Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
1/20
Organization (S): EDF-R & D/AMA
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
Document: U4.83.02
Operator CALC_FATIGUE
1 Goal
To calculate a field of damage of fatigue undergone by a structure and to determine the plan criticize in
which shearing is maximum.
Calculation of a field of damage: starting from a history of equivalent constraints (forced
von Mises signed) or of deformations equivalent (invariant of the second signed command) calculated to
nodes or at the points of Gauss and stored in a concept result of the evol_elas type, evol_noli
or dyna_trans, one calculates a field of size which contains the damage undergone by the structure in
each node or in each point of Gauss.
With this intention, in each node or each point of Gauss, CALC_FATIGUE:
·
reads in the structure of data result the equivalent constraint of von Mises signed
(VMIS_SG) or the second signed invariant (INVA_2SG),
·
extract by a method of counting of cycles (method RAINFLOW) elementary cycles
of loading (history of the equivalent constraint or equivalent deformation) undergone
by the structure,
·
determine the elementary damage associated with each elementary cycle,
·
determine the total damage undergone by the structure by a linear rule of office plurality while summoning
elementary damage.
Critical plan and maximum shearing: starting from a history of constraints calculated at the points of
Gauss (SIEF_ELGA, or SIEF_ELGA_DEPL) or with nodes (SIEF_NOEU_ELGA or SIGM_NOEU_DEPL)
and stored in a concept result of the evol_elas type or evol_noli, if the loading
is periodic, we calculate a field of size which contains inter alia: the half amplitude of
maximum shearing, the associated normal vector, the number of cycles to the rupture and the damage
corresponding to the points of Gauss or the nodes. If the loading is not periodical the field of
sizes contains the maximum damage and the normal vector associated the points of Gauss or
with the nodes.
Product a concept of the cham_elem_DOMMAG type or cham_elem_FACY_R or cham_no_FACY_R.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
2/20
2 Syntax
CHAM [cham_elem *] = CALC_FATIGUE (
TYPE_CALCUL =/“CUMUL_DOMMAGE”,
/
“FATIGUE_MULTI”,
# If TYPE_CALCUL = “CUMUL_DOMMAGE” - > calculation of the damage
# Choice of the option of calculation
OPTION
=/“DOMA_ELNO_SIGM”
,
/
“DOMA_ELGA_SIGM”
,
/
“DOMA_ELNO_EPSI”
,
/
“DOMA_ELGA_EPSI”
,
/
“DOMA_ELNO_EPME”
,
/
“DOMA_ELGA_EPME”
,
# Reading of the history of constraint or deformation
HISTOIRE = _F (
RESULTAT
=
LMBO,/
[evol_elas]
/
[evol_noli]
/
[dyna_trans]
EQUI_GD =
/
“VMIS_SG”, [DEFECT]
/
“INVA_2_SG”,
)
# Calculation of the damage
DAMAGE =/“WOHLER”,
/
“MANSON_COFFIN”,
/
“TAHERI_MANSON”,
/
“TAHERI_MIXTE”
,
MATER
=
to subdue,
[to subdue]
TAHERI_NAPPE
=
tablecloth,
/
[tablecloth]
/
[formula]
TAHERI_FONC
=
fonc,
/
[function]
/
[formula]
),
# Finsi
# If TYPE_CALCUL = “FATIGUE_MULTI” - > Calcul of the maximum shearing or of
maximum damage
TYPE_CHARGE =/“PERIODIC”,
/
“NON_PERIODIQUE”,
OPTION
=
/
“DOMA_ELGA”,
/
“DOMA_NOEUD”,
RESULTAT
=
LMBO,/
[evol_elas]
/
[evol_noli]
CHAM_MATER =
cham_mater,
[cham_mater]
# If TYPE_CHARGE = “PERIODIC”
CRITERION =/“MATAKE”,
/“DANG_VAN_MODI_AC”,
METHOD =/“CERCLE_EXACT”,
# Finsi
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
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Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
3/20
# If TYPE_CHARGE = “NON_PERIODIQUE”
CRITERION =/“DOMM_MAXI”,
/
“DANG_VAN_MODI_AV”,
/
“FATEMI_SOCIE”,
PROJECTION =/“UN_AXE”,
/
“DEUX_AXES”,
DELTA_OSCI =/delta,
[R]
/
0.,
[DEFAUT]
# Finsi
/
MAILLAGE
=
grid,
[grid]
/
GROUP_MA
=
grma,
[l_gr_maille]
/
MAILLE
=
my,
[l_maille]
/
GROUP_NO
=
grno,
[l_gr_noeud]
/
NOEUD
=
No,
[l_noeud]
COEF_PREECROU
=
/
coef_pre,
[R]
/
1.0, [DEFAUT]
# If (GROUP_MA!= Nun gold MAILLE!= Nun gold \
GROUP_NO!= Nun gold NOEUD!= Nun)
# Finsi
# Finsi
# Level
of impression
INFO =/1,
[DEFAUT]
/2,
)
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
4/20
3 Operands
3.1 Word
key
TYPE_CALCUL
This key word makes it possible to calculate is a field of damage of fatigue undergone by a structure, if
TYPE_CALCUL = “CUMUL_DOMMAGE”, is the critical plan in which shearing is maximum, if
TYPE_CALCUL = “FATIGUE_MULTI”.
