Code_Aster ®
Version
8.2
Titrate:
Operator POST_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.01-F1 Page:
1/24
Organization (S): EDF-R & D/AMA
Handbook of Utilization
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-Coffin 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 constraints 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 constraints 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.
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Operator POST_FATIGUE
Date:
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Count
matters
1 Goal ........................................................................................................................................................ 1
2 Syntax ................................................................................................................................................. 3
3 Operands ............................................................................................................................................ 5
3.1 Operand LOADING ................................................................................................................. 5
3.2 Key word HISTOIRE .......................................................................................................................... 5
3.2.1 Operand SIGM ..................................................................................................................... 5
3.2.2 Operand EPSI ..................................................................................................................... 5
3.2.3 Operands SIGM_XX/SIGM_YY/SIGM_ZZ/SIGM_XY/SIGM_XZ/SIGM_YZ 5
3.2.4 Operand EPSP ..................................................................................................................... 6
3.2.5 Operand TEMP ..................................................................................................................... 6
3.3 Operand DELTA_OSCI ................................................................................................................. 6
3.4 Key word COEF_MULT ........................................................................................................................ 7
3.4.1 Operand KT ......................................................................................................................... 7
3.5 Operand COUNTING ..................................................................................................................... 8
3.6 Operand CORR_KE ........................................................................................................................ 8
3.7 Operand DAMAGE ........................................................................................................................ 8
3.7.1 Methods based on uniaxial tests: method of Wöhler, method of Manson-
Whetstone sheath, methods of Taheri ................................................................................................... 8
3.7.2 Methods of Lemaître and Lemaître-Sermage ..................................................................... 11
3.8 Operand CORR_SIGM_MOYE ...................................................................................................... 12
3.9 Operand TAHERI_NAPPE ........................................................................................................... 12
3.10
Operand TAHERI_FONC .................................................................................................... 12
3.11
MATER operand ................................................................................................................. 13
3.12
Operand OFFICE PLURALITY ................................................................................................................. 13
3.13
Operands CRITERION ........................................................................................................... 13
3.13.1
Criterion of Crossland ............................................................................................... 13
3.13.2
Criterion of Dang Van-Papadopoulos ....................................................................... 14
3.13.3
Operand COEF_CORR ............................................................................................ 14
3.14
Operand INFORMATION ................................................................................................................... 15
3.15
Operand TITRATES ................................................................................................................. 15
3.16
Count produced ...................................................................................................................... 15
4 Examples ............................................................................................................................................ 16
4.1 Calculation of the damage of Wöhler (with correction of the average constraint) .............................. 16
4.2 Calculation of the damage of Taheri ..................................................................................................... 17
4.3 Calculation of the criteria of Crossland and Dang Van-Papadopoulos .................................................... 19
4.4 Calculation of the damage of Lemaître-Sermage ................................................................................. 20
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Date:
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:
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2 Syntax
tabl_post_fatig = POST_FATIGUE
(
# if purely uniaxial loading (or regarded as uniaxial)
/LOADING = “UNIAXIAL”,
HISTOIRE =
_F (
/SIGM = histsigm
/[function]
/
[formula]
/
EPSI
=
histepsi/
[function]
/
[formula]
),
COUNTING =/“RAINFLOW”
,
/
“RCCM”
,
/
“NATUREL”
,
DELTA_OSCI =/delta
, [R]
/
0.
, [DEFAUT]
COEF_MULT = _F (
KT
=
kt
),
[R]
CORR_KE = “RCCM”,
DAMAGE =/“WOHLER”
,
/
“MANSON_COFFIN”
,
/
“TAHERI_MANSON”
,
/
“TAHERI_MIXTE”
,
MATER
=
to subdue
,
CORR_SIGM_MOYE =/“GOODMAN”
,
/
“GERBER”
,
TAHERI_NAPPE
=
fnappe
,
/
[tablecloth]
/[formula]
TAHERI_FONC
=
ffonc
,
/
[function]
/[formula]
CUMUL
=
“LINEAIRE”
,
# Finsi
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# if loading periodic (for fatigue with great numbers of cycles and
for periodic cycles)
/LOADING = “PERIODIC”,
HISTOIRE = _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
,
[DEFAUT]
# Finsi
# if loading unspecified (damage of Lemaitre or Lemaitre-
Sermage)
/LOADING = “UNSPECIFIED”,
HISTOIRE = _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]
)
DOMMAGE
= “LEMAITRE”,
MATER
=
to subdue
,
CUMUL
=
“LINEAIRE”
,
# Finsi
INFO =/1,
[DEFAUT]
/2,
TITER
=
titrate
[l_Kn]
)
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Operator POST_FATIGUE
Date:
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3 Operands
3.1 Operand
CHARGEMENT
This key word makes it possible the user to specify the type of treated loading. The loading can be
“UNIAXIAL”, “PERIODIQUE” or “QUELCONQUE”. With each loading corresponds its (or its)
method (S) of evaluation of the damage by fatigue.
