson-whetstone sheath of material.
The calculation of the elementary damage of the following cycles is carried out by the algorithm described
below:
·
If
I
I
+
1
2
2
the calculation of the elementary damage of the cycle
()
I
+ 1
is determined by interpolation on
curve of Manson-Whetstone sheath.
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
11/24
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HT-62/06/004/A
·
If
I
I
+
<
1
2
2
one determines:
I
I
J I
I
Max
+
+
<
=
1
1
2
2
2
Fnappe
,
where
Fnappe
is a tablecloth introduced under the operand of
TAHERI_NAPPE
.
The value of the damage of the cycle
()
I
+ 1
is obtained by interpolation of
I
+ 1
2
on
curve of Wöhler of material.
1
+
I
rupt
NR
is the number of cycles to the rupture for the cycle
()
I
+ 1
1
+
I
rupt
NR
=
WÖHLER
I
+
1
2
and
1
+
I
Dom
is the damage of the cycle
()
1
+
I
.
1
/
1
1
+
=
+
I
rupt
I
NR
Dom
.
This method requires the data of the curve of Wöhler and the curve of Manson-Whetstone sheath
material which must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] (key word
factor
TIRE
).
3.7.2 Methods of Lemaître and Lemaître-Sermage
These two methods make it possible to calculate the damage
()
T
D
starting from the data of the tensor of
stresses
()
T
and of the plastic deformation cumulated
()
T
p
.
They thus apply to unspecified loadings and are used only in postprocessing of one
plastic or viscoplastic law having
p
like variable.
Evolution of
D
is defined by:
(
)
(
)
(
)
=
>
-
+
+
-
=
if not
if
0
2
1
2
3
1
3
1
1
1
2
2
2
D
p
p
p
ES
ES
D
D
D
S
H
eq
S
&
&
where
E
: Young modulus,
v
: Poisson's ratio,
S
and
S
: parameters material,
eq
: stress
equivalent of von Mises,
H
: hydrostatic pressure,
p
: cumulated plastic deformation and
D
p
:
threshold of damage.
DAMAGE = “LEMAITRE”,
Allows to calculate the damage of Lemaître or Lemaître-Sermage
()
T
D
starting from the data
tensor of the stresses
()
T
and of the cumulated plastic deformation
()
T
p
. To note that it
damage of Lemaître is obtained by assigning value 1.0 with the exponent
S
(
S
= 1).
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
12/24
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
3.8 Operand
CORR_SIGM_MOYE
CORR_SIGM_MOYE
=
/
“GOODMAN”
,
/
“TO STACK”
,
This operand is used only in the case of the calculation of the damage by the method of WOHLER.
If the part is not subjected to pure or symmetrical alternate stresses, i.e. if
mean stress of the cycle is not null, one can balance the curve of Wöhler to calculate
the number of effective cycles to the rupture using the diagram of Haigh [R7.04.01].
Starting from a cycle
(
)
S
S
alt
m
,
identified in the signal, one calculates the value of the alternate stress
corrected
S
alt
.
If the line of Goodman is used
=
-
S
S
alt
alt
m
U
S
1
.
If one uses the parabola To stack
=
-
S
S
alt
alt
m
U
S
1
2
.
The value of the limit to the rupture of material
S
U
must be introduced into the operator
DEFI_MATERIAU
[U4.43.01] (key word factor
TIRE
, operand
Known
).
3.9 Operand
TAHERI_NAPPE
TAHERI_NAPPE = fnappe,
This operand makes it possible to specify the name of a tablecloth.
max
,
2
fnappe
necessary to the calculation of the damage by the methods
TAHERI_MANSON
and
TAHERI_MIXTE
.
The tablecloth must have as parameters
X
and
EPSI
.
Tablecloth introduced under the operand
TAHERI_NAPPE
is the cyclic curve of work hardening with
prestressed material.
The cyclic curve of work hardening without pre-work hardening, given under key word TAHERI_FONC,
must be obligatorily one of the curves defining the tablecloth. This curve must be given
for X = 0.
3.10 Operand
TAHERI_FONC
TAHERI_FONC = ffonc,
This operand makes it possible to specify the name of a function
2
ffonc
necessary to the calculation of
damage by the method
TAHERI_MANSON
.
The parameter of this function must be
SIGM
.
This function is the cyclic curve of work hardening of material.
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3.11 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 contain the values of all the data materials necessary to
calculation of the damage.
3.12 Operand
OFFICE PLURALITY
OFFICE PLURALITY = “LINEAR”,
The methods of WOHLER, MANSON_COFFIN and TAHERI calculate a value of damage for
each elementary cycle extracted the uniaxial loading introduced by the user.