The following table indicates the key words which are usable according to the type of selected calculation.
TYPE_CALCUL
Key word
Paragraph
“CUMUL_DOMMAGE”
OPTION
3.2
“CUMUL_DOMMAGE”
HISTOIRE
3.3
“CUMUL_DOMMAGE”
DOMMAGE
3.4
“CUMUL_DOMMAGE”
MATER
3.5
“CUMUL_DOMMAGE”
TAHERI_NAPPE
3.6
“CUMUL_DOMMAGE”
TAHERI_FONC
3.7
“FATIGUE_MULTI”
TYPE_CHARGE
3.8
“FATIGUE_MULTI”
OPTION
3.9
“FATIGUE_MULTI”
RESULTAT
3.10
“FATIGUE_MULTI”
CHAM_MATER
3.11
“FATIGUE_MULTI”
CRITERE
3.12
“FATIGUE_MULTI”
METHODE
3.13
“FATIGUE_MULTI”
PROJECTION
3.14
“FATIGUE_MULTI”
DELTA_OSCI
3.15
“FATIGUE_MULTI”
GROUP_MA/MESH/GROUP_NO/NODE
3.16
“FATIGUE_MULTI” COEF_PREECROU
3.17
“FATIGUE_MULTI”
MAILLAGE
3.18
3.2 Word
key
OPTION
This key word factor makes it possible to specify the type of damage to be calculated:
·
“DOMA_ELNO_SIGM” for the calculation of the damage to the nodes starting from a field of
constraints.
The structure of data result specified under the key word factor RESULTAT must contain it
field of reference symbol EQUI_ELNO_SIGM (calculable by CALC_ELEM), which defines between
other the value of the equivalent constraint of von Mises signed (component VMIS_SG)
calculated with the nodes.
·
“DOMA_ELGA_SIGM” for the calculation of the damage at the points of Gauss starting from a field of
constraints.
The structure of data result specified under the key word factor RESULTAT must contain it
field of reference symbol EQUI_ELGA_SIGM (calculable by CALC_ELEM), which defines between
other the value of the equivalent constraint of von Mises signed (component VMIS_SG)
calculated at the points of Gauss.
·
“DOMA_ELNO_EPSI” for the calculation of the damage to the nodes starting from a field of
deformations.
The structure of data result specified under the key word factor RESULTAT must contain it
field of reference symbol EQUI_ELNO_EPSI, which defines the value of the invariant amongst other things
of a signed nature 2 (component INVA_2SG) calculated with the nodes.
·
“DOMA_ELGA_EPSI” for the calculation of the damage at the points of Gauss starting from a field of
deformations.
The structure of data result specified under the key word factor RESULTAT must contain it
field of reference symbol EQUI_ELGA_EPSI, which defines the value of the invariant amongst other things
of a signed nature 2 (component INVA_2SG) calculated at the points of Gauss.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
5/20
·
“DOMA_ELNO_EPME” for the calculation of the damage to the nodes starting from a field of
mechanical deformations, out-thermics: = B.u - HT.
The structure of data result specified under the key word factor RESULTAT must contain it
field of reference symbol EQUI_ELNO_EPME (calculable by CALC_ELEM), which defines between
other the value of the invariant of a signed nature 2 (component INVA_2SG) calculated with the nodes.
·
“DOMA_ELGA_EPME” for the calculation of the damage at the points of Gauss starting from a field of
mechanical deformations, out-thermics: = B.u - HT.
The structure of data result specified under the key word factor RESULTAT must contain it
field of reference symbol EQUI_ELGA_EPME, which defines the value of the invariant amongst other things
of a signed nature 2 (component INVA_2SG) calculated at the points of Gauss.
3.3
Key word factor HISTOIRE
This key word factor gathers all the phase of definition of the history of loading.
The history of loading is the evolution of a value of the constraint or deformation during
time.
3.3.1 Operand
RESULTAT
RESULTAT = LMBO
Name of the concept result containing the stress fields or the fields of deformation
defining the history of loading. More precisely, the concept result must contain one of
fields of reference symbol EQUI_ELNO_SIGM, EQUI_ELGA_SIGM, EQUI_ELNO_EPSI,
EQUI_ELGA_EPSI, EQUI_ELNO_EPME or EQUI_ELGA_EPME according to the desired option of calculation.
3.3.2 Operand
EQUI_GD
EQUI_GD =/“VMIS_SG”,
/
“INVA_2_SG”
To be able to calculate the damage undergone by a structure, a method of Wöhler, Manson-
Whetstone sheath or a method of Taheri, it is necessary to have a history of loading in constraints or in
deformations “uniaxial”. With this intention it is necessary to transform the tensor of constraints or the tensor of
deformations in a uniaxial field (scalar) “equivalent”.
“VMIS_SG”
to calculate the damage starting from a history of loading of the type
constraint of von Mises signed,
“INVA_2_SG” to calculate the damage starting from a history of loading of the type
invariant of a nature 2 signed of the deformation.
3.4 Operand
DOMMAGE
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. Method available in Code_Aster for
calculation of the damage by the method Wöhler or Manson-Coffin, is the method of counting of
extended in cascade or method of Rainflow [R7.04.01].