3.2 Word
key
HISTOIRE
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 constraint 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 command
POST_FATIGUE.
·
tensor of constraints in the course of time,
·
tensor of constraints, 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 constraints 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
constraints in the course of time. Each function or formula depends on parameter INST. All them
functions or formulas must be defined for the same moments.
In 2D are obligatory operands SIGM_XX, SIGM_YY, SIGM_ZZ and SIGM_XY.
In 3D are obligatory operands SIGM_XX, SIGM_YY, SIGM_ZZ, SIGM_XY, SIGM_XZ and
SIGM_YZ.
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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 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 constraints.
Operand EPSP must be used jointly with 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 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 constraints.
Operand TEMP must be used jointly with 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 constraint 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.
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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
=
)
5
(
- (4) < 0.9,
·
item 6 bus
=
(6) - (4) < 0.9,
·
item 12 bus
=
12
(
) -
)
11
(
< 0.9,
·
the point 13 bus
=
)
13
(
-
)
11
(
< 0.9.
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 kt report/ratio.
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3.5 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. 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].
/
“NATUREL”
,
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 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.
The values S
N
m
m,
and
are provided in operator DEFI_MATERIAU [U4.43.01] under the word
key factor FATIGUE and operands SM_KE_RCCM, N_KE_RCCM and M_KE_RCCM.
3.7 Operand
DOMMAGE
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-Coffin, 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 constraint 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-Coffin and Taheri use the deformations generated by
loading.
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The method of Wöhler uses the constraints generated by the loading.
DAMAGE = “WOHLER”,
For a history of constraints associated with a uniaxial loading, the number of cycles with
rupture is given using the curve of Wöhler of the Nrupt material =
WOHLER
.
2
The curve of Wöhler of material must be introduced into 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 FATIGUE, operand WOHLER),
·
analytical form of Basquin (key word factor FATIGUE, operands A_BASQUIN and
BETA_BASQUIN),
·
form “current zone” (key word factor FATIGUE, 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 constraints, 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 106
cycles, the corresponding constraint, 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
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.
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-Coffin of material
Nrupt =
MANSON_ WHETSTONE SHEATH
.
2
The curve of Manson-Coffin of material must be introduced into operator DEFI_MATERIAU
[U4.43.01] (key word factor FATIGUE, operand MANSON_COFFIN).
DAMAGE = “TAHERI_MANSON”,
This method of calculation of the damage applies only to loadings in deformations.
Are N cycles elementary (extracted by a method of counting) of half-amplitude
1,
2
K
N.
2
The value of the elementary damage of the first cycle is determined by interpolation on
curve of Manson-Coffin of material.
The calculation of the elementary damage of the following cycles is carried out by the algorithm described Ci
below:
+
·
If
I 1
I
2
2
the calculation of the elementary damage of the cycle (I +)
1 is determined by interpolation on
curve of Manson-Coffin of material,
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+
·
If
I 1
I
<
2
2
one determines:
I
I
J
+1 =
+1
Fnappe
, Max
2
2
j<i 2
*
i+1
i+1
=
Ffonc
2
2
where:
Fnappe is a tablecloth introduced under operand TAHERI_NAPPE,
Ffonc is a function introduced under operand TAHERI_FONC.
* i+ 1
The value of the damage of the cycle (I +)
1 is obtained by interpolation of
on the curve of
2
Manson-Coffin of material.
NR
is the number of cycles to the rupture of the cycle (I +)
1
I
rupt 1
+
I + 1
NR
= MANSON_COFFIN
I
rupt 1
+
2
and
I
Dom 1
+ is the damage of the cycle (I +)
1 = 1/Nrupt.
I + 1
The curve of Manson-Coffin of material must be introduced into operator DEFI_MATERIAU
[U4.43.01] (key word factor FATIGUE, operand MANSON_COFFIN).
DAMAGE = “TAHERI_MIXTE”,
This method of calculation of the damage applies only to loadings in deformations.