The operand
OFFICE PLURALITY
allows to ask the calculation of the total damage undergone by the structure in one
not.
The only rule available is the rule To mine, which consists in summoning all the damage
elementary
D
D
I
I
=
.
3.13 Operands
CRITERION
CRITERION =
/“CROSSLAND”,
/
“PAPADOPOULOS”
,
The criteria of Crossland and Dang Van-Papadopoulos apply to loadings
uniaxial or multiaxial periodicals.
The user introduces the values of each component of the tensor of the stresses into various
moments
(
)
NR
O
T
T
,
, K
, and it is supposed that
[
]
T T
O
NR
,
is one period of the loading.
The loadings must be in stresses.
The goal of these criteria is not to determine a value of damage, but a value of criterion
R
crit
such as:
R
R
crit
crit
>
0
0
no damage,
possible damage.
One can however determine a value of damage by extension [§3.13.3].
3.13.1 Criterion of Crossland
B
P
has
R
has
crit
-
+
=
max
where
() ()
cission
of
amplitude
is
0
1
~
~
2
1
0
T
S
T
S
Max
Max
T
T
T
has
-
=
1
T
0
0
with
~
S
diverter of the tensor of the stresses
maximum
that
hydrostati
pressure
is
trace
=
3
1
0
max
T
T
Max
P
alternated.
pure
N
compressio
traction
in
endurance
of
limit
is
alternated,
pure
NT
cisailleme
in
endurance
of
limit
is
with
and
-
=
-
=
0
0
0
0
0
0
:
3
3
D
B
D
D
has
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3.13.2 Criterion of Dang Van-Papadopoulos
R
K
p has
B
crit
=
+
-
*
max
where
R
K
=
*
with
R
radius of the smallest sphere circumscribed with the way of loading in
the space of the diverters of stresses
~
S
()
(
)
()
(
)
*
~
:
*
~
2
1
0
C
T
S
C
T
S
Max
R
T
T
-
-
=
where
()
(
)
()
(
)
E
hypersphèr
of
center
is
C
T
S
C
T
S
Max
Min
C
-
-
=
~
:
~
*
maximum
that
hydrostati
pressure
is
trace
=
3
1
0
max
T
T
Max
P
0
0
0
0
3
3
=
-
=
B
D
D
has
alternated.
pure
N
compressio
traction
in
endurance
of
limit
is
alternated,
pure
NT
cisailleme
in
endurance
of
limit
is
with
-
0
0
:
D
3.13.3 Operand
COEF_CORR
COEF_CORR = corr,
The criteria of Crossland and Dang Van-Papadopoulos allow for loadings
periodicals to calculate a value
R
crit
who indicates if there is damage or not for the number of
cycles associated with the limits with endurances
0
0
and
D
.
These criteria do not give a value of the damage, which can however be interesting.
With this intention, one proposes to use the value of the criterion and the curve of Wöhler of material, in
defining an equivalent stress
(
)
.
*
corr
×
+
=
B
R
crit
The value of the damage is obtained while applying
*
on the curve of Wöhler of material.
So that there is coherence between the criterion and the curve of Wöhler, it is necessary that:
>
too bad
too bad
of
not
0
0
*
for a curve of Wöhler defined in shearing and that:
>
too bad
too bad
of
not
0
0
*
D
D
for a curve of Wöhler defined in traction and compression.
The user can thus specify a value
CORR
, by taking account of the type of curve of Wöhler
it has.
The value taken by defect is
0
0
D
in coherence with curves of Wöhler in
traction and compression.
Note:
If
0
<
crit
R
, if the prolongation on the left of the curve of Wöhler is
linear (in DEFI_FONCTION (… PROL_GAUCHE = “LINEAR”…)), the user
a damage different from zero will obtain. To obtain a null damage when
0
<
crit
R
,
it is necessary that the prolongation on the left equal to “IS EXCLUDED” or “CONSTANT”.
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3.14 Operand
INFORMATION
INFORMATION =/1,
Impression:
·
elementary cycles determined by the method of counting chosen by the user,
·
elementary damage associated each cycle for methods WOHLER,
MANSON_COFFIN and TAHERI,
·
damage of LEMAITRE in each point of calculation,
·
total damage (if the user asked for his calculation).