For the calculation of the damage by methods TAHERI_MANSON and TAHERI_MIXTE, one uses
method of counting known as natural which consists in generating cycles in the order of their application.
Once the extracted elementary cycles, this operand makes it possible to specify the method of calculation of
damage for each elementary cycle.
DAMAGE =/“WOHLER”
For a history of loading of the type forced, the number of cycles to the rupture is
determined by interpolation of the curve of Wöhler of material for a level of constraint
alternated given (to each elementary cycle a level of amplitude of constraint corresponds
=
-
max
min and an alternate constraint Salt = 1/2).
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
6/20
One can use method WOHLER only for options “DOMA_ELNO_SIGM” or
“DOMA_ELGA_SIGM”. Moreover, it is necessary that the concept specified result contains it respectively
field of reference symbol EQUI_ELNO_SIGM or EQUI_ELGA_SIGM (calculable by
CALC_ELEM).
The curve of Wöhler of material must be introduced into operator DEFI_MATERIAU [U4.43.01],
under one of the three possible forms [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 word
key 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 one
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. a number of infinite acceptable cycle.
DAMAGE =/“MANSON_COFFIN”
For a history of loading of the deformations type, the number of cycles to the rupture is
determined by interpolation of the curve of Manson-Coffin of material for a level of
alternate deformation given (to each elementary cycle corresponds a level of amplitude of
deformation =
-
max
min and an alternate deformation Ealt = 1/2).
One can use method MANSON_COFFIN only for options “DOMA_ELNO_EPSI” or
“DOMA_ELGA_EPSI”, “DOMA_ELNO_EPME” or “DOMA_ELGA_EPME”. Moreover, it is necessary that it
concept specified result contains respectively the field of reference symbol
EQUI_ELNO_EPSI, EQUI_ELGA_EPSI, EQUI_ELNO_EPME or EQUI_ELGA_EPME (calculable by
CALC_ELEM).
The curve of Manson-Coffin must be introduced into operator DEFI_MATERIAU [U4.43.01] (word
key FATIGUE, operand MANSON_COFFIN).
DAMAGE =/“TAHERI_MANSON”
This method of calculation of the damage applies only to loadings of the deformation type,
i.e. for options “DOMA_ELNO_EPSI”, “DOMA_ELGA_EPSI”, “DOMA_ELNO_EPME” or
“DOMA_ELGA_EPME”. Moreover, it is necessary that the concept specified result contains it respectively
field of reference symbol EQUI_ELNO_EPSI, EQUI_ELGA_EPSI, EQUI_ELNO_EPME or
EQUI_ELGA_EPME (calculable by CALC_ELEM).
Are N cycles elementary of half amplitude
1,…
N.
2
2
The calculation of the elementary damage of the first cycle is determined by interpolation on the curve
of Manson-Coffin of material.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
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Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
7/20
The calculation of the elementary damage of the following cycles is determined by the algorithm described
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.
+
·
If
I 1
I
<
2
2
one determines:
+
I 1
i+1
J
= F
, Max
2
NAPPE
2
J I
<
2
* 1
+
I
i+1
= F
2
FONC 2
where FNAPPE is a tablecloth introduced under operand TAHERI_NAPPE.
FFONC is a function introduced under operand TAHERI_FONC.
*
The value of the damage of the cycle (I +)
1 is obtained by interpolation of
i+1 on the curve of
2
Manson-Coffin of the material (Nrupti+1 = a number of cycles to the rupture for the cycle
*
(I)
I
+ =
+
1
1
1
MANSON_ WHETSTONE SHEATH
and Dom
I + 1 =
).
2
i+1 = damage of the cycle (
)
Nrupti+1
The curve of Manson-Coffin must be introduced into operator DEFI_MATERIAU [U4.43.01] (word
key FATIGUE, operand MANSON_COFFIN).
Note:
1) The tablecloth or the formula introduced under operand TAHERI_NAPPE is in fact
cyclic curve of work hardening with prestressed material.
2) The function or the formula introduced under operand TAHERI_FONC is in fact
cyclic curve of work hardening of material.
3) The tablecloth or the formula introduced under operand TAHERI_NAPPE, must have “X” and
“EPSI” like parameters.
4) The function or the formula introduced under operand TAHERI_FONC, must have for
parameter “SIGM”.
DAMAGE =/“TAHERI_MIXTE”
This method of calculation of the damage applies only to loadings of the deformation type,
i.e. for options “DOMA_ELNO_EPSI”, “DOMA_ELGA_EPSI”, “DOMA_ELNO_EPME” or
“DOMA_ELGA_EPME”. Moreover, it is necessary that the concept specified result contains it respectively
field of reference symbol EQUI_ELNO_EPSI, EQUI_ELGA_EPSI, EQUI_ELNO_EPME or
EQUI_ELGA_EPME (calculable by CALC_ELEM).
Handbook of Utilization
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Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
8/20
Are N cycles elementary of half amplitude
1,…
N.
2
2
The calculation of the elementary damage of the first cycle is determined by interpolation on the curve
of Manson-Coffin of material.
The calculation of the elementary damage of the following cycles is determined by the algorithm described
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.
+
·
If
I 1
I
<
2
2
one determines:
+
I 1
i+1
J
= F
, Max
2
NAPPE
2
J I
<
2
where FNAPPE is a tablecloth introduced under operand TAHERI_NAPPE.