Are N cycles elementary (extracted by a method of counting) of half-amplitude
1
,
N
L
.
2
2
The value of the elementary damage of the first cycle is determined by interpolation on
curve of Manson-Coffin of material.
The calculation of the elementary damage of the following cycles is carried out by the algorithm described
below:
I + 1
·
If
I
2
2
the calculation of the elementary damage of the cycle (I +)
1 is determined by interpolation on
curve of Manson-Coffin.
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I + 1
·
If
I
<
2
2
one determines:
1
+
I
I + 1
I
= Fnappe
, Max
2
2
J < I 2
where Fnappe is a tablecloth introduced under the operand of TAHERI_NAPPE.
I +1
The value of the damage of the cycle (I +)
1 is obtained by interpolation of
on
2
curve of Wöhler of material.
NR
is the number of cycles to the rupture for the cycle (I +)
1
I
rupt 1
+
I + 1
NR
= WÖHLER
I
rupt 1
+
2
and
I
Dom 1
+ is the damage of the cycle (I
) 1
+.
Dom
1
=/
I 1
+
NR
.
I
rupt 1
+
This method requires the data of the curve of Wöhler and the curve of Manson-Coffin
material which must be introduced into operator DEFI_MATERIAU [U4.43.01] (key word
factor FATIGUE).
3.7.2 Methods of Lemaître and Lemaître-Sermage
These two methods make it possible to calculate the damage D (T) starting from the data of the tensor of
constraints (T) and of the plastic deformation cumulated p (T).
They thus apply to unspecified loadings and are used only in postprocessing of one
plastic or viscoplastic law having p like variable.
The evolution of D is defined by:
S
1
D & =
1
2
3
(1+) +
eq
(1 - 2)
2
p
if
&
p >
(
p
H
D
1 - D) 2s
3 ES
2 ES
D =
0
if not
where E: Young modulus, v: Poisson's ratio, S and S: parameters material: constraint
eq
equivalent of von Mises: hydrostatic pressure, p: cumulated plastic deformation and p:
H
D
threshold of damage.
DAMAGE = “LEMAITRE”,
Allows to calculate the damage of Lemaître or Lemaître-Sermage D (T) starting from the data
tensor of the constraints (T) and cumulated plastic deformation p (T). To note that it
damage of Lemaître is obtained by assigning value 1.0 with the exhibitor S (S = 1).
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3.8 Operand
CORR_SIGM_MOYE
CORR_SIGM_MOYE
=
/
“GOODMAN”
,
/
“GERBER”
,
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 constraints, i.e. if
average constraint 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 constraint
corrected Salt.
If the line of Goodman is used
S
S
=
alt
alt
.
1 - m
U
S
If one uses the parabola of Gerber
S
S
=
alt
alt
.
2
1 - m
U
S
The value of the limit to the rupture of the Su material must be introduced into the operator
DEFI_MATERIAU [U4.43.01] (key word factor FATIGUE, operand Known).
3.9 Operand
TAHERI_NAPPE
TAHERI_NAPPE = fnappe,
This operand makes it possible to specify the name of a tablecloth.
fnappe
, max necessary to the calculation of the damage by methods TAHERI_MANSON and
2
TAHERI_MIXTE.
The tablecloth must have as parameters X and EPSI.
The tablecloth introduced under 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
ffonc
necessary to the calculation of
2
damage by 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
CUMUL
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.
Operand CUMUL makes it possible to require the calculation of the total damage undergone by the structure in one
not.
The only rule available is the rule of Miner, which consists in summoning all the damage
elementary D =
Di.
I
3.13 Operands
CRITERE
CRITERE =
/“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 constraints into various
moments (to, T
K NR), and one suppose that [T, T
O
NR] is one period of the loading.
The loadings must be in constraints.
The goal of these criteria is not to determine a value of damage, but a value of criterion
Rcrit such as:
Rcrit 0 step of damage,
R
crit > 0 possible damage.
One can however determine a value of damage by extension [§3.13.3].