INFORMATION =/2,
Impression:
·
history of loading introduced by the user under the operands
SIGM
and
EPSI
,
·
peaks extracted the history of loading (introduced under the operands
SIGM
and
EPSI
),
·
elementary cycles determined by the method of counting chosen by the user,
·
elementary damage associated each cycle for methods WOHLER,
MANSON_COFFIN and TAHERI,
·
damage of LEMAITRE in each point of calculation,
·
total damage (if the user asked for his calculation).
The impressions are made in the file
message
.
3.15 Operand
TITRATE
TITRATE
= title
Titrate associated with the table.
3.16 Count
produced
The operator
POST_FATIGUE
create a table which is different according to calculations from postprocessing
carried out:
·
Loading uniaxial (Wöhler methods, Manson-Whetstone sheath and Taheri).
The table includes/understands five parameters:
NB_CYCL
: a number of elementary cycles extracted by the method of
counting,
VALE_MIN
: values of the stresses or minimal deformations of each cycle
elementary,
VALE_MAX
: values of the stresses or maximum deformations of each cycle
elementary,
TOO BAD
: values of the damage for each elementary cycle,
DOMM_CUMU: value of the total damage after office plurality on all the cycles
elementary.
·
Periodic loading (criteria of Crossland and Dang Van-Papadopoulos).
The table includes/understands five parameters:
CRITERION
: value of the criterion
PRES_HYDRO_MAX: value of the maximum hydrostatic pressure,
AMPLI_CISSION: value of the amplitude of cission
has
(if calculated),
RAYON_SPHERE
: value of the radius of the sphere circumscribed with the loading
K * (if calculated),
TOO BAD
: value of the damage of Wöhler (if requested by the user).
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·
Unspecified loading (damage of Lemaître and Lemaître-Sermage).
The table includes/understands two parameters:
TOO BAD
: value of the damage in each point of discretization
loading,
D_CUMULE
: value of the cumulated damage (if requested by the user).
The control
IMPR_TABLE
[U4.91.03] allows to print the produced table.
4 Examples
4.1 Calculation of the damage of Wöhler (with correction of the stress
average)
# Definition of the loading
taun = DEFI_FONCTION (
NOM_PARA = “INST”,
VALE = (0. , 50. ,
1. , 600. ,
2. , 50. ,
3. , - 500. ,
4. , 50. ,))
# Definition of the curve of Wöhler
wohl = DEFI_FONCTION (
NOM_PARA = “SIGM”,
INTERPOL = “LOG”,
PROL_DROIT = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
VALE = (138. , 1000000. ,
: :
.
2900., 10.,))
# Definition of Material
chechmate = DEFI_MATERIAU (
TIRE = _F (WOHLER = wohl)
RCCM = _F (KNOWN = 850. ))
# Calculation of damage
COUNT = POST_FATIGUE (
LOADING = “UNIAXIAL”,
HISTORY = _F (SIGM = taun),
COUNTING = “RCCM”,
MATER = chechmate,
DAMAGE = “WOHLER”,
OFFICE PLURALITY = “LINEAR”,
INFORMATION = 2)
This example results from test SZLZ100 (see [V9.01.100]).
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4.2
Calculation of the damage of Taheri
# Definition of the loading
taun = DEFI_FONCTION (
NOM_PARA = “INST”,
PROL_DROITE = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
VALE = (0. , 0. ,
1. , 3.5,
2. , 3. ,
3. , 3.5,
4. , 3. ,
5. , 3.5,
6. , 1. ,
7. , 2.5,
8. , 0. ,
9. , 0.5,))
# Definition of the Ffonc function: cyclic curve of work hardening of
# material
f_eps = DEFI_FONCTION (
NOM_PARA = “SIGM”,
PROL_DROITE = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
VALE = (0. , 0.,
1000., 10.,)
TITRATE = “Function of Taheri”
)
# Definition of the Fnappe tablecloth: cyclic curve of work hardening with pre
# forced of material
f_epsmax = DEFI_NAPPE (
NOM_PARA = “X”,
PROL_DROITE = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
PARA = (0.5, 1.,),
NOM_PARA_FONC = ' EPSI',
DEFI_FONCTION = (
_F (PROL_DROITE = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
VALE = (0. , 25.,
10. , 525.,)),
_F (PROL_DROITE = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
VALE = (0. , 50.,
10. , 550.,
))),
TITRATE = “TABLECLOTH OF TAHERI”)
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# Definition of the curve of Wöhler
f_wohl = DEFI_FONCTION (
NOM_PARA = “SIGM”,
PROL_DROITE = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
VALE = (0. , 200000.,
200. , 0.,),
TITRATE = “FUNCTION OF WOHLER”)
# Definition of the curve of Manson-Whetstone sheath
f_mans = DEFI_FONCTION (
NOM_PARA = “EPSI”,
PROL_DROITE = “LINEAR”,
PROL_GAUCHE = “LINEAR”,
VALE = (0. , 200000.,
2. , 0.,),
TITRATE = “FUNCTION OF MANSON-COFFIN”)
# Definition of material
mat0 = DEFI_MATERIAU (
TIRE = _F (WOHLER = f_whol,
MANSON_COFFIN = f_mans))
# Calculation of the damage
tabl1 = POST_FATIGUE (
LOADING = “UNIAXIAL”,
HISTORY = _F (EPSI = taun),
COUNTING = “RAINFLOW”,
DAMAGE = “TAHERI_MANSON”,
TAHERI_FONC = f_eps,
TAHERI_NAPPE = f_epsmax,
MATER = mat0,
OFFICE PLURALITY = “LINEAR”,
INFORMATION = 2)
tabl2 = POST_FATIGUE (
LOADING = “UNIAXIAL”,
HISTORY = _F (EPSI = taun),
COUNTING = “RAINFLOW”,
DAMAGE = “TAHERI_MIXTE”,
TAHERI_NAPPE = f_epsmax,
MATER = mat0,
OFFICE PLURALITY = “LINEAR”,
INFORMATION = 2)
This example results from test SZLZ108 (see [V9.01.108]).