The value of the damage of the cycle (I +)
1 is obtained by interpolation of
i+1 on the curve of
2
Wöhler of the material (Nrupti+1 = a number of cycles to the rupture for the cycle
(
+1
I
)
I
+ 1 =
1
WOHLER
and Dom
I + 1 =
).
2
i+1 = damage of the cycle (
)
Nrupti+1
This method requires the data of the curves of Wöhler and Manson-Coffin of the material, which
must be introduced into operator DEFI_MATERIAU [U4.43.01] (key word factor FATIGUE).
Note:
1) The tablecloth or the formula introduced under operand TAHERI_NAPPE is in fact
cyclic curve of work hardening with prestressed material.
2) The tablecloth or the formula introduced under operand TAHERI_NAPPE, must have “X” and
“EPSI” like parameters.
3.5 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 definition of the curve of Wöhler of material for the calculation of
damage by the methods “WOHLER” and “TAHERI_MIXTE” and the definition of the curve of
Manson-Coffin of material for the calculation of the damage by methods “MANSON_COFFIN”,
“TAHERI_MANSON” and “TAHERI_MIXTE”.
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
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Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
9/20
3.6 Operand
TAHERI_NAPPE
This operand makes it possible to specify the name of a tablecloth F
,
NAPPE 2
MAX necessary to the calculation of
damage by methods “TAHERI_MANSON” and “TAHERI_MIXTE”.
The tablecloth must have “X” and “EPSI” like parameters.
Note:
This tablecloth is in fact the cyclic curve of work hardening with prestressed material.
3.7 Operand
TAHERI_FONC
This operand makes it possible to specify the name of a function FFONC 2 necessary to the calculation of
damage by method “TAHERI_MANSON”.
The parameter of this function must be “SIGM”.
Note:
This function is in fact the cyclic curve of work hardening of material.
3.8 Operand
TYPE_CHARGE
This operand makes it possible to specify the type of loading applied to the structure:
·
PERIODIQUE, the loading are periodic;
·
NON_PERIODIQUE, the loading are not periodical.
3.9 Operand
OPTION
This operand makes it possible to specify the place where postprocessing will be made:
·
DOMA_ELGA, postprocessing are made at the points of Gauss of the grid;
·
DOMA_NOEUD, postprocessing are made with the nodes of the grid or part of the grid, cf.
operands: GROUP_MA, MAILLE, GROUP_NO and NO.
3.10 Operand
RESULTAT
RESULTAT = LMBO
Name of the concept result containing the stress fields defining the history of loading.
More precisely, the concept result must contain the field of reference symbol SIEF_ELGA and/or
SIEL_ELGA_DEPL and/or SIEF_NOEU_ELGA and/or SIGM_NOEU_DEPL.
3.11 Operand
CHAM_MATER
CHAM_MATER = cham_mater
Allows to specify the name of the field of the material cham_mater created by AFFE_MATERIAU
[U4.43.03].
The MATER material defined with the command DEFI_MATERIAU and which is used for the assignment of
material with the grid with command AFFE_MATERIAU must contain the definition of the curve
of Wöhler as well as information necessary to the implementation of the criterion, to see the key words
factors FATIGUE and CISA_PLAN_CRIT of command DEFI_MATERIAU [U4.43.01].
Handbook of Utilization
U4.8- booklet: Postprocessing and dedicated analyzes
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Operator CALC_FATIGUE
Date:
31/01/06
Author (S):
J. ANGLES, A. Key M. DONORE
:
U4.83.02-F1 Page:
10/20
3.12 Operand
CRITERE
CRITERION =/“MATAKE”,
/“DANG_VAN_MODI_AC”,
/“DOMM_MAXI”,
/“DANG_VAN_MODI_AV”,
/“FATEMI_SOCIE”,
Allows to specify the name of the criterion which half amplitude of shearing will have to satisfy to it
maximum.
:
Notation
N *
: normal
which
in
plan
with
amplitude
cisailleme
of
maximum
is
NT
;
(N)
: amplitude
cisailleme
of
normal
of
plan
one
in
constraint
in
NT
N;
(N)
: amplitude
cisailleme
of
déformatio
in
NT
normal
of
plan
one
in
N
N;
Nmax (N):
maximum
constraint
on
normal
normal
of
plan
N;
:
of
limit
cisailleme
in
endurance
pure
NT
;
alternated
0
D
:
of
limit
traction
in
endurance
- compressio
;
alternated
pure
N
0
P
:
hydrostati
pressure
that;
C
: being useful coeffician
T
count
in
to take
with
préécrouis
possible
one
;
wise
p
:
of
limit
elasticity.
y
Criterion of MATAKE
(N) * + NR has () * B éq
3.12-1
2
max N
where has and B are two constant data by the user under key words MATAKE_A and
MATAKE_B of the key word factor CISA_PLAN_CRIT of DEFI_MATERIAU, they depend on
characteristics materials and are worth:
D D
0
0
has = -
B =.
0
2
2
0
If the user has the results of two tensile tests compression, alternated and the other
not, the constant ones has and B are given by:
(
2 -
1)
has = (
1 -
2)
,
- 2 m
m
1
B = (
×
2 -
1)
,
+ 2
2
m
with
1 the amplitude of loading for the alternate case (= 0
m
) and
2 the amplitude of
loading for the case where the average constraint is nonnull (
0
m
).