3.13.1 Criterion of Crossland
R
= + P has
- B
crit
has
max
1
~
~
where
=
Max Max S
has
(1t) - S (t0)
amplitude
is
of cission
2 0t0 T
0
T
1
T
~
with S deviative of the tensor of the constraints
1
P
=
max
Max traces
is
pressure hydrostati
that maximum
0tT 3
D
has =
- 0
d0 and B =
0
3
0
3
with:
is
of
limit
cisailleme
in
endurance
pure
NT
alternated,
0
D
is
of
limit
traction
in
endurance
- compressio
alternated.
pure
N
0
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3.13.2 Criterion of Dang Van-Papadopoulos
R
K * has P
B
crit
=
+
-
max
where K * = R with R radius of the smallest sphere circumscribed with the way of loading in
~
the space of the diverters of constraints S
1
R =
Max
(~S (T) - C) * (~
: S (T) - C)
*
0 T T
2
~
where C * =
~
MinMax (S (T) C
-): (S (T) C
-)
center
is
of hypersphère
1
P
=
max
Max traces
is
pressure hydrostati
that maximum
0tT 3
D D
0
0
has =
-
B =
0
0
3 3
with:
is
0
of
limit
cisailleme
in
endurance
pure
NT
alternated,
D
is
0
of
limit
traction
in
endurance
- compressio
alternated.
pure
N
3.13.3 Operand COEF_CORR
COEF_CORR = corr,
The criteria of Crossland and Dang Van-Papadopoulos allow for loadings
periodicals to calculate a Rcrit value which indicates if there is damage or not for the number of
cycles associated with the limits with endurances and D.
0
0
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 constraint
* (
= R
+b
crit
) ×
.
corr
The value of the damage is obtained while applying * to the curve of Wöhler of material.
So that there is coherence between the criterion and the curve of Wöhler, it is necessary that:
*
no damage
0
>
too bad
0
for a curve of Wöhler defined in shearing and that:
* D
no damage
0
> D
too bad
0
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.
D
The value taken by defect is 0 in coherence with curves of Wöhler in
0
traction and compression.
Note:
If R
< 0, if the prolongation on the left of the curve of Wöhler is
crit
linear (in DEFI_FONCTION (… PROL_GAUCHE = “LINEAR”…)), the user
a damage different from zero will obtain. To obtain a null damage when R
< 0,
crit
it is necessary that the prolongation on the left is equal to “EXCLU” or “CONSTANT”.
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3.14 Operand
INFO
INFO =/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).
INFO =/2,
Impression:
·
history of loading introduced by the user under operands SIGM and EPSI,
·
peaks extracted the history of loading (introduced under 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
TITER
TITER = title
Titrate associated with the table.
3.16 Count
produced
Operator POST_FATIGUE creates a table which is different according to calculations from postprocessing
carried out:
·
Uniaxial loading (methods Wöhler, Manson-Coffin 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 constraints or minimal deformations of each cycle
elementary,
VALE_MAX
: values of the constraints or maximum deformations of each cycle
elementary,
DOMMAGE
: 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:
CRITERE
: 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),
DOMMAGE
: 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:
DOMMAGE
: value of the damage in each point of discretization
loading,
D_CUMULE
: value of the cumulated damage (if requested by the user).
Command IMPR_TABLE [U4.91.03] makes it possible to print the produced table.
4 Examples
4.1 Calculation of the damage of Wöhler (with correction of the constraint
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 Matériau
chechmate = DEFI_MATERIAU (
FATIGUE = _F (WOHLER = wohl)
RCCM = _F (KNOWN = 850. ))
# Calculation of damage
COUNT = POST_FATIGUE (
LOADING = “UNIAXIAL”,
HISTOIRE = _F (SIGM = taun),
COUNTING = “RCCM”,
MATER = chechmate,
DAMAGE = “WOHLER”,
OFFICE PLURALITY = “LINEAR”,
INFO = 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.,)
TITER = “Fonction de 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-Coffin
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 (
FATIGUE = _F (WOHLER = f_whol,
MANSON_COFFIN = f_mans))
# Calculation of the damage
tabl1 = POST_FATIGUE (
LOADING = “UNIAXIAL”,
HISTOIRE = _F (EPSI = taun),
COUNTING = “RAINFLOW”,
DAMAGE = “TAHERI_MANSON”,
TAHERI_FONC = f_eps,
TAHERI_NAPPE = f_epsmax,
MATER = mat0,
OFFICE PLURALITY = “LINEAR”,
INFO = 2)
tabl2 = POST_FATIGUE (
LOADING = “UNIAXIAL”,
HISTOIRE = _F (EPSI = taun),
COUNTING = “RAINFLOW”,
DAMAGE = “TAHERI_MIXTE”,
TAHERI_NAPPE = f_epsmax,
MATER = mat0,
OFFICE PLURALITY = “LINEAR”,
INFO = 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 (
FATIGUE = _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,
INFO = 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,
INFO = 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”,
INFO = 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.
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