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4.3
Calculation of the criteria of Crossland and Dang Van-Papadopoulos
# Definition of the loading
taun1 = DEFI_FONCTION (
NOM_PARA = “INST”,
VALE = (1. , 411.,
2. , 0.,
3. , - 411.,))
taun2 = DEFI_FONCTION (
NOM_PARA = “INST”,
VALE = (1. , 205.,
2. , 0.,
3. , - 205.,))
taun3 = DEFI_FONCTION (
NOM_PARA = “INST”,
VALE = (1. , 0.,
2. , 0.,
3. , 0.,))
# Definition of material
mat0 = DEFI_MATERIAU (
TIRE = _F (WOHLER = whol,
D0 = 540.97,
TAU0 = 352.,))
# Calculation of the criterion of Crossland
table1 = POST_FATIGUE (
LOADING = “PERIODIC”,
HISTORY = _F (SIGM_XX = TAUN1, SIGM_XY = TAUN2,
SIGM_YY = TAUN3, SIGM_XZ = TAUN3,
SIGM_ZZ = TAUN3, SIGM_YZ = TAUN3),
CRITERION = “CROSSLAND”,
MATER = mat0,
INFORMATION = 2)
# Calculation of the criterion of Dang Van-Papadopoulos
table2 = POST_FATIGUE (
LOADING = “PERIODIC”,
HISTORY = _F (SIGM_XX = TAUN1,
SIGM_YY = taun3,
SIGM_ZZ = taun3,
SIGM_XY = taun2,
SIGM_XZ = taun3,
SIGM_YZ = taun3),
CRITERION = “PAPADOPOULOS”,
MATER = mat0,
INFORMATION = 2)
This example results from test SZLZ107 (see [V9.01.107]).
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4.4
Calculation of the damage of Lemaître
# Definition of the loading
taun1 = DEFI_FONCTION (
NOM_PARA = “INST”,
VALE = (43.11, 300.,
100. , 300.,
1000. , 300.,
10000. , 300.,
20000. , 300.,
21000. , 300.,
22000. , 300.,
22200. , 300.,
22400. , 300.,))
taun2 = DEFI_FONCTION (
NOM_PARA = “INST”,
VALE = (43.11, 0.,
100. , 0.,
1000. , 0.,
10000. , 0.,
20000. , 0.,
21000. , 0.,
22000. , 0.,
22200. , 0.,
22400. , 0.,))
t_epsp = DEFI_FONCTION (
NOM_PARA = “INST”,
VALE = (43.11, 0.019996,
100. , 0.046384,
1000. , 0.46384,
10000. , 4.6384,
20000. , 9.2768,
21000. , 9.74064,
22000. , 10.20448,
22200. , 10.297248,
22400. , 10.390016,))
t_temp = DEFI_FONCTION (
NOM-PARA = “INST”,
VALE = (43.11, 20.,
100. , 20.,
1000. , 20.,
10000. , 20.,
20000. , 20.,
21000. , 20.,
22000. , 20.,
22200. , 20.,
22400. , 20.,))
t_e = DEFI_FONCTION (
NOM_PARA = “TEMP”,
VALE = (20. , 2.E+5,),
PROL_DROITE = “CONSTANT”,
PROL_GAUCHE = “CONSTANT”,)
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t_nu = DEFI_FONCTION (
NOM_PARA = “TEMP”,
VALE = (20. , 0.,),
PROL_DROITE = “CONSTANT”,
PROL_GAUCHE = “CONSTANT”)
t_s = DEFI-FONCTION (
NOM_PARA = “TEMP”,
VALE = (20. , 7.,),
PROL_DROITE = “CONSTANT”,
PROL_GAUCHE = “CONSTANT”,)
epsp_s = DEFI-FONCTION (
NOM_PARA = “TEMP”,
VALE = (20. , 0.02,),
PROL_DROITE = “CONSTANT”,
PROL_GAUCHE = “CONSTANT”,)
mat1 = DEFI_MATERIAU (
ELAS_FO = _F (E = t_e,
NAKED = t_nu),