Moreover, we define an equivalent constraint within the meaning of MATAKE, noted (N:
eq
) *
eq (N)
F
* = C p
(N) * + Nmax (N) has *,
2
T
where F/T represents the report/ratio of the limits of endurance in inflection and alternating torsion, and must be
informed under key word COEF_FLEX_TORS of the key word factor CISA_PLAN_CRIT of
DEFI_MATERIAU.
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Criterion DANG_VAN_MODI_AC
(N) * + aP B éq
3.12-2
2
where has and B are two constant data by the user under key words D_VAN_A and D_VAN_B
key word factor CISA_PLAN_CRIT of DEFI_MATERIAU, they depend on the characteristics
materials. If the user has two tensile tests compression, alternate
the other not the constant ones has and B are worth:
3
(
-
2
1)
m
1
= × has
B =
×
2 (
1 -
2) - 2 m
(
2 -
1)
,
+ 2
2
m
with
1 the amplitude of loading for the alternate case (= 0
m
) and
2 for the case where
average constraint is nonnull (
0
m
).
Moreover, we define an equivalent constraint within the meaning of DANG VAN, noted
(N
eq
)
*:
eq (N)
C
* = C p
(N)
* + P has,
2
T
where C/T represents the report/ratio of the limits of endurance in alternated shearing and traction, and must
to be well informed under key word COEF_CISA_TRAC of the key word factor CISA_PLAN_CRIT of
DEFI_MATERIAU.
For more information, to consult the document [R7.04.04].
Criterion DOMM_MAXI
Criterion DOMM_MAXI is an evolution of the criterion of MATAKE. Contrary to the two criteria
precedents, this criterion selects the critical plan according to the damage calculated in each
plan. It is the plan in which the damage is maximum which is retained. This criterion is adapted to
nonperiodic loadings, which induces the use of a method of counting of cycles so
to calculate the elementary damage. To count the cycles, we use the method
RAINFLOW.
The once known elementary damage is cumulated linearly to determine it
too bad.
To calculate the elementary damage we project the history of the constraints of
shearing on one or two axes in order to reduce this one to a unidimensional function time
= F
. After having extracted the elementary under-cycles from with method RAINFLOW
p
(T)
p
we define an elementary equivalent constraint for any elementary under-cycle I:
Max
Min
I
(I N I N -
I
N
I
N
1
p (), p2 ())
(1p (), p2 ())
eq (N)
= C
+
p
aMax (I
I
Nmax1 (N), Nmax2 (N) 0
,),
2
éq 3.12-3
with N the normal of the plan running, I
I
p1 (N) and p2 (N) values of shear stresses
projected under-cycle I and
I
NR
I
max1 (N) and NR max 2 (N) normal constraints maximum of
under-cycle I. From I
eq (N) and of a curve of fatigue we determine the number of cycles
with the elementary rupture
I
NR (N) and damage corresponding I
D (N)
I
= 1/NR (N). In
[éq 3.12-3] is a corrective term which makes it possible to use a curve of fatigue in
traction and compression. The constant ones has and must be indicated under the key words
DOMM_A and COEF_CISA_TRAC of the key word factor CISA_PLAN_CRIT of DEFI_MATERIAU.
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:
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We use a linear office plurality of damage. That is to say K the number of elementary under-cycles, for
a normal N fixed, the cumulated damage is equal to:
D (N)
K
= I
D (N). éq
3.12-4
I 1
=
To determine the normal vector *
N corresponding to the maximum cumulated damage we make
to vary N, the normal vector *
N corresponding to the maximum cumulated damage is then given by:
D (*
N) = Max (D (N).
N
Criterion DANG_VAN_MODI_AV
The step and the techniques implemented to calculate this criterion are identical to those
used for criterion DOMM_MAXI. The only difference lies in the definition of the constraint
equivalent elementary where the hydrostatic pressure p replaces the maximum normal constraint
Nmax:
Max
Min
I
(I N I N -
I
N
I
N
1
p (), p2 ())
(1p (), p2 ())
eq (N)
= C
+
p
aMax (I
I
1
P (N), 2
P (N) 0
,).
2
The constant ones has and are to be informed by the user under key words D_VAN_A and
COEF_CISA_TRAC of the key word factor CISA_PLAN_CRIT of DEFI_MATERIAU.
For more information to consult the document [R7.04.04].
Criterion of FATEMI_SOCIE
The criterion of FATEMI and SOCIE is defined by the relation:
N
NR
N
max
eq (N)
()
()
=
1+ K
2
y
where K is a constant which depends on the characteristics materials. Contrary to the others
criteria, it uses shearing in deformation instead of shearing in constraint. Moreover, them
various quantities which contribute to the criterion are multiplied and not added. The criterion of
FATEMI and SOCIE are usable after an elastic design or elastoplastic. This criterion selects
the plan criticizes according to the damage calculated in each plan. It is the plan in which
damage is maximum which is retained.
This criterion is adapted to the nonperiodic loadings, which leads us to use the method
of counting of cycles RAINFLOW to calculate the elementary damage. Damage
elementary are then cumulated linearly to determine the damage.
In order to calculate the elementary damage we project the history of shearing in
deformation on one or two axes in order to reduce this one to a unidimensional function time
F
p =
(T). After having extracted the elementary under-cycles with method RAINFLOW us
let us define an elementary equivalent deformation for any elementary under-cycle I:
Max
- Min
I
(I
I
I
I
1
p (N),
p2 (N))
(1p (N), p2 (N))
eq (N) = CP
(1+aMax (I
I
Nmax1 (N), Nmax2 (N), 0)
2
éq 3.12-5
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K
with A =
, N the normal in the plan running, I
p1 (N)
I
and p2 (N) values of shearings in
y
deformation projected of under-cycle I,
I
Nmax1 (N)
I
and Nmax2 (N) being two values of the constraint
maximum normal of under-cycle I. From I
eq (N) and of a curve of Manson-Coffin us
let us determine the number of cycles to the elementary rupture
I
NR (N) and corresponding damage
I
D (N)
I
= 1/NR (N).
In the equation [éq 3.12-5] is a corrective term which to use a curve of Manson-Coffin obtained
in traction compression. C p is a coefficient which makes it possible to take into account possible
préécrouissage.
The constant ones has and must be indicated under key words FATSOC_A and COEF_CISA_TRAC
key word factor CISA_PLAN_CRIT of command DEFI_MATERIAU.
As we use a linear office plurality of damage, if m is the number of under-cycles
elementary, then for a normal N fixed, the cumulated damage is equal to:
D (N)
m
= I
D (N)
i=1
To find vector normal N * corresponding to the maximum cumulated damage we vary N.
Normal vector N * associated the maximum cumulated damage is then given by:
D (N)
* = max (D (N)
N
3.13 Operand
METHODE
METHOD = “CERCLE_EXACT”
Allows to specify the name of the method which will be used to calculate to it half amplitude of
maximum shearing.
The method of the “CERCLE_EXACT” is used to determine the circle circumscribed at the points which are
in plans of shearing. This method rests on the process which consists in obtaining it
ring which passes by three points, cf document [R7.04.04].
3.14 Operand
PROJECTION
If the loading is not periodical, it is necessary to project the history of
shearing on one or two axes, cf document [R7.04.04].
·
UN_AXE, the history of shearing are projected on an axis;
·
DEUX_AXES, the history of shearing are projected on two axes.
3.15 Operand
DELTA_OSCI
DELTA_OSCI =/delta,
/
0.0,
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 weak
amplitude. For more information to see the documentation of command POST_FATIGUE,
[U4.83.01], even operand.
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3.16 Operands
GROUP_MA/MESH/GROUP_NO/NODE
GROUP_MA = lgma,
The options are calculated on the groups of meshs contained in the list lgma.
MAILLE = lma,
The options are calculated on the meshs contained in the list lgma.
GROUP_NO = lgno,
The options are calculated on the groups of nodes contained in the list lgno.
NOEUD = lno,
The options are calculated on the nodes contained in the list lno.
3.17 Operand
COEF_PREECROU
COEF_PREECROU =/coef_pre,
/
1.0,
This coefficient is used to take into account the effect of possible a préécrouissage.
3.18 Operand
MAILLAGE
MAILLAGE = grid,
Allows to specify the name of the grid given by the user.
3.19 Operand
INFO
INFO =/1
Impression:
·
no impression
/2
Impression:
·
parameters of the calculation of the damage (a number of the sequence numbers, numbers
points of calculation, type of the calculation of the damage (forced, deformations), localization
damage (nodes or points of Gauss), type of the equivalent component
(VMIS_SG or INVA_2SG), method of extraction of cycles (RAINFLOW) and method
of calculation of damage (WOHLER or MANSON_COFFIN or TAHERI_MANSON or
TAHERI_MIXTE).
·
point by point of the history of loading, of the cycles extracted and the value from
too bad.
·
field of damage.
The impressions are made in file MESSAGE.
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4 Example
One will be able to refer to test SZLZ105 concerning the damage and the office plurality of damage, with
tests SSLV135a and SSLV135b as regards relating to the periodic loadings like with the tests
SSLV135c and SSLV135d for the case where the loading is not periodical.
4.1
Calculation of the equivalent history of loading
DEPL
=
CALC_ELEM
(
reuse
=
DEPL,
MODELE
=
CPLAN,
CHAM_MATER =
MAT,
OPTION
=
(
“SIEF_ELGA_DEPL”,
“EPSI_ELGA_DEPL”,
“EQUI_ELGA_SIGM”,
“EQUI_ELGA_EPSI”,
“EQUI_ELNO_SIGM”,
“EQUI_ELNO_EPSI”,
),
RESULTAT
=
DEPL
)
4.2
Definition of the curve of Wöhler of material and associated damage
WOHL = DEFI_FONCTION (
NOM_PARA
=
“SIGM”,
VALE =
(
0.
,
1000.,
10.
, 0.,
),
PROL_DROITE
=
“LINEAIRE”,
PROL_GAUCHE
=
“LINEAIRE”,
TITER
=
'FONCTION
OF
WOHLER'
)
# Definition of material
= DEFI_MATERIAU SUBDUE (FATIGUE = _F (WOHLER = WOHL))
# Calculation of the damage to the nodes starting from the history of constraint of von
Settings signed (the loading being homogeneous with constraints, damage
calculate by interpolation on a curve of Wöhler of material).