DOMMA_LEMAITRE =_F (S = t_s,
EPSP_SEUIL = epsp_s,
EXP_S
= 1.0)
)
TAB_1 = POST_FATIGUE (
LOADING = “UNSPECIFIED”,
HISTORY = _F (SIGM_XX = TAUN1, SIGM_XY = TAUN2,
SIGM_YY = TAUN2, SIGM_XZ = TAUN2,
SIGM_ZZ = TAUN2, SIGM_YZ = TAUN2,
EPSP = t_epsp,
TEMP = t_temp),
MATER = mat1,
DAMAGE = “LEMAITRE”,
INFORMATION = 2)
This example results from test SZLZ109 (see [V9.01.109]).
4.5
Calculation of the damage of Lemaître-Sermage
TAUN1=DEFI_FONCTION (NOM_PARA=' INST',
VALE= (43.11, 300.,
100., 300.,
1000., 300.,
10000., 300.,
20000., 300.,
21000., 300.,
22000., 300.,
22200., 300.,
22400., 300.,))
TAUN2=DEFI_FONCTION (NOM_PARA=' INST',
VALE= (43.11, 0.,
100., 0.,
1000., 0.,
10000., 0.,
20000., 0.,
21000., 0.,
22000., 0.,
22200., 0.,
22400., 0.,))
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T_EPSP=DEFI_FONCTION (NOM_PARA=' INST',
VALE= (43.11, 0.019996,
100., 0.046384,
1000., 0.46384,
10000., 4.6384,
20000., 9.2768,
21000., 9.74064,
22000., 10.20448,
22200., 10.297248,
22400., 10.390016,))
T_TEMP=DEFI_FONCTION (NOM_PARA=' INST',
VALE= (43.11, 20.,
100., 20.,
1000., 20.,
10000., 20.,
20000., 20.,
21000., 20.,
22000., 20.,
22200., 20.,
22400., 20.,))
T_E=DEFI_FONCTION (NOM_PARA=' TEMP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
VALE= (20., 2.E+5,))
T_NU=DEFI_FONCTION (NOM_PARA=' TEMP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
VALE= (20., 0.,))
T_S=DEFI_FONCTION (NOM_PARA=' TEMP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
VALE= (20., 7.0,))
EPSP_S=DEFI_FONCTION (NOM_PARA=' TEMP',
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' CONSTANT',
VALE= (20., 0.02,))
MAT2=DEFI_MATERIAU (ELAS_FO=_F (E = T_E,
NAKED = T_NU,),
DOMMA_LEMAITRE=_F (S = T_S,
EPSP_SEUIL = EPSP_S,
EXP_S = 1.003,),);
TAB_2=POST_FATIGUE (CHARGEMENT=' QUELCONQUE',
HISTOIRE=_F (SIGM_XX = TAUN1,
SIGM_YY = TAUN2,
SIGM_ZZ = TAUN2,
SIGM_XY = TAUN2,
SIGM_XZ = TAUN2,
SIGM_YZ = TAUN2,
EPSP = T_EPSP,
TEMP = T_TEMP,),
MATER=MAT2,
DOMMAGE=' LEMAITRE',
CUMUL=' LINEAIRE',);
This example results from test SZLZ109 (see [V9.01.109]).
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One can find other examples in the tests:
SZLZ101 ([V9.01.101]): Calculation of the damage/Rainflow method.
SZLZ102 ([V9.01.102]): Tire with various methods counting.
SZLZ103 ([V9.01.103]): Tire counting by Rainflow method normalizes AFNOR.
Code_Aster
®
Version
8.2
Titrate:
Operator
POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES,
A. Mr. DONORE
Key
:
U4.83.01-F1
Page:
24/24
Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Intentionally white left page.