DMG_WOHL = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,
OPTION
=
“DOMA_ELNO_SIGM”,
HISTOIRE
=_F
(RESULT = DEPL,
EQUI_GD
=
“VMIS_SG”,
)
DOMMAGE =
“WOHLER”,
MATER
=
MATE,
INFO =
2
)
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4.3 Definition of the curve of Manson_Coffin of material and damage
associated
MANS = DEFI_FONCTION (
NOM_PARA
=
“EPSI”,
VALE =
(
0.
,
1000.,
10.
, 0.,
),
PROL_DROITE
=
“LINEAIRE”,
PROL_GAUCHE
=
“LINEAIRE”,
TITER
=
'FONCTION
OF
MANSON
COFFIN'
)
# Definition of material
MAT1 = DEFI_MATERIAU (FATIGUE = _F (MANSON_COFFIN = MANS))
# Calculation of the damage to the nodes starting from the history of the value of
the invariant of a nature 2 signed (the loading being homogeneous with deformations,
the damage is calculated by interpolation on a curve of Manson_Coffin of
material).
DMG_MCOF = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,
OPTION
=
“DOMA_ELNO_EPSI”,
HISTOIRE
=_F (RESULTAT
=
DEPL,
EQUI_GD
=
“INVA_2_SG”,
),
DOMMAGE =
“MANSON_COFFIN”,
MATER
=
MAT1,
INFO =
2
)
4.4 Definition of the curves of cyclic work hardening and work hardening
cyclic with prestressing
F_NAPPE = DEFI_NAPPE (
NOM_PARA = “X”,
PROL_DROITE
=
“LINEAIRE”,
PROL_GAUCHE
=
“LINEAIRE”,
PARA = (0.5, 1.,),
NOM_PARA_FONC
=
“EPSI”,
DEFI_FONCTION
=_F (
PROL_DROITE
=
“LINEAIRE”,
PROL_GAUCHE
=
“LINEAIRE”,
VALE
=
(
0.,
25.,
10., 525.,),
)
_F (
PROL_DROITE
=
“LINEAIRE”,
PROL_GAUCHE
=
“LINEAIRE”,
VALE
=
(
0. , 50.,
10., 550.,))),
TITER
=
'NAPPE
of
TAHERI'
)
F_FONC = DEFI_FONCTION (
NOM_PARA
= “SIGM”,
PROL_DROITE
=
“LINEAIRE”,
PROL_GAUCHE
=
“LINEAIRE”,
PARA =
(
0.,
0.,
100.,
10.,),
TITER=' FUNCTION
of
TAHERI')
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4.5 Calculation of the damage by methods “TAHERI_MANSON” and
“TAHERI_MIXTE”
MAT2 = DEFI_MATERIAU (
FATIGUE = _F (
WOHLER = WOHL,
MANSON_COFFIN
=
MANS
)
)
DMG_TMA = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,
OPTION
=
“DOMA_ELNO_EPSI”,
HISTOIRE
=_F (RESULTAT
=
DEPL,
EQUI_GD
=
“INVA_2_SG”
)
DOMMAGE =
“TAHERI_MANSON”,
MATER
=
MAT2,
TAHERI_NAPPE
=
F_NAPPE,
TAHERI_FONC
=
F_FONC,
INFO =
2
)
DMG_TMI = CALC_FATIGUE (
TYPE_CALCUL = “CUMUL_DOMMAGE”,
OPTION
=
“DOMA_ELNO_EPSI”,
HISTOIRE
=_F (RESULTAT
=
DEPL,
EQUI_GD
=
“INVA_2_SG”
),
DOMMAGE =
“TAHERI_MIXTE”,
MATER
=
MAT2,
TAHERI_NAPPE
=
F_NAPPE,
INFO =
2
)
4.6
Calculation of the half amplitude of maximum shearing by the method:
“CERCLE_EXACT”
This example is drawn from the case test SSLV135a. Ici the loading is periodic and the damage is calculated
at the points of Gauss.
STEEL = DEFI_MATERIAU (ELAS =_F (E = 200000.,
NAKED = .3,
ALPHA = 0. ),
TIRE =_F (WOHLER = WHOL,),
CISA_PLAN_CRIT =_F (CRITERION = “MATAKE”,
COEF_FLEX_TORS = 1.5,
MATAKE_A = 1.0,
MATAKE_B = 2.0,)
)
CHECHMATE = AFFE_MATERIAU (GRID = CUBIC,
AFFE =_F (ALL = “YES”,
MATER = STEEL,
TEMP_REF = 20. )
)
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SOL_NL = STAT_NON_LINE (TITLE =
“TEST ALTERNATE TRACTION AND COMPRESSION - CRITICAL PLAN”,
MODEL = TROISD,
CHAM_MATER = CHECHMATE,
EXCIT =_F (LOAD = TR_CS,
FONC_MULT = COEFF,
TYPE_CHARGE = “FIXE_CSTE”),
COMP_ELAS =_F (RELATION = “ELAS”,
DEFORMATION = “SMALL”,
ALL = “YES”),
INCREMENT =_F (LIST_INST = LINST,),
NEWTON =_F (MATRIX = “ELASTIC”,
REAC_INCR = 0))
FATI_NL=CALC_FATIGUE (TYPE_CALCUL = “FATIGUE_MULTI”,
OPTION = “DOMA_ELGA”,
TYPE_CHARGE = “PERIODIC”,
RESULT = SOL_NL,
CHAM_MATER = CHECHMATE,
CRITERION = “MATAKE”,
COEF_PREECROU = 1.0,
METHOD = “CERCLE_EXACT”
)
4.7
Calculation of the damage when the loading is not periodical
This example is drawn from the case test SSLV135d. Ici the loading is not periodic, the damage is
calculated at the points nodes on part of the whole of the grid: “FACE1”, “FACE3” and
“FACE5”.
STEEL = DEFI_MATERIAU (ELAS =_F (E = 200000.,
NAKED = .3,
ALPHA = 0. ),
TIRE =_F (WOHLER = WHOL,),
CISA_PLAN_CRIT =_F (CRITERE= “DANG_VAN_MODI_AV”,
D_VAN_A = 1.0,
D_VAN_B = 2.0,
COEF_CISA_TRAC = 1.5)
)
CHECHMATE = AFFE_MATERIAU (GRID = CUBIC,
AFFE =_F (ALL = “YES”,
MATER = STEEL,
TEMP_REF = 20. ))
SOL_L = MECA_STATIQUE (TITLE =
“TEST ALTERNATE TRACTION AND COMPRESSION - DANG_VAN_MODI_AV”,
MODEL = TROISD,
CHAM_MATER = CHECHMATE,
EXCIT =_F (LOAD = TR_CS,
FONC_MULT = COEFF),
LIST_INST = LINST,
)
SOL_L = CALC_ELEM (reuse = SOL_L,
RESULT = SOL_L,
OPTION = “SIGM_ELNO_DEPL”,
)
SOL_L = CALC_NO (reuse = SOL_L,
RESULT = SOL_L,
OPTION = “SIGM_NOEU_DEPL”
)
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FATI_LNO2=CALC_FATIGUE (TYPE_CALCUL = “FATIGUE_MULTI”,
OPTION = “DOMA_NOEUD”,
TYPE_CHARGE = “NON_PERIODIQUE”,
RESULT = SOL_L,
CHAM_MATER = CHECHMATE,
GROUP_MA = (“FACE1”, “FACE3”, “FACE5”),
GRID = CUBIC,
CRITERION = “DANG_VAN_MODI_AV”,
COEF_PREECROU = 1.0,
PROJECTION = “DEUX_AXES”,
)
4.8
Calculation of the damage with criterion FATEMI_SOCIE
This example is drawn from the case SSLV135e test. Here the loading is not periodic, the damage is
calculated with the nodes on part of the whole of the grid: “FACE1”, “FACE2” and “FACE3”.
STEEL = DEFI_MATERIAU (ELAS =_F (E = 200000.,
NAKED = 0.3,
ALPHA = 0.0),
TIRE =_F (MANSON_COFFIN = MANCOF,),
CISA_PLAN_CRIT =_F (CRITERION = “FATEMI_SOCIE”,
FATSOC_A = 1.0,
COEF_CISA_TRAC = 1.5)
)
CHECHMATE = AFFE_MATERIAU (GRID = CUBIC,
AFFE =_F (ALL = “YES”,
MATER = STEEL,
TEMP_REF = 20. ))
# CALCULATION WITH STAT_NON_LINE
# -------------------------
SOL_NL = STAT_NON_LINE (TITLE =
“TEST ALTERNATE TRACTION AND COMPRESSION - FATEMI_SOCIE”,
MODEL = TROISD,
CHAM_MATER = CHECHMATE,
EXCIT =_F (LOAD = TR_CS,
FONC_MULT = COEFF,
TYPE_CHARGE = “FIXE_CSTE”),
COMP_ELAS =_F (RELATION = “ELAS”,
DEFORMATION = “SMALL”,
ALL = “YES”),
INCREMENT =_F (LIST_INST = LINST,),
NEWTON =_F (MATRIX = “ELASTIC”,
REAC_INCR = 0))
SOL_NL = CALC_ELEM (reuse = SOL_NL,
RESULT = SOL_NL,
OPTION = (“EPSI_ELGA_DEPL”,
“SIEF_ELNO_ELGA”,
“EPSI_ELNO_DEPL”)
)
SOL_NL = CALC_NO (reuse = SOL_NL,
RESULT = SOL_NL,
ALL = “YES”,
GROUP_MA_RESU = (“FACE1”, “FACE2”, “FACE3”),
OPTION = (“SIEF_NOEU_ELGA”, “EPSI_NOEU_DEPL”)
)
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F_NLNO2A=CALC_FATIGUE (TYPE_CALCUL = “FATIGUE_MULTI”,
OPTION = “DOMA_NOEUD”,
TYPE_CHARGE = “NON_PERIODIQUE”,
RESULT = SOL_NL,
CHAM_MATER = CHECHMATE,
COEF_PREECROU = 1.0,
GROUP_MA = (“FACE1”, “FACE2”, “FACE3”),
GRID = CUBIC,
CRITERION = “FATEMI_SOCIE”,
PROJECTION = “DEUX_AXES”,
)
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